MODULAR PLATFORMS WITH MULTI-ROTOR COPTERS MOUNTED ON HINGES OR GIMBALS TO FORM MECHANICALLY CONSTRAINED FLIGHT FORMATIONS CROSS-REFERENCE TO RELATED PATENT APPLICATIONS [0001] The present application claims the benefit of and priority to U.S. Provisional Patent Application No.63/069,487, filed on August 24, 2020, the entire disclosure of which is incorporated by reference herein. BACKGROUND [0002] Multi-rotor copters, such as the most popular quad-rotor copters with fixed propeller axes, have several limitations. The copter’s main frame is limited to orientations that are nearly horizontal, thus limiting the copter’s manipulability and agility. Payload is limited by the size, speed, numbers of rotors, and their kinematic configurations. Accordingly, a solution to these and other limitations remains desirable. Underwater vehicles propelled by rotors have similar limitations. SUMMARY [0003] At least one embodiment relates to an aerial flying unit. The aerial flying unit can include a modular mechanical platform. The modular mechanical platform can include a frame. The flying unit can include a plurality of multiple-rotor copters detachably coupled to the mechanical platform by a portion of the frame. The mechanical platform can be reconfigurable. The multiple-rotor copters can coupled to the mechanical platform by a passive pad. [0004] At least one embodiment relates to a modular unit. The modular unit can include a center structure and a plurality of arms extending from the center structure. The modular unit can include an attachment to couple to a standard quad copter at the end of each of the plurality of arms. Each arm of the plurality of arms can couple to the attachment by a rotational joint. The attachment can include a one degree of freedom rotational motion. [0005] At least one embodiment relates to an aerial flying unit. The aerial flying unit can include a plurality of modular units. The aerial flying unit can include a first modular unit of the plurality of modular units mechanically coupled to a portion of a second modular unit of the plurality of modular units. The first and second modular units can form a formation. Each of the plurality of modular units can include a modular and reconfigurable mechanical platform and a plurality of multiple-rotor copters coupled to the mechanical platform. BRIEF DESCRIPTION OF THE DRAWINGS [0006] The accompanying drawings constitute a part of this specification, illustrate embodiments of the disclosure, and together with the specification, explain the methods, systems disclosed herein. The accompanying drawings are not intended to be drawn to scale. For purposes of clarity, not every component may be labeled in every drawing. The present embodiments will be described with reference to the attached drawings, wherein: [0007] FIG.1 depicts a schematic of a thrust-vectoring propulsion unit, according to an exemplary embodiment. [0008] FIG.2 depicts a thrust-vectoring propulsion unit, according to an exemplary embodiment. [0009] FIG.3 depicts a schematic of a module with a plurality of thrust-vectoring propulsion units coupled via hinges, according to an exemplary embodiment. [0010] FIG.4 depicts a schematic of a module with a plurality of thrust-vectoring propulsion units coupled via gimbals, according to an exemplary embodiment. [0011] FIG.5 depicts a top view of a schematic of a plurality of modules coupled to one another to form a chain, according to an exemplary embodiment. [0012] FIG.6 depicts a side view of the chain of FIG.5, according to an exemplary embodiment. [0013] FIG.7 depicts a module with a plurality of thrust-vectoring propulsion units, according to an exemplary embodiment. [0014] FIG.8 depicts a thrust-vectoring propulsion unit, according to an exemplary embodiment. [0015] FIG.9 depicts a graphic illustration of a control system loop of a module with a plurality of thrust-vectoring propulsion units, according to an exemplary embodiment. [0016] FIG.10 depicts a schematic of a control system of a module with a plurality of thrust-vectoring propulsion units, according to an exemplary embodiment. [0017] FIG.11 depicts a graphic illustration of a tilting angle of a module with a plurality of thrust-vectoring propulsion units, according to an exemplary embodiment. [0018] FIG.12 depicts a graphic illustration of a distribution of a central controller loop time, according to an exemplary embodiment. [0019] FIG.13 depicts an experimental implementation of a module with a plurality of thrust-vectoring propulsion units, according to an exemplary embodiment. [0020] FIG.14 depicts an experimental implementation of a module with a plurality of thrust-vectoring propulsion units, according to an exemplary embodiment [0021] FIG.15 depicts a graphic representation of various characteristics of a module with a plurality of thrust-vectoring propulsion units, according to an exemplary embodiment [0022] FIG.16 depicts a graphic representation of results of a first case of experimental implementation of FIG.13, according to an exemplary embodiment. [0023] FIG.17 depicts a graphic representation of results of a second case of experimental implementation of FIG.13, according to an exemplary embodiment. [0024] FIG.18 depicts a graphic representation of results of a third case of experimental implementation of FIG.14, according to an exemplary embodiment. DETAILED DESCRIPTION [0025] The present embodiments are generally directed to modular platforms with multi-rotor copters mounted thereon. As set forth above, multi-rotor copters, such as the most popular quad-rotor copters with fixed propeller axes, have several limitations. Conventional multi-rotors have coupling between position and attitude control due to under-actuation in dynamics. Mechanical modifications with tiltable thrusting actuators were proposed to address this issue, but usually with the price of increased mechanical complication, additional actuators and introduced disturbance torques during operations. Furthermore, the copter’s main air frame is limited to orientations that are nearly horizontal, thus limiting the copter’s manipulability. Payload is limited by the size, speed, and numbers of rotors. [0026] To address these problems, the existing public domain knowledge is generally classified into two categories. The first category is multi-rotor copters with fixed