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Title:
METHOD AND SYSTEM FOR CALCULATING AND MODELLING INVERSE KINEMATICS IN COMPLEX SYSTEMS
Document Type and Number:
WIPO Patent Application WO/2023/007517
Kind Code:
A1
Abstract:
A method and system for calculating and modelling inverse kinematics in a complex system using a Jacobian technique is disclosed. The method includes computing one or more joint parameters, using a Jacobian technique, wherein the Jacobian kinematic technique uses a difference in a position between a starting point and a desired position. The Jacobean technique is used to compute the joint parameters iteratively by minimizing the error. The Jacobean technique is an incremental method and wherein one or more joint parameters are recomputed multiple times as the end-effector moves towards the desired endpoint.

Inventors:
SALINS PAUL CHRISTADAS (IN)
Application Number:
PCT/IN2022/050683
Publication Date:
February 02, 2023
Filing Date:
July 28, 2022
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
SALINS PAUL CHRISTADAS (IN)
International Classes:
G05B19/408; B25J9/16
Foreign References:
US20140107841A12014-04-17
Attorney, Agent or Firm:
ORAON, Pallavi (IN)
Download PDF:
Claims:
CLAIMS

I/We Claim :

1. A method for calculating and modelling inverse kinematics in a complex system, the method comprises: computing one or more joint parameters, using a Jacobian technique, wherein the Jacobian kinematic technique uses a difference in a position between a starting point and a desired position, and wherein the Jacobean technique is used to compute the joint parameters iteratively by minimizing the error; and wherein the Jacobean technique is an incremental method and wherein one or more joint parameters are recomputed multiple times as the end- effector moves towards the desired endpoint, and wherein the Jacobean matrix is computed for each value of displacement of link, and wherein the data required for calculating inverse kinematics using the Jacobian technique are the starting position A (xl, yl, 01), the ending position B (x2, y2, 02), and the angle of each link with respect to the frame of reference of the previous link.

2. A method for calculating inverse kinematics for a complex adaptive kinematic system in robots, the method comprises: obtaining a plurality of overlaps between a plurality of systems comprising kinetic, sensory, motor, and artificial intelligence systems; processing the data from each of the plurality of systems one of: separately or in combination; and

'changing the joint parameters of the kinematics using the complex adaptive robotic system to preserve the structural economy of the system depending either on the task or function; wherein with the functional overlap between a plurality of systems, the kinematics of each system depends upon the signature of an overall system, and wherein the shift in kinematics is observed and calculated from the shift in the signature of individual systems, and wherein the kinematic signature is calculated upon the interaction with all the variables in the kinematic chain, and wherein the end-effector is moved along the actual trajectory, and wherein the kinematics depends on the links, angles, orientation and varies with the functionality of the other systems comprising at least sensory feedbacks, motor performance, forces, stress, strain, and torques acting on the links and joints, material characteristics and external fluid resistance, and wherein the variables are converted to a dynamic signature pattern.

3. The method of claim 2, wherein a dynamic signature is obtained for the displacement vector (e) and the joint angle vector (q), and wherein the dynamic signature provides a kinematic signature shift that heuristically assigns the joint angles to achieve the movement of the end- effector from a first point to a second point instead of calculating individual joint angles.

4. A method for calculating the dynamic continuum kinematic profile for a hyper redundant robot, the method comprising: obtaining a signature of the continuum kinematic profile from a plurality of over lapping functions of at least one of: kinematics, kinetics, sensorimotor, and control systems of the hyper redundant robot, comprising at least one of: a current orientation, and a posi tion of all the end effector, a range of motion of the end effector, a spline of the current joint kinematic, a force/torque profile of the structure of the robot, data about the environ ment from other sensors and a dynamic activation strength of the motors; and obtaining at least one of: a desired continuum kinematics profile and a kinematic signature from the shift in a current kinematic signature with a desired endpoint; wherein the continuum kinematic profile is a unique kinematic status of biome chanical or robotic object which gives the entire dynamics of the object in order for the controller or the brain to process the inverse and forward kinematics, smooth acceleration, and optimized movements.

5. The method of claim 4, wherein the step of obtaining at least one of: the desired continuum kinematics profile and kinematic signature comprises: obtaining the data from at least one of: the kinematics, kinetics, sensory re sponses through various sensors; normalizing the data using min-max normalization; generating a grid with at least one of: the kinematics, kinetics, and sensory re sponse data; juxtaposing at least one of: the primary, secondary, tertiary, and quaternary data into different grid patterns; and obtaining a dynamic relationship profile portfolio of the kinematic chain.

