INTERNATIONAL PATENT APPLICATION Mitigation of Chemical Absorption Across Multiple Robots TECHNICAL FIELD [0001] The present application relates to operation of large numbers of robots that absorb a chemical from surrounding fluid. BACKGROUND [0002] Large numbers of remote robots, often referred to as a “swarm”, can utilize their collective operational capabilities to accomplish certain tasks more readily than a single larger robot or small number of larger robots would be able to. Such robots may operate within a fluid system and may absorb a chemical of particular interest from the surrounding fluid as part of their designed function. Such absorption could be achieved by using one or more chemical-extracting components (hereafter referred to as “pumps”) capable of absorbing the chemical of interest from the surrounding fluid. One example of such a pump is a component that draws fluid through an intake duct, passes it through a chemically-selective membrane to filter out a selected chemical from the fluid flow (either restraining the chemical from the flow or passing the chemical through while restraining the remainder of the flow), and then ejects the resulting chemical-depleted fluid via an output duct. Small-scale pumps and valves are well-known in the art, (Zhang, Xing et al., "Micropumps, microvalves, and micromixers within PCR microfluidic chips: Advances and trends," Biotechnol Adv, 5, 2007), (Nguyen, Huang et al., "MEMS-Micropumps: A Review," Journal of Fluids Engineering, 2, 2002), (Amirouche, Zhou et al., "Current micropump technologies and their biomedical applications," Microsystem Technologies, 5, 2009) and some examples are taught in U.S. Patents 6,955,670; 8,343,425; and 10,220,004; and U.S. Publications 2008/0161779, 2008/0202931, 2010/0284924, and 2012/0015428. Alternatives to the use of semi-permeable or selectively-permeable membranes include passing the fluid across chemically-selective binding sites, and/or using Zeolites (crystal structures with holes sized to fit certain molecules) to separate a chemical from the flow. (Jones, Tsuji et al., "Organic-functionalized molecular sieves as shape-selective catalysts," Nature, 6680, 1998; Martínez and Corma, "Inorganic molecular sieves: Preparation, modification and industrial application in catalytic processes," Coordination Chemistry Reviews, 13-14, 2011). One application for the use of micro- or nano-scale robot swarms is the operation of such robots operating inside the body of an organism for medical or veterinary purposes. [0003] Larger-scale robots (100mm and larger, for example) can be fabricated using conventional construction techniques. For smaller scale robots (such as MEMS and NEMS robots), such robots and their constituent parts are manufactured in a variety of ways, including lithography and etching, micromachining, e-beam deposition, atomic layer deposition, and others. These techniques and others, including the integration of circuitry with the robots, are known in the appropriate fields (e.g., ("Handbook of Silicon Based MEMS Materials and Technologies," Micro and Nano Technologies, William Andrew, 2010); (Ghodssi and Lin, "MEMS Materials and Processes Handbook," MEMS Reference Shelf, Springer, 2011); (Schulz, Shanov et al., "Nanotube Superfiber Materials: Changing Engineering Design," Micro and Nano Technologies, William Andrew, 2013); (Morris and Iniewski, "Nanoelectronic Robot Applications Handbook," Robots, Circuits, and Systems, CRC Press, 2013); (Choudhary and Iniewski, "MEMS: Fundamental Technology and Applications," Robots, Circuits, and Systems, CRC Press, 2013); (Sharapov, Sotula et al., "Piezo-Electric Electro-Acoustic Transducers," Microtechnology and MEMS, Springer, 2013). Additionally, three dimensional printers are available which are capable of far sub- micron feature sizes (e.g., OWL Nano, sold by Old World Technologies, Virginia Beach, VA, USA; Photonic Professional GT from Nanoscribe, Germany; and the f100 aHead from FEMTOprint SA, Switzerland). Also falling under the category of small-scale robots, biorobots have been created which use, for example, flagella from micro-organisms for motile power, and which can be steered using electrical fields, light, or other means. (Sakar, "MicroBioRobots for Single Cell Manipulation," Electrical and Systems Engineering, 284, University of Pennsylvania, 2010); (Paprotny and Bergbreiter, "Small-Scale Robotics From Nano-to-Millimeter-Sized Robotic Systems and Applications," First International Workshop, microICRA 2013, Karlsruhe, Germany, Springer, 2013). SUMMARY [0004] The following Summary is provided to aid in understanding the novel and inventive features set forth in the appended claims and is not intended to provide a complete description of the inventive features. Any limitations of the following summary should not be interpreted as limiting the scope of the appended claims. [0005] Where a large number of robots operate in a fluid system to absorb a particular chemical (hereafter referred to as a “reactant”), they may cause depletion of the reactant to such a degree as to materially affect the functioning of the fluid system. In such case, the impact of the collective absorption by the robots effectively makes them a part of the fluid system that alters its operation. Where a certain concentration of the reactant is needed, either by the robots themselves or by other reactant-using features associated with the fluid system, the combined absorption capability of the robots may create situations in which the concentration of the reactant is insufficient for proper functioning of the fluid system. To prevent such situations, robots may need to limit their absorption of the reactant to avoid creating such depletion of reactant. In some cases, the fluid system has at least one region where reactant is abundant (hereafter referred to as a “high-reactant region”); in such cases, some or all robots may be configured to absorb and store reactant when in such a high- reactant region, and later release the reactant for use when in a region where the reactant is depleted or otherwise would become depleted. [0006] As one example to illustrate the above concepts, the circulatory system of an organism can be considered as a fluid system, and a swarm of robots can be configured to operate in the circulatory system, absorbing oxygen and glucose from blood as reactants to provide power to operate. In such cases, available oxygen is frequently a limiting factor, as oxygen is extracted both for use as a reactant to power the robots and by cells, and the lungs or gills provide a high-reactant region where oxygen is readily available. The proper functioning of the fluid system in such case includes keeping the oxygen concentration at any particular location in the circulatory system high enough to provide power for robots as well as supplying sufficient oxygen for use by cells. If a large enough number of robots are present and absorbing oxygen, they can impact the ability of the fluid system to fulfill its function of transporting and distributing oxygen to the cells, and their combined absorptive capability can materially affect the function of the fluid system. Typically, this is of greatest concern near the “end” of the circuit, before the blood re-enters the lungs/gills where oxygen is replenished. [0007] A swarm of robots that operate as part of a fluid system in which a selected reactant is present in the fluid can be operated so as to mitigate the impact of their combined absorption. In one general method for performing such operation, a large number of robots operate in the fluid system and can each absorb the selected reactant from the surrounding fluid, with the combined absorption capability of the robots being great enough to materially affect the functioning of the fluid system with respect to the reactant. The robots (or at least a subset of the robots) can be operated to determine when a particular robot is in an absorption- limiting need condition. Responsive to such determination, the particular robot can then be operated so as to limit its absorption of reactant from the surrounding fluid. The step of determining when a particular robot is situated in an absorption-limiting need condition could make such determination based, at least in part, on sensed conditions (such as concentration of the selected reactant or another chemical, a related parameter such as rate of concentration change, a physical parameter such as temperature, pressure, etc.) at the location of the particular robot, and/or can include making a determination of the location of the particular robot in the fluid system. In many cases, such determination is made in anticipation of the reactant level eventually becoming depleted if absorption by the robot were not limited. In some cases, robots may be assumed to be in an absorption-limiting need condition as a default, until some absorption-limiting triggering event is determined to occur, indicating that the robot should no longer limit its absorption (examples of such triggering events are discussed below). [0008] In some cases, the fluid system has at least one region having a high concentration of the selected reactant (a “high-reactant region”), and the combined absorption capability of the robots is such that it can create a concentration gradient of the selected reactant that decreases in concentration with increasing distance from the high-reactant region. The fluid may circulate through such a high-reactant regions, or even through multiple such regions. In fluid systems having a high-reactant region, the step of determining when a particular robot is situated in an absorption-limiting need condition can include determining that the particular robot has exited the high-reactant region; one scheme is to assume that an absorption-limiting need condition exists upon the robot exiting the high- reactant region, until an absorption-limiting triggering event is determined to have occurred. In many cases, such triggering event is indicative of a need for the robot to operate in a relatively high-energy mode of operation to perform some task, such as computation, communication, and/or some diagnostic or therapeutic operation. Examples of triggering events that could determine when a particular robot is no longer in an absorption-limiting need condition include making a determination that the robot has circulated a set number of times through the high-reactant region (which may indicate that the robot has collected a sufficient amount of data to communicate), is within a specified region of the fluid system (which could be a region suitable for communication to a receiver, a region where a diagnostic and/or therapeutic task must be done, a region where significant data collection is required, or simply a region where it is expected that reactant levels are sufficient that limiting absorption is unnecessary), has stored a set amount of data, has achieved a prescribed mission-related task to a prescribed degree, and/or requires performing a high-energy task. Where the fluid system is the circulatory system of a biological organism having capillaries, organs, and skin, and the triggering event could be determining that the robot is within a specified region of the fluid system, further specifying the determination that the robot has passed into a capillary, is within a specified distance of the skin (and thus positioned to transmit data to an external receiver), and/or has passed into a specified organ. In some cases, determining that the robot is within a vessel of a specified minimum size and within a specified distance of a wall of the robot can be the basis for determining that an absorption- limiting need condition exists, and the robot can be operated to limit its absorption and/or (where the robot has a locomotion capability) move away from the vessel wall. [0009] Various approaches to limiting absorption of reactant by a particular robot can be employed. Typically, robots can turn off some or all of their pumps, and/or operate some or all pumps at a different rate (such as at a different power level and/or different duty cycle). One approach for a number of robots that are absorbing reactant is for them to maintain their position within a specified distance of one another, such that the presence of additional robots in close proximity limits the available reactant for each robot to absorb. [0010] In fluid systems where the fluid has at least one high-reactant region (hereafter discussed in the singular, although multiple high-reactant regions could be present), the robots may include at least a subset of robots that can store the reactant and later release the stored reactant for use by themselves and/or for use by another robot. In such cases, a determination can be made of when a particular robot with such storage capability is located in the high-reactant region, and operating such robot to absorb and store reactant responsive to such determination. A determination can subsequently be made that a reactant need condition exists in the vicinity of the robot, and the robot operated to release stored reactant responsive to such determination. Many of the criteria discussed above for determining when an absorption-limiting need condition no longer exists could also be employed to determine when a reactant need condition exists, where these criteria indicate a need for the robot to operate in a high-power mode (such as to communicate data after the robot’s mission has been completed to a prescribed degree and/or after the robot has accumulated a prescribed amount of data). The determination of when a reactant need condition exists could be made based on sensed conditions, such as sensing that the concentration of reactant in the particular region is (or will soon be) below a specified threshold (or by sensing a related parameter such as rate of decrease in concentration), and/or based on determining when a particular robot that can store reactant is located within a specified region of the fluid system (which could be a region based on absolute location, location in a specific type of region, or a relative location such as a specified distance away from the high-reactant region, as determined by distance traveled, elapsed time in circulation, etc.) For a circulating fluid system, relative location could be determined by elapsed time or distance as an absolute value or as a percentage of the circulation path, such as the time or distance equivalent to traveling 50%, 70%, 80% or 90% of the circulation path (or average circulation path, if there are multiple possible routes through the circuit – in such cases, the determination might be that the robot has traveled 100% of the average, indicating that it is in a longer and/or slower route than average). Such reactant need condition could also be indicated by receiving a communication from an external transmission source, such as another robot in need of more reactant (as discussed in greater detail below), or by an external source (such as another robot or other device monitoring conditions in the fluid system) that has determined that more reactant is needed. When absorbing and storing reactant, a robot may remain in the high-reactant region until a determination is made that a specified threshold amount of reactant has been stored. Where the fluid system circulates through the high-reactant region, the robot could anchor itself within the high-reactant region, select a path through the high-reactant region that takes the fluid longer to circulate through, and/or could delay full-power operation until it has passed several times through the high-reactant region (for example, operating in a low-power mode of operation until it has passed 5 times, 10 times, 15 times, 20 times, or 25 times through the high-reactant region), and/or stored a threshold amount of reactant (as determined by pressure, weight, etc.) Where the fluid system contains other sources of reactant (for example, oxygen stored in red blood cells in an organism’s circulatory system), robots could be configured to extract the reactant from such source to store for later release. In some cases, robots could store a reactant, move to another location, and release it at the new location in order to more evenly distribute reactant through a portion of the fluid system. Such redistribution may help to avoid the impact of robot absorption and/or may provide a more consistent distribution of reactant through vessels of the fluid system in order to make the actual conditions experienced by the robots conform better to generalized models used to design and implement robot missions. [0011] In some situations, the group of robots can include a subset of robots that serve as mission robots and a subset of robots that serve as supply robots, where the supply robots can store the selected reactant for later use by the mission robots (the mission robots may also be able to store reactant, typically for their own use). In such cases, determining when a reactant need condition exists can (possibly in addition to one or more of the criteria discussed above) include determining when a mission robot in the vicinity of a supply robot has insufficient reactant available to perform a desired operation, and operating such mission robot to communicate a reactant need signal to such supply robot, in response to which the supply robot receiving the reactant need signal can be operated to release stored reactant for use by the mission robot communicating the reactant need signal. Where such a supply robot releases reactant, it could release stored reactant into the surrounding fluid (to be absorbed by the mission robot), and/or could dock with the mission robot before releasing stored reactant to it. [0012] Instructions for directing a group of robots to perform any of the methods described above can be stored on a medium suitable for providing instructions to direct the operation of a group of robots. A group of robots can be configured to perform any of the methods described above. [0013] A group of robots for operating as part a fluid system in which a selected reactant is present in the fluid can comprise a large number of robots, each of which is configured to absorb the selected reactant from surrounding fluid, and wherein the combined absorption capability of such robots is great enough to materially affect the functioning of the fluid system with respect to the selected reactant. At least a subset of the robots serve as mission robots, and each have controller housed therein and at least one mission instruction set for directing the controller to operate the mission robot so as to perform the operations of determining when the mission robot is in an absorption-limiting need condition and, responsive to such determination, operating the mission robot to limit its absorption of reactant from the surrounding fluid. The determination that the mission robot is in an absorption-limiting need condition could be made based on the various criteria discussed above with regard to methods, and could include criteria such as one or more of the sensed conditions at the location of the mission robot, the location of the mission robot in the fluid system, and/or a determination that the mission robot has exited a high-reactant region. In this latter case, an absorption-limiting need condition could be assumed to exist after exiting a high-reactant region until an absorption-limiting triggering event is determined to have occurred. Examples of such triggering events include determining that the mission robot has circulated a set number of times through the high-reactant region, that the mission robot is within a specified region of the fluid system, that a set amount of data has been stored by the mission robot, that a prescribed mission-related task has been achieved to a prescribed degree, and/or that a high-energy task is required by the mission robot. [0014] A group of robots can include robots that can absorb and store reactant and later release stored reactant for use by themselves or by another robot. Such robots that store and release reactant could be mission robots, which operate as discussed above. Mission robots (with or without storage capability) could be supplemented with a number of supply robots that are provided primarily to supply reactant to the mission robots, each of such supply robots having controller housed therein and at least one supply instruction set for directing the controller to operate the supply robot so as to perform the operations of determining when the supply robot is in a high-reactant region and absorbing and storing reactant responsive to such determination, and determining when a reactant need condition exists in the vicinity of the supply robot, and releasing reactant for use responsive to such determination (note that when mission robots store reactant, they can have a storage and release instruction set that operates similarly, although they may employ different criteria to determine when a reactant need condition exists and may only release reactant from storage internally, for use by the mission robot itself). The determination of when a reactant need condition exists could be made based on the various criteria discussed above with regard to methods, and could include sensed conditions, such as sensing that the concentration of reactant in the particular region is below a specified threshold, based on determining when a particular robot that can store reactant is located within a specified region of the fluid system, and/or based on receiving communication from a nearby robot that that robot needs reactant. When reactant is released from storage, it could be released into the surrounding fluid, or the supply robot could dock with a particular mission robot to transfer reactant directly to that mission robot. The composition of the group of robots may be selected such that the number of supply robots is at least 5x, 10x, 15x, 20x, 30x, or 40x greater than the number of mission robots. The robots may be configured such that the supply robots have an average size no greater than half the size (by volume) than the mission robots, and may be considerably smaller, such as ¼ the volume, 1/8 the volume, 1/16 the volume, or 1/32 the volume. When operating to absorb and store reactant, robots that are determined to be in the high-reactant region may make a determination of whether a reactant storage triggering event has occurred, and ceasing storage in response to such triggering event. Such triggering event could be a determination that a prescribed amount of reactant has been stored, that the robot has spent a prescribed amount of time in the high-reactant region or made a prescribed number of passages therethrough (where the fluid circulates), or similar criteria related to the amount of reactant that the robot is able to absorb and store while in the high-reactant region. [0015] A robot for operating in a fluid environment with similar robots could have circuitry housed in the robot at least one mission instruction set for directing the circuitry to operate the robot so as to perform the operations of determining when the robot is in an absorption-limiting need condition, and operating the robot in such a manner as to limit its absorption of reactant from the surrounding fluid responsive to such determination. In some cases, the robot has at least one fuel cell housed therein, which is configured to consume the reactant to generate electrical energy to power the circuitry (and frequently other capabilities of the robot). The robot may have at least one pump for absorbing reactant from surrounding fluid and supplying absorbed reactant to the at least one fuel cell. The robot may have at least one storage tank housed therein that is connectable to the at least one pump to receive and release reactant therefrom, and at least one supply instruction set for directing the circuitry to operate the robot so as to perform the operations of determining when the robot is located in the high-reactant region and operating such robot to absorb and store reactant responsive to such determination, and determining when a reactant need condition exists in the vicinity of the robot and operating the robot to release stored reactant responsive to such determination. Where the robot is intended for use as a supply robot, it may have only the supply instruction set, and not include the mission instruction set for determining when to limit absorption. Where the robot has one or more reactant storage tanks, such tanks may have a volume between 2% and 25% of the total volume of the robot. The fraction of the robot surface may be greater than 2% and may be about 5%. The robot radius may be greater than 0.25 µm. Where the robot operates in a fluid that contains other sources of reactant, the robots could be configured to extract the reactant from such source for its own use at the time and/or to store for later release. [0016] Where particular determinations of conditions and corresponding responses are discussed for apparatus, those determinations and responses discussed when addressing the method could be employed for such apparatus, and vice versa. BRIEF DESCRIPTION OF THE FIGURES [0017] FIG.1 is a flow chart illustrating one example of a method for mitigating the absorption effect of a swarm of robots by determining when an absorption-limiting need condition exists for particular robots and operating such robots to limit their absorption of a reactant. [0018] FIG.2 is a flow chart illustrating one example of a routine that could be employed in the method shown in FIG.1 to determine when an absorption-limiting need condition exists. [0019] FIG.3 illustrates one example of a static fluid system having a high-reactant region at its surface. Robots located near the surface are in the high-reactant region, while robots at greater depths may cause depletion of the reactant at such depths. [0020] FIG.4 illustrates one example of a fluid system where a liquid circulates through a high-reactant region, and robots travel in the circulating fluid. [0021] FIG.5 is a flow chart illustrating one example of a method for mitigating absorption by having robots store reactant when located in a high-reactant region, and later releasing such stored reactant. [0022] FIG.6 is a flow chart illustrating one example of a reactant storage routine that could be employed in the method shown in FIG.5, for the case of a circulating fluid system. [0023] FIG.7 illustrates one example of a robot suitable for performing an absorption-limiting method such as shown in FIG.1. [0024] FIG.8 illustrates one example of a robot similar to that shown in FIG.7, but which is also suitable for performing storage and release of