rotor axes, where the orientations of the axes with respect to the main frames are designed to be non- parallel. The second category is multi-rotor copters, where some or all of the rotor axes are actively adjustable in real-time while the remaining axes are fixed orientations with respect to the copter main frames. [0027] Among other things, it is recognized that both of these categories represent significant deviations from the most popular quad-copters and require a new mechanical design process. It’s also infeasible to increase the number of rotors on-site in reconfigurable and modular fashions for increasing payload or improving manipulability. The adjustable rotor axes also require additional actuators to steer the orientation angles, thus reducing payload. Overview [0028] Addressing the aforementioned challenges, a modular and reconfigurable mechanical aerial platform as a main frame is configured to host a plurality of multiple-rotor copters to form one flying unit. Each quad-copter can couple to a mechanically passive pad, which can have either one degree-of-freedom (e.g., utilizes a hinge) or two degree-of- freedom (e.g., utilizes a gimbal) of rotational axes. The pads can passively couple to the frame by the hinges or gimbals. The orientation angles of each passive hinged or gimbaled pad can be established by active control of the multiple (typically four) rotors of the copters attached to the pad. The rotors of the copters can be controlled to establish the orientation angles and thrust forces with a direction that is correlated to the hinge’s or gimbal’s orientation angles. A plurality of hinges and gimbals can couple with multi-rotor copters to form a modular flying unit. A plurality of modular units can mechanically couple to each other in a formation to form a larger unit. The attachments of the copters to the pads and the interconnections among these modular units can be designed so that the engagement and disengagement may be operated in the airfield in a controlled manner. Thus, this modular unit is both modular and reconfigurable, capable of being organized pre-flight on the ground or in-situ in the airfield. The presented systems and methods also apply to under water vehicles. [0029] In various embodiments, a modular flying unit includes a reconfigurable mechanical frame and a plurality of rotors coupled to the frame. For example, the flying unit may include, but is not limited to, a vehicle or device to travel through air, land, or water. In various embodiments, the flying unit is an unmanned aerial vehicle (UAV). Propulsion Unit [0030] FIG.1 depicts a thrust-vectoring propulsion unit 100, according to an exemplary embodiment. For example, the propulsion unit 100 is one example of a portion of the modular aerial flying unit (e.g., the module 300 as discussed below) that includes a multi- rotor. As shown in FIG.1, and among others, the propulsion unit 100 can include a basic structure (e.g., connecting structure 110) in which a plurality or rotors 105 are coupled. For example, the connecting structure 110 may include any commercially available multi-rotor components capable of fixing one or more rotors 105 to the structure 110. The connecting structure 110 may include a plurality of rotors 105 coupled to (e.g., mounted on, attached to, etc.) the structure 110 via one or more mechanical hinges or gimbals (e.g., via gimbal 120 or hinge 125). [0031] In various embodiments, the multiple-rotor copters are quad-rotor copters 130. For example, the propulsion unit 100 may include four rotors 105 (e.g., a quad-rotor) coupled to the connecting structure 110, as shown in FIG.1, and among others. In various embodiments, the mass center of the rotors 105 are located at or close to the center of the gimbal 120 (or the center line of the hinges) to provide one or more passive rotational joints, as depicted by the directional rotation about an axis (e.g., arrows 115). For example, the gimbal 120 can couple to the propulsion unit 100 proximate the center of mass of the sum of the rotors 105 (e.g., the center point or midpoint of the structure 110, as shown in FIG.1). The angle and magnitude of the thrust vectoring propulsion unit 100 can be controlled by adjusting the individual speed of each rotor 105. For example, the speed of each rotor 105 can be individually or simultaneously increased and/or decreased to accommodate varying control of the whole propulsion unit 100, as discussed in greater detail below. [0032] In various embodiments, the rotors 105 can couple to a mechanically passive pad 135, which can have either one degree-of-freedom (hinge 125) or two degree-of-freedom (gimbal 120) of rotational axes. For example, the passive pad 135 may include various attachment components to facilitate coupling the rotors 105 to a frame 310, as discussed in greater detail below. In various embodiments, the pads 135 are connected to the structure 110 by the hinges 125 or gimbals 120. A hinge 125, as shown throughout the figures, is when one of the two rotational degree-of-freedom (DOF) gimbal 120 is fixed. A quad-rotor copter 130 (e.g., four rotors 105) mounted on a hinge 125 or gimbal 120 makes a prominent example of such unit. [0033] FIG.2 depicts an example of thrust-vectoring propulsion unit 100, according to an exemplary embodiment. The propulsion unit 100 of FIG.2 includes another configuration of a gimbal 120 mechanism, according to an exemplary embodiment. As shown in FIG.2, and among others, the propulsion unit 100 can include a plurality of rotors 105 coupled to the connecting structure 110 of the propulsion unit 100 by various types of gimbals 120. Referring generally to the figures, the propulsion unit 100 configuration of coupling a quad-rotor copter 130 (e.g., four rotors 105) to a hinge 125 or gimbal 120 provides an example in which the speed of each of the four rotors 105 can be controlled to generate desired angles (e.g., roll and pitch) and a desired magnitude of a thrust force, as discussed in greater detail below.. [0034] In various embodiments, the orientation angles of each passive hinged or gimbaled pad 135 is established by active control of the multiple rotors 105 of the quad-rotor copters 130 coupled to the pad 135. In various embodiments, the rotors 105 of the quad-rotor copters 130 are controlled to establish the orientation angles and thrust