6. A system for calculating and modelling inverse kinematics in a complex system, the system comprising: a memory storing one or more executable modules; and a processor configured to execute the one or more executable modules for calculating and modelling inverse kinematics, the one or more executable modules comprising: a kinematics module configured to employ a Jacobian technique to determine the inverse kinematics for the complex adaptive kinematic system, wherein the Jacobian kine matic technique uses the difference in the position between the starting position/point and desired position; wherein the Jacobean technique is used to compute the joint parameters iteratively by minimizing the error; and wherein the Jacobean technique is an incremental method, where the joint parameters are recomputed several times as the end-effector moves towards the desired endpoint, and wherein the Jacobean matrix is computed for every possible value of displacement of link.

7. The system of claim 6, wherein the data required for calculating inverse kinematics using the Jacobian technique are the starting position A (xl, yl, 01), the ending position B (x2, y2, 02), and the angle of each link with respect to the frame of reference of the previous link and wherein the data is stored in the memory.

Description:
METHOD AND SYSTEM FOR CALCULATING AND MODELLING INVERSE

KINEMATICS IN COMPLEX SYSTEMS

CROSS-REFERENCE TO RELATED APPLICATION [0001] The present application claims the priority of the Indian Provisional Patent Appli cation (PPA) with serial number 202141033946 filed on 28th July 2021 with the title" METHOD AND SYETEM FOR CALCULATING AND MODELLING INVERSE KINEMATICS IN COMPLEX SYSTEMS". The contents of abovementioned PPA are included in entirety as refer ence herein.

BACKGROUND Technical Field

[0002] The present invention is generally related to a complex kinematics system. The present invention is particularly related to a kinematics of complex adaptive robotics system, bio logical system, hyper redundant robotics system and biological hyper redundant systems. The pre sent invention is particularly related to a method and a system for calculating and modelling in verse kinematics in a complex system in the field of robotics, animation, kinematic design, and biomechanics.

Description of the Related Art

[0003] Typically, the functions of a complex adaptive system are not independent but in tertwined as all the variables and elements in the complex adaptive system take part in performing any specific function. The percentage contribution of these variables and elements is given by the specific to unknown parameters affecting the function. Let us consider a simple example of a sim ple linear system with four inputs (xl, x2, x3, x4) and two outputs (yl, y2), the transfer function of the system is given by G and this function depends upon the outputs over the given inputs.

G = {blyl+b2y2]/{alxl+a2x2+a3x3+a4x4} - >eq.l

[0004] The output coefficients bl, b2 represent the magnitude of the output variable yl and y2, and the input coefficients al, a2, a3, a4 represent the magnitude of the input variables xl, x2, x3, and x4 respectively. If the same system is represented as a complex adaptive system, then the transfer function G is given by,

G = {BAY}/{ABX} - > eq.2 where B = [bl, b2], A = [al, a2, a3, a4], X = [xl, x2, x3, x4], and Y = [yl, y2]

[0005] The magnitude of output coefficients not only depends upon the output variables but also on the input variable. In order to achieve a transfer function Gl, the input-output variable and coefficients can be arranged in multiple ways (structural hyper redundancy), and also by ad justing just coefficients of the input-output variables, multiple transfer functions can be derived (functional hyper redundancy).

[0006] Further, biological systems are a unique genre of a hyper-redundant complex adap tive system. It is unique in that the natural healing capacity of biological systems leverage a prin ciple of functional hyper-redundancy that is paradoxically coupled to structural economy. This is in contradistinction to conventional mechanical systems where functional hyper-redundancy is al most always consequent to provision of a structural excess, as in the case of increase in the power of the motor in a mechanical system such as a motor car. On the other hand, biological systems amplify functional capability of individual units by creating a syncytial shared systems architecture where each system seamlessly shares work of another and the two together compliment other sys tems enabling increase in the load of one system to be distributed across several. However, such shared architecture of structure and function demands prioritization of function across shared structural units e.g., shared swallowing and airway means you can’t perform both activities to gether. As a consequence, defects in one or two systems may not immediately manifest to be di- agnosable but lead to variety of compensatory changes and structural accommodation that can be only diagnosed by an analytical system that represents the functioning of whole syncytial complex system and identifies subtle shifts in the normal overall/ aggregate signature of performance before the threshold of diagnosability as a perturbation of concern or breakdown in any one of its com ponent systems. [0007] Consider for example, the biomechanics of walking in human being, for simplifi cation let us constrain the inputs to the environment, senses from eyes, ears, and proprioception, and friction, the outputs to the muscle forces in the foot, calves, and thighs, position or displace ment, joint angles of the ankle, knee and pelvis, arm swing, and spine angle. Even for an oversim plified version of the biomechanics of walking, all the inputs and output variables are intertwined and a model similar to eq.2 can be derived for such a system.