reactant. [0025] FIGS.9 and 10 illustrate a group of robots that includes a mission robot and multiple supply robots that can store reactant and supply it for use by the mission robot. FIG. 9 illustrates two supply robots releasing reactant from storage tanks into the surrounding fluid near the mission robot. FIG.10 illustrates one of the supply robots docked with the mission robot to transfer reactant directly to it. [0026] FIG.11 illustrates an aggregated model of a circulatory fluid system, showing an example where the fluid system is a circulatory system of a human. [0027] FIG.12 is a graph of distance over time of blood traveling through the circulatory system shown in FIG.11, from the time of leaving the lung to returning to the lung. Vertical lines near the center indicate passage through capillaries. [0028] FIG.13 is a compartment model of oxygen within blood, used when determining changes in concentration as the blood flows through the circulatory system. [0029] FIG.14 is a graph showing how robot available power (limited by available oxygen) varies during a circulation loop, for the case where all robots consume oxygen as fast as it diffuses to their surfaces, without taking any mitigation efforts. Results are shown for three different numbers of robots in a swarm distributed throughout the circulatory system. [0030] FIGS.15A and 15B are graphs showing how oxygen concentration in plasma (FIG.15A) and red blood cell saturation (FIG.15B) vary during a circulation loop. Results are compared for the numbers of robots in the swarm as shown in FIG.14, along with the values for a case without robots. [0031] FIG.16 is a graph showing tissue power (relative to its maximum with unlimited oxygen) over the time interval when the blood flows through the capillaries, for numbers of robots as shown in FIGS.14, 15A, & 15B, and for the case without robots as shown in FIGS.15A & 15B. [0032] FIGS.17A & 17B are graphs showing how robot available power (FIG.17A) and oxygen concentration in plasma (FIG.17B) decrease with distance along in a 1mm capillary, for a case where robots operate just in the capillaries. [0033] FIGS.18A & 18B illustrate two examples of placement of five robots anchored to the wall of a 34µm long segment of an 8µm-diameter capillary. FIG.18A shows the case where the robots are positioned on alternating sides of the vessel, while FIG.18B shows the robots all positioned on the same side. [0034] FIGS.19A & 19B are graphs showing robot power (FIG.19A) and oxygen concentration in plasma (FIG.19B) with 25% overall hematocrit, for comparison to the case shown in FIGS.14 and 15A (for normal hematocrit). The reduced hematocrit simulates the effect for a patient with reduced ability to store oxygen in their blood, such as an anemic patient. [0035] FIG.20 illustrates a cross section of a robot capable of storing oxygen in a spherical storage tank. [0036] FIG.21 is a graph of fraction of surface occupied by pumps needed to collect all oxygen molecules arriving at the robot surface, as a function of robot size. [0037] FIG.22 shows three constraints on robot and tank fractional size for supply robots to carry enough oxygen to provide each mission robot with sufficient oxygen. [0038] FIG.23 illustrates a main mission robot and an oxygen supply robot, where the supply robot is optimized according to the parameters shown in FIG.22. [0039] FIG.24 is a graph of the power available to a robot through the circulation loop for three different scenarios where 10 ¹² robots are in the swarm, comparing available power to a case where power is not limited (the same as the curve for 10 ¹² robots from FIG. 14). The scenarios compared are where all robots are limited to a specified maximum power, and where robots are limited based on their location in the circuit. [0040] FIG.25 is a graph showing how oxygen concentration in plasma varies for the three cases shown in FIG.24. Note that the curve for unlimited power use is the same as the curve for 10 ¹² robots in FIG.15A. [0041] FIG.26 is a transition graph showing a Markov stochastic process for the amount of data stored by robots (in numbers of capillaries for which data is stored), where each edge corresponds to the robot making a single circulation through the body. [0042] FIG.27 is a graph showing how concentration near the wall of a 2mm diameter straight blood vessel changes with distance for a distributed swarm of 10 ¹² robots, in three cases. In the first case, robots fully consume all oxygen reaching their surface. In the second case, robots within 0.3mm of the vessel wall do not consume oxygen. In the third case, only half the robots consume oxygen but without regard to their position in the vessel. [0043] FIG.28 is a graph showing the same three cases as for FIG.27, but for merging vessels with asymmetric branching where two 2mm-diameter branches merge into a 2.5mm vessel. [0044] FIG.29 illustrates five robots positioned along a vessel similar to that shown in FIGS.18A & 18B, but where successive robots are offset about the longitudinal axis of the vessel by an angle Θ, shown in FIG.29 for the case where Θ = 30° (the arrangements shown in FIG.18A & 18B respectively correspond to Θ = 180° and Θ = 0°). [0045] FIGS.30A & 30B are graphs showing how average robot power and power for the last downstream robot vary as a function of the offset angle Θ shown in FIG.29, relative to the power that would be available with all robots aligned along the vessel wall (i.e., with Θ = 0° as shown in FIG.18B). FIG.30A shows the case for an average fluid speed of 1mm/s, while FIG.30B shows the case for average fluid speed of 0.2mm/s. [0046] FIGS.31A & 31B illustrate five robots in a vessel similar to that shown in FIGS.18A, 18B, & 29, but where the distance between successive robots increases quadratically. FIG.31A shows this distribution for robots aligned along the same side of the vessel (i.e., Θ = 0°), while FIG.31A shows the distribution where robots are on alternating sides of the vessel (i.e., Θ = 180°). [0047] FIGS.32A & 32B are graphs showing the average power for the robots and for the last robot as a function of the offset angle Θ, relative to the situation of uniformly- spaced robots aligned along the vessel wall (as shown in FIGS.30A & 30B), for fluid flow speeds of 1mm/s (in FIG.32A) and 0.2mm/s (in FIG.32B). [0048] FIG.33 is a graph of the dimensions of blood vessels as a function of time through the circuit shown in FIG.12, with the size of larger vessels ignored to show the range of sizes where hematocrit varies with vessel size. [0049] FIG.34 is a schematic view of blood vessel branching to illustrate increased aggregated cross section in smaller vessels. [0050] FIG.35 is an aggregated vessel cross section showing increased cross section and reduced hematocrit in smaller vessels. [0051] FIGS.36-38 illustrate gradients in concentration that result in merged vessels when the flows from smaller vessels having differing concentrations combine in the merged vessel. DETAILED DESCRIPTION [0052] When a large number of robots operate in a fluid system and absorb a selected chemical (hereafter “reactant”) as a function of their operation, their combined absorption of the chemical may potentially deplete its concentration to such a degree as to materially affect the function of the fluid system with regard to that reactant. As used herein, “materially affect” means that the concentration of the reactant can be reduced to such a degree in some locations in the fluid system that available reactant is insufficient for some intended purpose. In some cases, the operation of the robots is dependent on an adequate supply of the reactant (such as where the robots employ the reactant to generate operating power), and such insufficiency occurs when the available reactant in some location is too low for the robots in that location to operate as intended. In some cases, the fluid system serves primarily to distribute the reactant (such as in the circulatory system of an organism, where the blood distributes oxygen to cells throughout the body of the organism), and such insufficiency occurs where there is insufficient reactant in some regions compared to the concentration that is intended to be provided by distribution. In many cases, both of these situations exist, and insufficiency could be based on either or both of the intended needs of the robots themselves or the need of some other reactant-absorbing feature associated with the fluid system. To prevent such insufficiencies, the robots can be operated to limit their absorption under circumstances where it is appropriate, mitigating the effect of absorption of the reactant by such robots; in many cases, operation of the robots is adjusted in anticipation of an insufficient concentration of reactant that would arise later if operation were not adjusted at the present time. In some cases, robots can absorb and store reactant when in a location where the reactant is readily available (a “high-reactant region”), and later release such reactant for use when in a circumstance where available reactant is insufficient. While the examples discussed are directed to systems where the fluid is a liquid, the same techniques could be employed in systems where the fluid is a gas, in such cases where the absorption action of the robots is capable of causing material depletion of the reactant. [0053] FIG.1 is a flow chart that illustrates one example of a method 100 for mitigating absorption by limiting the absorption of robots when circumstances warrant such limiting action. At the start, a large number of robots are present in the fluid system, each of the robots being configured to absorb a selected reactant that is present in the fluid system, and where the combined absorption capacity of the robots is great enough that it can materially affect the function of the fluid system by causing depletion of the reactant in one or more regions, unless absorption is limited. In normal operation, the robots absorb the reactant (step 102). Some or all of the robots are operated such that a determination is made as to whether or not each such robot is in an absorption-limiting need condition (step 104); that is, a determination is made as to whether the current situation of the robot is such that it should limit its absorption of the reactant to avoid the creation of a depleted region. Responsive to a determination that an absorption-limiting need condition exists, the robot is operated so as to limit its absorption of the reactant from the surrounding fluid (step 106). The determination step 104 is repeated, and if an absorption-limiting need condition is determined to still exist, then the robot continues to limit its absorption of the reactant. If it is determined in step 104 that no absorption-limiting need condition currently exists for the robot, then it can resume operating in a manner where it does not limit its absorption of the reactant. 102 – Robots absorb reactant 104 – Determine whether absorption-limiting need condition exists 106 – Operate to limit absorption [0054] Prior to the start of the method, the robots can be introduced into the fluid system in a manner appropriate to the available access to the fluid system. Where the system is open at some location, the robots can be introduced at such location. Where the fluid system is fully enclosed, the robots can be introduced through an existing port or through a port installed, temporarily or permanently, for the purpose of introducing the robots. As one example, where the fluid system is the circulatory system or organ of a living organism, an injection or infusion device such as known in the medical and veterinary arts could be employed as a port to introduce the robots at a desired location (e.g., into a blood vessel or into the organ of interest). [0055] There are various criteria that could be used in step 104 to determine when an absorption-limiting need condition exists, and the specific criteria selected are typically dependent on the particular fluid system, reactant distribution, and intended operation of the robots. Typically, determining that an absorption-limiting need condition exists is made based on the anticipation that a reactant deficiency would result in some region of the fluid system in the future if absorption is not limited at the present time. One parameter that might be monitored to determine such a condition would be the rate of depletion of the reactant. In some cases, the location of the robot in the fluid system is one basis, or the only basis, for determining that an absorption-limiting need condition exists. For example, in a case where the fluid system has a high-reactant region, the absorption by the robots upon leaving such high-reactant region could create a gradient where the concentration of reactant decreases as the distance from the high-reactant region increases. If absorption is not limited, the reactant concentration at locations further from the high-reactant region may be insufficient for the needs of the robots and/or other reactant-using features associated with the fluid system. In such case, a routine 120 such as shown in FIG.2 could be employed in performing the step 104 of the method 100. [0056] In the example of the absorption-limiting need condition determining routine 120, a determination is made as to whether the robot has exited the high-reactant region (step 122). Upon such determination, an absorption-limiting need condition is assumed to exist (step 124), and the robot is operated to limit its absorption of the reactant, according to step 106 of the method 100. A determination is then made as to whether a triggering event has occurred (step 126), where such triggering event is indicative of the robot being in a situation where limiting its absorption is no longer required and/or desirable. A typical class of such triggering events occur when it is determined that the robot has reached a location and/or a stage of mission completion where it needs to use the reactant at a higher rate than can be supplied through limited absorption. For example, where the reactant is used to power the robots, a robot may need to perform a high-energy task (such as transmitting data) upon reaching a particular location in the fluid system, and/or upon having completed its mission to a particular degree. Some specific examples are determining that the robot has reached a particular location in the fluid system, has passed through a particular part of the fluid system a prescribed number of times, or that it has stored a prescribed amount of data. Upon determining in step 126 that such a triggering event has occurred, the robot returns (step 128) to operating in a mode in which it does not limit absorption of the reactant. 122 – Determine whether robot has exited high-reactant region 124 – Absorption-limiting need condition is assumed to exist 126 – Determine whether absorption condition triggering event has occurred [0057] FIGS.3 and 4 illustrate two examples of fluid systems having high-reactant regions. FIG.3 illustrates a static fluid system 150 where the fluid is a liquid 152, having a surface 154 that is in gas exchange with an atmosphere 156 that contains a reactant. The supply of dissolved reactant at the surface 154 creates a high-reactant region 158 near the surface, where the reactant is abundant. Robots 160 having a locomotion capability (such as ability to swim and/or ability to adjust their buoyancy) are distributed in the liquid 152, and those located in the high-reactant region 158 can absorb reactant without creating a deficiency, so long as their absorption rate is less than the rate at which dissolved reactant is replaced by gas interchange at the surface 154. As the robots 160 move, some exit the high- reactant region 158 near the surface 154 to operate at greater depths in the liquid 152. The absorption of such robots 160 may deplete the reactant in lower depths faster than the reactant can be replaced by diffusion, and would create a region at some depth where the concentration of reactant would be insufficient for the robots 160 to operate properly. To avoid this, robots 160 can limit their absorption of the reactant upon leaving the high-reactant region 158, and only resume full absorption when it is determined that they are in a condition, based on location, mission profile, or other considerations, that it is desirable for them to have more reactant available in order to perform their desired operation (such as to absorb a reactant used to generate power when the situation warrants a higher rate of power consumption to allow the robot to perform mission tasks), or simply when they are again in the high-reactant region 158. [0058] FIG.4 illustrates a fluid system 170 where a liquid 172 circulates through a circuit 174 that includes a high-reactant region 176 where reactant is supplied to the liquid 172 (one of example of such a circulating system is the circulatory system of a living organism, discussed in greater detail below, where the lungs/gills provide a high-reactant region where oxygen is replenished in the blood). Robots 178 can circulate with the liquid 172, and may be provided with a locomotion capability (allowing them to move relative to the flowing liquid 172) and/or an anchoring capability (allowing them to anchor to a wall of the circuit 174 so as to remain in place against the flow of liquid 172). As the liquid 172 circulates away from the high-reactant region 176, the absorption of reactant by the robots 178 causes a reduction in the concentration of the reactant (typically creating a gradient where concentration decreases with increasing distance from the high-reactant region 176), and may result in the reactant being insufficient for its intended function in regions of the circuit 174 that are distant from the high-reactant region 176, such as an end region 180 located before the liquid 172 returns to the high-reactant region 176. Again, such an insufficiency can be avoided if the robots 178 limit their absorption when exiting the high- reactant region 176, until such time as their situations are such that they need to absorb the reactant at a greater rate in order to perform mission tasks. [0059] There are a number of schemes that can be used in step 106 of method 100 to operate a particular robot to limit its absorption. One simple scheme is for the robot to cease the operation of the component(s) it uses to absorb the reactant. Some or all of such components could be deactivated, or the operation of such components could be adjusted to reduce their rate of absorption while they remain active (such as by reducing the operation rate or duty cycle). Another scheme is to operate the robot in such manner that the reactant available for it to absorb is limited, such as by traveling in a group with similar robots such that the group depletes the reactant in its close vicinity, and diffusion limits the available reactant for each robot in the group. Where alternative reactants are available, such as for use as a fuel, some robots could limit absorption of one reactant by switching to a different one. [0060] FIG.5 is a flow chart that illustrates one example of a method 200 for mitigating absorption by having robots store reactant when located in a high-reactant region, and later releasing such stored reactant. Depending on the situation, a particular robot could operate according to this method by itself or could operate according to this method as well as according to a method for limiting absorption, such as the method 100 discussed above. In some cases, some robots act as supply robots that are operated according to a reactant storage and release method, while other robots act as mission robots and operate according to an absorption-limiting method (although such robots may also employ a storage and release method as well). [0061] At the start of the method 200, a large number of robots are operating in the fluid system (step 202), where the fluid system has at least one high-reactant region and at least some of the robots are each configured to absorb and store reactant from the surrounding fluid. For purposes of discussion, only those robots that are operated to store and release reactant are addressed when describing this method; other robots that absorb the reactant may also be present. Similarly, while more than one high-reactant region could be present, the discussion addresses the case for a singular high-reactant region; where multiple high-reactant regions exist, the method could be applied to any of the high-reactant regions. The robots are operated such that a determination is made as to whether or not each such robot is in the high-reactant region (step 204). Such determination could be made based on sensing concentration of the reactant, by sensing fluid flow parameters that characterize the high-reactant region, and/or by use of location determination techniques. Responsive to such determination, the robot is operated to absorb and store reactant (step 206). So long as the robot is in the high-reactant region, it may continue to absorb and store reactant until such time as it is determined in step 204 that it is no longer in the high-reactant region. Optionally, the robot may stop absorbing upon determination that a triggering event has occurred (step 208), such as the storage capacity of the robot being reached (as determined by time spent absorbing, pressure, weight, etc.) When it is determined in step 204 that the robot is no longer located in the high-reactant region, it may optionally be operated to cease absorbing and storing reactant (step 210). Note that such action would also correspond to the step of limiting absorption in an absorption-limiting method, where an absorption-limiting need condition can be assumed to exist when a robot exits a high-reactant region. Alternatively, the robot could continue to absorb reactant normally after leaving the high-reactant region (i.e., skipping optional step 210). [0062] A determination is made as to whether a reactant need condition exists in the vicinity of each robot that is no longer in the high-reactant region (step 212). Such determination could be based on criteria similar to those discussed for determining when an absorption-limiting need condition no longer exists, such as by concentration sensing, fluid flow parameter sensing, and/or location determination, but could also be based on communication of such condition from an outside source, such as another robot. Upon such determination that a reactant need condition exists, the robot is operated to release stored reactant for use (step 214). Such release could be release from storage within the robot, to provide itself with reactant, or could be released for use by another robot, in which case the reactant could be released into the surrounding fluid or released directly to the other robot (when the two robots are docked together). 202 – Robots operate in fluid 204 – Determine whether robot is in high-reactant region 206 – Operate robot to absorb and store reactant 208 – Determine whether reactant storage triggering event has occurred 210 – Operate to limit absorption 212 – Determine whether reactant need condition exists 214 – Operate to release reactant [0063] FIG.6 illustrates one example of a reactant storage routine 230 that could be employed in the method 200, and which is suitable for fluid systems where the circulation of the fluid may pass the robot through the high-reactant region before the robot has had an opportunity to store a desired amount of reactant. In some cases, such situation could be avoided by the robot taking action to prolong its time in the high-reactant region, such as anchoring to a wall, actively moving against the flow of circulation, or positioning itself where the flow of fluid through the high-reactant region is slower. However, in cases where the robot flows with the fluid, the storage routine 230 could be employed. In the storage routine 230, after the determination has been made in step 204 that the robot is no longer in the high-reactant region, a determination is made as to whether or not the robot has a prescribed amount of reactant stored (step 232). This determination could be made by sensing a parameter such as pressure and/or or weight, or could be assumed from the robot having spent a sufficient time in the high-reactant region or made a sufficient number of passages therethrough (where the fluid circulates). If it is determined in step 232 that the prescribed amount of reactant has not been stored, the robot is operated in a low-use mode of operation (step 234) until such time as the determination in step 204 indicates that the robot is again in the high-reactant region. In the low-use mode of operation, the operation of the robot is adjusted to reduce its need to use the reactant. In cases where the reactant is used to generate power for the robot, the low-use mode of operation may be provided by limiting the function of the robot to reduce its power consumption. When in the low-use mode, the robot may ignore any determination of whether or not it is in a reactant need condition according to step 212. When it is determined in step 204 that the robot is again in the high-reactant region (or in a different high-reactant region, in a fluid system where more than one exists), the robot is again operated to absorb and store reactant in step 206. Once it is determined in step 204 that the robot has exited the high-reactant region, the determination is made again in step 232 whether or not the prescribed amount of reactant has been stored. Eventually, after some amount of time and/or number of passes through the high-reactant region, the step 232 determines that the prescribed amount of reactant has been stored, at which time the robot can be operated in a different mode than the low-use mode, and responds to a determination in step 212 that a reactant need condition exists in its vicinity by releasing stored reactant according to step 214. 