forces with a direction that is correlated to the hinge’s or gimbal’s orientation angles, as discussed in greater detail below. Modular Unit Comprising a Plurality of Propulsion Units [0035] In various embodiments, a plurality of hinges 125 and gimbals 120 with attached multi-rotor copters forms the modular flying unit. For example, FIG.3 depicts a flying or underwater module 300, according to an exemplary embodiment. The module 300 can include a basic structure (e.g., frame 310) in which a plurality of the thrust-vectoring propulsion units 100, composed of hinges 125, are coupled to a vehicle frame 310. For example, the vehicle frame 310 can include various platforms, fixtures, attachments, fasteners, or other components to facilitate coupling a plurality of propulsion units 100 to one another. [0036] In various embodiments, the module 300 can include a plurality of arms 305 that branch out from the frame 310. For example, each arm 305 may facilitate coupling to a single-DOF rotational joint to couple to the quad-rotor copter 130 at the end of each arm 305. In various embodiments, the center of the frame 310 can be used to carry a load (e.g., payload, battery, etc.). The center of the frame 310 can branch out into any number of arms 305. For example, the frame 310 can include one arm 305, two arms 305, or three or more arms 305. Four arms 305 are shown in FIG.3 for illustrative purposes only. In various embodiments, the arms 305 may facilitate attaching the one or more rotors 105 to the frame 310 via a single-DOF rotational joint (e.g., hinge 125). These joints, represented as arrow 115, are generally passive and unconstrained. For example, the hinges 125 provide the arms 305 in connection with the rotors 105 with full rotational motion. In various embodiments, the ends of each arm 305 contain a platform or attachment, such as the passive pad 135, to couple to a standard quadcopter 130. In various embodiments, the passive pad 135 may include, but is not limited to, platforms, fasteners, joints, and various other attachment components configured to facilitate coupling the rotors 105 to a portion of the frame 310 (e.g., one or more arms 305). [0037] In various embodiments, the module 300 can include a plurality of arms 305 that branch out from the frame 310 and couples to a basic gimbal 120 mechanism. For example, in such embodiments, two passive joints are kinematically linked allowing for two DOF of rotational motion. The arms 305 may facilitate coupling to a standard quad-rotor copter 130 at the end of each basic gimbal 120 mechanism. FIG.4 depicts an example flying or underwater module 300 in which a plurality of the thrust-vectoring propulsion units 100 is coupled to the frame 310 via gimbals 120. FIG.4 depicts a basic gimbal 120 mechanism shown in which two passive joints (shown via arrows 115) are kinematically linked allowing for two DOF of rotational motion. In various embodiments, these joints (shown as arrows 115) are passive. For example, in various embodiments, the rotational joints are passive and unconstrained (fully rotational motion). The gimbal 120 mechanism depicts in FIG.4 is for illustrative purposes only. Various configurations and types of similar gimbal 120 mechanisms may be used to facilitate connecting the rotors 105 with the frame 310. For example, the gimbal 120 mechanism shown in FIG.2 may be used in the embodiment shown in FIG.4. While four arms 305 are shown in the exemplary embodiment depicted in FIG.4, any number of arms 305 can be added in any configuration of the module 300. While the arms 305 shown in the exemplary embodiments of FIGS.3 and 4 are depicted as planar members, the arms 305 may vary in shape, size, and configuration in various implementations. The arms 305 are not limited to a planar form, as illustrated. Chain of Modular Units [0038] In various embodiments, a plurality of modular units 100 (e.g., module 300) may mechanically couple to one other in a formation, wherein each module 300 can include a modular and reconfigurable mechanical platform (e.g., frame 310) and a plurality of multiple- rotor copters (e.g., quad-rotor copter 130) coupled to the frame 310. A plurality of propulsion units 100 or modules 300 can be coupled together to form a chain 500 of units 100, or modules 300. For example, a plurality of modular propulsion units 100 coupled together to form a module 300 can couple to a second module 300 via one or more joint connectors 510, as depicted in FIG.5. In various embodiments, the joint connectors 510 can couple to one or more portions of the frame 310 of the module 300. For example, as depicted in FIG.5, a plurality of joint connectors 510 can facilitate connecting a plurality of modules 300 together. For example, the joint connectors 510 may include various fasteners, hinges, gimbals, ball- and-socket joints, or the like. In various embodiments, the frame 310 of the module 300 may include a rectangular shape to facilitate forming a linear chain 500, as depicted in FIG.5. In various embodiments, the frame 310 of the module 300 may include various other shapes to facilitate coupling each propulsion unit 100 to one another. For example, the frame 310 may be any polygonal shape. [0039] FIG.5 depicts a top view of an example of joining a plurality of modules 300 together to form a single chain 500 of linkages. While the exemplary embodiment in FIG.5 depicts a chain 500 of four individual modules 300, the chain 500 may include more or less modules 300. While the exemplary embodiment depicted in FIG.5 includes one quad-rotor copter 130 coupled to each module 300, the modules 300 may include more quad-rotor copters 130. In various embodiments, the modules 300 may couple to one another to form various shapes of chains 500. For example, the modules 300 can couple at multiple portions to create a plane of linkages (e.g., the modules 300 couple both laterally and longitudinally to each other). In various embodiments, each module 300 can include joint connectors 510 that provide one or two angles of rotation. For example, the joint connectors 510 may include hinges or gimbals (similar to those discussed in greater detail above). In various embodiments, the joint connectors 510 may provide the chain 500 of modules 300 freedom to rotate by fixed-angle mechanisms. For example, the joint connectors 510 may include various