Multi-modular robot optimal coordination control method, equipment and medium

Abstract

The invention discloses a multi-modular robot optimal coordination control method and device and a medium, and relates to the field of robot control. Firstly, a kinematic model of a modular robot collaborative handling task is established, and secondly, through the combination of robot joint torque feedback and Newton-Euler iteration, the kinematic model of the modular robot collaborative handling task is established; the method comprises the following steps: establishing an overall dynamic model of the modular robot and a target object, observing cross-linking coupling terms between joint subsystems of the modular robot through a neural network observer, and then respectively constructing performance index functions of an inner layer and an outer layer; and then approximation is performed on the performance index functions of the inner layer and the outer layer by using a radial basis function neural network, a Hamiltonian-Jacobi equation is solved to obtain an optimal control law and an optimal internal force, and coordination control of the multi-modular robot system is realized. According to the method, the interaction strategy among the multiple modular robots is optimized while the internal cooperation problem of the modular robots is considered, so that the accuracy, optimality and stability of the system are ensured.

Description

Technical Field

[0001] The present application relates to the field of robot control, and in particular to a method, device and medium for optimal coordinated control of multi-modular robots. Background Art

[0002] With the implementation of the concept of Industry 5.0, the handling capabilities of robots have been comprehensively and deeply applied in many fields such as deep space exploration, disaster prevention and relief, and industrial production. However, as the mission scenarios and working conditions become increasingly complex, the weaknesses of a single robot, such as insufficient load capacity and limited working scenarios, are gradually exposed when faced with the task of handling large objects with complex shapes. Therefore, when faced with such complex tasks, the demand for multiple robots to collaboratively handle target objects is becoming increasingly strong. Controlling multiple robots to collaboratively complete the task of handling target objects through coordinated control algorithms has become a popular frontier research direction.

[0003] Each joint subsystem of the modular robot is independently equipped with sensing, driving, communication, control and other units. The robot subsystems can be reconfigured to make the modular robot system present different configurations to adapt to different task scenarios. Compared with traditional fixed-configuration robots, modular robots have many advantages such as strong scalability, good maintainability, low cost and strong portability.

[0004] Optimal control is a control method that studies how to optimize the specific performance indicators of a given controlled system through appropriate control strategies. It is an indispensable part of modern control theory and also one of the important research directions of modular robot system control.

[0005] Existing control methods only focus on differential games between modular robot subsystems, or analyze the game process between robots and human collaborators separately. This method works well when facing relatively simple systems, but for complex systems with multiple levels and multiple agents, it is difficult to effectively handle the interactions between different levels within the system, and it is impossible to guarantee the accuracy, optimality and stability of the system. Summary of the invention

[0006] The purpose of this application is to provide a multi-modular robot optimal coordination control method, device and medium, which can achieve in a complex multi-layer game system, while taking into account the internal collaboration problems of modular robots, optimizing the interaction strategies between multiple modular robots to ensure the accuracy, optimality and stability of the system.

[0007] To achieve the above objectives, this application provides the following solutions:

[0008] In a first aspect, the present application provides an optimal coordinated control method for a multi-modular robot, which is applied to a multi-modular robot system; the multi-modular robot system includes a plurality of modular robots, each of which includes a plurality of joint subsystems; the optimal coordinated control method for the multi-modular robot includes:

[0009] Establish a kinematic model for modular robot collaborative handling tasks;

[0010] Based on the kinematic model of the modular robot collaborative handling task, the overall dynamic model of the modular robot and the target object is established according to the robot joint torque feedback and Newton-Euler iteration;

[0011] Based on the overall dynamics model of the modular robot and the target object, a neural network observer is constructed to observe the cross-linking coupling terms between the joint subsystems of the modular robot, and a radial basis neural network is used to approximate the cross-linking coupling terms to obtain the update rate expression of the weights.

[0012] Construct the performance index function of the two-layer Nash game, and use the radial basis neural network to approximate the performance index function of the two-layer Nash game, and determine the weight update rate of the two-layer Nash game according to the weight update rate expression;

[0013] The Hamilton-Jacobi equation corresponding to the performance index function of the double-layer Nash game is solved according to the weight update rate of the double-layer Nash game, and the optimal control law and optimal internal force are obtained to achieve coordinated control of the multi-modular robot system.