[0008] Even though the basic mechanics of walking requires only the joint angle and dis placement to determine the function, the biomechanics is an aggregate function of all the input and output variables, i.e., the function is hyper redundant. Hyper redundancy has an effective ad vantage on adaptivity over perturbation. For example, during a walking in the dark and a walking with the lights on, the coefficient of the optic sensors is shifted to high sensitivity or lower thresh old, the joint angles and spine angle are optimized selectively for balance, the arm swing is re duced, and the friction is increase. In total, the coefficient of the input and output variable shifts to compensate the required functionality.

[0009] Hence, there is a need for a system and method for calculating and modelling in verse kinematics in complex systems such as complex adaptive robotics system, biological system, hyper redundant robotics system and biological hyper redundant systems in the field of robotics, animation, kinematic design, and biomechanics. Further there is a need to determine a dynamic continuum kinematic profile for a hyper redundant robot.

OBJECTIVES OF THE EMBODIMENTS HEREIN [0010] The primary objective of the present invention is to provide a method and system for calculating and modelling inverse kinematics in a complex system.

[0011] Another objective of the present invention is to provide a method and system for calculating and modelling inverse kinematics for a complex adaptive kinematic system using a

Jacobian technique. [0012] Yet another objective of the present invention is to provide a system and method for calculating inverse kinematics for a complex adaptive kinematic system in robots by determin ing dynamic signature patterns.

[0013] Yet another objective of the present invention is to provide a system and method for calculating inverse kinematics for a complex adaptive kinematic system in for a hyper redun dant robot by determining a dynamic continuum kinematic profile.

[0014] These and other objects and advantages of the present invention will become read ily apparent from the following detailed description taken in conjunction with the accompanying drawings.

SUMMARY

[0015] The following details present a simplified summary of the embodiments herein to provide a basic understanding of the several aspects of the embodiments herein. This summary is not an extensive overview of the embodiments herein. It is not intended to identify key/critical elements of the embodiments herein or to delineate the scope of the embodiments herein. Its sole purpose is to present the concepts of the embodiments herein in a simplified form as a prelude to the more detailed description that is presented later.

[0016] The other objects and advantages of the embodiments herein will become readily apparent from the following description taken in conjunction with the accompanying drawings. It should be understood, however, that the following descriptions, while indicating preferred embod iments and numerous specific details thereof, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the embodiments herein with out departing from the spirit thereof, and the embodiments herein include all such modifications.

[0017] In an aspect, a method for calculating and modelling inverse kinematics in a com plex system is provided. The method includes computing one or more joint parameters, using a Jacobian technique. The Jacobian kinematic technique uses a difference in a position between a starting point and a desired position. [0018] According to an embodiment, the Jacobean technique is used to compute the joint parameters iteratively by minimizing the error.

[0019] According to an embodiment, the Jacobean technique is an incremental method, and one or more joint parameters are recomputed multiple times as the end-effector moves towards the desired endpoint.

[0020] According to an embodiment, the Jacobean matrix is computed for each value of displacement of link.

[0021] According to an embodiment, the data required for calculating inverse kinematics using the Jacobian technique are the starting position A (xl, yl, 01), the ending position B (x2, y2, 02), and the angle of each link with respect to the frame of reference of the previous link.

[0022] In another aspect, a method for calculating inverse kinematics for a complex adap tive kinematic system in robots is provided. The method includes obtaining a plurality of overlaps between various systems like kinetic, sensory, motor, and artificial intelligence. The method fur ther includes processing the data from each of the systems either separately or in combination. The method further includes changing the joint parameters of the kinematics using the complex adap tive robotic system to preserve the structural economy of the system depending either on the task or function.

[0023] According to an embodiment, with the functional overlap between a plurality of systems, the kinematics of each system depends upon the signature of an overall system. The shift in kinematics is observed and calculated from the shift in the signature of individual systems.

[0024] According to an embodiment, the kinematic signature is calculated upon the inter action with all the variables in the kinematic chain. The end-effector is moved along the actual trajectory.

[0025] According to an embodiment, the kinematics depends on the links, angles, orienta tion and varies with the functionality of the other systems including at least sensory feedbacks, motor performance, forces, stress, strain, and torques acting on the links and joints, material char acteristics and external fluid resistance.

[0026] According to an embodiment, the variables are converted to a dynamic signature pattern.

[0027] According to an embodiment, a dynamic signature is obtained for the displacement vector (e) and the joint angle vector (q).

[0028] According to an embodiment, the dynamic signature provides a kinematic signature shift that heuristically assigns the joint angles to achieve the movement of the end-effector from a first point to a second point instead of calculating individual joint angles.