locks, latches, or the like. In various embodiments, the joint connectors 510 may provide the chain 500 with a combination of hinges, gimbals, or fixed-angle mechanisms. For example, the chain 500 may include propulsion units that are both adjustably coupled to one another and locked by latching mechanisms. [0040] FIG.6 depicts a side view of a plurality of modules 300 as a mosaic structure chain 500. As depicted in FIG.6, the chain 500 can include various degrees of motion to form a blanket over an uneven surface 515. For example, the flexible or passive joint connections 510 can facilitate providing the chain 500 one or more degrees of freedom to maneuver over various terrains. The uneven surface 515 shown in FIG.6 is shown for illustrative purposes only. The chain 500 can be configured to maneuver over various terrains including, but not limited to, ground surfaces, uneven surfaces, and objects in the air. While the exemplary embodiment depicted in FIG.6 shows the chain 500 as a mosaic linear configuration, a closed chain mosaic structure like a ring, cube, or soccer ball can also be formed of the modules 300 in various embodiments. Dynamic Modeling of Modular Unit Overview [0041] Example processes of calculating various characterization of exemplary embodiments of the module 300 are described in detail below. These processes are for demonstrative purposes only and is in no way intended to limit the scope of the present disclosure. In various embodiments, various other calculations, experiments, processes may be used. [0042] FIG.7 depicts a perspective view of a module 300 having a plurality of quad- rotor copters 130 coupled to the module 300 via the frame 310, according to an exemplary embodiment. FIG.7 illustrates one example of the degrees of freedom of the module 300 connected via hinges 125. For illustration purposes only, each of the four quad-rotor copters 130 of the module 300 in FIG.7 are labeled i with a corresponding number as reference to the following equations and various calculations. [0043] FIG.8 depicts a portion of the module 300 shown in FIG.7. For example, FIG.8 depicts a singular propulsion unit 100 including a single quad-rotor copter 130. As shown in FIG.8, and among others, the quad-rotor copter 130 includes four individual rotors 105. For illustration purposes only, each of the four rotors 105 of the propulsion unit 100 in FIG.8 are labeled j with a corresponding number as reference to the following equations and various calculations. [0044] First, as depicted in FIG.7, a world inertia frame (e.g., coordinate reference system of a surrounding environment as shown through coordinate system 705) can be defined under North-East-Down (NED) convention, defined as FW below. The frame of inertia of the vehicle frame 310 (e.g., coordinate reference system of the center of the frame 310, as shown through coordinate system 710) can be defined as FB below. The quad-rotor copter 130 frame of inertia (e.g., coordinate reference system of the individual propulsion unit 100 as shown through coordinate system 805) can be defined as FQi below. [0045] The quad-rotor copters 130 in the module 300 depicted in FIG.7 are ordered The distance of each center of the quad-rotor copter 130 to the center of central frame 310 is assumed identical (e.g., assuming each arm 305 is identical in shape and length) and is defined as l. The propellers (e.g., the rotors 105) of each quad-rotor copter 130 are ordered in FIG.8. The distance of each rotor 105 to the center of the quad-rotor copter 130 (e.g., the lateral length from the center of hinge 125 to the center of each rotor 105) is assumed identical and is defined as a. [0046] Next, the position of the center of the vehicle frame 310 can be defined in reference to the world frame of inertia FW as [0047] The Euler angle of platform attitude in the world frame of inertia FW can be described by intrinsic rotation. The corresponding Tait–Bryan angles in the roll-pitch-yaw convention can be defined as [0048] The angular velocity of the module 300 in the frame of inertia of the vehicle frame 310 FB can be defined as where v is the angular velocity of the module 300. [0049] The tilting angle of quad-rotor copter 130 (i) with respect to the central frame 310 is defined as αi, as shown by directional arrow 810 in FIG.8. Next, the rotation matrix can be defined as as the rotation matrix from the central frame 310 of inertia to the world frame of inertia (FB to FW) according to the Tait–Bryan angles defined in Equation (4), and as the rotation matrices from the quad-rotor copter 130 frame of inertia to the central frame 310 of the module 300 frame of inertia (FQi to FB). [0050] For notation simplicity, the following is denoted: Thrust Force and Torque [0051] Generally, still referring to FIGS.7 and 8, tilting angle platforms are usually driven by four actively tilting thrust forces, therefore requiring two sets of actuators. A first set of thrust actuators can generate thrust forces, and a second set of tilting actuators can rotate the thrust actuators to change direction of the thrust actuators. The module 300, however, can use the quad-rotor copters 130 to achieve both actual and tilting simultaneously and independently. For example, a rotor 105 (j) in the quad-rotor copter 130 (i) can generate a thrust force f _ij and a torque t _ij along the normal direction (e.g., in an upward direction) of its spinning plane. The thrust force of each rotor 105 fij and torque tij can be defined as [0052] Here w _ij represents the angular velocity of each rotor 105 and K _T and K _τ are constants related to various rotor 105 specifications and aerodynamics. Collectively, the quad-rotor copter 130 (i) generates four independent inputs: [0053] Here Ti along coordinate axis zQ is the thrust force of the module 300, while refer to the external torques in the quad-rotor copter 130 frame of inertia FQi. Therefore, the thrusting actuation is controlled by the thrust force of the module 300 Ti, and the tilting actuation is controlled by , as the quad-rotor copter 130 is passively hinged (e.g., via hinges 125) onto the central frame 310 along the coordinate axis yQi, as shown in FIG.8. [0054] Assuming the Center-of-Mass (CoM) of the quad-rotor copter 130 on the rotation axis (e.g., the axis of rotation as depicted about arrow 810), the tilting dynamics