[0014] Optionally, based on the kinematic model of the modular robot collaborative handling task, according to the robot joint torque feedback and Newton-Euler iteration, an overall dynamic model of the modular robot and the target object is established, including:

[0015] Establish the dynamic model of the modular robot based on the robot joint torque feedback;

[0016] Establish the dynamic model of the target object according to Newton-Euler iteration;

[0017] Based on the kinematic model of the modular robot's collaborative handling task, the dynamic model of the modular robot and the dynamic model of the target object, an overall dynamic model of the modular robot and the target object is established.

[0018] Optionally:

[0019] The kinematic model of the modular robot collaborative handling task is:

[0020] x=δ 1 (q 1 )=δ 2 (q 2)=...=δ n (q n )=...=δ N (q N );

[0021]

[0022] Among them, x represents the pose vector of the target object, represents the speed of the target object, represents the acceleration of the target object, q n represents the joint angles of the nth modular robot, represents the joint velocity of the nth modular robot, represents the joint acceleration of the nth modular robot, δ n () represents the relationship between the pose vector of the target object and the joint angle of the nth modular robot, Denotes δ n The first-order derivative of (), Jcjn represents the Jacobian matrix from the center of mass of the target object to the joint of the nth modular robot, Indicates J cjn The first-order derivative of , n = 1, 2, ..., N, N represents the number of modular robots;

[0023] The dynamic model of the modular robot is:

[0024]

[0025] Among them, I n represents the moment of inertia vector of the motor of the nth modular robot, γ n represents the reduction ratio vector of the harmonic reducer of the nth modular robot, f n represents the friction torque of the nth modular robot, I cn represents the cross-coupling term between the joint subsystems of the nth modular robot, τ jn represents the torque measured by the joint torque sensor of the nth modular robot, f oen represents the force exerted by the target object on the end of the nth modular robot, J ejn represents the Jacobian matrix from the end to the joint of the nth modular robot, Indicates J ejn The transpose of n represents the output torque of the motor of the nth modular robot;

[0026] The dynamic model of the target object is:

[0027]

[0028] Among them, M W (x) represents the inertia matrix of the target object, Represents the Coriolis force and centrifugal force matrix of the target object, G W (x) represents the gravity term acting on the target object, f o represents the resultant force of N modular robots acting on the target object;

[0029] The overall dynamic model of the modular robot and the target object is:

[0030]

[0031] Among them, M zn represents the inertia matrix of the nth modular robot, C zn represents the Coriolis force and centrifugal force of the nth modular robot, G zn represents the gravity term of the nth modular robot, Indicates J cjn The transpose of n (t) represents the load distribution matrix of the nth modular robot at time t, f ni represents the internal force of the nth modular robot.

[0032] Optionally, the neural network observer is:

[0033]

[0034] Among them, x n2 represents the second component of the state vector of the nth modular robot, represents the observer state vector of the nth modular robot, express The first derivative of represents the observation of the cross-coupling term between the joint subsystems of the nth modular robot, Ω n represents the positive definite observation gain matrix of the nth modular robot, u n represents the control input of the nth modular robot, M zn -1 Indicates M zn The inverse of.

[0035] Optionally, the performance index function of the double-layer Nash game includes: an inner-layer Nash game performance index function and an outer-layer Nash game performance index function;

[0036] The inner Nash game performance index function is:

[0037]

[0038] in, represents the inner Nash game performance indicator function, represents the utility function of the inner Nash game, represents the speed error, express The transpose of represents the inner error quadratic positive definite matrix, represents the inner interaction control input penalty matrix, u nm represents the control law of the mth joint subsystem of the nth modular robot, Indicates u nm The transpose of , m = 1, 2, ..., M, M represents the number of joint subsystems, τ represents the independent variable of time integration;

[0039] The outer Nash game performance index function is:

[0040]

[0041] in, represents the outer Nash game performance index function, represents the outer error quadratic positive definite matrix, represents the outer interaction control input penalty matrix, represents the internal force positive definite matrix, represents f ni The transpose of .