232 – Determine whether prescribed amount of reactant stored 234 – Operate in low-use mode [0064] FIG.7 illustrates one example of a robot 300 suitable for performing an absorption-limiting method such as the example of the method 100 illustrated in FIG.1; robots suitable for practicing the methods discussed may not have all components and functionalities shown and described, and in some cases may have functional equivalents to the components illustrated. The robot 300 has a housing 302 and a controller 304 (provided by a microprocessor or similar logic and control component) located inside the housing 302. The controller 304 has an associated memory 306, containing an appropriate storage medium for containing instructions, in which a mission instruction set 308 is stored. A communication transceiver 310 may be provided, which can receive inputs to the controller 304, and can be operated by the controller 304 to transmit messages and/or data to other robots and/or to one or more remote receivers located within or outside the fluid system (for simplicity, some connections of various components with the controller 304 are not shown). The robot 300 has a number of intake pumps 312, which communicate with the exterior of the housing 302 and can absorb the selected reactant from the surrounding fluid. In the particular example of the robot 300, the intake pumps 312 serve to absorb a reactant that is used to generate power to operate the robot, and provide the reactant to a fuel cell 314 (while not shown, similar pumps could be employed to absorb a different reactant from the fluid for supply to the fuel cell for reacting with the selected reactant, such as one set of pumps absorbing oxygen and another set absorbing glucose). [0065] The robot 300 may be provided with various sensors, represented in this example by sensors 316, 318, and 320. The type of sensors employed is typically determined by the intended mission, and the sensor types shown merely represent some examples that could be used. In this example, the sensors include a concentration sensor 316, an array of surface stress sensors 318, and a location sensor 320. The concentration sensor 316 provides the controller 304 with a signal indicative of the concentration of the selected reactant at the location of the robot 300. The stress sensors 318 provide the controller 304 with signals indicative of the distribution of stresses about the housing 302, which can be processed to provide information about relative location, fluid flow, and/or characteristics of the fluid system, as disclosed in US Patent 11,526,182. While the stress sensors 318 could provide information on the location, the location sensor 320 can be provided to supplement or replace them and provide the robot 300 with an indication of its current location in the fluid system. Examples of location sensors (other than stress sensors) could include a clock and sensors to determine flow speed (to navigate by dead reckoning), sensors for receiving location signals from a network or array of transmitters, sensors capable of determining nearby tissue, cell, and/or microbe types, sensors for detecting specific environmental conditions (chemical, pressure, thermal, etc.), sensors for detecting features for comparison to a stored map, or other sensors appropriate for navigation within the particular fluid system. [12]. It should be noted that some sensors could provide the functions of others; for example, a concentration sensor could indicate that the robot is within a region where the concentration of the particular chemical being sensed is known to be high or low (such as determining when the robot is within a high-reactant region) and thus serve as a location sensor, stress sensors could be used to determine that the robot is located in a vessel of a certain size and serve as location sensors, etc. [0066] The sensors (316, 318, 320) may be sufficient to allow the robot 300 to perform its intended mission, such as when mapping the distribution of a chemical of interest or mapping the vessels of a fluid system. In some cases, one or more mission-specific components are provided, as indicated by mission-specific component 322. The mission- specific component 322 can be any component designed to aid the robot 300 in performing a desired mission, typically in cooperation with sensors such as the sensors (316, 318, 320) to determine when it is appropriate for the robot 300 to take a particular action. Examples of mission-specific components could include a mission port to release a mission-related chemical (such as a pharmaceutical agent, an agent that changes fluid viscosity, a marker agent that is remotely detectable, etc.), an energy transmitter to direct electromagnetic radiation, acoustic energy, thermal energy, etc. at a target site, an electrode to electrically stimulate or monitor current or voltage at a target site, a mechanical manipulator, a diagnostic probe, and/or a sample collector. [0067] The robot 300 may be provided with a locomotion component 324 and/or an anchoring component 326, either or which can be employed when it is desired for the robot 300 to not be freely carried by the fluid. The locomotion component allows the robot 300 to move through the fluid, while the anchoring component 326 allows the robot to anchor to a wall of the fluid system so as to remain in place while the fluid flows past. In some cases, the anchoring component 326 could be designed to allow joining to another robot. [0068] Depending on the particular mission that the robot 300 is designed for, some components as described may not be present or may function differently than described. For example, where the robot only needs to respond to transmitted instructions, the “transceiver” 310 could only receive, and where the robot only needs to transmit data and/or message, the “transceiver” 310 could only transmit. [0069] The mission instruction set 308 can include instructions for operating the robot 300 to perform one or more intended missions, which may make use of the sensors (316, 318, 320) and, optionally, one or more mission-specific components 322. In addition to whatever instructions are needed to operate the robot 300 to perform its intended mission functions, the mission instruction set 308 includes instructions for directing the controller 304 to operate the robot 300 to perform the operations of determining when the robot 300 is in an absorption- limiting need condition (similar to step 104 of the method 100), and responsive to the determination that the robot 300 is in an absorption-limiting need condition, operating the robot 300 in such a manner as to limit its absorption of reactant from the surrounding fluid (similar to step 106 of the method 100). In making the determination and operating the robot to limit its absorption, any of the techniques discussed above with regard to examples of methods for operating a swarm of robots could be employed. The determination could be made based on information obtained by the sensors (316, 318, 320), based on information stored in the memory 306, and/or messages received by the transceiver 310. Limiting the absorption could be achieved by adjusting the operation of one or more of the intakes pumps 312 and/or by changing the location of the robot 300 by operating the locomotion component 324. [0070] FIG.8 illustrates one example of a robot 350 that is similar to the robot 300, but which is also suitable for performing storage and release of reactant, such as discussed in the example of the method 200 illustrated in FIG.5. The robot 350 has a storage and release instruction set 352 stored in the memory 306, and a reactant storage tank 354 which can receive reactant from the intake pumps 312 and can release the stored reactant. The reactant could be released to the fuel cell 314 via an optional supply duct 356, and/or could be released to an optional outlet port 358 (which in turn can release reactant into the fluid surrounding the robot 350 or could be designed to dock with another robot and release the reactant directly to an intake pump or other component of that robot). The storage and release instruction set 352 includes directions for the controller 304 to operate the robot 350 so as to perform the operations of, determining when the robot 350 is in a high-reactant region (similar to step 204 of the method 200) and, responsive to such determination, operating the 350 robot to absorb and store reactant (similar to step 206 of the method 200), as well as instructions for determining when a reactant need condition exists in the vicinity of the robot 350 (similar to step 212 of the method 200), and responsive to such determination, operating the robot 350 to release reactant (similar to step 214 of the method 200). The storage and release instruction set could also be considered as a supply instruction set; in general, where the reactant is released from storage for use by the robot itself (such as releasing reactant from the storage tank 354 to the fuel cell 314 via the supply duct 356), it is a “storage and release instruction set”, and when released for use by another robot (such as releasing reactant from the storage tank 354 via the outlet port 358), it is a “supply instruction set”. In practice, some robots may include both options, releasing reactant for their own use when necessary for their own operation, and releasing reactant for use by another robot when necessary for that robot’s operation. In some cases, reactant may be released into the surrounding fluid for the operation of some feature associated with the fluid system which is not another robot, to offset depletion of the reactant by robots in some region of the fluid system. In making the determinations and operating the robot, any of the techniques discussed above with regard to examples of methods for operating robots to store and release reactant could be employed. The determinations of when the robot 350 is in a high-reactant region and when a reactant need condition exists could be made based on information obtained by the sensors (316, 318, 320), based on information stored in the memory 306, and/or messages received by the transceiver 310. The action of absorbing and storing the reactant is typically achieved by operating the pumps 312 and the storage tank 354, but may also make use of the locomotion component 324 and/or the anchoring component 326 to allow the robot 350 to remain for a longer time in the high-reactant region. The action of releasing the reactant operates the storage tank 354 and one or more of the supply duct 356 and the outlet port 358, and may again make use of the locomotion component 324 (such as to move towards another robot to dock with it to directly transfer reactant) and/or the anchoring component 326 (such as when it is desired for the robot 350 to remain within a particular location in the fluid system while releasing reactant to the surrounding fluid). Where the robot 350 is intended primarily for storing reactant for later release at a different location (i.e., a “supply robot”), it typically would not have any mission-specific component 322, and may lack other components and/or functionalities shown. [0071] FIGS.9 and 10 illustrate one example of a group 400 of robots 402 & 404 where the robot 402 is designed to perform a desired mission, and the robots 404 are each designed to store reactant and supply it for use by the mission robot 402 (or another mission robot, not shown); for purposes of illustration, only the small group 400 is shown, but in practice a very large number of robots (402, 404) of each type would be employed, distributed throughout the fluid system. The robots (402, 404) can include components as discussed above for the robots 300 & 350, but for clarity only a subset of the components are illustrated in FIGS.9 & 10. [0072] FIG.9 illustrates one option for releasing stored reactant, where two supply robots 404 in close proximity to the mission robot 402 release reactant from storage tanks 406 through outlet ports 408 into the surrounding fluid (as indicated by the arrows pointing out of ports 408). This release increases the concentration of the reactant in this region, and the reactant can be absorbed by pumps 410 on the mission robot 402 (as indicated by the arrows pointing into pumps 410). FIG.10 illustrates one alternative option, where one of the supply robots 404 docks with the mission robot 402 to transfer reactant directly to it via mating ports 412, 414 (which could also serve respectively as an outlet port 408 and a pump 410). To move together to dock, either or both of the robots (402, 404) could employ a locomotion component 416. [0073] The group 400 includes several supply robots 404 for a single mission robot 402, and the supply robots 404 are each smaller in size than the mission robot 402. Smaller size allows optimizing the supply robots for more rapidly absorbing and storing reactant while in a high-reactant region, since reactant diffuses more quickly to a large number of smaller robots than to a smaller number of larger robots. Additionally, as their only function is to supply reactant to mission robots 402, the supply robots only require the sensors, instruction sets, and other components to perform their storage and release operations, and typically require less interior space to accommodate the components needed to perform their function. For many situations, the number of supply robots is significantly greater than the number of mission robots, such as at least 5x, 10x, 20x, or 40x the number of mission robots. The supply robots may be no greater than half the size (by volume) than the mission robots, and may be considerably smaller, such as ¼ the volume, 1/8 the volume, 1/16 the volume, or 1/32 the volume. Smaller robots have a greater ratio of surface area to volume, and thus are able to fill storage tanks faster than larger robots. The rate molecules arrive at the robot is proportional to its radius r _robot (see Eq.1 below), while tank capacity is related to its volume, which is proportional to r _robot ³ (assuming the tank occupies a set fraction of the robot volume); thus the time to fill a tank scales as r _robot ² . EXAMPLE [0074] The particular robots to be employed and method of employment can be designed for a particular intended application. The following discussion addresses one possible example of a circulating fluid system, where oxygen is the reactant and is used to power the robots. The discussion addresses several considerations in limiting absorption of oxygen by a swarm of robots operating in the fluid system. For this example, the fluid system is a model of a human circulatory system, where blood flowing through vessels of the fluid system is recharged with oxygen in the lungs and becomes gradually depleted of oxygen as it flows through the body before returning to the lungs. Most of the circulation through the body passes through a single capillary network between arteries and veins, and this typical case is the basis for the model fluid system described. Other situations, such as portal flows where the blood flows through two sets of capillaries, require generalizing the model considered here. This particular example illustrates the type of considerations used for designing and operating robots for a particular application. The general principles for determining parameters, as well as particular features, behaviors, criteria for making determinations, and other details described with respect to this example should be applicable to alternative applications, modified as necessary to suit the particular situation. [0075] For purposes of discussion, the model assumes the use of robots powered by fuel cells that oxidize glucose. Oxygen is the rate-limiting chemical for this reaction, since its concentration in the blood is much lower than that of glucose, and the maximum possible power for robots is when they use all oxygen reaching their surfaces. Throughout this example, “power” may be used interchangeably with “oxygen” when discussing the availability of the reactant to the robots. [0076] When the distance between neighboring robots is large compared to their size, a good approximation of robot oxygen collection is that of an absorbing sphere. Such a robot in blood plasma with oxygen concentration c absorbs oxygen at the rate [5]: ( ¹⁾ where D _O 2 is oxygen’s diffusion coefficient in plasma and r _robot is the robot radius. Absorption can be close to this value even when only a few percent of the robot surface absorbs oxygen [5]. [0077] The reaction energy of glucose oxidation and rate of oxygen absorption determine the power generated by the fuel cell. Not all of that power is available for robot operations due to losses in the power system. These losses include dissipation in wires connecting fuel cells to loads in the robot and internal losses in the fuel cell, e.g., due to membrane transport and incomplete catalysis. We characterize these losses by the fuel cell efficiency, f _robot : the fraction of the full reaction energy available to the robot. The power available to the robot from glucose oxidation is: (2) where e is the energy released by oxidizing a glucose molecule and the factor of 1/6 arises from the need for six oxygen molecules to oxidize each glucose molecule. [0078] A small number of robots in the bloodstream have no systemic effect on oxygen concentration. In that case, the normal concentrations found in the circulation determine the power available to the robots and nearby tissue, whether the robots are widely separated or form aggregates [19]. However, large numbers of robots may consume a significant fraction of the oxygen in the blood. Red blood cells carry most of the oxygen in blood. These cells release oxygen in partial compensation for that consumed by the robots. This replenishment depends on the concentration of red blood cells, i.e., the hematocrit. In small vessels, cells typically travel a bit faster than plasma, leading to a reduced hematocrit in these vessels [28]. In addition, tissue consumes oxygen from nearby capillaries. [0079] Estimating systemic effects of robot oxygen consumption does not require precise vessel geometry of each of the many circulatory paths through the body. Instead, vessels of each size can be considered as an aggregate, with the flow through an average aggregated structure for a single loop around the circulation being shown in FIG.11, illustrating circulation from lungs 1102 to the rest of the body 1104 and back to the lungs 1102; the lungs 1102 in this case provide a high-reactant region that the fluid circulates through. This loop starts as fully oxygenated blood leaves a lung capillary 1102 via a pulmonary vein 1106 and continues through the heart 1108, aorta 1110, body 1104, and vena cava 1112 and back though the heart 1108, until the blood next reaches a lung capillary from a pulmonary artery 1114 (while passage through the lung capillary at the end of the circuit contributes to the total circulation time, it is not addressed in this model as even 10 ¹² robots do not significantly alter the oxygen available in lung capillaries). A useful simplification for evaluating the typical power available to robots is to average over the vessel cross section, which gives a one-dimensional model of the blood flow. Further discussion of the model used for the present example is provided below in the section “Vessel Circuit Model”. [0080] A circulation loop takes about one minute average (actual time to complete a circuit depends on where the blood goes, e.g., shorter times for transit through the head than through the feet). Evaluating behavior on this time scale averages over the short-term variations in flow speeds, particularly in arteries, due to heart beats. The present model also considers a fixed, resting pose for the body and does not treat longer-term variations from changes in activity level or environmental factors. This temporal averaging leads to a steady- state profile of oxygen concentration in a typical circulation loop. The change in oxygen concentration in each part of the circuit depends on its transit time and hematocrit. A blood vessel model can define both the fraction of the blood volume occupied by red blood cells (the “hematocrit”) and the transit time (based on flow speed) as functions of vessel diameter. For the hematocrit, the fluid flow in small vessels tends to push cells toward the center of the vessel where they move faster than the average speed of the flow. This Fahraeus effect decreases the hematocrit in small vessels. On average, the hematocrit in vessels greater than 1mm varies little (h ≈ 0.45), while in smaller vessels the hematocrit decreases with size, such that 8µ dia. capillaries have a hematocrit (h = 0.34). Blood flow speed is dependent on vessel size, and aggregated vessels provides a circuit transit time model as shown in FIG.12 where the vertical Axis indicates distance in millimeters and the horizontal axis indicates time in seconds. The vertical lines near the center indicate passage through a capillary. Dashed lines show regions where interpolation is used to model arteries and veins of changing size. [0009] Considering a small volume of blood moving through the circulation, containing plasma, blood cells, and robots, a concentration model as shown in FIG.13 consists of four compartments. Blood vessels contain three of these compartments: blood plasma 1302, blood cells 1304, and robots 1306, where robots occupy a small fraction of the plasma volume, and are assumed to move with cells, rather than with plasma. The fourth compartment in this model is the tissue 1308 around capillaries. Oxygen concentration in the moving volume of blood changes due to the combination of consumption by robots and tissue, and oxygen release by red blood cells to maintain equilibrium. Table 1 [0081] Table 1 lists some typical values for proposed swarm applications [12] for use in determining robot power and oxygen concentration in the model shown in FIG.13. Nanocrit is the fraction of the blood volume occupied by robots (in analogy with hematocrit, which is the fraction occupied by cells). The robot spacing is the typical distance between neighboring robots. The value for large vessels is the cube root of the average blood volume per robot. In capillaries, the spacing is from the blood volume in an 8µm-diameter vessel, up to a maximum capillary length of 1mm. The spacing in the body is the cube root of the average body volume per robot for a nominal 50L body volume. The largest number of robots considered here, 10 ¹² , have a combined mass of several grams and volume of a few milliliters. The table gives typical spacings between robots in large vessels, within capillaries and between nearby small vessels. These spacings are much larger than the size of the robots so that the robots typically do not directly compete with neighboring robots for oxygen, in contrast to situations where robots operate in close proximity [19]. In large vessels the nearest robots are within the same vessel, but in small vessels, the nearest robot may be in a neighboring vessel. [0082] Micron-size robots (i.e., robots with a radius on the order of about 1µm) have considerably smaller volume than red blood cells, so even the largest number of robots considered here occupy less than 0.1% of the blood volume, compared to 45% typically occupied by blood cells. This small fraction of robots does not significantly affect blood rheology [12], allowing the model to use typical flow speeds in the absence of robots. Devices are assumed to have sufficient power-generating capability to consume all oxygen reaching their surface, so that oxygen concentration in the plasma and its diffusion rate to the robot surface are the limiting factors for the power available to the robots. [0083] To model oxygen consumption as the blood circulates, the flow of the blood can be considered as flowing through a single aggregated vessel consisting of two compartments, plasma 1302 and cells 1304, where the cross sections of these compartments varies along the length of the vessel as the larger vessels branch into smaller vessels (increasing the aggregated cross section) and then the smaller vessels join together again into larger vessels (decreasing the aggregated cross section), and where the fraction occupied by cells (i.e., the hematocrit) is smaller in smaller vessels (see FIGS.34 & 35). Robots 1306 are a small portion of the blood and can be ignored for purposes of determining flow. The plasma and blood cell compartments exchange oxygen with each other, and with robots and tissue. The section “Oxygen Concentration in Vessels” discusses concentration changes, first considering how oxygen concentration changes in vessels with variable cross section for a single vessel, then for an aggregated vessel having two compartments exchanging oxygen, to determine how concentration changes in a volume of fluid moving with the flow in one of these compartments. This differs from behavior in vessels of a fixed cross section, due to the changing cross section and fraction of the total cross section occupied by each of the two compartments. To determine the power available to a robot throughout the circulation loop, the concentration in a volume of blood (containing the robot) moving through the circulatory system is determined using this compartment model. [0084] FIG.14 shows how robot power varies during a circulation loop in the case where robots consume oxygen as fast as it diffuses to their surfaces, so robot power is given by Eq.2 above. FIG.14 shows power in picowatts as a function of time in seconds, for three different total numbers of robots distributed through the circulation loop. FIG.14 shows the power used starting when a robot leaves a lung capillary (0 seconds) and ending just before it next enters a lung capillary, with the light vertical lines indicating when the robot is in a capillary. Robot power decreases as the robot moves from the lung: hundreds of picowatts in the arteries, an abrupt reduction in the capillary where tissue competes with the robots for oxygen, and a continued gradual decrease as the robot travels through veins back to the lung. The consequences of this variation in power during a circuit depend on how well it matches the power requirements of the robots’ tasks. For instance, if the robots require a significant amount of power to maintain their activity, the minimum power available during the circulation (i.e., just before returning to the lung) is a significant result from this model. If this minimum is below the required power, either the task needs to use fewer robots or the robots need sufficient onboard energy storage to support their activities until they return to the lung. Some applications could have flexible timing of robot power demand. These tasks could include computation to evaluate sensor measurements, maintenance tasks such as checking robot functionality, and communicating information to other robots. In such cases, robots could wait until there is abundant power to perform these tasks, e.g., while passing through arteries. In other cases, the robots might have their highest power demand during the short time they pass through capillaries. For instance, robots might need to move to cells near the capillary that are emitting chemicals into the blood, thereby requiring the robots to measure, compute and propel themselves while in the capillaries [17]. In this case, a significant result from FIG.14 is the power