can be defined as where p and q are defined in the angular velocity of Equation (5). Here, are independent auxiliary inputs, which can be set zero for control simplicity, or exploited to extend control capability, as described below. Translational Dynamics [0055] Still referring to FIGS.7 and 8, the translational dynamics of the module 300 can be expressed as where m refers to the total mass of the module 300, G refers to the gravitational acceleration in the world frame of inertia FW and (e.g., the total thrust vector of quad-rotor copter 130 (i) in the quad-rotor copter 130 frame of inertia FQi). Here where Rotational Dynamics [0056] Still referring to FIGS.7 and 8, assuming a constant inertial matrix I, the rotational dynamics of the module 300 in the central frame 310 frame of inertia FB can be defined as where is the total external torque exerted on the module 300. [0057] Generally, for aerial modules (e.g., module 300) with four tiltable thrusting actuators (e.g., four quad-rotor copters 130), the external torque consists of three major components [0058] Here τT is the torque generated by the four tilting thrust vectors (e.g., four quad-rotor copters 130), and is calculated as [0059] It has been mentioned that each single spinning rotor 105 generates a drag torque when providing thrust force, as indicated in (7). The total sum of these torques is denoted as τM, and can be calculated by [0060] Here Mi is the drag torque of each thrusting actuator (e.g., each quad-rotor copter 130) in the quad-rotor copter 130 frame of inertia FQi. In the module 300, according to Equation (8). Here, the zero element is related to the passive hinge 125 along axis yQi. As mentioned earlier, are independent inputs. Therefore, in the module 300 is decoupled from τT and can be determined freely. [0061] Finally, τR refers to the reaction torque when tilting the thrusting actuators (e.g., quad-rotor copters 130), which, in the module 300, tilting actuation is merely an interaction of the quad-rotor copter 130 and the air due to the passive hinge 125 connection. Therefore, holds at all time. Hovering Analysis [0062] Still referring to FIGS.7 and 8, it can be shown that the dynamics of the module 300 is able to provide an analytical solution set of inputs α _i , T _i and M _i to collectively generate any desired accelerations under arbitrary attitude η without the consideration of input saturation. First, substitute into Equations (10) and (14), then the translational dynamics becomes and the rotational dynamics is rewritten as [0063] The unique dynamics of the module 300 decouples τT and τM, as demonstrated in (16) and (18). Therefore, setting and defining then Equations (21) and (22) can be reformulated in the matrix form as where [0064] Here, W and p are known. Next, solving for T, [0065] So there always exist a matrix such that where I6 refers to the identity matrix of dimension 6. [0066] Therefore, one particular solution of T for Equation (25) can be and the null space of T is explored as [0067] As such, N(W) is supposed to have 2 free variables. By proper calculation, Equation (30) can be reduced to where [0068] Therefore, the general solution of Equation (25) is [0069] Equation (33) can be explicitly calculated as [0070] As the thrust forces Ti ≥ 0, it can be calculated by [0071] The tilting angles αi can be uniquely determined by for [0072] When Ti = 0, any tilting angle αi satisfies the corresponding solution in Equation (34). [0073] In addition, Equation (23) has a trivial solution for Mi as [0074] Therefore, Ti, αi and Mi can be calculated by Equations (35), (36) and (38) respectively with the results in Equation (34), indicating that a set of inputs always exists to generate any specific translational and rotational accelerations of the module 300 at arbitrary attitude η without the consideration of input saturation. In fact, the result proposed shows that the goal can be achieved with only Ti and α, suggesting that Mi can be utilized as auxiliary inputs to further improve control performance and robustness. Control System of Modular Unit Overview [0075] Referring now to FIG.9, a computationally-effective and easily-implemented controller can be designed to demonstrate the independent control of position and attitude for the module 300. Such control architecture is depicted in the control loop 900, shown in FIG. 9. [0076] As depicted in FIG.9, the outer loop 905 takes in the 6 DoF errors in the 3D space and calculates the desired total external force Fd and torque τd on the module 300, as discussed above. The force and torque are then allocated onto each quad-rotor copter 130 as desired thrusting force and tilting angle by the mapper M, depicted as box 920. In various embodiments, a servo controller can run on each quad-rotor copter 130 to follow the trajectories of thrust force and tilting angle. The outer loop 905 also displays the dynamics P of the module 300, shown as box 925. [0077] For controller simplicity, the mapper is set then Position and Attitude Controllers [0078] The controllers Cξ and Cη (shown as boxes 910 and 915) in the outer loop 905 can calculate the desired total external force Fd and torque τd on the module 300 from 6 DoF errors in the 3D space, while compensating the gravitational effect, as [0079] Here are controller tuning parameters. The errors are defined in as Mapper [0080] The mapper (box 920 of FIG.9) allocates the desired total external force Fd and torque τd onto each quad-rotor copter 130 as desired tilting angle and thrust forces It can be observed from Equations (10) and (16) that αi and Ti are nonlinearly coupled in dynamics by multiplication. Therefore, a two-stage mapping scheme is proposed, where the desired tilting angles are determined in the first stage, and used as determined values in the second stage to calculate the desired thrust forces . [0081] Notice that the mapper has 6 inputs and 8 outputs, so additional constraints are required. It has been derived that the module 300 roll/pitch angles φ, θ and actuator tilting angles αi have the relationship at any equilibrium point during hovering. Adjusting this relationship to include the influence of desired forces in the xBOByB plane (e.g., of coordinate system 710) gives the first stage of mapping as [0082] Here φd and θd are the desired roll and pitch angles of the platform respectively. are