[0042] Optionally, the weight update rate of the double-layer Nash game includes: the weight update rate of the inner Nash game and the weight update rate of the outer Nash game;

[0043] The weight update rate of the inner Nash game is:

[0044]

[0045] in, represents the weight update rate of the inner Nash game, λ nm represents the learning rate of the inner Nash game radial basis neural network, e cnm represents the error function of the inner Nash game radial basis neural network, σ Inm represents the basis function of the inner Nash game radial basis neural network, represents the acceleration error, represents partial derivative;

[0046] The weight update rate of the outer Nash game is:

[0047]

[0048] in, represents the weight update rate of the outer Nash game, λ on represents the learning rate of the outer Nash game radial basis neural network, e con represents the error function of the outer Nash game radial basis neural network, Represents the basis functions of the outer Nash game radial basis neural network.

[0049] Optionally, the Hamilton-Jacobi equation is:

[0050]

[0051] Among them, J Inm represents the inner Nash game performance index function of the mth joint subsystem of the nth modular robot, Indicates J Inm The transpose of J On represents the outer Nash game performance index function of the nth modular robot, express The transpose of represents the dynamic characteristic matrix of the system, represents the control input matrix, represents the expected acceleration.

[0052] Optionally:

[0053] The optimal control law is:

[0054]

[0055] in, represents the optimal control law of the mth joint subsystem of the nth modular robot, represents the optimal performance index function of the inner Nash game of the m-th joint subsystem of the n-th modular robot, Representation Matrix The inverse, Representation Matrix The transpose of

[0056] The optimal internal force is:

[0057]

[0058] Among them, f ni * represents the optimal internal force of the nth modular robot, Represents the optimal performance indicator function of the outer Nash game of the nth modular robot.

[0059] In a second aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the optimal coordinated control method for multiple modular robots.

[0060] In a third aspect, the present application provides a computer program product, including a computer program, which, when executed by a processor, implements the optimal coordinated control method for multiple modular robots.

[0061] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0062] The present application provides a method, device and medium for optimal coordinated control of multiple modular robots. First, a kinematic model of the collaborative handling task of modular robots is established. Secondly, the overall dynamic model of the modular robot and the target object is established by combining the robot joint torque feedback and Newton-Euler iteration. The cross-linked coupling terms between the joint subsystems of the modular robot are observed by a neural network observer. Subsequently, the performance index functions of the inner and outer layers are constructed respectively. Then, the radial basis neural network is used to approximate the performance index functions of the inner and outer layers respectively, and the Hamilton-Jacobi equation is solved to obtain the optimal control law and the optimal internal force, so as to realize the coordinated control of the multi-modular robot system. The present application proposes a double-layer Nash game theory framework, which can optimize the interaction strategies between multiple modular robots while taking into account the internal collaboration problems of modular robots in a complex multi-layer game system, thereby ensuring the accuracy, optimality and stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0064] Figure 1 A schematic diagram of a multi-modular robot system provided in this application performing a handling task;

[0065] Figure 2 A flowchart of the optimal coordinated control method for multiple modular robots provided in this application;

[0066] Figure 3 A diagram of the execution steps of the optimal coordinated control method for multiple modular robots provided in this application. DETAILED DESCRIPTION

[0067] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0068] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0069] In an exemplary embodiment, the present application provides an optimal coordinated control method for a multi-modular robot, which is applied to a multi-modular robot system. Figure 1 As shown, the multi-modular robot system includes several modular robots, each of which includes several joint subsystems. Figure 2 and Figure 3 As shown, the multi-modular robot optimal coordination control method includes the following steps 101 to 105.

[0070] Step 101: Establish a kinematic model of the modular robot collaborative handling task.

[0071] The kinematic model of the modular robot collaborative handling task is as follows:

[0072] x=δ 1 (q 1 )=δ 2 (q 2 )=...=δ n (q n )=...=δ N (q N ), (1)

[0073] The above formula expresses the relationship between the robot's end position and posture and each joint variable. (p) T ,x (o) T ] T ∈R dt Represents the position x of the target object (p) ∈R p and direction x (o) ∈R o The pose vector, d t (d t =p+o) represents the degree of freedom of the target object, where p represents the dimension of the target object position vector, o represents the dimension of the target object posture vector, and q n represents the joint angle of the nth modular robot, δn () represents the relationship between the pose vector of the target object and the joint angle of the nth modular robot, n = 1, 2, ..., N, N represents the number of modular robots, and R represents a real number.