available while robots pass through capillaries. [0085] To further illustrate the consequences of robots using oxygen for power, FIGS. 15A and 145B show oxygen concentration (in units of 10 ²² oxygen molecules / m ³ ) in the plasma (FIG.15A) and red cell saturation (FIG.15B) as a function of time in seconds, and compares the values shown for different numbers of robots in FIG.14 with the values for a situation without robots (top line), in which case the only oxygen consumption occurs in tissue around the capillaries. In FIG.15A, oxygen concentration in plasma is expressed in molecules per unit volume (macroscopic studies usually express concentrations in more readily measurable quantities such as moles of chemical per liter of fluid or grams of chemical per cubic centimeter, and discussions of gases dissolved in blood often specify concentration indirectly via the corresponding partial pressure of the gas under standard conditions; as an example of these units, oxygen concentration CO ₂ = 10 ²² molecule/m ³ corresponds to a 17µM solution, 0.53µg/cm ³ and to a partial pressure of 1600Pa or 12mmHg, and this concentration corresponds to 0.037cm ³ O2/100cm ³ tissue with oxygen volume measured at standard temperature and pressure). In FIG.15B, relative oxygen saturation of red cells is shown, where 1 is fully saturated cells (as they exit the lungs). The light vertical lines indicate when the flowing blood is in a capillary. For the cases where the swarm contains 10 ¹⁰ or 10 ¹¹ robots, the diffusion limit on the rate oxygen reaches the robot surface (i.e., Eq.1) prevents the robots from fully depleting oxygen in the blood. That is, as is the case without robots, the blood returns to the lungs with much of the oxygen it originally took from them. By contrast, a swarm having one trillion (10 ¹² ) robots that consume oxygen as fast as possible completely depletes oxygen by the end of the circuit. This would significantly impair the ability of the fluid system to provide the intended function with regard to providing sufficient oxygen to power the robots. Such depletion could also impair the function of the fluid system in supplying oxygen to vein walls near the end of the circuit, before the blood re-enters the lungs. [0086] Values for parameters used for the present example are presented in Table 2 below. The sources for these values are given in the section “Model Parameters” below. Table 2 [0087] A significant consequence of robots consuming oxygen is their effect on oxygen available to tissue. Robots consume oxygen in arteries bringing oxygen to capillaries, and compete with tissue for oxygen in the capillaries. Much of the oxygen that robots use comes from red cells, which limits the decrease in concentration in plasma. Nevertheless, robot consumption leads to some reduction by the time blood reaches the capillaries, as shown in FIG.15A. The extent to which this reduced concentration affects tissue depends on the minimum oxygen that tissue requires to support its metabolism. Tissue demand leads to the abrupt reduction in concentration in capillaries seen in FIG.15A. Even with the largest number of robots considered here, the concentration in capillaries is sufficient to support resting tissue demand. Specifically, cellular functions continue to operate normally until oxygen partial pressure is below 5mmHg [9], corresponding to concentration 0.4 × 10 ²² molecule/m ³ . This is lower than the capillary concentrations seen in FIG.15A. [0088] The conclusion of sufficient oxygen for tissue also follows from treating the tissue surrounding the vessel as homogeneous and metabolizing oxygen at the rate that produces power according to: (3) where is the nominal demanded power density (i.e, power per unit volume) of the tissue and is the concentration of O ₂ giving half the maximum reaction rate. When oxygen concentration is substantially larger than Ktissue, tissue power is nearly independent of oxygen concentration. [0089] FIG.16 shows tissue power relative to its maximum value with unlimited oxygen, for the time (in seconds) when the blood flows through the capillaries, for the case of no robots or for the three numbers of robots as in FIGS.14-15B. The reduction in oxygen in capillaries due to robots has only a minor effect on tissue power in the case considered here, i.e., resting metabolic demand. Blood typically transports much more oxygen than required by tissue (such as to support peak metabolic rate, which can be as high as 200kW/m3 [27]) and so provides a buffer for any localized increase in tissue metabolic demands. [0090] While FIG.16 illustrates power available in the capillaries (which is most relevant for availability of oxygen for tissues), FIG.15A shows that the lowest oxygen concentrations occur toward the end of the circulation loop, as robots return to the heart and then to the lungs. Normally, blood returning to the lungs contains a significant portion of the oxygen originally collected in the lungs. Robots can make use of this oxygen without concern of reducing oxygen available to tissue since this blood has already passed through capillaries to deliver oxygen to tissue. A caveat to this conclusion is that cells comprising the walls of blood vessels consume a portion of the oxygen carried in those vessels. Specifically, small arteries and veins, and the inner portion number of walls of larger vessels, receive nutrients that diffuse into the wall from the blood carried in the vessel [34]. These cells form a small fraction of the body tissue so their oxygen use is not a significant contribution to total tissue oxygen consumption. Moreover, the small diffusion distance of oxygen and the relatively large volume of the vessels compared to capillaries means consumption by the vessel walls does not significantly alter the concentration in the vessels during the time blood flows through them, and this oxygen consumption can be ignored in the model. [0091] However, the lowered oxygen concentration in veins due to the robots could be a safety issue. For example, normal leg veins have oxygen concentrations of about 30– 40mmHg and red cell saturation 50–70% [25], where 30mmHg is 2.5 × 10 ²¹ /m ³ . These ranges are a bit below the values toward the end of the circulation loop with 10 ¹¹ robots. This comparison suggests lowered concentration in veins should not be an issue when using that many robots, but could be significant for larger numbers of robots. The oxygen requirements of vein walls may place more stringent constraints on robot oxygen consumption than the requirements of most tissue, which receives nutrients from capillaries. Quantifying this constraint requires determining the minimum concentration these cells can tolerate for various amounts of time. An initial assessment is to assume these cells have requirements similar to those of resting tissue. In that case, FIG.15A shows that 10 ¹² robots could be detrimental to vessel walls over the last 15 second or so of the circulation unless their absorption is limited. [0092] Robot power production adds heat to the body, arising from the full reaction energy in the fuel cells, not just the fraction available for the robot’s use. The total dissipation from all the robots equals the average available power over a circulation, multiplied by the number of robots and divided by the fuel cell efficiency. Table 3 gives values for average power over the circulation time, minimum power (just before returning to the lungs), and total energy dissipation from the oxygen consumed by all the robots, for the three cases using the numbers of robots in Table 1. For comparison, typical basal metabolism is 100W or 2000kcal/day. The table shows that 10 ¹⁰ robots, each consuming as much oxygen as it can, add less than 10% to basal metabolism. On the other hand, 10 ¹² robots add more than twice the basal amount, thereby adding significant heat to the body. This is well below the heat dissipation during exercise [12], but nevertheless may be a limiting factor during prolonged robot operation. Table 3 [0093] The oxygen concentration profile produced by robots alters assumptions underlying some clinical measurements, particularly the relation between direct measurements and inferred properties based on causal relationships in the body [4]. For instance, normally oxygen is only removed from blood in capillaries so the arterial concentration is the same throughout the body. This is the basis for pulse oximetry, a common, noninvasive measurement of respiratory heath and oxygen supply to organs [29]. Large numbers of robots consume oxygen in arteries, leading to significant concentration reduction in the vessels between the lung and capillaries, as shown in FIG.15A. In the presence of such robots, pulse oximetry may require modified calibration to account for variation in arterial oxygen depending on body location and the time since the blood left the lung. These systemic changes could also affect the interpretation of other large-scale functional oxygen measurement techniques, such as photoacoustic imaging [6]. The model described here indicates how oxygen varies with location and could aid in calibrating and interpreting these measurements. [0094] As compensation for their alteration of conventional clinical measurements, robots should be able to measure oxygen concentration throughout the body at micron length scales, thereby far surpassing the accuracy and quantity of external measurements. Interpreting such measurements may need to account for the systemic changes in concentration produced by the robots. In spite of this robot capability, recalibrated conventional sensors remain useful as checks on robot performance and to allow comparison with established clinical practice. Moreover, receiving measurements from robots may be delayed due to communication limits, e.g., if robots must wait until they are near the skin to send information out of the body. Delays or reduced information could also occur if continual communication takes too much power away from the robots’ main tasks. In such cases, the improved sensing capability of robots may not be as readily available as measurements from conventional sensors. Robots in Capillaries [0095] In some applications, robots would perform most of their tasks in capillaries, e.g., to monitor or act on individual cells accessed from capillaries. In this case, robots could initially travel through the circulation until they reach capillaries, at which point they attach to the capillary walls to perform their primary function. Robots in lung capillaries would have access to the oxygen not taken by red cells, as discussed below. However, robots in capillaries of the systemic circulation would only consume oxygen from blood passing through capillaries, rather than during the entire circulation. [0096] Applying the model described above to robots positioned in systemic capillaries requires two modifications. First, there is no robot oxygen consumption in arteries or veins, since they do not contain robots. Second, since these capillaries contain about 5% of the total blood volume [12], the number density of robots in capillaries is about 20 times larger than when they are distributed throughout the blood volume. With these modifications, FIGS.17A & 17B illustrate how robot power (FIG.17A) and oxygen concentration (FIG. 17B) vary in a capillary with typical length of 1mm (arterial flow arriving from the left). Since there is no oxygen consumption in arteries in this scenario, the oxygen concentration in blood entering the capillary does not depend on the number of robots. Oxygen concentration and robot power decrease through the capillary, so robots near the venous end of the capillary have less power. If necessary, robots near the arterial end of the capillary could reduce their power to leave more available for downstream robots. FIG.17A shows the decrease in robot power (in picowatts) with distance (in millimeters) along the capillary, while FIG.17B shows decrease in oxygen concentration (in 10 ²² molecules per cubic meter) in plasma with distance. Comparing FIG.17B with FIG.15A shows that the oxygen concentration in blood after passing through a capillary is similar to that when robots are distributed throughout the blood and consume all oxygen reaching their surface. In both cases, the robots extract about the same amount of oxygen from circulating blood, up to the time it passes through a capillary. The average power per robot and their total dissipation are similar to the values in Table 2. However, this power is entirely generated in capillaries, giving a much larger power density in the blood as it passes through capillaries. For example, 10 ¹⁰ robots heat capillaries at an average rate of about 30kW/m ³ . This is several times the resting tissue power demand used in this model (see Table 2), and comparable to the power density for cells with high metabolic demands, such as heart or kidney cells [12]. Nevertheless, heat transport by blood and through tissue is rapid enough at these small scales that this increased power density does not result in much local temperature increase, even when robots are close enough to come into contact [19]. This indicates that even when all robots operate in capillaries, the main heating issue is for the body as a whole due to the large number of robots, as discussed above, rather than local heating in capillaries. [0097] While FIGS.17A & 17B show the average behavior in capillaries, the small blood volume in individual capillaries leads to considerable variation due to differences in capillary type [12], flows within a network of connected capillaries, and the precise locations of robots in a capillary. For instance, at the lower range of the numbers of robots considered here, each capillary has only a few robots, on average, so that the actual number of robots varies considerably among capillaries, including many capillaries with no robots. [0098] The circulation model considered here does not evaluate variation in oxygen concentration at micron length scales, such as oxygen diffusion across a vessel. Moreover, the model assumes robots are sufficiently far apart that they do not compete with neighboring robots for oxygen. From Table 1, this is reasonable even when all the robots are in capillaries, up to about 10 ¹¹ robots or so. However, with 10 ¹² robots in capillaries, the distance between neighboring robots is only somewhat larger than their diameter, and that many robots create some competition for oxygen, reducing the oxygen they collect and the power they generate compared with the model’s predictions. [0099] To illustrate the effect of competition among neighboring robots and diffusion across capillaries, the effect of oxygen diffusing in the fluid moving through the vessel can be modeled using common software, such as Comsol, to compute the concentration distribution in the fluid to compare two situations, as shown in FIGS.18A & 18B, where robots 500 are positioned in a small segment of a capillary 502 with the average spacing corresponding to 10 ¹² robots in the capillaries, where five robots 500 are anchored to the inner wall 504 of an 8µm-diameter vessel with 5.5µm spacing along the vessel. The vessel segment 502 shown here is 34µm long. These examples differ in the positioning of successive robots: alternating between opposites sides of the vessel (FIG.18A) or all on the same side (FIG.18B). Modeling was conducted for each of the two robot positions shown in FIGS.18A & 18B, for each of two fluid flow speeds (0.2mm/s and 1mm/s) that are within a typical range for capillaries [12], using the oxygen diffusion coefficient from Table 2. The models showed large variations in concentration along the vessel, particularly near each of the robots. This contrasts with the monotonically decreasing concentration from the averaged circulation model shown in FIG.17B. For the slower flow speed, oxygen concentration decreased significantly before reaching the third robot in both arrangements, and varied across the width of the vessel with a lower concentration on the side nearest a robot. The concentration variation across the vessel was particularly large at the higher flow speed, where oxygen does not have enough time to diffuse throughout the vessel cross section while the fluid passes the robots. Robots positioned on the same side of the vessel increase the difference in oxygen concentration between the two sides of the vessel compared to robots on alternate sides. An interesting result is that robots farther downstream have more available oxygen when the robots are on the same side vs. on different sides, as the side opposite is less depleted, allowing more oxygen to diffuse across the vessel at the point where the downstream robots are located. The differences in oxygen concentration around the robots leads to variation in the rate oxygen molecules reach the robot surface, depending on robot position and fluid speed. [0100] While the large-scale model shown in FIGS.17A & 17B describes behavior averaged over capillaries, the oxygen concentration and robot power may vary considerably from this average in individual capillaries, because of both variations in the number of robots in the small volume of blood in a capillary and the positions of the robots on the capillary walls. There could be additional variations due to features of the flow not included in this model of oxygen transport in capillaries. For instance, it neglects oxygen consumption by nearby tissue cells, the possibility of oxygen diffusing out of the vessel and then back to the robots due to the large concentration gradient near their absorbing surfaces. Moreover, the model assumes the oxygen saturation of passing blood cells remains in equilibrium with the concentration in the fluid. Accounting for tissue consumption, diffusion outside the vessel, and the kinetics of oxygen release from blood cells gives similar large concentration gradients near absorbing robots on a vessel wall [19]. Additional changes to the oxygen concentration could arise from blood cells as they distort to move past robots anchored to the vessel wall. [0101] An additional consideration for robots remaining in capillaries rather than moving with the blood is the extent to which such robots increase the vascular resistance of the flow, particularly in the narrowest capillaries, since vascular resistance of these vessels is inversely proportional to the fourth power of their diameter according to Poiseuille’s law [16]. As an example, the pressure drop for a vessel without robots compared to a vessel with robots such as shown in FIGS.18A & 18B indicates that the robots increase the vascular resistance by about 20% in each case (slightly higher for offset robots, but a difference likely beyond the accuracy of the model used). Robots on vessel walls may further increase the resistance by changing how blood cells distort as they move past the robots. As an extreme, robots could block passage of the cells. If this increased resistance reduces the blood flow, robots and the tissue around the capillaries would not receive new oxygenated blood as rapidly as assumed by the circulation model. Alternatively, the body may compensate for the increased resistance by a corresponding increase in the blood pressure. Avoiding injury from robot blockage or increased blood pressure may limit the number of robots that can be stationed in capillaries, and how long they can remain there. This could be a significant limitation on applications that require longitudinal data on individual cells over an extended period of time. [0102] An alternative way to collect information from the same cell over a period of time that avoids blocking capillary blood flow is by using robots that move with the blood, as considered by the average circulation model, where the robots collect data while passing through a capillary. By collecting sufficient data to uniquely identify the capillary and their location within it, post-processing could match data collected by different robots at different times from the same capillary, thereby reconstructing longitudinal observations with single- cell resolution. Instead of continuously monitoring cells, this would collect snapshots each time a robot passes through a capillary near the cell. On average, each of n robots completes a circulation in t = 60s and passes through about 1.25 capillaries in the systemic flow (including a portion portal flows that pass through more than one capillary during a single circuit [10]). On average, robots pass through a given capillary at the rate r = 1.25n/t/N where N ≈ 2×10 ¹⁰ is the number of capillaries in the systemic circulation [12]. The average time between successive robots is 1/r. For example, with n = 10 ¹² robots, a robot passes through a capillary about once a second, though with considerable variation around this average value. If this is adequate temporal resolution for the task, and robots can collect data while moving with the flow instead of, e.g., requiring probes into the vessel wall, then collecting data as robots move through capillaries is a viable alternative to robots attached to the wall. In either case, the robots would mainly be active and consuming oxygen during the time they are in capillaries, so FIGS.17A illustrates their average power. This alternative does place larger demands on robot data storage, since the robots need to collect not only the cell measurements of interest but also the data required provide the unique identifications. On the other hand, robots moving in capillary networks could also use their interactions with the flow and other robots to perform distributed microfluidic computation [31] to provide useful information on the microcirculation. Patient Variation [0103] Disease and injury could alter oxygen availability and affect the power available to robots treating sick or injured people. In this regard, one relevant health status is anemia, i.e., having lower than normal hematocrit. Such patients have less ability to replenish the oxygen robots remove from plasma than people with normal hematocrit. FIG.14 shows power available to robots in an individual with normal hematocrit. This model can also illustrate the effect of low blood cell count (i.e., anemia) by reducing the hematocrit parameter. As an example, FIGS.19A & 19B show robot power (FIG.19A showing power in picowatts as a function of time in seconds) and oxygen concentration (FIG.19B showing concentration in 10 ²² molecules per cubic meter) in plasma with 25% overall hematocrit, for the same numbers of robots as in FIG.14. Even with this lowered hematocrit, the available oxygen from circulating cells provides significant power for all but the largest number of robots considered here. However, 10 ¹² robots remove all oxygen before blood reaches capillaries. For the lower range of robot numbers, anemia does not significantly change the situation for robots using chemical power, but the low oxygen reserve in cells with this reduced hematocrit significantly increases oxygen depletion with a large number of robots. This example shows how models developed here can not only evaluate robot capabilities but can also evaluate the suitability of patients for applications of microscopic robots. Personalized versions of such models could help develop mission plans for the robots and provide a baseline to compare with robot measurements during early stages of a mission to identify and respond to deviations from the plan before they become harmful. This extends to microscopic robots the current use of computational models to help plan conventional medical procedures [39]. [0104] As described above, conventional monitoring may have reduced accuracy when large numbers of robots are consuming oxygen. The variation in response to large numbers of robots based on the patient’s health status suggests a staged approach of gradually increasing the number of robots in the body. Another way to achieve a similar effect is by having robots initially limit their power use and gradually increase that limit to the level required for their mission. During this initial stage, the robots could monitor their effect on oxygen concentration and other body processes to determine whether full power would exceed safety limits prior to fully activating all the robots. This evaluation would allow determining patient-specific trade-offs in treatment options. For example, a treatment could use fewer robots or have them operate at lower power with the tradeoff of longer treatment duration or less frequent communication with the robots. In particular, monitoring body function at the start, and during, a mission would allow adapting robot behavior and mission parameters to far more detailed measurements than would be available from conventional macroscopic sensors. Continual comparison with personalized versions of the general model discussed here could aid in the interpretation of these measurements and anticipate the likely effect of increasing the number of robots and/or increasing their power use. Mitigation Strategies [0105] As discussed above, oxygen absorption by robots raises concerns for extremely large numbers (10 ¹² ) of robots, and may raise concerns in some situations even when smaller numbers of robots are employed. To address these concerns, various strategies to mitigate the impact of such absorption can be employed. Broadly, these strategies fall into two approaches, saving oxygen for later release, and limiting absorption by robots under circumstances where full-power operation is not needed. [0106] With regard to the approach of storing oxygen for later release, oxygen in lung capillaries is normally more than sufficient to fully saturate blood plasma and red cells. The amount of additional oxygen depends on the health of the lungs: patients with limited lung capacity may not have sufficient additional available oxygen for robots to collect. However, under normal conditions, robots could store some of the remaining available oxygen in pressure tanks without reducing oxygen collected by red blood cells. The lungs serve as a high-reactant region. There are several ways that stored oxygen could supplement the oxygen available to the robots at a particular location after circulating away from the lungs. Robots could also fill tanks from oxygen in vessels other than lung capillaries. However, this would reduce the oxygen available later in the circulation in the same way as robots collecting, and immediately using, all oxygen reaching their surfaces. In addition, if the treatment includes passing the patient’s blood through an external oxygen exchanger, robots could remain in that exchanger as long as needed to fill oxygen tanks. However, typical treatments using microscopic robots would