controller tuning parameters. are the desired total external forces along axes xB and yB, of the coordinate system 710 and are calculated by [0083] The inverse tangent function is a selected bounded monotonic function to shape the influence curve of , and is subject to change with specific requirements. The second stage of mapping is based on inverse dynamics where [·]† refers to the operator of Moore-Penrose pseudo inverse. [0084] The proposed mapper is computationally effective, and smoothens trajectories for desired tilting angles αi. Servos [0085] Still referring to FIG.9, the four identical control loops represent the servos running on quad-rotor copters 130 to track the desired tilting angles and thrust forces as shown as the inner loops 950 in FIG.9 The tracking controller Cα (box 930) is the tracking controller for tilting angle αi, which can calculate the required torque along the direction of passive hinge, denoted as The second mapper MS (shown as box 935) is the mapper that allocates inputs onto thrust forces of each rotor 105 fi as [0086] The mapper MP (box 940) is the reverse mapping curve from rotor 105 thrust forces fi to motor servo commands ui. The dynamics of the quad-rotor copters 130 PQi (shown as box 945) refers to the tilting dynamics of the quad-rotor copter 130 (i). Experimental Simulation of Control System Overview [0087] FIG.10 depicts an example of a control system 1000 of the module 300. As depicted in FIG.10, the control system 1000 may be controllable by, for instance, manual controls, computer applications, remote controls, and/or stored control routines (e.g., such as within a database). In various embodiments, the control system 1000 can include one or more client devices 1010, shown in station 1005. For example, one or more devices of the control system 1000 can operate with a database, such as, for example, a computer disc, hard disc, centralized server, mobile device, or any other computer memory storage device, for processing data. The control system 1000 can operate with an end user of a client device 1010 by, for example, utilizing a graphical user interface, as another example. The control system 1000 can be accessed by a computer processing device locally, such as off of local hard disk space, or alternatively the control system 1000 can be accessed or stored remotely from a central server or other storage device over a network such as, for example, a LAN, WAN or Internet. In various embodiments, the control system 1000 can be interfaced or communicated with the devices of a computer, mobile device, or the like, so as to provide a user interface for an end user to implement controls, operate, or otherwise analyze a module 300. [0088] In various embodiments, the one or more client devices 1010 may utilize various processors and circuits to operate the module 300. For example, various computing algorithms may be executed via the client devices 1010. In various embodiments, the client devices 1010 may be configured to send various control commands (e.g., Td and αd) of each quad-rotor copter 130 of the module 300. For example, the client devices 1010 may communicably couple to one or more portions of the control system 1000 wirelessly (e.g., via various antennas, radios, etc.) or through wires. [0089] In various embodiments, a motion capture system 1015 (e.g., the OptiTrack motion capture system) may measure the position ξ and attitude η of the module 300. In various embodiments, the motion capture system 1015 can send various signals corresponding to the measurements to the client devices 1010 either wirelessly (e.g., a wireless connection point) or through various wires (e.g., Ethernet cable, UDP, etc.). The attitude of each quadcopter ηQi can be measured, filtered, and exploited to calculate the tilting angle αi by comparing with the attitude of the platform η. In various embodiments, the motion capture system 1015 is tested to have a maximum stable updating rate of 160 Hz, and the servo controllers (as shown in FIG.9) are running at 500 Hz. The loop time of central controller follows a stochastic distribution as a result of CPU task management logic and wireless communication, as discussed in greater detail below. In various embodiments, the motion capture system 1015 may include a plurality of cameras, video cameras, or similar devices for capturing 2D of 3D images to receive position data. The motion capture system 1015 may include a plurality of sensors to facilitate depicting the position data. Identification of Servo Dynamics [0090] FIG.11 depicts a graphic comparison 1100 of identified servo dynamics (e.g., a fitted model of the module 300) with real dynamics under a 0.25 rad step input against experimental data. For example, for the fitted model, multiple sets of step response data regarding the tilting actuation α of a single quad-rotor copter 130 is averaged, and used to calculate the impulse response (e.g., output when presented with a brief input signal). It can then be fitted with a 3 ^rd order balances realization due to the singular value decomposition of the corresponding Hankel matrix (e.g., square matrix). In FIG.11, line 1105 represents the step reference (e.g., 0.25 rad step input), line 1110 (dotted line) represents the identified model, and line 1115 (solid line) represents the experimental data. As can be seen in FIG.11, the identified model closely represents the experimental data. Characterization of Central Controller Loop Time [0091] FIG.12 depicts an example histogram 1200 of the loop time of the central controller (e.g., outer loop 905 of FIG.9), denoted as tD with unit millisecond. The histogram of FIG.12 follows a stochastic distribution due to various variances of the control system 1000 (e.g., such as the client device 1010, CPU logic, and wireless communication). The histogram in FIG.12 includes a total of 37,287 data points of loop time tD gathered from multiple experiments for different tasks at different time to address generality. The normalized histogram, denoted as h(tD), is calculated by statistical analysis, and is shown as the bars 1205 in FIG.12. In various embodiments, the wireless communication of the control system 1000 may have failures. For example, if data transmission fails in the first attempt, the sender will request a second try. This may explain the two peaks in the