[0074] The first derivative of the pose vector represents the velocity of the target object:

[0075]

[0076] The second derivative of the pose vector represents the acceleration of the target object:

[0077]

[0078] in, represents the speed of the target object, represents the acceleration of the target object, represents the joint velocity of the nth modular robot, represents the joint acceleration of the nth modular robot, express The first derivative of cjn represents the Jacobian matrix from the center of mass of the target object to the joints of the nth modular robot, Indicates J cjn The first derivative of .

[0079] Step 102: Based on the kinematic model of the modular robot collaborative handling task, an overall dynamic model of the modular robot and the target object is established according to the robot joint torque feedback and Newton-Euler iteration.

[0080] First, the dynamic model of the modular robot is established based on the robot joint torque feedback. The dynamic model of the nth modular robot is as follows:

[0081]

[0082] in, represents the moment of inertia vector of the motor of the nth modular robot, represents the reduction ratio vector of the harmonic reducer of the nth modular robot, represents the friction torque of the nth modular robot, represents the cross-coupling term between the joint subsystems of the nth modular robot, represents the torque measured by the joint torque sensor of the nth modular robot, f oen ∈R M represents the force exerted by the target object on the end of the nth modular robot, J ejn represents the Jacobian matrix from the end to the joint of the nth modular robot, represents the transpose of the Jacobian matrix from the end to the joint of the nth modular robot, τ n ∈R M Represents the output torque of the motor of the nth modular robot.

[0083] Secondly, the dynamic model of the target object is established according to Newton-Euler iteration. The dynamic model of the target object is as follows:

[0084]

[0085] Among them, M W (x) represents the inertia matrix of the target object, Represents the Coriolis force and centrifugal force matrix of the target object, G W (x) is the gravitational force acting on the target object, and f o represents the resultant force of N modular robots acting on the target object, which can be decomposed into:

[0086]

[0087] Among them, f ecn represents the force applied by the nth modular robot on the target object. ecn and f oen The relationship can be expressed as:

[0088] f ecn =J ecn T f oen , (7)

[0089] Among them, J ecn The Jacobian matrix J represents the distance from the end of the nth modular robot to the center of mass of the target object. ecn T Indicates J ecn The transpose of ecn can be decomposed into the internal force f ni With external force f ne The sum of the forms:

[0090] f ecn =f ni +f ne , (8)

[0091] The sum of the internal forces is zero, that is:

[0092]

[0093] Therefore (5) can be written as:

[0094]

[0095] In other words ne It can also be written as the total external force multiplied by the load distribution matrix:

[0096]

[0097] Among them, d n (t) is a time-dependent load distribution matrix, which represents the load distribution matrix of the nth modular robot at time t, and thus:

[0098]

[0099] in, Indicates J ecn The pseudo-inverse of , where the superscript T indicates the transpose of the matrix.

[0100] Finally, based on the kinematic model of the modular robot's collaborative handling task, the dynamic model of the modular robot and the dynamic model of the target object, an overall dynamic model of the modular robot and the target object is established.

[0101] The overall dynamic model of the modular robot and the target object is as follows:

[0102]

[0103] Among them, M zn represents the inertia matrix of the nth modular robot, C zn represents the Coriolis force and centrifugal force of the nth modular robot, G zn represents the gravity term of the nth modular robot, τ n Represents the output torque of the motor of the nth modular robot.

[0104] M zn It can be specifically expressed as:

[0105]

[0106] C zn It can be specifically expressed as:

[0107]

[0108] G zn It can be specifically expressed as:

[0109]

[0110] in, Indicates J cjn The transpose of .

[0111] The control input and state vector are defined as:

[0112] u n =τ n , (17)

[0113]

[0114] Among them, u n is the control input of the nth modular robot, x n is the state vector of the nth modular robot, and the first component x of the state vector of the nth modular robot n1 =q n Represents the joint position, the second component of the state vector of the nth modular robot Representing the joint velocity, the state space equation of the multi-modular robot collaborative handling task can be obtained as:

[0115]

[0116] Among them, the intermediate parameter l n and g n They are:

[0117]

[0118] g n =M zn -1 . (twenty one)

[0119] Among them, M zn -1 Indicates M zn The inverse of.