likely not need such an exchanger. Moreover, this external circulation would alter the typical circulation time assumed for the model described above. The discussion here does not include these options for collecting oxygen, but instead focuses on robots obtaining oxygen in lung capillaries. [0107] A robot can store oxygen in a pressure tank [12]. FIG.20 is a cross section of an oxygen-storing robot 550 (which can be functionally equivalent to the robot 350 shown in FIG.8) having a spherical oxygen tank 552 defined by a tank wall 554 with wall thickness t and interior volume that is a fraction f of the robot’s volume (as enclosed by a robot surface 556). For clarity, the wall thickness is exaggerated compared to the other dimensions, and the drawing is not to scale. The amount of oxygen the robot 550 can store during a single pass through a lung capillary (a “high-reactant region”) is limited by three factors: the rate at which the robot 550 absorbs oxygen, the time it spends in the lung capillary, and the capacity of the storage tank 552. These three factors are discussed below. [0108] Oxygen absorption rate for the robot 550 depends on how fast molecules diffuse to the robot surface 556 and the fraction of the surface 556 that captures arriving oxygen, using pumps 558 (functionally equivalent to the pumps 312 of the robot 350 shown in FIG.8). Eq.1 gives the rate oxygen diffuses to the robot surface. The corresponding flux to the surface is _{Jrobot/(4πrrobot} ² ₎ . For a 1µm-radius robot _Jrobot = 1.8 × 10 ⁹ molecules/s in lung capillaries, corresponding to a flux of 1.4 × 10 ²⁰ molecules/m ² /s. [0109] For maximum absorption, the pumps 558 must have sufficient capacity to collect molecules as fast as they reach the pump 558. However, the pumps 558 have a maximum operating rate (assuming sufficient supply of molecules) J _pump = (4πr _robot ² )sF _pump where s is the fraction of the robot surface 556 used by the pumps 558 and Fpump is their maximum pump capacity. For molecular sorting rotors, a plausible capacity is Fpump = 10 ²² molecules/m ² /s [12]. Capturing all the molecules requires that J _pump ≥ J _robot . With Eq.1, the minimum surface coverage required is: (4) with c being the oxygen concentration in lung capillaries. [0110] Another constraint on pump surface fraction arises from diffusion. When pumps do not cover the entire surface, an oxygen molecule diffusing to the robot surface 556 does not necessarily reach a pump. Nevertheless, once a molecule reaches any part of the robot surface 556, it usually moves for a considerable time near the surface 556 before diffusing away. This means that pumps 558 that only cover a few percent of the surface 556 can collect oxygen nearly as well as a completely absorbing surface [5]. This provides a lower limit on the fraction of the surface 556 used by the pumps 558. An additional constraint arises from the multiple uses the robot 550 may have for its surface, e.g., for sensing, structural support, communications, locomotion, etc., which prevent the pumps 558 from occupying the entire surface 556. [0111] FIG.21 illustrates the net effect of the three constraints of pump capacity, diffusion to reach a pump, and the maximum surface area available to pumps in determining what fraction of the surface area must be used by pumps (vertical axis) in order to collect nearly all available oxygen molecules while the device is in a lung capillary, as a function of device size (radius in in µm). The calculations use Eq.1 for diffusion as a function of device size and the value for pump capacity cited above. In the shaded area 2102 on the left, molecules arrive faster than the pumps can collect them, even if they cover the entire surface of the robot. In the shaded area 2104 on the right, surface coverage is 5%, which is sufficient for pumps to capture most of molecules reaching the robot surface. For intermediate sizes between these shaded regions, the surface fraction is a function of the robot radius from Eq. 4. In this case, the minimum fraction is 5%, which allows capturing most arriving oxygen [5]. The maximum in FIG.21 is for the theoretical case of pumps covering the entire surface. Even if the other components that the robot 550 needs on its surface 556 limit the pumps 558 to no more than 25% of the surface, FIG.21 shows that this limit only applies to robots significantly smaller (~r ≤ 0.06µm) than those used in the scenarios discussed herein, and therefore pump capacity should not be a limiting factor for oxygen absorption. [0112] For time spent in a lung capillary, blood passes through a lung capillary in about 0.75s [10], and this can be used as the oxygen collection time for robots moving with the blood, although robots might have somewhat less time as they move with cells, due to the reduced hematocrit in small vessels. Robots could increase the filling time in several ways. Robots moving passively with the blood could use several circulations through the lungs to fill their tanks. Active robots could extend their filling time by sticking to capillary walls or selecting longer routes through the lung capillary network. [0113] The tank 552 stores oxygen at high pressure. For a spherical tank of radius r with a thin wall of thickness t, Laplace’s law gives its maximum pressure as [12] (5) where σ is the failure strength of the wall 554. For a wall 554 formed of covalently-bonded carbon, a conservative estimate of the failure strength is σ = 10 ¹⁰ Pa, about 20% of diamond’s failure strength [12]. For example, a tank with radius r = 0.3µm and wall thickness t = 5nm has maximum pressure near 3000atm. The scenarios discussed in this example use tanks storing oxygen at about one-third of this maximum pressure. At these storage pressures and body temperature, common gases such as oxygen deviate somewhat from the ideal gas law. To account for this deviation, the tank storage capacity is estimated using the van der Waals equation of state for oxygen [12]. [0114] During a 0.75s transit through a lung capillary [10], 1.3×10 ⁹ molecules diffuse to the surface of a 1um radius robot. For example, at body temperature and tank pressure of 1000atm, the number density of oxygen molecules is 1.26 × 10 ²⁸ molecule/m ³ [12], which is far larger than the concentration in blood (see Table 2). A tank 552 with radius 0.3µm could store all the collected molecules. This tank 552 would occupy about 3% of the robot’s volume, including a 5nm-thick wall 554. [0115] From Eq.2, a robot collecting oxygen as fast as it diffuses to its surface while passing through a lung capillary collects enough oxygen to provide about 7pW for the duration of a 60s circulation loop. This is well below the power available from oxygen in the blood during the circulation with even as many as 10 ¹² robots, except for the last ten seconds or so of the loop. If the stored oxygen were only used during the last ten seconds of the circulation, it would provide about 50pW. This oxygen storage is not sufficient for robots requiring around 100pW or so, and hence can not completely alleviate depletion by large numbers of robots consuming oxygen. However, stored oxygen would be useful as a supplemental power source for brief intervals of reduced oxygen, such as when a robot is next to a white blood cell moving through a capillary, so the plasma around the robot is temporarily not replenished by nearby red blood cells. It would also be useful on its own for somewhat smaller numbers of robots, and/or robots with somewhat lower power requirements. [0116] As another illustration of oxygen storage, suppose robots collect enough oxygen to provide 100pW for the 60s duration of the average circulation loop, which corresponds to 1.8×10 ¹⁰ oxygen molecules. Storing this much oxygen in a pressure tank at one-third its maximum pressure requires about one third of the robot volume for a tank with 10nm thick walls. Filling this tank requires 10s in a lung capillary, which is much longer than typical transit times. To fill its tank, a robot could remain in a lung capillary rather than flow with the blood, e.g., by anchoring itself to the capillary wall. Lung capillaries contain 70mL of blood [10], so if robots stay in capillaries long enough to fill their tanks, lung capillaries would hold about 15% of the robots in only 1.2% of the blood volume. For 10 ¹² robots, this scenario gives a nanocrit of 0.01 in lung capillaries, about ten times larger than the overall nanocrit (see Table 1). The distance between robots in a capillary would be correspondingly reduced, to about 10µm. This spacing is small enough that nearby robots compete for oxygen, thereby somewhat increasing the filling time beyond that determined here for isolated robots [19]. These estimates indicate the trade-offs required for robots to carry enough oxygen for 100pW without consuming oxygen from the blood during the circulation. In particular, this scenario requires a large fraction of robot volume for storage, significantly increases robot concentration in lung capillaries, and requires robots have the capability to anchor themselves in capillaries. [0117] An alternative (or supplement) to oxygen tanks in the robots performing the medical mission is to use additional specialized oxygen supply robots [11], in a manner similar to the group 400 of robots (402, 404) shown in FIGS.9 & 10. The supply robots collect oxygen while passing through the lungs and deliver it to the main mission robots in the systemic circulation. This oxygen delivery contrasts with transport robots intended to serve as artificial red blood cells that also collect carbon dioxide for return to the lungs [11], as such robots require power to collect and compress molecules while in the systemic circulation, which robots that only deliver oxygen do not need (as they only collect and compress molecules while in the high-reactant region of the lungs, where ample oxygen for power is present). Such oxygen supply robots face the same limit on extracting oxygen from lung capillaries as discussed above, depending on their size and tank capacity. However, the supply robots can be optimized to address these limitations without compromising other requirements of the main mission. [0118] For example, considering the scenario where robots cannot fill their tanks during a single transit through a lung capillary, supply robots could be designed to fill their tanks in this time by exploiting the geometry of diffusion: from Eq.1 the rate molecules arrive at the robot is proportional to its radius r _robot , while tank capacity is related to its volume, which is proportional to r _robot ³ when tanks use a fixed fraction of the robot volume and a fixed storage pressure. The time to fill a tank scales as r _robot ² . This means that instead of a single large tank in one robot, using proportionally smaller tanks in many robots, with the same overall storage capacity, can collect the same amount of oxygen in a shorter time. For example, decreasing the robot size by a factor of two reduces the time required to fill its tank by a factor of four. Increasing the number of robots by a factor of eight gives the same total volume of robots and the amount of oxygen they can transport. [0119] To quantify the design trade-offs for these robots, consider n oxygen supply robots as shown in FIG.20, each of radius r with a fraction f of its volume for oxygen storage. Scaling the entire geometry with robot size means the thickness of the oxygen tank wall is proportional to r. From Eq.6, this scaling has the same maximum pressure for the storage tank in robots of different sizes. Specifically, the wall thickness in this example is t = 20nm × (r/r _robot ) where r _robot = 1µm is the radius of the mission robots. The wall cannot be less than one atomic layer, so this scaling does not apply for arbitrarily small robots (e.g., with a minimum t ≥ 1nm thickness, this relation applies for r _robot ≥ 0.05µm - the supply robots considered here are larger than this size). As discussed above, tanks can store oxygen at one- third of their maximum pressure. With these specifications of the supply robots, the number of robots, their size, and volume devoted to oxygen (i.e., values for the parameters n, r and f) can be selected such that the robots in aggregate carry 1.8 × 10 ¹⁰ oxygen molecules for each of the mission robots, duplicating the amount of stored oxygen as discussed above. In addition to this requirement, three constraints on the choice of these parameters for supply robots are considered. [0120] First, the robots should be small enough so that favorable diffusion scaling allows them to fill their tanks with a single transit of the lung capillaries. This includes setting the fraction of the surface used by pumps as shown in FIG.21 so the robots can collect nearly all the oxygen available to them in the lung capillary. Second, the volume of the robot outside its oxygen tank must be sufficient to contain its other components. These additional components include pumps to collect oxygen and mechanisms to control the operation of the robot. It is assumed here that determining oxygen concentration in the fluid around the robot is used to decide when to collect or release oxygen; other considerations besides concentration could be employed, such as location in the circulatory system and/or receipt of a request for oxygen from a nearby mission robot. For the volume used by the pumps, each pump is assumed to have size d = 10nm [12] so the total volume of pumps is 4πr ² sd. The controller and other components are assumed to require a fixed minimum volume v = 0.1µm ³ that was estimated for transport robots delivering oxygen to tissue [11]. This gives the required volume for other components as: (6) [0121] The third constraint is on energy required by the supply robots. Their main energy use is to fill their tank. This consumes part of the received oxygen while they are in the lung capillary, thereby increasing the filling time. Comparing the pump energy required to compress oxygen [12] with the rate at which the robots receive oxygen in lung capillaries (as discussed above) indicates that a robot should only need about 3% of the oxygen it collects to operate the pumps, so the energy required for filling the tank has a negligible effect on filling time. [0122] Supply devices need energy for their operation after leaving the lung. This includes sensing when oxygen concentration is low (or other condition for release of stored oxygen) and determining when to release oxygen, which are tasks that do not depend on robot size. Supply robots could obtain energy using oxygen from the blood outside the lung capillaries in the same way as the mission robots. However, that would decrease the oxygen available to the mission robots, partially negating the benefit of using supply robots to mitigate oxygen reduction in the blood. Instead, the supply robots could use their stored oxygen to power their operation outside the lungs. For effective oxygen transport, this consumption should be a small fraction of the stored oxygen so that a supply robot can deliver almost all its oxygen to the mission robots. One measure of this power requirement is the average use over the 60s circulation loop. For instance, 0.1pW is an estimate of the power needed for computation by robots supplying oxygen to tissue [11]. After supply robots leave the lung, their main activity is determining when to release stored oxygen, so computation determines their energy demand, and 0.1pW is a plausible estimate of their required power for continuous operation. In practice, supply robots would only need to check oxygen concentrations intermittently, thereby reducing their average power use below this value. A reasonable requirement for a supply robot is that its tank can hold enough oxygen to provide at least 1pW, on average, during a circulation loop. This provides sufficient energy for the robot while using only a small portion (1%) of its stored oxygen. [0123] FIG.22 shows these three constraints on robot and tank fractional size for supply robots to carry enough oxygen to provide each mission robot with 100pW for 60s, the same oxygen requirement as discussed above; the vertical axis is the fraction of robot volume used for oxygen storage, and the horizontal axis is robot radius in µm. In the region at the upper right of insufficient time curve 2202, tank capacity and robot size are such that diffusion is too slow to fill the tanks during a single lung capillary transit. In the region to the left of the generally-vertical too small curve 2204 in the center, the robot is too small and/or the oxygen tank too large to leave enough room for other robot components. Finally, in the region at the lower left of insufficient power curve 2206, the oxygen tank is too small to both provide enough power to the supply robot during the circulation and to deliver most of its oxygen to the mission robots (i.e., the tank cannot store at least 1pW*60s worth of oxygen). The point 2208 is the design choice satisfying the constraints with the smallest value of the total volume of the supply robots given in Eq.7 below. Robots satisfying all the constraints (i.e., the region 2210 of FIG.22 between the insufficient time curve 2202 and the insufficient power curve 2206 and to the right of the insufficient room for components curve 2204) are feasible designs. Selecting among these designs can optimize operational or production goals. Operational goals include minimizing the nanocrit, i.e., the total volume of the supply robots and reducing their size to simplify passage through small vessels or slits of the spleen [13]. Production cost depends on the number of robots and the manufacturing cost of each robot. A proxy for manufacturing cost is the number of atoms required for their structure and mechanisms, in analogy with 3D printing with cost dominated by time and materials rather than the complexity of the printed structure. This proxy is proportional to the volume of the robot other than the interior of the oxygen tank. This proxy for production cost is the total volume of all the supply robots multiplied by 1 – f (where f is the fraction of each robot volume for oxygen storage): (7) An example of optimized parameters are those that minimize the total volume of the supply robots. These parameters correspond to the point 2208 in FIG.22, where the supply robots have radius r = 0.32µm and an oxygen volume fraction f = 0.23. FIG.23 illustrates this optimized design by comparing cross sections of such an oxygen supply robot 550 and a main mission robot 560 having a radius of 1µm (Table 2). These parameters also minimize Vproduction in Eq.7. This choice of r and f provides both an operational benefit of minimizing the nanocrit and a production benefit of minimizing the volume proxy for manufacturing cost. Table 4 shows how number and volume of the supply robots compare to the main mission robots with these parameters. Carrying the same amount of oxygen per main mission robot (100pW for 60s) requires about 43 supply robots for each mission robot. The mission robots and supply robots together have a nanocrit about 2.4 times larger than for the mission robots alone. Table 4 [0124] When considering a typical placement of robots in a cube of blood with 20µm edge length, for the case of 10 ¹² mission robots in a blood vessel whose diameter is larger than the size of the cube and where cells and robots are uniformly distributed, such a cube typically contains one of the mission robots (see Table 1), and 43 supply robots (see Table 4), while blood cells (each with a typical red cell volume of 100µm ³ [12]) occupy about 40% of the cube volume. This is an approximation to the actual distribution, since smaller objects (such as the robots of both types) tend to concentrate toward the vessel wall [12]. [0125] Due to their larger numbers, the spacing between supply robots in capillaries is smaller than those for the mission robots given in Table 1. However, the supply robots are also smaller, so their spacing measured in terms of their size is reduced to a lesser extent. For example, with 10 ¹² mission robots, supply robots are separated by about 8 times their radius in straight capillaries used for the estimate in Table 1. This suggests that neighboring supply robots compete to some extent for oxygen in lung capillaries, which may somewhat increase their filling time compared to the estimate assuming independent diffusion to each robot. However, lung capillaries have a complex network structure [41] which could alter the extent of this competition, especially due to the variation in paths and transit times. [0126] For the supply robot 550 shown in FIG.23, the pump volume is a small fraction of the component volume in Eq.6. If pump size and surface coverage are larger than assumed here, an additional optimization is allowing for a smaller number of pumps than indicated by FIG.21. This would trade a longer filling time due to fewer pumps for additional volume for other robot components. This would give another parameter to optimize, in addition to robot radius and tank fractional size shown in FIG.22. The specific optimal robot 550 and tank 552 sizes shown in FIG.23 depend on the robot component size and power requirements (i.e., the second and third constraints in FIG.22). This example illustrates how multiple design constraints combine to determine the choice of robot parameters. These constraints arise both from the robot’s external environment (e.g., the diffusion rate of oxygen) and the robot’s internal capabilities (e.g., the power required for its operation). Better estimates of these parameters require more detailed design of the robot components. Depending on these values, there could be no feasible design (i.e., no region in FIG.22 meeting all three criteria) for some situations. That would indicate that the robots’ component volumes or power requirements are too large to provide this oxygen. In that case, oxygen supply robots could provide less than the 100pW used in this scenario, or the mission robots could use another mitigation strategy to avoid low oxygen concentration. [0127] Using supply robots increases nanocrit. While likely not a significant issue for the scenarios of Table 1, large nanocrit from supply robots could alter blood flow [12] or require a compensatory reduction in the number of main mission robots. Moreover, increasing the number of robots collecting oxygen in the lungs eventually extracts all available oxygen. At this point, additional robots would not increase the total collected oxygen and would reduce the reserve available to the body by increasing blood perfusion in the lungs. [0128] Supply robots carry oxygen from the lungs to the systemic circulation. In the case of passive flow, supply robots release oxygen into the surrounding blood plasma when deemed necessary, such as when they detect low oxygen concentrations. Some of that released oxygen diffuses to nearby robots. The rest remains in the blood plasma or diffuses into tissue or red cells. This means the blood carries some of the released oxygen back to the lung without providing robot power. This wasted oxygen is particularly significant when released in the veins, where it does not diffuse into tissue. This is a likely scenario since the lowest concentrations occur in veins. This diffusive oxygen delivery by specialized robots is not as effective as when robots carry their own oxygen, as described above. [0129] Robots could partially offset the limitation of diffusive transport by releasing oxygen only when they are close to a main mission robot, as determined, for example, via short range communication [12,20]. This proximity allows more of the released oxygen to reach the receiving robot’s surface. If necessary to support high burst power, multiple supply robots could aggregate around a mission robot and simultaneously release oxygen (as shown in FIG.9). This temporarily produces a high oxygen concentration in that region. However, as not all of that oxygen reaches the robot, the total release must be limited to avoid tissue damage due to excessive oxygen, i.e., hyperoxia, which is a particular concern in the brain [43]. This safety limit due to released oxygen not reaching a mission robot limits how rapidly a group of supply robots can deliver oxygen, thereby reducing their ability to support high burst power that robots could obtain if they carry their own oxygen. [0130] For greater efficiency, oxygen supply robots could directly transfer oxygen to the mission robots by docking with them (as shown in FIG.10). Direct transfer provides oxygen in the same way as an onboard tank. In this approach, supply robots act as external oxygen tanks for the mission robots. Using separate robots to carry oxygen allows them to selectively provide power to robots that most need it. For example, this selectivity could allow one robot in a group to have a burst of high power for long range communication of a summary of data collected by the group. While this flexibility is a potential benefit, some amount of power variation within a group of robots can also be achieved if most robots limit their oxygen demands, as described below. Direct transfer requires more complicated robots than releasing oxygen into the blood and relying on diffusion. In particular, docking requires locomotion and navigation on the part of the transport or mission robots, or both, to find each other in the constantly changing fluid environment as the robots and cells move. If the mission robots need locomotion capability for their mission, they could also use that capability to reach oxygen supply robots. In that case, there is no need for the supply robots to also have locomotion capability, thereby simplifying their design and providing more room for them to carry oxygen. An additional issue is if a supply robot delivers oxygen by completely emptying its tank while docked, direct oxygen delivery would produce a population of supply robots with a declining fraction of those with full tanks. Devices with full tanks become harder to find, and the robots may need a communication protocol to identify those supply robots that have available stored oxygen. [0131] FIG.14 shows that 10 ¹² robots deplete oxygen toward the end of the circulation loop, i.e., in veins. A rechargeable reservoir with control over oxygen release could be formed from robots small enough to travel through the circulation and able to attach to vein walls. These could be the same type of circulating oxygen supply robots as discussed above, but used as a reservoir fixed to vessel walls rather than traveling in the blood along with the main mission robots. As an example of this scenario, consider a reservoir capable of supplying enough oxygen for 100pW