[0029] In yet another aspect, a method for calculating the dynamic continuum kinematic profile for a hyper redundant robot is provided. The method includes obtaining a signature of the continuum kinematic profile from various overlapping functions of at least one of kinematics, ki netics, sensorimotor, and control systems of the hyper redundant robot, such as, current orientation, and position of all the end effector, range of motion of the end effector, the spline of the current joint kinematic, force/torque profile of the structure of the robot, data about the environment from other sensors and dynamic activation strength of the motors. The method further includes obtaining either a desired continuum kinematics profile or a kinematic signature from a shift in a current kinematic signature with a desired endpoint.

[0030] According to an embodiment, the continuum kinematic profile is a unique kine matic status of biomechanical or robotic object which gives the entire dynamics of the object in order for the controller or the brain to process the inverse and forward kinematics, smooth accel eration, and optimized movements.

[0031] According to an embodiment, the method to obtain continuum kinematic profile includes obtaining the data from at least one of the kinematics , kinetics, sensory responses through various sensors. The method further includes normalizing the data using min-max normalization. The method further includes generating a grid with at least one of the kinematics, kinetics and sensory response data. The method further includes juxtaposing at least one of the primary, sec ondary, tertiary, and quaternary data into different grid patterns. The method further includes ob taining a dynamic relationship profile portfolio of the kinematic chain.

[0032] In another aspect a system for calculating and modelling inverse kinematics in a complex system is provided. The system includes a memory storing one or more executable mod ules and a processor configured to execute the one or more executable modules for calculating and modelling inverse kinematics, the one or more executable modules including a kinematics module configured to employ a Jacobian technique to determine the inverse kinematics for the complex adaptive kinematic system. The Jacobian kinematic technique uses the difference in the position between the starting position/point and desired position.

[0033] According to an embodiment, the Jacobean technique is used to compute the joint parameters iteratively by minimizing the error.

[0034] According to an embodiment, the Jacobean technique is an incremental method, where the joint parameters are recomputed several times as the end-effector moves towards the desired endpoint.

[0035] According to an embodiment, the Jacobean matrix is computed for every possible value of displacement of link.

[0036] According to an embodiment, the data required for calculating inverse kinematics using the Jacobian technique are the starting position A (xl, yl, 01), the ending position B (x2, y2, 02), and the angle of each link with respect to the frame of reference of the previous link and the data is stored in the memory.

[0037] These and other aspects of the embodiments herein will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following descriptions, while indicating pre- ferred embodiments and numerous specific details thereof, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the embodiments herein without departing from the spirit thereof, and the embodiments herein include all such mod ifications.

[0038] The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The other objects, features and advantages will occur to those skilled in the art from the following description of the preferred embodiment and the accompanying drawings in which:

[0040] FIG. 1A illustrates a block diagram of a system for calculating and modelling in verse kinematics in a complex system.

[0041] FIG. IB illustrates a schematic representation of a model indicating the resources required for a hyper redundant robot in a complex adaptive kinematic system, according to an embodiment of the present invention.

[0042] FIG.2 illustrates a schematic view of an inverse kinematics problem of a kinematic chain on a plane in a two-dimension manner for a hyper redundant robot, in a complex adaptive kinematic system, according to an embodiment of the present invention.

[0043] FIG. 3 illustrates an example kinematic chain for a hyper redundant robot in a com plex kinematic system, according to an embodiment of the present invention.

[0044] FIG. 4 illustrates a functional block diagram of various operations for a hyper re dundant robot in a complex adaptive kinematic system, according to an embodiment of the present invention.

[0045] FIG. 5 illustrates a schematic representation of a functional overlap of various op erations for a hyper redundant robot in a complex adaptive kinematic system, according to an embodiment of the present invention. [0046] FIG. 6 illustrates a method for calculating inverse kinematics for a hyper redundant robot in a complex adaptive kinematic system, according to one embodiment of the present inven tion.

[0047] FIG.7 illustrates a dynamic signature pattern obtained by converting the variables for a hyper redundant robot in a complex adaptive kinematic system, according to an embodiment of the present invention.

[0048] FIG.8 illustrates a shift in the dynamic signature pattern for a hyper redundant robot in a complex adaptive kinematic system, according to an embodiment of the present invention.

[0049] FIG.9 illustrates a dynamic continuum kinematic profile for a hyper redundant ro bot in a complex adaptive kinematic system, according to one embodiment of the present inven tion.

[0050] FIG. 10 illustrates a change in an angle of joints and a continuous change along with a profile of a structure of a hyper redundant robot, in a complex adaptive kinematic system according to one embodiment of the present invention.

[0051] FIG. 11 illustrates a grid for a dynamic continuum kinematic profile or signature for a hyper redundant robot, in a complex adaptive kinematic system according to one embodiment of the present invention.

[0052] FIG. 12 illustrates a movement of the joint from one position to another for creating multiple limbs for a hyper redundant robot, in a complex adaptive kinematic system according to one embodiment of the present invention.

[0053] FIG. 13A-13C illustrates the steps involved in generating a continuum kinematic profile.