[0120] Step 103: Based on the overall dynamic model of the modular robot and the target object, a neural network observer is constructed to observe the cross-linked coupling terms between the joint subsystems of the modular robot, and a radial basis neural network is used to approximate the cross-linked coupling terms to obtain an update rate expression of the weights.

[0121] The observation of unknown cross-linked coupling terms between joint subsystems of modular robots is completed through neural networks. The specific method is as follows:

[0122] First, substituting (16), (17), and (18) into the state space equation (19) yields:

[0123]

[0124] Construct a neural network observer to observe the unknown cross-coupling terms between the joint subsystems of the modular robot:

[0125]

[0126] in, represents the observer state vector of the nth modular robot, express The first derivative of represents the observation of the cross-coupling term between the joint subsystems of the nth modular robot, Ω n is a positive definite observation gain matrix of the nth modular robot. The error dynamics of the observer can be expressed as:

[0127]

[0128] The observation error can be expressed as: express The first-order derivative of . The cross-linked coupling term is approximated by a radial basis neural network:

[0129] I cn =W cn T σ cn +ε cn , (25)

[0130] Among them, W cn represents the ideal weight, σ cn represents the basis function, ε cn is the approximate error, from which we can get:

[0131]

[0132] and Respectively represent I cn and W cn The approximation of , and then the update rate expression of the weight is obtained:

[0133]

[0134] Among them, η cn is a normal number.

[0135] Step 104: construct a performance indicator function of the double-layer Nash game, and use a radial basis function neural network to approximate the performance indicator function of the double-layer Nash game, and determine the weight update rate of the double-layer Nash game according to the weight update rate expression.

[0136] Among them, the performance index function of the double-layer Nash game includes: the performance index function of the inner Nash game and the performance index function of the outer Nash game; the weight update rate of the double-layer Nash game includes: the weight update rate of the inner Nash game and the weight update rate of the outer Nash game.

[0137] The inner Nash game performance indicator function is constructed as follows:

[0138]

[0139] This performance indicator function indicates that the error is the optimization target of the control system, where represents the inner Nash game performance indicator function, represents the utility function of the inner Nash game, is a function of time t, representing the velocity error, x 2 =[x n12 ,...,x nm2 ,...,x nM2 ] T , represents the joint velocity, represents the expected speed, represents the inner error quadratic positive definite matrix, represents the inner interaction control input penalty matrix, u nm represents the control law of the mth joint subsystem in the nth modular robot, Indicates u nm The transpose of , m = 1, 2, ..., M, M represents the number of joint subsystems, τ represents the independent variable of time integration. From this, the expression of the inner Nash game Hamiltonian function can be obtained:

[0140]

[0141] The Hamiltonian function is the partial derivative of the performance index function with respect to time. The purpose is to find the extreme value of the performance index function to achieve optimal control. Indicates J Inm The partial derivative of the velocity error is represents the dynamic characteristic matrix of the system, represents the control input matrix. Therefore, the optimal performance index function of the mth joint subsystem in the nth modular robot can be expressed as:

[0142]

[0143] It means that by selecting a suitable control strategy, the integral of the utility function is minimized, thereby achieving the purpose of optimizing system performance. By taking the partial derivative of (29) with respect to the control law, we can obtain:

[0144]

[0145] According to (31), the optimal control law expression of the mth joint subsystem in the nth modular robot can be obtained as:

[0146]

[0147] It indicates that the optimal control law of the joint subsystem is determined by the gradient of the performance index function and the penalty matrix is ​​input by the inner interactive control and the control input matrix Correction.

[0148] The outer Nash game performance indicator function is constructed as follows:

[0149]

[0150] in, represents the outer Nash game performance index function, u n =[u n1 ,...,u nm ,...u nM ] T represents the control law vector of the nth modular robot, Q On represents the outer error quadratic positive definite matrix, represents the outer interaction control input penalty matrix, represents the positive definite matrix of internal forces, f ni Indicates internal force, represents f ni The transpose of . From this, we can get the expression of the outer Nash game Hamiltonian function:

[0151]

[0152] in, Indicates J On The partial derivative of , thus, the optimal performance index function of the outer Nash game can be expressed as:

[0153]

[0154] By taking the partial derivative of (34) with respect to the internal force, we can obtain:

[0155]

[0156] According to (36), the optimal internal force expression of the outer Nash game can be obtained:

[0157]

[0158] Among them, f ni * represents the optimal internal force of the nth modular robot, Represents the optimal performance indicator function of the outer Nash game of the nth modular robot.