to each of 10 ¹² mission robots during the last 20s of their circulation. The supply robots in the reservoir could do so by releasing oxygen into the blood, but only a portion of that would diffuse to the mission robots, while the rest would return to the lung unused. Instead, circulating mission robots could find and dock with the reservoir supply robots to receive oxygen from them directly. With uniform distribution of robots, the last 20s of the circulation contains about a third of the robots. To provide the mission robots with sufficient oxygen to generate 100pW each during the last 20s of circulation, the reservoir would need to supply 10 ²⁰ molecules/s. To maintain this rate for a single circulation time, the reservoir would need to start with 6 × 10 ²¹ oxygen molecules. As an example, if the reservoir consists of 1µm-radius supply robots using 80% of their volume to store oxygen in tanks with 20nm-thick walls and at one-third the tanks’ maximum pressure, each supply robot could store 4.6×10 ¹⁰ molecules and the exterior volume of the tank (i.e., including the tank wall) would occupy 85% of the supply robot’s volume. If a supply robot uses 10pW to support its operation, it would consume about 4% of its stored oxygen during a 60s operation time. With these parameters, the reservoir would require 1.4 × 10 ¹¹ supply robots to provide oxygen to the 10 ¹² circulating mission robots. A reservoir supply robot with these parameters would require 26s to fill its tank in a lung capillary, compared to the typical 0.75s transit time through a lung capillary. If the supply robots move passively with the circulation rather than concentrating in lung capillaries for the required time, and do not use power while circulating, each would require 35 circulations through the lung to fill its tank, which would take about half an hour. In this scenario, using a reservoir would provide oxygen to support 100pW for mission robots during the last third of a circulation loop only once in every 35 circulations. In the remaining circulations, the mission robots would have little power during the last third of their circulation, or no power if they stop using power to avoid extremely low oxygen concentration and cell saturation toward the end of the circulation loop. [0132] Robots could mitigate their effect on oxygen concentration by limiting their power use, particularly early in the circulation loop (i.e., in arteries) where oxygen is plentiful. Examples of strategies that robots could use for limiting power are discussed below. Since 10 ¹² robots consuming oxygen as fast as possible leads to significant oxygen reduction (as shown in FIGS.15A & 15B), this case is used for evaluating the effects of strategies for limiting power use. [0133] A fixed limit on robot oxygen consumption could be implemented in hardware by reducing the number or capacity of pumps on the robot surface, or limiting fuel cells inside the robot. This would prevent the robot from using all oxygen reaching its surface when the concentration is high, i.e., shortly after leaving the lungs. The more flexible and targeted power limitation methods discussed in this section require robots to alter pump capacity based on sensor measurements of quantities such as oxygen concentration, location in the body, or distance to vessel walls. Moreover, software-based limits would allow some robots to use all the oxygen when occasions arise that could benefit from high burst power. [0134] An alternative method for limiting oxygen collection in large vessels is for the robots to travel in groups, analogous to the grouping of blood cells in some blood vessels [12]. Such groups could form from robots waiting in moderate-sized vessels, such as lung veins, for a group to accumulate, or robots could search for others to form a group while moving with the blood; groups could be formed by robots joined together and/or robots that simply travel in close proximity to each other. If the group is large and compact enough that some robots are completely surrounded by others, the robots at the surface of the group could share collected oxygen with those inside, or the robots could occasionally change positions so each robot spends part of the time at the surface of the group. When vessels become too small for the group, the robots could disperse. Such grouping reduces absorption per robot by exploiting the competition for oxygen among nearby robots, which is the opposite of the improved absorption by smaller robots discussed above. For example, suppose n robots join to form a spherical group of radius R. To accommodate the volume of these robots, R ≈ r _robot 3 _√ ^{^^} . From Eq.1, the rate this group collects oxygen is proportional to R. The oxygen collected per robot in the group is reduced from that of isolated robots by a factor of (R/r _robot )/n ≈ n ^−2/3 . For example, 100 robots of radius 1µm could form a group with R ≈ 5µm and then each robot would receive about 5% of the oxygen that isolated robots would collect. For this method of power reduction, the groups need not all have the same size nor contain all the robots in large vessels. For example, if among 200 robots, 100 form a group while the others remain isolated, the total oxygen consumed by those robots would be about half what they would consume without any grouping. [0135] The simplest approach to limiting robot oxygen consumption is for all of the robots to have a fixed maximum power generation rate. FIG.24 shows one example of this approach for 10 ¹² robots, comparing the cases where power is not limited (curve 2402, which is the same as the curve for 10 ¹² robots from FIG.14), the case where all robots are limited to a maximum of 200pW (curve 2404), and a case where robots are limited based on their location in the circuit (curve 2406, discussed below). As with FIG.14, the plot shows available robot power in picowatts as a function of time in seconds as the robots move through the circulation loop. The light dashed curves 2408 and 2410 show the power available to a robot for the two power-limiting strategies, if the robot in question were not following the strategy and instead consumed all oxygen reaching its surface, provided that no more than an insignificant number of other robots exceed their limits, so oxygen is not significantly reduced by the few robots that do switch to maximum power. The imposition of a 200pW limit for all robots extends the range of a circuit throughout which robots have power, but power still falls to zero before returning to the lung. To provide some power throughout the circulation loop with this many robots would require a somewhat lower power limit. The dashed curves 2408 and 2410 in FIG.24 indicate power available to a robot from the oxygen concentration in the plasma around that robot. This is the power a single robot would have if it switches from limited-power to using all available oxygen, but while most or all of the other robots in the fluid system operate to limit their power consumption (applying the 200pW limit for curve 2408 or the location-based limit for curve 2410). If only a few robots switch to a higher-consumption mode of operation, they do not significantly lower the oxygen, so the dashed curve indicates the power available to a few robots (e.g., for occasional burst activity) provided that only a tiny fraction of the robots make use of that additional power at any given time. [0136] By limiting their power production when oxygen is plentiful, robots leave more oxygen for robots later in the circulation loop. In effect, the robots use blood cells as external oxygen storage tanks to shift when and where robots utilize oxygen. This is conceptually similar to oxygen provided by additional supply robots discussed above, without the need for additional robots. On the other hand, specialized supply robots could deliver oxygen more effectively, especially if they use pumps for transfer rather than relying on diffusion. [0137] Instead of a fixed power limit, robots could use a specified percentage of the oxygen reaching their surface. Unlike a fixed power limit, such as 200pW, a percentage limit would adjust to the decreasing oxygen concentration as robots move through a circulation loop. For example, 10 ¹² robots using only 10% of the oxygen would have the same effect on oxygen concentration as 10 ¹¹ robots using all available power (which would provide adequate power throughout the circuit, as shown in FIG.14). The robots would have a few tens of picowatts. This would only be a worthwhile alternative to using 10 ¹¹ robots if there is a benefit of having ten times as many robots, each with one-tenth the power. For instance, if the mission is to have at least one robot pass through every capillary to look for a target location, e.g., recognized by a rare pattern of chemicals, and this detection can be done with low power. In that case, a larger number of robots can complete the survey more rapidly than a smaller number of robots. Moreover, if the response to the detection requires much more power, such power should be available to the few robots finding the target due to the higher oxygen concentration left by most other robots using only a small fraction of the available power. [0138] The above discussion of power limits supposes those limits are always in effect. Another possibility is limits that apply occasionally so robots alternate between consuming much or all of the available oxygen and limiting their consumption. For example, robots could consume significant oxygen only every second or third circuit. If such duty cycling occurs independently among robots, it would reduce the number of active robots by the corresponding factor, i.e, 2 or 3 in this example. On the other hand, if robots synchronize their schedules, oxygen in the circulation would alternate between high and low levels. This could be beneficial if the harm from continuous moderately low oxygen is worse than switching between very low and normal concentrations. [0139] A more sophisticated limitation method is for the limits to depend on the robot’s location rather than using a single overall limit. Such a strategy would be particularly useful if the main operation of a robot occurs when it is in a capillary (e.g., measuring properties of nearby tissues). In this case, robots could reduce power use while in arteries, to have more available for the short time they spend in capillaries. They could also defer some power consumption (e.g., analyzing measurements they collected in the capillary), until they reach vessels with more available oxygen. This could be in veins, where additional reduction in oxygen saturation of red cells would no longer affect oxygen available to tissues. This strategy should include some adjustment for portal flows, e.g., in the portal vein, where blood flows through another capillary, in the liver, before returning to the lungs. In that case, the robot could wait until it has passed a liver capillary before increasing its power use (variations in flow paths such as the portal flow are discussed in the section “Variations in Circulation Paths”). Location-based limit curve 2406 in FIG.24 shows an example for 10 ¹² robots using this method, where robots are limited to 20pW in arteries, 200pW while in capillaries, and unlimited use in veins. With these parameters, this approach provides power throughout the circulation loop. In particular, it provides higher power when robots are in the veins compared to robots using all available power or using an overall power limit. In the arteries, additional power is available for a small number of robots that do not follow the location-based limit, as indicated by the curve 2410. FIG.25 shows the effect of this limit on oxygen concentration by curve 2502, showing oxygen concentration (in 10 ²² molecules per cubic meter) as a function of time (in seconds). FIG 25 also shows curve 2504 for the case discussed above where power to all robots is limited to 200pW and curve 2506 for the case where robots do not limit their power consumption. [0140] Implementing location-dependent limits on power may require that robots determine the type of vessel they are in. Robots could do so in a variety of ways, with trade- offs between complexity for robot processing and accuracy. One approach is to use an onboard clock to measure the time since a robot left the high-oxygen environment of a lung capillary. They could use a fixed time, e.g., 30 seconds, to decide when they have likely reached a vein and can increase power use. This approach does not adjust for variation in circulation speed due to changes in heart rate, nor variations in circulation path lengths, but is a simple approach that avoids the need for robots to determine when they have passed through a capillary. [0141] Alternatively, robots could measure oxygen concentration in the surrounding plasma. This is high in arteries, decreases as the robot passes through a capillary where tissue consumes oxygen, and is relatively low in veins. Concentration thresholds required to distinguish these types of vessels depends on the concentration of robots and the power- consumption method of the robots (see FIG.25). This variation could be predefined based on these choices. More challenging for estimating location from oxygen concentration is the variation in tissue use in different organs and at different times, and variation in hematocrit in small vessels. These variations limit the accuracy of using oxygen concentration to determine the type of vessel the robot is in. [0142] Combining a variety of measures can identify vessel type more accurately. Most circuits through the body move through arteries of decreasing size, through a capillary, and then through veins of increasing size. Changes in pressure and how much it varies over the duration of a heartbeat distinguishes arteries from veins [12]. For small vessels, changes in fluid flow near the robot allow estimating vessel size [18]. It should be noted that these techniques for determining location could be used in other situations where the operation of a robot is to be adjusted based on its location in the circuit. [0143] In addition to adjusting power based on the type of vessel a robot is in, a robot could adjust its power based on its macroscopic location in the body. For example, robots could use information on which organ they are in [12] to set their power limits. This would allow robots to adjust power generation to match organ-specific tasks. As an extreme case, if robots only need to be active in one organ, then a number of robots large enough to deplete oxygen if they all use power would instead consume much less oxygen and mainly affect that organ and tissue downstream from that organ. This would avoid depleting oxygen in veins throughout the body, but could lead to significant local oxygen reductions, particularly in the small veins leaving those organs before the blood reaches larger veins, where it mixes with blood from other organs. [0144] The most severe reduction in oxygen with 10 ¹² robots occurs near the end of the circuit, i.e., after blood has mixed into large veins. For robots limiting power use to one or a few organs, that extreme reduction would not occur: instead, blood from other organs would partially restore oxygen in the vein. Organ-specific power use could tolerate larger numbers of robots than if all robots consume oxygen. A trade-off in this scenario is that only the portion of robots in the target organ at any given time would be actively performing their tasks while the majority of robots simply move passively with the blood. Alternatively, robots with locomotion could target the organs of interest, thereby providing sufficient concentration to perform their mission with a smaller total number of robots. [0145] Another application for power limits based on location within the body is to adjust to organ-specific variations in tissue demand, beyond those compensated for by variation in tissue capillary density or changes in blood flow in response to those variations. That is, robots may need to reduce their oxygen consumption in tissue with higher than usual oxygen demand. At a local scale, robots could determine such limits from measuring oxygen concentration. However, by the time a robot reaches the tissue, and encounters the lowered oxygen concentration, it may be too late for limiting power in small arteries leading to that tissue and where oxygen concentration may still be relatively high. In this case, a robot could limit power more effectively using information on which organ it is entering and the overall tissue demand of that organ. [0146] Instead of a power limit on all robots, the limit could be selective by depending on the recent history of each robot. The benefit of a history-dependent limit depends on the fraction of robots requiring significant power at any given time, as determined by their current configuration and their local environment. For example, if only 10% of robots need significant power, then the effective number consuming oxygen is reduced by that fraction. If this reduction is, at least roughly, uniform throughout the body, the robot power affects oxygen according to the effective number of active robots. For instance, if only 10% of a trillion robots generate significant power and do so at their maximum possible rate, the effect on oxygen concentration corresponds to 10 ¹¹ robots consuming oxygen as rapidly as they can. [0147] One situation leading to history-dependence arises in robots with oxygen storage and considerable variation in power requirements, depending on where they travel in the body. Such a robot could limit its oxygen intake and supplement that intake with oxygen from its storage tank. When the tank is nearly empty, the robot could absorb more rapidly to fill it. This would be useful if neighboring robots share data and only one of them needs to expend significant power to process or communicate the data: the robot using burst power would deplete its tank and need to refill it. Another case of history-dependent power is if robots only need high power when handling rare events. This could occur when a robot detects a specific chemical in the blood and needs to use locomotion capability to move toward its source [17], or if such a robot requires confirmation from other nearby robots before taking action, to reduce the number of false positives. In this latter situation, the detecting robot could increase its power use to communicate with nearby robots and evaluate their responses. In this case, the originating robot may need sufficient power to send a significant number of bits (e.g., a summary of the data it collected), whereas responding robots could just send a short response indicating whether their information is consistent with that from the detecting robot. [0148] As a quantitative example of history-dependent power, consider robots that measure chemical concentrations in capillaries and communicate their readings when they are in range of external receivers on the skin. One way in which robots could determine they are close to a receiver is for receivers to emit a beacon signal that robots can detect when they pass through nearby vessels in the skin. Suppose the relevant data for this mission occurs in tissue other than the lung or skin. In this case, the relevant property of each circulation loop is whether the robot goes to the skin, and, if not, whether it flows through a portal system, thereby measuring two capillaries before returning to the lung for another loop through the circulation. With typical resting perfusion rates [10], 8% of the blood flows to the skin and 20% flows through the portal vein, which is the major circulation path passing through two capillaries. The rest of the blood flows through a single capillary that is not in the skin before returning to the heart. Suppose a robot can store measurements from up to 5 capillaries and has time to transmit the data from up to 3 measurements while near the skin. [0149] Due to the mixing of blood in the heart, where a robot goes in the body during each circulation loop is independent of where it went previously. This leads to a Markov stochastic process for the amount of data stored by a robot with the transition graph shown in FIG.26. Each edge in the graph corresponds to the robot making a single circulation through the body. For instance, a robot with empty data storage is most likely to store data from one capillary during its next circulation. A robot could also go to the skin, in which case it does not collect data, or through a portal system, in which case it collects data from two capillaries. The number in each node in FIG.26 is the number of capillary measurements the robot has currently stored. The thickness of the edges correspond to the transition probabilities. After multiple loops, the Markov process approaches its stationary distribution, in which about 70% of the robots have filled data storage. Such robots are unable to collect any additional data until they have had an opportunity to transmit, and delete, some of their collected data during their next passage near the skin. Moreover, most of the robots reaching the skin would have data on at least 3 capillaries, and hence have enough data to transmit at their maximum rate while near the skin. [0150] Suppose the robots mainly require power during data collection. The 70% of robots with full data storage then use only a minimal amount of power. In terms of power use, 10 ¹² robots would be comparable to 3 × 10 ¹¹ robots consuming oxygen as fast as they can. This would be similar to an overall limit of robots using 30% of available power, but with history dependence so that the power use is targeted to those robots that most need it, rather than a reduction for all robots. [0151] Low oxygen concentrations in veins could affect cells on the vessel wall. Addressing this issue suggests another location-based limit, namely for robot power limits to apply only when a robot is close to the vessel wall. This could be useful in vessels whose diameter is at least a millimeter or so since, for vessels of that size, diffusion limits oxygen transport to a relatively small fraction of the vessel diameter during the time a robot passes through the vessel. Specifically, the low oxygen concentration with 10 ¹² robots occurs during the last 10 to 20 seconds of the circulation loop. The characteristic diffusion distance of oxygen during = 0.3mm, with D _O2 given in Table 2. Robots could avoid creating low concentration near vein walls by reducing their oxygen consumption when they are near the vessel wall, e.g., as determined by measuring fluid stresses on their surfaces [18]. Alternatively, if robots have locomotion capability, they could move away from the vessel wall. In this case, the low oxygen concentration would occur in the central portion of the vessel only. The effectiveness of limiting oxygen consumption based on distance to the vessel wall depends on how much mixing occurs during transport in moderate-sized veins, including the effect of merging vessels and cell motion. For veins whose diameter is substantially larger than the size of cells, this could be evaluated by approximating the blood as a uniform fluid. For smaller vessels, this evaluation may require simulations including deformable cells, e.g., in vessels with diameters up to hundred microns or so [2]. The main advantage of limiting power use near vessel walls arises in vessels large enough that oxygen does not have time to diffuse across the vessel, and there is not significant mixing from the flow. In general, mixing is slow in laminar flow [36] found in such vessels. [0152] As a quantitative example of this mitigation method, consider the flow in a 40mm-long portion of a vein with diameter of 2mm. Suppose oxygen is well-mixed through the blood as it enters this vessel segment, has a relatively low concentration of 0.5 × 10 ²² /m ³ and there are 10 ¹² robots in the circulation. Oxygen transport in the vessel segment can be evaluated assuming a parabolic (i.e., Poiseuille) flow profile with average speed of 2.5mm/s. Oxygen transport is a combination of convection with that flow, diffusion, consumption by robots and replenishment by red cells; as this vessel is a vein, there is no significant consumption by tissue. In this case, the mixing due to the motion of blood cells is a minor addition to the diffusion of small molecules, such as oxygen, in the blood [12]. The Peclet number (roughly corresponding to the number of vessel diameters required for diffusion to spread oxygen across the vessel) for this oxygen transport is: (8) where v is the flow speed, d a characteristic distance and D _O 2 the diffusion coefficient, and from Eq.8 above for the case here is Pe = 2500, so oxygen mainly flows along the vessel with relatively little diffusion across the vessel. This leads to considerable variation in oxygen concentration across the vessel, as robots in the slowly moving blood near the walls deplete oxygen much more thoroughly than robots traveling with the faster flow near the center of the vessel. [0153] Robots could mitigate the rapid concentration decrease near the wall by reducing their oxygen consumption. As an example, FIG.27 shows how the concentration (in 10 ²² molecules per cubic meter) near the vessel wall changes with distance along the vessel (in millimeters) in three cases for a straight vessel of 2mm diameter, in the case of 10 ¹² robots distributed throughout the entire circulatory system. In the first case, shown by curve 2702, robots fully consume oxygen reaching their surface. In the second case, shown by curve 2704, only half the robots consume oxygen (or, equivalently, each robot consumes only half the oxygen reaching its surface), without regard to their position in the vessel. In the third case, shown by curve 2706, robots within 0.3mm of the vessel wall do not consume oxygen, with that distance corresponding to oxygen’s characteristic diffusion distance discussed above. This distance to the vessel wall accounts for about half the total cross-sectional area of the vessel, and only about half the robots are consuming oxygen (i.e., those in the central portion of the vessel). As seen in FIG.27, the approach of an overall reduction in power (curve 2704) reduces the rate of oxygen depletion near the wall, but is much less effective than when robots limit power based on their distance to the wall (curve 2706). [0154] The example shown in FIG.27 is for flow in a single straight vessel. The flow from the merging of veins of various sizes could somewhat increase the mixing and thereby reduce the benefit provided by robots limiting consumption near the wall. To evaluate this effect, FIG.28 illustrates an example