[0054] FIG.14 illustrates the flowchart of method for calculating and modelling inverse kinematics in complex systems, in accordance with an embodiment.

[0055] FIG.15 illustrates the flowchart of a method for calculating inverse kinematics for a complex adaptive kinematic system in robots, in accordance with an embodiment. [0056] FIG.16 illustrates the flowchart of a method for calculating the dynamic continuum kinematic profile for a hyper redundant robot in accordance with an embodiment.

[0057] Although the specific features of the present invention are shown in some drawings and not in others. This is done for convenience only as each feature may be combined with any or all of the other features in accordance with the present invention.

DETAILED DESCRIPTION OF THE DRAWINGS [0058] In the following detailed description, reference is made to the accompanying draw ings that form a part hereof, and in which the specific embodiments that may be practiced is shown by way of illustration. These embodiments are described in sufficient detail to enable those skilled in the art to practice the embodiments and it is to be understood that the logical, mechanical, and other changes may be made without departing from the scope of the embodiments. The following detailed description is therefore not to be taken in a limiting sense.

[0059] The various embodiments of the present invention provide a method and a system for calculating and modelling inverse kinematics in a complex system. According to an embodi- ment of the present invention, the method is used to determine the inverse kinematics for the com plex adaptive kinematic system using a Jacobian technique. The Jacobian kinematic technique uses the difference in the position between the starting position/point and desired position. The Jacobean technique is used to compute the joint parameters iteratively by minimizing the error. The Jacobean technique is an incremental method, where the joint parameters are recomputed several times as the end-effector moves towards the desired endpoint.

[0060] According to an embodiment of the present invention, the Jacobian matrix of a kinematic chain is given by the following equation, where Q is the joint angle and S is the dis placement of the link.

J ίb) [0061] The Jacobean matrix is computed for every possible value of S, as the end-effector moves across the plane to reach the desired endpoint. This method requires a lot of time and com putational resources to calculate the optimal matrix as the end-effector moves across the plane. This becomes more and more complex when the degree of freedom of the kinematic system in creases. For a two-dimensional system like the kinematic chain as shown in FIG.l, The Jacobean is given by a 4x4 matrix for each instance in time. This becomes more complex for a kinematic chain for robots as shown in FIG.2.

[0062] According to an embodiment of the present invention, a method for calculating inverse kinematics for a complex adaptive kinematic system in robots is provided. The kinematics of the complex adaptive robotic systems has multiple overlaps between various systems like ki netic, sensory, motor, artificial intelligence, etc. As the data from each of the systems are pro cessed, separately or in combination, but with the complex adaptive robotic system, the functional overlap introduces hyper redundancy. The kinematics not just depends only on the links, angles, orientation but now varies with the functionality of the other systems like sensory feedbacks, motor performance, forces, stress, strain, and torques acting on the links and joints, material characteris tics, external fluid resistance, etc. Some of the systems are interdependent and thus complex adapt ability evolves with overlap between these systems. Depending upon the task or function now the complex adaptive robotic system changes the joint parameters of the kinematics to preserve the structural economy of the system.

[0063] According to an embodiment of the present invention, the data required for calcu lating inverse kinematics using the Jacobian technique are the starting position A (xl, yl, 01), the ending position B (x2, y2, 02), and the angle of each link with respect to the frame of reference of the previous link. For a complex adaptive kinematics system, the variables are converted to the dynamic signature patterns.

[0064] According to an embodiment of the present invention, a dynamic signature is ob tained for the displacement vector (e) and the joint angle vector (q). This dynamic signature provides a kinematic signature shift that heuristically assigns the joint angles to achieve the move ment of the end-effector from point A to point B instead of calculating individual joint angles.

[0065] With the functional overlap between various systems, the kinematics of the system depends upon the signature of the overall system. The shift in kinematics is observed and calcu lated from the shift in the signature of few (individual) systems.

[0066] Since the kinematic signature is calculated upon the interaction with all the varia bles in the kinematic chain, the end-effector is moved along the actual trajectory instead of a linear approximation of the trajectory given by the solutions of the current techniques, thereby preventing jerky movements with fewer computational resources.

[0067] According to an embodiment of the present invention, a method for calculating the dynamic continuum kinematic profile for a hyper redundant robot is provided.

[0068] According to an embodiment of the present invention, the continuum kinematic profile is a signature obtained from various overlapping functions of kinematics, kinetics, sen sorimotor, and control systems of the hyper redundant robot, such as, current orientation, and position of all the end effector, range of motion of the end effector, the spline of the current joint kinematic (i.e., the shape of the kinematic chain with respect to the position), force/torque profile of the structure of the robot (i.e., the force/strain distribution along the spline of the kinematic chain), data about the environment from other sensors ( obstruction, multiple available pathways, etc.,), and dynamic activation strength of the motors. The desired continuum kinematics profile or kinematic signature is obtained from the shift in the current kinematic signature in accordance with the desired endpoint.