[0159] Use radial basis neural network to approximate the inner Nash game performance index function:

[0160]

[0161] Among them, W Inm represents the ideal weight of the inner Nash game radial basis neural network, σ Inm represents the basis function of the inner Nash game radial basis neural network, ε Inm It represents the approximation error of the inner Nash game radial basis neural network.

[0162] According to (38), we can deduce:

[0163]

[0164] in, represents the optimal control law of the mth joint subsystem of the nth modular robot, represents the optimal performance index function of the inner Nash game of the m-th joint subsystem of the n-th modular robot, Representation Matrix The inverse, Representation Matrix The transpose of represents the partial derivative of the basis function with respect to the error, It represents the gradient of the approximation error.

[0165] The approximate optimal performance index function can be expressed as:

[0166]

[0167] in, represents the estimated weights of the inner Nash game.

[0168] The ideal Hamiltonian function H Inm It can be expressed as:

[0169]

[0170] Approximate Hamiltonian function It can be expressed as:

[0171]

[0172] Define the error function expression:

[0173]

[0174] According to the gradient descent method, the weight update rate can be obtained as:

[0175]

[0176] in, represents the weight update rate of the inner Nash game, λ nm represents the learning rate of the inner Nash game radial basis neural network, e cnm represents the error function of the inner Nash game radial basis neural network, σ Inm represents the basis function of the inner Nash game radial basis neural network, represents the acceleration error, represents partial derivative, E cnm Represents the inner error gradient function.

[0177] Use radial basis neural network to approximate the outer Nash game performance index function:

[0178]

[0179] in, represents the ideal weights of the outer Nash game radial basis neural network, Represents the basis function of the outer Nash game radial basis neural network, It represents the approximation error of the outer Nash game radial basis neural network.

[0180] According to (45), we can deduce:

[0181]

[0182] in, represents the partial derivative of the basis function with respect to the error, It represents the gradient of the approximation error.

[0183] The approximate optimal performance index function can be expressed as:

[0184]

[0185] in, represents the estimated weights of the outer Nash game.

[0186] Ideal Hamiltonian function It can be expressed as:

[0187]

[0188] Approximate Hamiltonian function It can be expressed as:

[0189]

[0190] Define the error function expression:

[0191]

[0192] According to the gradient descent method, the weight update rate can be obtained as:

[0193]

[0194] in, represents the weight update rate of the outer Nash game, λ on represents the learning rate of the outer Nash game radial basis neural network, e con represents the error function of the outer Nash game radial basis neural network, represents the basis function of the outer Nash game radial basis neural network, E con Represents the outer error gradient function.

[0195] Step 105: Solve the Hamilton-Jacobi equation corresponding to the performance index function of the double-layer Nash game according to the weight update rate of the double-layer Nash game to obtain the optimal control law and the optimal internal force to achieve coordinated control of the multi-modular robot system.

[0196] Among them, for the inner Nash game, the control strategy is improved through strategy iteration. The specific process is as follows:

[0197] Step 1: Set variable k = 0 and select the initial admissible control strategy And choose a very small positive constant ε nm .

[0198] Step 2: When k>0, based on Approximate solution of the Hamilton-Jacobi equation based on the weight update rate And find the performance index function And there is

[0199] Step 3: Pass Update control strategy

[0200] Step 4: When When , the policy iteration process ends and the optimal control law is obtained, otherwise it returns to the second step and sets k = k + 1.

[0201] For the outer Nash game, the corresponding Hamilton-Jacobi equation is The iterative solution process is similar to that to obtain the optimal internal force.