of merging vessels with asymmetric branching where two branches, each with diameter of 2mm, merge into a vessel with diameter of 2.5mm (typically when blood vessels merge, the total cross section of the two branches exceeds that of the main vessel, so flow speed in the branches is somewhat slower than in the main vessel). To focus on the effect of the merging vessels, the example included only 8mm in each branch and in the main vessel (16mm total, compared to the 40mm-long straight vessel discussed with FIG.27). Accounting for the effect of the branches required solving for the fluid flow through the vessels, with the flow exiting the main vessel assumed to be parabolic with average speed 2.5mm/s, and the inlet pressure assumed to be the same for both branches. The fluid flow with these boundary conditions was laminar, and the merging flows provided some mixing where the branches joined. The behavior of the concentration was similar to that seen in the straight-vessel example, with oxygen becoming depleted near the vessel wall. FIG.28 shows the reduction in oxygen concentration along the upper wall of the upper branch and main vessels for the same three oxygen consumption cases as shown for the straight vessel in FIG.27, with curve 2802 showing the case where robots do not limit power, curve 2804 showing the case where robots reduce their consumption by 50% regardless of location, and curve 2806 showing the case where robots do not consume oxygen when within 0.3mm of the vessel wall. Even in this last case (curve 2806), the concentration near the wall eventually gets very small, although it does not become completely depleted as occurs when robots do not limit absorption (curve 2802) or where robots consume 50% of oxygen reaching their surfaces regardless of their location (curve 2804). In the context of these examples, the main benefit of this mitigation is extending the range of the circulation loop by a few centimeters compared to when robots consume all oxygen or limit consumption to 50%. This increase in range could be especially beneficial in a vein just before it merges with other veins that contain blood from shorter circuits and hence have more remaining oxygen than the model estimates for an average circulation loop. In that case, avoiding fully depleted oxygen for a few additional centimeters could be sufficient to avoid extremely low concentrations near the walls of any veins, without requiring all robots in those vessels to reduce their power generation. Alternatively, achieving the same increase in range with a power limit on all robots would require a much larger reduction in power than the 50% reduction that corresponds to robots near the wall consuming no oxygen while the rest of the robots consume at their maximum rate. The usefulness of this distance-based limit on oxygen consumption compared to limiting all robots depends on the benefit some robots obtain from more power while in the veins compared to the additional complexity of robots required to determine their distance to the vessel wall. [0155] Capillaries are of particular interest, as they allow robots to operate close to tissues of interest while remaining in a blood vessel. The small volume of capillaries leads to relatively large variation in robot numbers as discussed above. Those capillaries that contain significantly more robots than average have less power. Robots could reduce this variation by moving away from particularly close neighbors, including moving to other capillaries that have fewer robots. Within a single vessel, robots in close proximity compete for oxygen; such robots could improve oxygen distribution using a small-scale version of the power limiting strategies discussed above. In addition, the flow of oxygen to robots depends on their positions along the vessel wall, which provides an additional mitigating strategy for small groups of nearby robots: improving power distribution by deliberately adjusting their positions relative to their neighbors. Computer modeling of oxygen distribution suggests that there are competing effects on the oxygen delivered to robots, as a robot directly upstream of another absorbs much of the oxygen that would otherwise go to the downstream robot, but where placing all robots on one side of the vessel allows more oxygen to reach downstream on the other side of the vessel, which can then diffuse across the vessel to downstream robots. The relative importance of these effects depends on the ratio of convective to diffusive transport of the oxygen, i.e., the Peclet number of the oxygen transport [36] as discussed above. [0156] To illustrate the potential of position adjustment, consider 5 robots 500 positioned along a vessel wall with neighbors offset by an angle θ, as shown in FIG.29. In this example, five 2µm diameter robots 500 are arranged in a vessel 502 of 8µm diameter (the same situation as illustrated in FIGS.18A & 18B). Successive robots 500 are offset around the wall 504 by the angle θ about a longitudinal axis 506 and spaced along the vessel by 5.5µm (the arrangements shown in FIG.18A & 18B respectively correspond to θ = 180° and θ = 0°). This arrangement is analogous to the angular spacing of leaves around the stem of a plant, where angles related to the golden ratio can minimize the extent to which higher leaves cast shadows on lower ones [38]. However, unlike the direct path of light, diffusion allows some oxygen to reach robots that are directly downstream of others on the vessel wall. FIGS.30A & 30B show curves for the average robot power (curve 3002) and power for the last downstream robot 500’ (curve 3004) for the case of 5 robots in a vessel, as a function of the offset angle θ (in degrees), relative to the power that would be available with all robots aligned along the vessel wall (i.e., with θ = 0 as shown in FIG.18B), for two flow speeds. The solid curves 3002 show the average power for the 5 robots 500 with average fluid speed 1mm/s (FIG.30A) and 0.2mm/s (FIG.30B) while the dashed curves 3004 show the power available to the fifth robot 500’ for these same fluid speeds. FIGS.30A & 30B show that the offset angle has a different effect on the average robot power than it does on power for the last robot 500’, which receives the least oxygen. Specifically, offsetting neighboring robots 500 by 180 ^◦ increases the average power by a few percent, with larger effect for faster moving fluid. On the other hand, positioning all robots 500 on the same side of the vessel 502 (i.e., θ = 0) increases power for the last robot 500’ even though it is directly downstream of all the other robots 500 in the group. Computer models show that this occurs because robots on one side of the vessel allow more oxygen to reach downstream along the other side of the vessel and then diffuse to the last robot, and that this effect is larger for slower moving fluid (where the upstream robots have greater opportunity to deplete the fluid of oxygen before it flows past). The robots could select among these placement options based on the relative importance of maximizing power for the group as a whole vs. ensuring that all robots have at least a minimum amount of power and/or depending on the size of the vessel and/or fluid speed. [0157] Robots 500 could use nonuniform positions along the vessel to provide more power to downstream robots by having upstream robots closer to each other than downstream ones. As an example, in addition to the angular separation around the vessel discussed above, suppose the robot positions along the direction of the vessel increase quadratically, starting with a difference of 2.5r _robot for the first two robots 500 and occupying the same total distance along the vessel as the uniformly spaced robots discussed above. FIG.31A shows this distribution for the case of zero offset angle between neighbors (i.e., θ = 0°), where the distance between facing surfaces of the first two robots 500 is 0.5r _robot , while FIG.31B shows the distribution for θ = 180°, where successive robots 500 are on opposite sides of the vessel. The fluid flows from left to right in each case. The larger distance between the last robot 500’ and the others allows the last robot 500’ to collect oxygen from a larger portion of the fluid than when robots 500 are uniformly spaced (as is shown in FIGS.18A, 18B, and 29). FIGS. 32A & 32B show the average power for the robots (curve 3202) and power for the last robot 500’ (curve 3204) as a function of the offset angle θ, relative to the situation of uniformly- spaced robots aligned along the vessel wall as used in FIGS.30A & 30B, again for the same two fluid flow speeds (1mm/s in FIG.32A and 0.2mm/s in FIG.32B). The nonuniform spacing has little effect on the average power, but aligned, nonuniformly spaced robots provide 20% more power to the last robot 500’ than uniformly spaced robots. [0158] The choice of robot positions on the vessel wall alters the power available to downstream robots in a manner similar to that of robots limiting their power use, as discussed above, but without requiring the robots to continually monitor and adjust their power consumption. Instead, robots attaching to a vessel wall for extended operation could determine their positions during their setup and then avoid devoting any computation to maintaining power limits while they perform their tasks while attached to the vessel wall. On the other hand, actively adjusted power limits provide more flexibility in distributing power to downstream robots. Robots could adopt a hybrid approach of positioning themselves to best achieve their goals and having upstream robots limit their power consumption when downstream robots indicate they require more power. [0159] As described above, robots moving passively with the blood and attaching to capillary walls can lead to significant variations in the number of robots in each capillary. In addition to adjusting their position in individual capillaries, robots could alter how they divide among nearby capillaries in a network of vessels. For example, robots could preferentially position themselves in some of the capillaries in a network of vessels while leaving others with few or no robots. In that case, the increased vascular resistance due to robots would tend to direct blood cells away from branches of the network containing many robots, thereby contributing to the heterogeneity of paths that cells take through a network of small vessels [37]. Provided the open paths interleave closely with the vessels blocked by robots, the flow through the open paths could be sufficient to support the surrounding tissue with less disruption to the overall flow than if robots were positioned in all the capillaries. The possibility of using just a portion of capillaries to perfuse tissue arises because resting tissue can contain more capillaries than required for adequate perfusion [10], though with considerable variation among locations in the body [1]. [0160] In addition to managing oxygen concentration, a concern when large numbers of robots consume oxygen is that they add significant heat to the body. Mitigating oxygen depletion by transporting more oxygen using supply robots as discussed above does not address issues arising from heating. Instead, providing more oxygen allows robots to increase their power use, and hence produce more heat. Limiting power production can both reduce oxygen depletion and reduce the heat generated by the robots, and is typically the better approach in situations where the large number of robots might lead to significant problems due to both oxygen depletion and heating. Another method to mitigate heating is to modify the location-based power limiting strategies discussed above, to change where the heating occurs. In particular, robots could shift their high-power activity and the resultant heat production to regions of the body that readily dissipate the heat. Such regions might be detected by having a lower temperature than the core of the body, such as near the skin. This approach to heat mitigation is particularly suitable for missions where high power demands occur near the skin (e.g., for robots communicating information to external receivers when they are near the skin). An alternative communication strategy of network message-passing through hubs located throughout the body would distribute power use and resultant heating throughout the body rather than concentrating heating near the skin. With enough robots that heating becomes an issue, heat dissipation could constrain the choice of communication method, in addition to constraints on transmission rates, latency, and/or reliability. Vessel Circuit Model [0161] The circuit considered for the example discussed above starts as blood leaves a lung capillary, where its oxygen concentration is set by that from the air in the lung, after which oxygen concentration decreases due to consumption by robots and tissue. The circuit continues through the body and back to the lung, ending as the blood is about to enter a lung capillary where it will be oxygenated and start a new circuit. The time to complete a circuit depends on where the blood goes, e.g., shorter times for transit through the head than through the feet. The example considers an average circulation time of about one minute, i.e., the time required for the resting heart rate, 5L/min, to pump the entire blood volume, Vblood. Oxygen concentration in the plasma at any location determines the power available to a robot, this concentration being determined by the combination of oxygen removal (by robots and tissue) and replenishment from red blood cells. As replenishment depends on the number of cells in the plasma (i.e., the hematocrit), evaluating available robot power requires characterizing the variation in hematocrit during a typical circulation loop. [0162] Blood carries most of its oxygen bound to hemoglobin in red blood cells. The number of red cells in blood is commonly expressed by the fraction of the blood volume occupied by cells, i.e., the hematocrit, which is typically around 45% [12]. This is the average value over the entire blood volume. However, in small vessels the fluid flow tends to push cells toward the center of the vessel where they move faster than the average speed of the flow. This Fahraeus effect decreases the hematocrit in small vessels. While there is considerable variation among such vessels, on average the hematocrit h in a vessel of diameter d (measured in microns) is approximately [32] where hfull is the hematocrit of the entire blood volume. For example, when overall hematocrit is hfull = 0.45, Eq. A.1 gives h = 0.34 in a capillary with diameter d = 8µm. Eq.9 is used to determine hematocrit in the example, thereby treating hematocrit as only depending on vessel diameter. [0163] From Eq.9, hematocrit only deviates significantly from hfull in those vessels whose diameters are less than about a millimeter, so it is unnecessary to distinguish diameters larger than this to determine hematocrit. The model used in this example only explicitly accounts for vessel diameter during the portion of the circuit through small vessels. Transport through large-diameter vessels and the heart, which all have the same hematocrit, can be grouped to produce a circuit with the following parts: 1. a sequence of small veins of increasing diameters starting from the end of a lung capillary 2. large pulmonary veins, the heart, large arteries 3. a sequence of small arteries of decreasing diameters to the start of a body capillary 4. a body capillary 5. a sequence of small veins of increasing diameters from the end of a body capillary 6. large veins, the heart, large pulmonary arteries 7. a sequence of small arteries of decreasing diameters to the start of a lung capillary [0164] Passage through the lung capillary at the end of the circuit contributes to the total circulation time but is not explicitly included in the model. Instead, the concentration is specified at the start of the circuit (i.e., just after passing through a lung capillary) as a boundary condition. This simplification is reasonable because the transit time through lung capillaries is more than sufficient to saturate red cells with oxygen even if they enter the capillary with low oxygen saturation [10]. Moreover, the large spacing between robots in capillaries, even at the largest number of robots considered here (10 ¹² ), means that robots do not significantly alter the oxygen available in lung capillaries. [0165] Without consumption by robots, the change in oxygen concentration in each part of the circuit depends on its transit time and hematocrit. Eq.9 gives hematocrit equal to hfull in the large-vessel parts of the circuit, i.e., circuit parts 2 and 6. The transit time for these parts is set so the total circuit time equals one minute when combined with the estimates of transit times through small vessels discussed below. For the capillary part of the circuit, typical capillary diameter and transit time are used. Eq.9 gives the hematocrit in the body capillary based on its typical diameter. [0166] For the remaining parts of the circuit, consisting of small branching vessels, hematocrit is estimated from the vessel diameter, d, via Eq.9, and transit time from vessel geometry: diameter, d, length, l, and number of such vessel segments, Nvessel. There is considerable variation in these values. For the purpose of this model average values are used, analogous to using the average relation between vessel diameter and hematocrit in Eq.9. These geometric parameters are related to transit time in the vessels of a given type (i.e., artery, capillary or vein) and diameter. In aggregate, small vessels have larger cross section than large vessels, which leads to slower speeds in those vessels [24]. Nevertheless, the short length of the small vessels more than offsets their slower flow speed, so blood spends most of the circuit time in large vessels. The aggregate cross section of vessels with diameter d is π(d/2) ² Nvessel. The entire blood volume passes through this aggregate cross section, when neglecting the relatively small portion of the flow through portal systems, so that (10) where v is the average flow speed in the vessels and T is average transit time for the blood volume V _blood (i.e, about one minute). This relation gives v in terms of d and N _vessel . This velocity determines the segment’s transit time as t = l/v. [0167] As described above, the geometric parameters of small branching vessels are used to quantify those parts of the circuit, using representative average branch geometry. For this example, vessel branching is based on branching of vessels in the lung for which data on complete vascular trees is available [21, 35,40,41]. Although the structure of capillary networks in the lung differs from that in other parts of the body [40], the branching of small arteries and veins in the lung is taken as representative of such vessels for a typical circuit through the body. The measured geometry of arterial and venous trees in the lungs [21] indicates that most of the flow is through vessels of successive branch orders. Flow that skips a few branch orders corresponds to blood that reaches capillaries through fewer branchings than blood that goes through all orders. For this model of average flow, vessel branching is taken to follow the main flow through successive orders, giving a sequence of vessel lengths, diameters and number of branches at each branching order for both arterial and venous trees [21, Tables 2 and 5]. Doubling the number of branches to account for flow through both lungs, Eq.10 determines transit speed, and hence transit time, for each level of branching. [0168] Large arteries branch into successively smaller vessels until they reach capillaries, and then merge into increasingly large veins. For circulation through a sequence of vessels i = 1,2,..., the total length is and the total passage time is which equals the typical total transit time T. Subtracting the transit time through small vessels from the total time T gives the time in the circuit parts corresponding to large vessels, i.e., circuit parts 2 and 6 above. To partition this time between these two large-vessel parts (i.e., arteries and veins) to and from a capillary, respectively, the time in veins is taken to be 1.5 times larger than in arteries, corresponding to somewhat slower flow speed in the veins. Combining these vessel properties results in the circuit model as shown in FIG.12. For purposes of illustration, the transit through each side of the heart is shown as taking 1s to transverse 50mm. Since hematocrit is the same in the heart and in large vessels, the precise time spent in the heart has no effect on the model results. FIG.12 illustrates transit through large vessels as an interpolation (dashed curves) between the heart and the branching through small vessels to and from a capillary. This interpolation matches typical average flow speed of blood leaving and entering the heart. Specifically, flow speed in the aorta averaged over a heartbeat is around 110mm/s and speed in the vena cava is around 135mm/s [14]. This interpolation illustrates the flow through large vessels. However, the model of oxygen consumption only depends on the transit time through those vessels, not the specific shape of the dashed curves in FIG.12. [0169] Fig.33 shows the vessel diameters (in millimeters) for the vessel circuit on a log scale, as a function of time (in seconds) through the vessel circuit, highlighting the diameters of small vessels where hematocrit deviates from its overall value. For small vessels, the diameters and transit times are the values described above. The diameters for large vessels are not shown in FIG.33, and the diameters are not relevant for this model as such vessels are large enough that hematocrit equals the overall value hfull (see Eq.9). [0170] FIG.34 is a schematic illustration of vessel branching. Smaller vessels have larger total cross section and lower hematocrit than larger vessels; these are illustrated in the aggregated model of the vessels shown in FIG.35. Such a simplified model can be employed because flow speed and hematocrit are relevant to robot oxygen consumption, while the details of vessel branching can be ignored. In this aggregated model shown in FIG.35, the circulation consists of a single vessel 3500 with volumes for plasma 3502 and blood cells 3504, where the aggregated vessel cross section is larger corresponding to smaller vessels, and where the fraction of volume occupied by cells (hematocrit) 3504 is smaller relative to the volume of plasma 3502 in the smaller vessels. [0171] To evaluate robot oxygen consumption over a minute or so, a one-dimensional model of vessel flow is averaged over the variation in speed due to heart contractions. This gives flow speed v(x) depending on the location x along the aggregated vessel, but not depending on time or how close the fluid is to the vessel wall. With this time averaging, the total cross section A(x) is independent of time. Considering the flow in a vessel with cross section area A(x) and flow speed v(x) at position x, fluid flows through the cross section at x at a rate ρv(x)A(x) where ρ is the fluid density. This rate is constant throughout the vessel for incompressible fluid, as given in Eq.10. Speed is inversely proportional to cross section area: (11) where v ₀ and A ₀ are the speed and cross section at an arbitrarily specified position along the circuit. The total cross section A(x) varies with position, as does hematocrit, as shown in FIG. 35. Since the fraction of the total cross section corresponding to plasma and cells varies in the aggregate vessel a model of aggregated vessels with two compartments, plasma and cells, can be employed, where the relative cross sections change with the changing hematocrit in the vessels. [0172] Evaluating how much cells replenish oxygen in blood plasma requires specifying the average speed of cells and plasma, v _cell and v _plasma , respectively. Due to changing hematocrit, these speeds are not the same and vary with the changing cross section of the vessel. One relation among these speeds is the average speed v in terms of hematocrit: ⁽¹²⁾ In this expression, v is the average speed in the vessel, taken from the parameters of the circuit in Fig.12. This relation assumes the addition of any robots to the blood does not noticeably alter the speed, which is reasonable with the small fraction of the volume occupied by robots [12]. This expression splits the blood volume between plasma and cells, ignoring the tiny volume occupied by robots. [0173] Another relation among these speeds arises from conservation of flow. For a small volume of blood with hematocrit h containing plasma and cells in a vessel with cross section area A, the volume of plasma and cells moving across that area in a small time ∆t are (1 − h)Av _plasma and hAv _cell , respectively. Over the time of a circuit (e.g., about a minute), neither plasma nor cell volumes change significantly, so the flow rates of plasma and cells must be the same throughout the circuit, i.e., equal to some constants αplasma and αcell. That is, (1 − h)Avplasma = αplasma and hAvcell = αcell. These relations imply that the ratio of cell speed to plasma speed is independent of the total cross section: (13) The Fahraeus effect does not apply to large vessels, where cells and plasma move together with the average flow of the blood, i.e, vcell = vplasma and hematocrit is hfull. For this case, Eq. 13 gives αcell/αplasma = hfull/(1 − hfull), and Eq.13 becomes (14) Combined with Eq.9, this gives the velocity ratio as a function of vessel diameter. For example, with the range of hematocrits used here for large and small vessels, Eq.14 gives a velocity ratio around 1.7 in small vessels, which matches reported values [3]. [0174] The aggregated vessel diameters (illustrated in Fig.35) and Eq.9 give the variation in h(x) in the aggregated vessels. This value, combined with Eq.12 and 14, gives the speeds v _plasma (x) and v _cell (x) as a function of position in the circuit. With these speeds, transit time can be calculated, and with transit time and hematocrit, oxygen concentration at different locations in the circuit can be determined. Oxygen Concentration in Vessels [0175] The aggregate vessel model shown in Fig.35 consists of two compartments, plasma and cells, and the cross sections of these compartments vary along the length of the aggregate vessel. These compartments exchange oxygen with each other, and with robots and tissue. Robots are a small portion of the blood and not treated as a separate compartment for the discussion of this section. This section describes how oxygen concentration changes in vessels with variable cross