[0069] The various embodiments of the present invention disclose a method and system for calculating and modelling inverse kinematics in a complex system.

[0070] FIG. 1A illustrates a block diagram of a system for calculating and modelling in verse kinematics in a complex system. The system comprises a memory 103 storing one or more executable modules and a processor 101 configured to execute the one or more executable modules for calculating and modelling inverse kinematics. The one or more executable modules comprises a kinematic module 102. The kinematics module 102 is configured to employ a Jacobian technique to determine the inverse kinematics for the complex adaptive kinematic system, wherein the Jaco bian kinematic technique uses the difference in the position between the starting position/point and desired position. The Jacobean technique is used to compute the joint parameters iteratively by minimizing the error. The Jacobean technique is an incremental method, where the joint parame ters are recomputed several times as the end-effector moves towards the desired endpoint. The Jacobean matrix is computed for every possible value of displacement of link. The data required for calculating inverse kinematics using the Jacobian technique are the starting position A (xl, yl, 01), the ending position B (x2, y2, 02), and the angle of each link with respect to the frame of reference of the previous link and wherein the data is stored in the memory.

[0071] FIG. IB illustrates a schematic representation of a model indicating the resources required for a hyper redundant robot in a complex adaptive kinematic system, according to an embodiment of the present invention. The FIG. IB indicates the resources required for executing two different functions and the common resources used in both the functions.

[0072] According to an embodiment of the present invention, the Jacobian matrix of a kinematic chain is given by the following equation, where 0 is the joint angle and S is the dis placement of the link. j(e\ ...

[0073] The Jacobean matrix is computed for every possible value of S, as the end-effector moves across the plane to reach the desired endpoint. This method requires a lot of time and com putational resources to calculate the optimal matrix as the end-effector moves across the plane. This becomes more and more complex when the degree of freedom of the kinematic system in creases. [0074] FIG. 2 is a schematic view of an inverse kinematics problem of a kinematic chain on a plane in a two-dimension manner. The complex kinematic chain for robots as shown in FIG.2.

[0075] FIG. 3 is an example kinematic chain of a complex kinematic system. The inverse kinematics is the process of calculating a vector of joint variables which produces the desired end- effector location of a kinematic chain relative to the start of the chain. Given the joint parameters, the kinematic chain’s end-effector location can be calculated directly, applying essential trigono metric functions. Still, the inverse operation is much more challenging. The inverse kinematics problem is that there is no unique joint variable vector to attain the desired end-effector location. Unfortunately, the inverse kinematics problem can be ill-posed because there are no solutions or many solutions.

[0076] The inverse kinematics problem had been a problem in the field of robotics, anima tion, kinematic design, and biomechanics for decades. Solving the inverse kinematics problem develops more robust kinematic systems for Robots and virtual models, thus generating smooth and real movements with optimal energy expenditure. There have been numerous mathematical and computational solutions proposed to solve this problem currently being used in these fields. The most popular yet complex approach is the jacobian kinematic technique.

[0077] Jacobian kinematic technique: The Jacobian kinematic technique uses the differ ence in the position between the starting and desired position and computes the joint parameters iteratively by minimizing the error. It is an incremental method, where the joint parameters are recomputed several times as the end-effector moves towards its desired endpoint. The jacobian matrix of a kinematic chain is given by the following equation, where Q is the joint angle and S is the displacement of the link.

../I# :

[0078] This matrix is computed for every possible value of S, as the end-effector moves across the plane to reach the desired endpoint. This method requires a lot of time and computational resources to calculate the optimal matrix as the end-effector moves across the plane. This will become more complex if the degree of freedom of the kinematic system increases. For a two- dimensional system like the kinematic chain shown in FIG. 2, the jacobian is given by a 4x4 matrix for each instance in time. This will become more complex for a kinematic chain as shown in the FIG. 3.

[0079] FIG. 4 illustrates various operations in a complex adaptive kinematic system, in accordance with an embodiment.

[0080] FIG. 5 illustrates a functional overlap of a complex adaptive kinematic system, in accordance with an embodiment. As the robots are becoming more autonomous, the kinematics of the same should be self-adaptive in nature, the current kinematics numerical and computational models rely on the iterative mathematical procedure to solve the current inverse kinematic prob lem. This model will be so resource-intensive for a self-adaptive autonomous robot with complex overlapping kinematic and sensory systems, the entire equation becomes more complex and diffi cult to solve when more redundancy is included. Redundancy is not a problem but a benefactor to the system. The redundancy can be achieved by incorporating the functional overlap of different kinematic blockchains.