[0202] The derivation process of the above formula proves that compared with the traditional method of only focusing on the differential game between the joint subsystems of the modular robot, or only analyzing the game process between the modular robot and the human collaborator, the theoretical method proposed in this application takes into account the internal collaboration problems of the modular robot subsystems in a complex multi-layer game system, while optimizing the interaction strategies between multiple modular robot systems. It can obtain the optimal control law of each subsystem within the modular robot and obtain the optimal internal force.

[0203] In summary, this application proposes a two-layer Nash game theory framework to achieve the optimization of the interaction strategy between multiple modular robot systems while taking into account the internal collaboration problems of modular robot subsystems in a complex multi-layer game system. In addition, this application solves the problem of the Hamilton-Jacobi equation in the optimal control problem, which is difficult to obtain an analytical solution, by applying the adaptive dynamic programming method. At the same time, the game theory is incorporated to treat the multiple joint subsystems in the modular robot and the multiple modular robot systems when collaboratively transporting the target object as participants in the game theory. Through the inner and outer two-layer Nash games, the optimal control problem of the modular robot system is transformed into a game problem of multiple subsystems and multiple robots.

[0204] In an exemplary embodiment, the present application further provides a computer device, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0205] In an exemplary embodiment, the present application further provides a computer-readable storage medium storing a computer program, which implements the steps in the above-mentioned method embodiments when executed by a processor.

[0206] In an exemplary embodiment, the present application further provides a computer program product, including a computer program, which implements the steps in the above-mentioned method embodiments when executed by a processor.

[0207] In this application, all actions to obtain signals, information or data are carried out in compliance with the relevant data protection laws and policies of the country where the application is located, and with the authorization of the corresponding device owner. It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant legal provisions.

[0208] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0209] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0210] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0211] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. An optimal coordination control method for multi-modular robots, characterized in that: Applied to a multi-modular robot system; the multi-modular robot system includes a plurality of modular robots, each modular robot includes a plurality of joint subsystems; the multi-modular robot optimal coordination control method includes: Establish a kinematic model for modular robot collaborative handling tasks; Based on the kinematic model of the modular robot collaborative handling task, the overall dynamic model of the modular robot and the target object is established according to the robot joint torque feedback and Newton-Euler iteration; Based on the overall dynamics model of the modular robot and the target object, a neural network observer is constructed to observe the cross-linking coupling terms between the joint subsystems of the modular robot, and a radial basis function neural network is used to approximate the cross-linking coupling terms to obtain the update rate expression of the weights. Construct the performance index function of the two-layer Nash game, and use the radial basis neural network to approximate the performance index function of the two-layer Nash game, and determine the weight update rate of the two-layer Nash game according to the weight update rate expression; The Hamilton-Jacobi equation corresponding to the performance index function of the double-layer Nash game is solved according to the weight update rate of the double-layer Nash game, and the optimal control law and optimal internal force are obtained to achieve coordinated control of the multi-modular robot system.

2. The optimal coordination control method of multi-modular robots according to claim 1, characterized in that: Based on the kinematic model of the modular robot collaborative handling task, the overall dynamic model of the modular robot and the target object is established according to the robot joint torque feedback and Newton-Euler iteration, including: Establish the dynamic model of the modular robot based on the robot joint torque feedback; Establish the dynamic model of the target object according to Newton-Euler iteration; Based on the kinematic model of the modular robot's collaborative handling task, the dynamic model of the modular robot and the dynamic model of the target object, an overall dynamic model of the modular robot and the target object is established.