section: first for a single vessel, then for two such vessels treated as two compartments exchanging oxygen. These behaviors determine how concentration changes in a volume of fluid moving with the flow in one of these vessels. This differs from behavior in vessels of a fixed cross section due to the changing cross section and fraction of the total cross section occupied by the two compartments. [0176] A chemical in the fluid moves by convection with the fluid’s motion as well as diffusion. For the scales and flow speeds considered here, diffusion is a minor contribution to changing concentration. In particular, the Peclet number (as discussed above in Eq.8) characterizes the relative importance of convection and diffusion [36]. For flow through a vessel of diameter d, Pe roughly corresponds to the number of vessel diameters required for diffusion to spread the chemical across the vessel. For motion along the vessel, the distance at which Pe ≈ 1, i.e., d = D _O2 /v, is the distance at which diffusion and convection have about the same effect on mass transport in a moving fluid. At significantly longer distances, convection is the dominant effect. [0177] The distance over which diffusion is important is largest in the vessels with slowest flow, i.e., the capillaries. Capillary flow speeds are around 1mm/s for which DO ₂ /v = 2µm. This distance, comparable to the size of the robots, is considerably smaller than a typical capillary length, i.e., a millimeter, and the length of the full circulation loop (e.g., as indicated in Fig.12) relevant for evaluating systemic effects of robot oxygen consumption. Moreover, the typical distance between neighboring robots is larger than DO ₂ /v in the scenarios considered here, so neighboring robots do not directly compete with each other for oxygen. This is unlike the case of closely spaced robots (such as aggregates on vessel walls) where robots significantly reduce oxygen available to their neighbors [19]. In light of these observations, diffusive transport can be ignored in modeling the change in oxygen on the scale of the circulation loop. [0178] For convective flow, the chemical flux at position x along the vessel is J(x) = v(x)c(x) where c(x) is the chemical’s concentration. In a small section of vessel between x and x+∆x, in time ∆t, J(x)A(x)∆t molecules enter that section of vessel, and J(x+∆x)A(x+∆x)∆t leave it. In addition, reactions such as release of oxygen by cells or consumption by tissue change the concentration at a rate R. Combining these contributions to concentration change gives: From Eq.11, at position x, JA = v0A0c so the rate of change of concentration is (15) with v given by Eq.11. [0179] As described below in the section “Processes that Change Oxygen Concentration”, the time constant for robot oxygen consumption is less than a minute. Typical operations for the robots are likely to occur over time periods of at least tens of minutes, corresponding to many circulations, so a reasonable simplification is to focus on the steady-state concentration profile in the vessels, in which case Eq.15 becomes (16) For transient operations (e.g., for a few seconds after robots start consuming oxygen) robots will have more oxygen than indicated by the steady-state analysis considered here. [0180] As illustrated in FIG.35, the aggregated vessel consists of two main compartments: plasma 3502 and blood cells 3504 which have separate flow speeds (Eq.14). Each compartment acts as a separate vessel in terms of flow, but they can exchange oxygen. Generalizing Eq.16 to account for this exchange gives the behavior of the concentrations, c1 and c ₂ , in the two compartments: (17) where Rfrom 2 is the change of concentration in compartment 1 due to chemicals from compartment 2, R _{to 1} is the decrease of concentration in compartment 2 from chemicals that move to compartment 1, and Ri is the rate concentration changes in compartment i due to production of chemical in that compartment (with a negative value for chemical consumed). The two compartments share the total cross section of the aggregated vessel model, A(x). With hematocrit h(x), the cross sections of the two compartments are A1 = (1 − h(x))A(x) and A2 = h(x)A(x) (assuming that robots occupy a negligible fraction of the vessel volume). Conservation of flow means v ₁ (x)A ₁ (x) and v ₂ (x)A ₂ (x) are independent of x. R _{from 2} and R _{to 1} are rates of concentration change in the two compartments from oxygen moving from compartment 2 to compartment 1. These rates must account for different volumes, i.e., a given amount of oxygen makes a larger change to concentration in a smaller volume. The number of molecules in volume element i, extending from x to x + ∆x, is A _i (x)∆xc _i . The rate molecules move from compartment 2 to compartment 1 is both Rto 1A2∆x and Rfrom 2A1∆x. These must be the same, so (18) For example, when h is small, the transfer of a given amount of oxygen has a much larger effect on the concentration in compartment 2 than it does on that of compartment 1. [0181] With the above model, a robot moving in a small volume of fluid in compartment 2 can be considered. Eq.17 describes the steady-state concentration profile in two compartments, determining how the concentration in that fluid volume changes as it moves through a circuit such as illustrated in FIG.12. In time ∆t, the fluid volume moves from position x to x+v2∆t, and the time rate of change of concentration in the volume element of compartment i, due to motion with the speed v2 is dci/dt = v2∂ci/∂x. Thus Eq.17 gives (19) for the rate that concentration changes in the two compartments from the viewpoint of a volume moving with the flow in compartment 2. The circulation shown in Fig.12 starts with blood leaving lung capillaries, so the initial condition for Eq.19 is the concentration in the lung. Processes that Change Oxygen Concentration [0182] In this example, robots are assumed to move with cells rather than with plasma (i.e., flow pushes robots away from vessel walls in a manner similar to the behavior of blood cells [42]). This is reasonable in capillaries where cells move through single-file: robots are too large to fit in the gap between cells and the vessel wall, so robots move between cells, and hence at similar speed. In somewhat larger vessels, if robots are pushed closer to the vessel wall than the cells, robots would move somewhat more slowly. The difference in speeds between cells and the average flow rate is largest when hematocrit differs most from its overall value (i.e., in small vessels). Even then, the difference is relatively minor due to the short time (a few seconds out of the one minute circulation) that robots spend in those vessels, so the model results are not very sensitive to the accuracy of this assumption. [0183] With the assumption that robots travel with the speed of compartment 2 discussed above, the model of concentration change requires specifying the reaction rates appearing in Eq.19. During the circulation, robots and tissue consume oxygen from the plasma, and red cells replenish it. Fig.13 illustrates the processes that change oxygen concentration. In terms of Eq.19, R ₁ = R _robot + R _tissue is the rate, per unit volume, that robots and tissue remove oxygen from the plasma. There is no consumption within cells so R2 = 0. The rates Rfrom 2 and Rto 1 are the transfer rates from cells to plasma that maintains the equilibrium of Eq.20 below. [0184] Oxygen removed from blood plasma is replaced by oxygen released from nearby red blood cells. The time scale for this process is less than 100ms [7], which is much shorter than the one minute circulation time considered here, and even the one second capillary transit time during which tissue extracts oxygen from the blood. A reasonable approximation is that oxygen bound inside red cells is in equilibrium with the concentration in the surrounding plasma. Oxygen bound in red cells is characterized by the hemoglobin saturation S: the fraction of hemoglobin capacity in a cell which has bound oxygen [26]. The oxygen concentration in the cell is where is the concentration in the cell when all the hemoglobin has bound oxygen. Quantitatively, the equilibrium saturation, conventionally expressed in terms of the equivalent partial pressure p of O ₂ in the fluid around the cell, is described by the Hill equation [15,30]: (20) where a = p/p ₅₀ is the partial pressure ratio, p ₅₀ is the partial pressure at which half the hemoglobin is bound to oxygen and n characterizes the steepness of the change from low to high saturation. The saturation ranges from near 1 in the lungs to around 1/3 in working tissues. Henry’s Law relates the partial pressure to the oxygen concentration in the plasma around the cell: p = H _O2 C _O2 with the proportionality constant H _O2 depending on the temperature. Thus, a = (HO2/p50)CO2 = CO2/Chalf where Chalf = p50/HO2, which is about 2.2 × 10 ²² molecule/m ³ . This is comparable to lower range of oxygen concentration in tissue. This model does not consider deviations from Eq.20, which mainly occur at low saturations [15, 30], and variations in its parameters with changing blood chemistry, such as pH and carbon dioxide concentration. [0185] For determining oxygen removal by robots, a small volume ∆V of blood with oxygen concentration c in the plasma contains νrobot∆V robots, where νrobot is the robot number density in the blood. With each robot absorbing at the rate given by Eq.1, the total rate robots remove oxygen per unit volume of plasma is R _robot = γ _robot c (21) with rate constant γrobot = 4πDO2r _robot νrobot/(1 − h). This absorption rate assumes each robot draws oxygen independently from a fluid with concentration c (that is, robots are assumed to be sufficiently far apart that they do not compete with their neighbors to reduce the local oxygen concentration and hence robot absorption rate [19]). Such competition is insignificant for robots separated by at least about ten times their size [5], which is the case for the numbers of robots considered here. The time constant for robots removing oxygen from plasma is τ _robot = 1/γ _robot . τ _robot ≈ 10s for 10 ¹⁰ robots. τ _robot is correspondingly smaller for the scenarios with larger numbers of robots, so concentration changes due to robots reach steady- state within a single circulation time. [0186] Tissue extracts oxygen from blood passing through capillaries. In terms of the aggregated vessel model, consumption by tissue occurs over a short distance around the peak in total cross section shown in Fig.35, which corresponds to capillaries. A simple model of tissue oxygen consumption uses a cylindrical region of tissue around each capillary [23, 30]. The radius of this tissue cylinder, rtissue, corresponds to a typical maximum distance of tissue supplied from a capillary, which is a few cell diameters. In this model, the volume of tissue receiving oxygen from a length ∆x of capillary, with radius rcap is π(rtissue ² − rcap ² )∆x, so the ratio of tissue to vessel volume is (rtissue/rcap) ² − 1. A consistency check on this model is that multiplying the total capillary volume by the tissue to capillary volume ratio should equal the total body volume. The total capillary volume is about 4 × 10 ⁵ mm ³ [12]. The ratio of tissue to capillary volume is about 100, giving corresponding tissue volume of about 0.04m ³ , which is comparable to body volume. [0187] Models of oxygen use and power generation in tissues can account for tissue structure [30]. A simpler approach [27], adopted for this example, treats the tissue surrounding the vessel as homogeneous and metabolizing oxygen at the rate that produces power according to Eq.3 above. When oxygen concentration is substantially larger than Ktissue, tissue power is nearly independent of oxygen concentration, and tissue metabolic demand, rather than available oxygen, limits tissue power. Dividing Ptissue by the reaction energy per oxygen molecule consumed gives the rate of oxygen consumption per unit volume of tissue. Oxidizing a single glucose molecule consumes six oxygen molecules, so the energy per oxygen molecule is e/6, with e being the energy from oxidizing one glucose molecule. [0188] For the resting tissue power demand considered in this example, oxygen concentration in tissue is nearly constant as a function of distance from the capillary [23], even with additional consumption from robots [19]. For evaluating tissue oxygen consumption from capillaries, the oxygen concentration in the tissue is considered to be the same as that of the plasma in the capillary. That is, in Eq.3 C _O2 is set equal to the oxygen concentration in the capillary surrounded by the tissue. In this case, Ptissue is constant within the tissue cylinder and total tissue consumption is Ptissue multiplied by the tissue volume around the capillary. Tissue takes oxygen from plasma in the capillary, so the rate it reduces concentration in the plasma is enhanced by the ratio of tissue to capillary volume given above, and the fraction of the vessel volume that is plasma (i.e., 1−h). Combining these factors, the rate tissue reduces oxygen concentration in the plasma is (22) in the capillaries, and zero elsewhere in the circuit. Model Parameters [0189] Table 2 gives the parameter values used to evaluate robot power in the circulation in the example discussed. For tissue, Ktissue is from Ref. [27], and the blood cell parameters are from Refs. [7] and [30]. The oxygen concentration in the lung corresponds to arterial concentration [12]. Concentrations of glucose in blood plasma are in the millimolar range (about 10 ²⁴ molecule/m ³ ), far larger than the oxygen concentrations [12]. [0190] For evaluating the rate oxygen diffuses to the robot surface (e.g., in Eq.1), it is convenient to express oxygen concentration in terms of molecules per unit volume. By contrast, macroscopic studies usually express concentrations in more readily measurable quantities. These include moles of chemical per liter of fluid (i.e., molar, M) and grams of chemical per cubic centimeter. Discussions of gases dissolved in blood often specify concentration indirectly via the corresponding partial pressure of the gas under standard conditions. As an example of these units, oxygen concentration CO ₂ = 10 ²² molecule/m ³ corresponds to a 17µM solution, 0.53µg/cm ³ and to a partial pressure of 1600Pa or 12mmHg. This concentration corresponds to 0.037cm ³ O ₂ /100cm ³ tissue with oxygen volume measured at standard temperature and pressure. [0191] Tissue power demands vary considerably, depending on the tissue type and overall activity level. For this example, is set to a typical resting power demand [12]. For comparison, peak metabolic rate in human tissue can be as high as 200kW/m ³ [27]. [0192] Conventional fuel cells have efficiencies around 50% [12]. While the efficiency of the fuel cells required for micron-size robots remains to be determined, for definiteness the example uses fuel cell efficiency f _robot = 50%. Variations in Circulation Paths [0193] The above discussion addresses average circulation times. However, circulation paths differ depending on the length of the circuit. Paths through organs close to the heart typically have shorter paths than average, while paths through the legs typically are longer than average. Additional variation occurs due to differences in flow speed, such as slow flow of blood through the spleen. Additional distance and/or time may cause oxygen depletion in longer/slower circuits that would not occur for the same number of robots in average circulation. Modeling such variation has found that the impact of such variations is relatively minor for numbers of robots either 10 ¹¹ or fewer, or 10 ¹² or more. For intermediate numbers, such as 3 x 10 ¹¹ robots, variation in circulation path length and/or flow speed can have a significant impact on oxygen availability in the later portions of the circuit, and it may therefore be beneficial to adjust the operation of individual robots based on the circulation path they are currently in. Robots having a locomotive capability could select an appropriate circulation path to avoid situations where insufficient oxygen is available (such as avoiding longer/slower paths when an insufficient amount of oxygen has been stored, avoiding capillaries with a large number of other robots, etc.) or to take advantage of shorter/faster circuits when greater availability of oxygen would be beneficial (such as when conducting high-power tasks or when filling the robot’s storage tank). [0194] In general, if robots can detect that they are on a shorter/faster circulation path they may be able to ignore criteria that would otherwise determine that they are in an absorption-limiting need condition, and thus can continue to absorb oxygen to operate in a higher-power mode. Similarly, robots could delay high-energy tasks (computation, long- range communication, maintenance routines, etc.) until they detect that they are in a short circulation loop. Information that robots could employ to determine that they are on a shorter circuit path could include analyzing rate of change of branch size, overall location information (such as external navigation information provided by acoustic transducers or other transmitters), elapsed time or distance before reaching a capillary, temperature, and/or chemical variation.[12] [0195] Robots that can detect that they are on a longer/slower circulation path may apply more strict criteria to determine that they are in an absorption-limiting need condition, to reflect that there is a longer time before oxygen can be replenished in the lung capillaries (or before merging with less-depleted blood from shorter circuits in larger veins). Robots that store oxygen could make a determination that a reactant need condition exists based on detecting that they are in a longer/slower circuit, or by criteria such as time elapsed or distance traveled since leaving the lung capillaries. For example, since the average circuit time is one minute, robots could wait one minute after leaving a lung capillary to release reactant (either internally for the robot’s own use or externally to supply other robots), as such time would indicate the robot to be on a longer/slower path. Such determination of a reactant need condition could be combined with additional considerations discussed above. For example, a robot could release stored oxygen after one minute only after already having stored a prescribed amount of oxygen during multiple passages through the lung capillaries. Where the robots flow through the capillaries due to blood circulation (i.e., without employing locomotion or anchoring to prolong their period in the lung) a model of circulation paths that accounts for variations of length and flow speed shows that a robot of 1µm radius with 1/3 of its volume used for storage should have a full tank after 20 passages through the lungs. In such a case, the storage tank remains relatively full if the robot operates at 100pW using stored oxygen after one minute for most circulation paths, but may be depleted on an especially long/slow path. Alternatively, a robot could use stored oxygen after one minute whenever stored oxygen is available (a similar model of circulation paths shows that robots operating at 100pW using stored oxygen after one minute can run out of oxygen on longer paths, and do not fill more than 30% of their tank capacity, and thus a smaller fraction of robot volume may be devoted to storage when such an operation scheme is employed). [0196] Variation in circulation paths may result in robots in any particular location in the fluid system having varying amounts of stored oxygen, depending on how much they have been able to store and how much they have used due to their history of traveling on shorter or longer circulation paths. Robots may be able to take advantage of such variation by having those robots with ample stored oxygen undertake high-energy tasks (computation, long-range communication, maintenance routines, etc.) using data communicated to them over short range by robots with less stored oxygen, allowing those robots to operate in a lower-power mode. Active Mixing [0197] The variation in circulation paths discussed above gives rise to another example of robot operation to reduce the impact of a large number of robots absorbing a chemical of interest, when intermediate-size veins from paths of different lengths/times merge together. In the case where a vein carrying blood from a longer/slower circuit path merges with a vein carrying blood from a shorter/faster circuit path, they blood from the longer path typically has a lower oxygen concentration due to consumption by robots over a greater time since leaving the lungs. For veins of intermediate size (generally in the range of millimeters), the combined flow in the larger vessel has a gradient of oxygen concentration across its section for some distance downstream of the merge. This gradient results from the time it takes for convection and diffusion to distribute the oxygen from the oxygen-rich blood from the shorter path vein across the vessel to mix with the oxygen-depleted blood from the longer path vein. As a result, when robots continuously absorb and consume oxygen, such continued absorption may deplete the oxygen in one region of the merged vessel to the point where it is insufficient for robot operation and/or be detrimental to cells in the vessel wall in such region. This is particularly a concern for robots located at or near the vessel wall in such region, where blood flow is slower and thus absorption takes place for a longer time. [0198] FIGS.36 and 37 illustrate such a case, where two veins (3602, 3604) that are each 2mm in diameter merge together into a 2.5 diameter vessel 3606 and where 10 ¹² robots of 1 µm radius are distributed throughout the bloodstream and absorbing all the oxygen that reaches their surfaces (similar geometry to the case discussed for FIG.28). The axes show dimensions in millimeters, and the gradation of shading represents the concentration of oxygen, ranging from the darkest shade (starting point of vein 3604) representing 2.0 x 10 ²² oxygen molecules per cubic meter and the lightest shade representing no oxygen. Vein 3602 carries blood from a longer circuit path, having a uniform concentration of 0.5 x 10 ²² oxygen molecules per m ³ at its start, 8mm upstream of the merge. Vein 3604 carries blood from a shorter circuit path, having a uniform concentration of 2.0 x 10 ²² oxygen molecules per m ³ at its start. FIG.37 shows the concentration across the merged vessel 3606 at a location 8mm downstream of the merge (section 37 of FIG.36). Due to limited mixing of oxygen across the vessel and continued absorption by the robots, the merged flow is still largely separated into an oxygen-depleted region 3608 (where robots in the flow from vein 3602 have continued to absorb the remaining oxygen, which has not been sufficiently replaced by diffusion or convection) and a higher-oxygen region 3610 (where robots in the flow from the vein 3604 have continued to absorb oxygen, but where there is still ample oxygen available due to the higher initial concentration). The higher-oxygen region 3610 can be considered as a high- reactant region. [0199] To mitigate the impact of such gradient, robots can be programmed to actively transport oxygen across the merged vessel to actively distribute oxygen across the section. In effect, the oxygen-rich region of the vessel serves as a high-reactant region, and robots absorb and store reactant when in such region, and then release such reactant from storage when conditions indicate that they have reached (or are statistically likely to have reached) a location where a reactant need condition exists. One simple operational scheme is for the robots to periodically store reactant when they determine that they are in a high-reactant region, move in series of randomly-directed segments, and then release the stored reactant. This would have the effect of increasing the diffusion coefficient for the reactant. Other schemes could be more directed to increase efficiency of redistribution (at the expense of requiring more complex robot behavior). Examples of such directed transport include detecting the reactant gradient and moving to a location of low reactant before releasing stored reactant, determining vessel diameter and moving along the vessel wall to an opposite location (based on travelling a distance of half the vessel circumference), moving responsive to other robots communicating that the location of a low-reactant region, etc. [0200] As an example of the effect of increased diffusion that could be provided by such active mixing, FIG.38 shows merging blood flows with similar parameters to those used for FIG.36, but for a smaller vessel where the relative contribution of diffusion to convection in distributing oxygen across the vessel after merging is greater, and thus the Peclet number (see Eq.8) is lower. In FIG.38, two 100µm diameter vessels (3802, 3804) merge into a 125µm diameter vessel 3806. Because of the smaller diameter, flow speed is accordingly lower (see Eq.11), so the flow speed is 30% of the speed in the vessels shown in FIG.36. The Peclet number for the vessels shown in FIG.38 is 45, compared to 3000 for the vessels shown in FIG.36. For the vessels shown in FIG.36, using active transport by robots to increase the effective diffusion rate by a factor of about 70 would result in a distribution of oxygen in the merged vessel 3606 similar to that seen in the smaller merged vessel 3806 due to increased diffusion. In this case, the gradient in the merged vessel 3806 decreases in a small distance downstream of the merger, and there is no zone where the flow from the longer-path vein 3802 becomes increasingly oxygen-depleted. [0201] Increased mixing to avoid having a reactant-depleted region may be necessary for proper operation of the fluid system, but could also be advantageous for averaging the concentration to increase the accuracy of generalized modeling of the fluid system by making the concentration at any particular point more consistent with the generalized model. While providing such active mixing may complicate the design and operation of individual robots, it can provide more accurate modeling to simplify the design and implementation of overall robot operations and mission planning, as the actual situations encountered by individual robots will more closely match the generalized conditions assumed in models of the fluid system. [0202] The above discussion, which employs particular examples for illustration, should not be seen as limiting the spirit and scope of the appended claims. 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