histogram, where the corresponding loop times 6 millisecond and 19 millisecond refers to the nominal loop time for one-time and two-time transmissions, respectively. In the exemplary embodiment depicted in FIG.12, the central controller is running on one particular algorithm system (e.g., Ubuntu operating system), however the control system 1000 may be configured to utilize various other operating system. Due to its task distribution logic, the completing time is stochastic and generally follows the Poisson Distribution [0092] Here λ refers to the peak of density, or the nominal loop time. Therefore, the loop time tD is characterized as a weighted Poisson Distribution [0093] Here w refers to the success rate of first-time transmission, and is calculated by the optimization where fD and h refers to the batch vectors of fD(tD) and h(tD) respectively. The fitted distribution is shown as line 1210 in FIG.12. Maximum Hovering Attitude and Independent Control of Position and Attitude [0094] Example cases of simulation of the module 300 are depicted in FIGS.13 and 14. The pitch angle is tracking a consecutive stair reference signal, while the roll, yaw and position of the module 300 are regulated at 0. The stair reference initiates with 0.1 rad and increments 0.5 rad/stair. The stair is maintained at each level for 5 s so that the platform can reach steady state. Consistent results are demonstrated in simulation and experiment, where the control fails after reaching the step of θ = 0.3 rad. At the failure, the desired thrust forces exceed the input saturation. As the platform is symmetric in xB and yB, identical maximum achievable angle can be expected for the roll angle. Therefore, all attitude trajectories for roll and pitch angles are constrained within this range. The results also verifies that the simulation model captures features of the real module 300. [0095] Three example cases are described in detail below to demonstrate the decoupling of position and attitude control of the module 300. These cases are for illustrative purposes only and are not intended to be limiting. The first two cases (shown in FIG.13) track combined trajectories of Tait-Bryan angles while the module 300 is kept hovering (e.g., in air) at a specific point. For example, at point 1305, the module 300 is at position 1 of case 1, in which the roll and pitch angles are zero. At point 1310, the module 300 is at position 2 of case 1, in which the roll angle is 0.2 rad and the pitch angle is -0.2 rad. At point 1315, the module 300 is at position 3 of case 1, in which the roll angle is -0.2 rad and the pitch angle is 0.2 rad. At point 1320, the module 300 is at position 1 of case 2, in which the pitch and yaw angles are zero. At point 1325, the module 300 is at position 2 of case 2, in which the pitch angle is 0.2 rad and the yaw angle is -0.6 rad. At point 1330, the module 300 is at position 3 of case 2, in which the pitch angle is -0.2 rad and the yaw angle is 0.6 rad. [0096] The last case (shown in FIG.14), tracks moving trajectories 1400 of the module 300 for position and attitude. For example, as shown in FIG.14, the module 300 travels in a specified square trajectory (e.g., a 1 meter square). Accordingly, the roll and pitch angles are measured across various positions. [0097] FIG.15 depicts a graphic representation of a maximum hovering attitude and a thrust force limit with respect to an exemplary embodiment of the module 300. Graphic 1505 depicts a simulation of the maximum hovering attitude, while graphic 1510 depicts experimental results of the maximum hovering attitude. Graphic 1515 depicts a simulation of the desired thrust force, while graphic 1520 depicts experimental results of the desired thrust force. [0098] FIG.16 depicts the graphic representation of the results of Case 1: Tracking roll and pitch angles of the module 300 while hovering (e.g., in the air at a specific position). The trajectories of roll and pitch angles are bounded by rad, and cover both directions, as shown in FIG.13 and discussed above. The position of the module 300 is regulated at a fixed location at all time. FIG.17 depicts the graphic representation of the results of Case 2: Tracking pitch and yaw angles of the module 300 while hovering (e.g., in the air at a specific location). The trajectories of pitch and yaw angles are bounded by rad and rad respectively, and cover both directions, as shown in FIG.13 and discussed above. The position of the module 300 is still regulated at a specific location. FIG.18 depicts a graphic representation of the results of Case 3: Tracking roll and pitch angles of the module 300 while tracking a square trajectory in position simultaneously. The trajectories of roll and pitch angles are bounded by rad, and cover both directions. In this case, position trajectory is a 1 meter square in space with constant height. The cases described are solely for experimental illustration. In various other implementations, any other experimental setups may be utilized. [0099] The rooted-mean-square (RMS) errors of the 3 aforementioned cases are summarized in Table I below. As shown from FIGS.16-18 and Table I, it can be observed that the error for simulation and experiment of the same case is of the same level, indicating that the simulation model maintains the main features of the prototype. Comparing the errors of case 1 and case 3 shows that switching the position control from hovering to following a changing trajectory does not influence the tracking error of attitude, which verifies the decoupling of position and attitude control. However, it can be noticed that the position RMS error increases significantly from case 1 to case 3. That may be because the mapper in the proposed controller (e.g., in FIG.9), though computationally effective and avoiding abrupt changes in the tilting angle αi under smooth reference signals for attitude with inverse tangent function as the shaping function, sacrifices the dynamic property of position tracking. [00100] Comparing with case 1 and case 2 for the desired thrust forces, it can be noticed that ripples occur every time there is a non-differentiable point in the attitude reference. However, the ripples in case 2 is more significant. This can be explained by Equation (46). As the tilting angles αi is relatively small, cαi is larger than sαi, so a change of