[0081] Many biological systems are adaptive in nature as a function of hyper redundancy. The kinematic function of the biological system is hyper redundant with overlapping of multiple functions such as motor, sensory, propericeptory, and structural functions. The structural economy of the biological system increases with the increase in redundancy and the increase in the func tional overlap.

[0082] The kinematics of the complex adaptive robotic systems will have multiple over laps between various systems like kinetic, sensory, motor, artificial intelligence, etc. The tradi tional approach will process the data from each of the systems separately or in combination but with the complex adaptive robotic system, the functional overlap introduces hyper redundancy. The kinematics not just depends only on the links, angles, orientation but now varies with the functionality of the other systems like sensory feedbacks, motor performance, forces, stress, strain, and torques acting on the links and joints, material characteristics, external fluid resistance, etc. Some of the systems are interdependent and thus complex adaptability evolves with overlap be tween these systems. Depending upon the task or function now the complex adaptive robotic sys- tern will change the joint parameters of the kinematics to preserve the structural economy of the system.

[0083] FIG. 6 illustrates a method for calculating inverse kinematics for a complex adap tive kinematic system, according to one embodiment of the present invention. The data required for calculating inverse kinematics using the Jacobian technique are the starting position A (xl, yl, 1), the ending position B (x2, y2, 02), the angle of each link with respect to the frame of reference of the previous link.

[0084] For a complex adaptive kinematics system, the variables are converted to the dy namic signature patterns, for the same example problem from the previous FIG. 5, a dynamic signature is obtained for the displacement vector (e) and the joint angle vector (q). This will pro- vide a kinematic signature shift that heuristically assigns the joint angles to achieve the movement of the end-effector from point A to point B instead of calculating individual joint angles as in the traditional approach.

[0085] With the functional overlap between various systems, the kinematics of the system depends upon the signature of the overall system. The shift in kinematics can be observed and calculated from the shift in the signature of few systems.

[0086] Since the kinematic signature is calculated upon the interaction with all the varia bles in the kinematic chain, it moves the end-effector along the actual trajectory instead of a linear approximation of the trajectory given by the solutions of the current techniques. This will prevent jerky movements with fewer computational resources. [0087] FIG.7 illustrates a dynamic signature pattern obtained by converting the variables for a hyper redundant robot in a complex adaptive kinematic system, according to an embodiment of the present invention.

[0088] FIG.8 illustrates a shift in the dynamic signature pattern for a hyper redundant robot in a complex adaptive kinematic system, according to an embodiment of the present invention. The hyper redundant robots are kinematic systems with more degrees of freedom, and no joints. The biological hyper redundant kinematic systems like an elephant’s trunk, octopus’s tentacles, or a snake’s torso, the movement is smooth and there are no joint parameters involved in measuring the kinematics of such a system and it doesn’t need any Jacaboian vectors. Continuum robots are close to the biological hyper redundant systems that are hyperflexible with infinite degrees of free dom capable of maneuvering complex curvilinear pathways. Different materials use their viscoe lastic properties and physics of such materials to achieve hyper redundancy in kinematics without joints. With the application of continuum robots from medicine to nuclear science, and with data communication at faster speeds, the system delays imposed by joint kinematics computation will be disastrous. A unified computational system that can calculate a dynamic continuum curvilinear profile for the hyper redundant kinematic robots. This computational system calculates the kine matics profile from the physical and material properties of the structure and its overlapping func tions with the external parameters.

[0089] According to an embodiment of the present invention, a method for calculating the dynamic continuum kinematic profile for a hyper redundant robot is provided. Currently, all kin ematics are measured, and executed in vector or Euler’s space (i.e., Linear approximation), for a hyper-flexible or continuum robot, the kinematics cannot be measured or executed in a vector space but requires a dynamic continuum kinematic profile. The dynamic continuum kinematic profile is given as shown in the FIG. 9.

[0090] According to an embodiment, a continuum kinematic profile of a hyper redundant robot is obtained from a synthetic cognition model wherein the input to the model is kinematics of the robots such as the joint angles, positions, velocity, and acceleration, kinetics such as the forces and torque acting on the joints, forces producing acceleration, etc, other sensory inputs from other sensors shape of the robot during various positions, environmental parameters, etc. The overlap ping functions are added into the grid as secondary, tertiary, and quaternary data to create a more sensitive and specific continuum kinematic profile. The overlapping functions are known as hyper redundancy and the continuum kinematic profile helps us visualize the hyper-redundancy of the kinematic chain.

[0091] FIG. 10 is an example illustration in which a change in the angle of the joints con stitutes a continuous change along with the profile of the structure of the robot is depicted, accord ing to one embodiment of the present invention.

[0092] Consider a hyper redundant system as shown in the FIG. 10, for the end-effector to move from point A to point B, unlike the joint kinematics, the joint angle vector cannot be calcu lated with just the current position and orientation of the end effector and desired endpoint using iterative linear approximation technique.