required torque in zB requires larger changes in the thrust forces than xB or yB. [00101] Another interesting finding is that ez in experiments are smaller than simulation for all 3 cases. This is expected as the simulation model does not include damping from the air. As the experiments are conducted in a constrained attitude space, the projection of the experimented module 300 on the z axis is much larger than that in x or y axis, resulting in larger damping and thus smaller RMS error in the z direction. [00102] As used herein, the singular terms “a,” “an,” and “the” may include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to an object may include multiple objects unless the context clearly dictates otherwise. [00103] As used herein, the term “set” refers to a collection of one or more objects. Thus, for example, a set of objects can include a single object or multiple objects. [00104] As used herein, the terms “connect,” “connected,” and “connection” refer to an operational coupling or linking. Connected objects can be directly coupled to one another or can be indirectly coupled to one another, such as via one or more other objects. [00105] As used herein, the terms “substantially” and “about” are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. When used in conjunction with a numerical value, the terms can refer to a range of variation of less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%. For example, a first numerical value can be “substantially” or “about” the same as or equal to a second numerical value if the first numerical value is within a range of variation of less than or equal to ±10% of the second numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%. [00106] References to “or” may be construed as inclusive so that any terms described using “or” may indicate any of a single, more than one, and all of the described terms. References to at least one of a conjunctive list of terms may be construed as an inclusive OR to indicate any of a single, more than one, and all of the described terms. For example, a reference to “at least one of ‘A’ and ‘B’” can include only ‘A’, only ‘B’, as well as both ‘A’ and ‘B’. Such references used in conjunction with “comprising” or other open terminology can include additional items. [00107] The term “coupled” and variations thereof, as used herein, means the joining of two members directly or indirectly to one another. Such joining may be stationary (e.g., permanent or fixed) or moveable (e.g., removable or releasable). Such joining may be achieved with the two members coupled directly to each other, with the two members coupled to each other using a separate intervening member and any additional intermediate members coupled with one another, or with the two members coupled to each other using an intervening member that is integrally formed as a single unitary body with one of the two members. If “coupled” or variations thereof are modified by an additional term (e.g., directly coupled), the generic definition of “coupled” provided above is modified by the plain language meaning of the additional term (e.g., “directly coupled” means the joining of two members without any separate intervening member), resulting in a narrower definition than the generic definition of “coupled” provided above. Such coupling may be mechanical, electrical, or fluidic. [00108] The term “exemplary” and variations thereof, as used herein to describe various embodiments, are intended to indicate that such embodiments are possible examples, representations, or illustrations of possible embodiments (and such terms are not intended to connote that such embodiments are necessarily extraordinary or superlative examples). [00109] In the description of some embodiments, a component provided or disposed “on” or “over” another component can encompass cases where the former component is directly on (e.g., in physical or direct contact with) the latter component, as well as cases where one or more intervening components are located between the former component and the latter component. [00110] Additionally, amounts, ratios, and other numerical values are sometimes presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified. For example, a ratio in the range of about 1 to about 200 should be understood to include the explicitly recited limits of about 1 and about 200, but also to include individual ratios such as about 2, about 3, and about 4, and sub-ranges such as about 10 to about 50, about 20 to about 100, and so forth. [00111] While the disclosure has been described with reference to the specific embodiments thereof, it should be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the true spirit and scope of the disclosure as defined by the appended claim(s). In addition, many modifications may be made to adapt a particular situation, material, composition of matter, method, operation or operations, to the objective, spirit and scope of the disclosure. All such modifications are intended to be within the scope of the claim(s) appended hereto. In particular, while certain methods may have been described with reference to particular operations performed in a particular order, it will be understood that these operations may be combined, sub-divided, or re-ordered to form an equivalent method without departing from the teachings of the disclosure. Accordingly, unless specifically indicated herein, the order and grouping of the operations is not a limitation of the disclosure. [00112] The present disclosure contemplates methods, systems and program products on any machine-readable media for accomplishing various operations. The embodiments of the present disclosure can be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwired system. Embodiments within the scope of the present disclosure include program products comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine- readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions. [00113] Although the present embodiments have been particularly described with reference to preferred examples thereof, it should be readily apparent to those of ordinary skill in the art that changes and modifications in the form and details may be made without departing from the spirit and scope of the present disclosure. It is intended that the appended claims encompass such changes and modifications.