[0093] Instead of using just the current position and orientation, for calculating the kine matics, the method uses the current continuum kinematic profile. The continuum kinematic profile is a signature obtained from various overlapping functions of kinematics, kinetics, sensorimotor, and control systems of the hyper redundant robot, such as,

1. Current orientation, and position of all the end effectors.

2. Range of motion of the end effectors.

3. The spline of the current joint kinematic (i.e., the shape of the kinematic chain with respect to the position).

4. The force/torque profile of the structure of the robot (i.e., the force/strain distribu tion along the spline of the kinematic chain).

5. Data about the environment from other sensors (obstruction, multiple available pathways, etc.,) 6. Dynamic activation strength of the motors.

7. Endpoint orientation, and position of all the end effectors.

[0094] Current continuum kinematics profile + Endpoint -> Desired continuum kinematics profile. The desired continuum kinematics profile or kinematic signature is obtained from the shift in the current kinematic signature in accordance with the desired endpoint.

[0095] FIG. 11 is an example illustration in which a grid for the dynamic continuum kin ematic profile or signature is depicted, according to one embodiment of the present invention.

[0096] Hyper redundancy by functional distribution: The complexity of the kinematics of a hyper redundant robotic limb can be increased by introducing a moving joint. The position of the joint is in accordance with different functions, this introduces hyper redundancy by functional distribution, and thus two or more function doesn’t have to share the same structural resources. By just changing the position of the joint, the length of the limbs can be adjusted thus changing the kinematic structure of the system.

[0097] FIG. 12 is an example illustration in which the joint is moved from one position to another creating multiple limbs, according to one embodiment of the present invention. In the FIG. 12, when the joint moves from point A to point B, the number of limbs increases from 2 to 3 thus altering the kinematic structure to perform complex functions.

[0098] FIG. 13A-13C illustrates the steps involved in generating a continuum kinematic profile. According to an embodiment, the continuum kinematic profile is a unique kinematic status of biomechanical or robotic object which gives the entire dynamics of the object in order for the controller or the brain to process the inverse and forward kinematics, smooth acceleration, and optimized movements.

Step 1:

Data from the kinematics , kinetics, sensory responses are otained through various sensors.

Step 2:

Data is normalized using min-max normalization

Step 3: A grid is generated with the kinematics, kinetics and sensory response data.

Step 4:

The primary, secondary, tertiary, and quaternary data are juxtaposed into different grid pat terns as shown in FIG.13 A and a dynamic relationship profile portfolio of the kinematic chain is obtained as shown in FIG.13B. [0099] FIG.14 illustrates a flowchart of a method for calculating and modelling inverse kinematics in complex systems, in accordance with an embodiment. At step 1402, one or more joint parameters is computed, using a jacobian technique, wherein the jacobian kinematic tech nique uses a difference in a position between a starting point and a desired position.

[0100] FIG.15 illustrates a flowchart of a method for calculating inverse kinematics for a complex adaptive kinematic system in robots, in accordance with an embodiment. At step 1502, a plurality of overlaps is obtained between various systems like kinetic, sensory, motor, and artificial intelligence. At step 1504, the data is processed from each of the systems either separately or in combination. At step 1506, the joint parameters of the kinematics are changed using the complex adaptive robotic system to preserve the structural economy of the system depending either on the task or function. [0101] FIG.16 illustrates the flowchart of a method for calculating the dynamic continuum kinematic profile for a hyper redundant robot. At step 1602, a signature of the continuum kinematic profile is obtained from a plurality of overlapping functions of at least one of: kinematics, kinetics, sensorimotor, and control systems of the hyper redundant robot, comprising at least one of: a cur- rent orientation, and a position of all the end effector, a range of motion of the end effector, a spline of the current joint kinematic, a force/torque profile of the structure of the robot, data about the environment from other sensors and a dynamic activation strength of the motors. At step 1604, at least one of: a desired continuum kinematics profile and a kinematic signature are obtained from the shift in a current kinematic signature with a desired endpoint. [0102] The foregoing of the specific embodiments will so fully reveal the general nature of the embodiments herein that others can, by applying current knowledge, readily modify and/or adapt for various applications such specific embodiments without departing from the generic con cept, and, therefore, such adaptations and modifications should and are intended to be compre hended within the meaning and range of equivalents of the disclosed embodiments. [0103] It is to be understood, that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore, while the embodiments herein have been described in terms of preferred embodiments, those skilled in the art will recognize that the embodiments herein can be practiced with modification within the spirit and scope of the appended claims. [0104] Although the embodiments herein are described with various specific embodi ments, it will be obvious for a person skilled in the art to practice the embodiments herein with modifications.