3. The optimal coordination control method for multi-modular robots according to claim 2, characterized in that: The kinematic model of the modular robot collaborative handling task is: x=δ1(q1)=δ2(q2)=...=δ n (q n )=...=d N (q N ); Among them, x represents the pose vector of the target object, represents the speed of the target object, represents the acceleration of the target object, q n represents the joint angles of the nth modular robot, represents the joint velocity of the nth modular robot, represents the joint acceleration of the nth modular robot, δ n () represents the relationship between the pose vector of the target object and the joint angle of the nth modular robot, Denotes δ n The first derivative of (), J cjn represents the Jacobian matrix from the center of mass of the target object to the joints of the nth modular robot, Indicates J cjn The first-order derivative of , n = 1, 2, ..., N, N represents the number of modular robots; The dynamic model of the modular robot is: Among them, I n represents the moment of inertia vector of the motor of the nth modular robot, γ n represents the reduction ratio vector of the harmonic reducer of the nth modular robot, f n represents the friction torque of the nth modular robot, I cn represents the cross-coupling term between the joint subsystems of the nth modular robot, τ jn represents the torque measured by the joint torque sensor of the nth modular robot, f oen represents the force exerted by the target object on the end of the nth modular robot, J ejn represents the Jacobian matrix from the end to the joint of the nth modular robot, Indicates J ejn The transpose of n represents the output torque of the motor of the nth modular robot; The dynamic model of the target object is: Among them, M W (x) represents the inertia matrix of the target object, Represents the Coriolis force and centrifugal force matrix of the target object, G W (x) represents the gravity term acting on the target object, f o represents the resultant force of N modular robots acting on the target object; The overall dynamic model of the modular robot and the target object is: Among them, M zn represents the inertia matrix of the nth modular robot, C zn represents the Coriolis force and centrifugal force of the nth modular robot, G zn represents the gravity term of the nth modular robot, Indicates J cjn The transpose of n (t) represents the load distribution matrix of the nth modular robot at time t, f ni represents the internal force of the nth modular robot.

4. The optimal coordination control method of multiple modular robots according to claim 3 is characterized in that: The neural network observer is: Among them, x n2 represents the second component of the state vector of the nth modular robot, represents the observer state vector of the nth modular robot, express The first derivative of represents the observation of the cross-coupling term between the joint subsystems of the nth modular robot, Ω n represents the positive definite observation gain matrix of the nth modular robot, u n represents the control input of the nth modular robot, M zn -1 Indicates M zn The inverse of.

5. The optimal coordination control method of multiple modular robots according to claim 4 is characterized in that: The performance index function of the double-layer Nash game includes: an inner layer Nash game performance index function and an outer layer Nash game performance index function; The inner Nash game performance index function is: in, represents the inner Nash game performance indicator function, represents the utility function of the inner Nash game, represents the speed error, express The transpose of represents the inner error quadratic positive definite matrix, represents the inner interaction control input penalty matrix, u nm represents the control law of the mth joint subsystem of the nth modular robot, Indicates u nm The transpose of , m = 1, 2, ..., M, M represents the number of joint subsystems, τ represents the independent variable of time integration; The outer Nash game performance index function is: in, represents the outer Nash game performance index function, represents the outer error quadratic positive definite matrix, represents the outer interaction control input penalty matrix, represents the internal force positive definite matrix, represents f ni The transpose of .

6. The optimal coordination control method of multiple modular robots according to claim 5, characterized in that: The weight update rate of the double-layer Nash game includes: the weight update rate of the inner Nash game and the weight update rate of the outer Nash game; The weight update rate of the inner Nash game is: in, represents the weight update rate of the inner Nash game, λ nm represents the learning rate of the inner Nash game radial basis neural network, e cnm represents the error function of the inner Nash game radial basis neural network, σ Inm represents the basis function of the inner Nash game radial basis neural network, represents the acceleration error, represents partial derivative; The weight update rate of the outer Nash game is: in, represents the weight update rate of the outer Nash game, λ on represents the learning rate of the outer Nash game radial basis neural network, e con represents the error function of the outer Nash game radial basis neural network, Represents the basis functions of the outer Nash game radial basis neural network.

7. The optimal coordination control method of multiple modular robots according to claim 6, characterized in that: The Hamilton-Jacobi equation is: Among them, J Inm represents the inner Nash game performance index function of the m-th joint subsystem of the n-th modular robot, Indicates J Inm The transpose of represents the outer Nash game performance index function of the nth modular robot, express The transpose of represents the dynamic characteristic matrix of the system, represents the control input matrix, represents the expected acceleration.

8. The optimal coordination control method for multiple modular robots according to claim 7, characterized in that: The optimal control law is: in, represents the optimal control law of the mth joint subsystem of the nth modular robot, represents the optimal performance index function of the inner Nash game of the m-th joint subsystem of the n-th modular robot, Representation Matrix The inverse, Representation Matrix The transpose of The optimal internal force is: Among them, f ni * represents the optimal internal force of the nth modular robot, Represents the optimal performance indicator function of the outer Nash game of the nth modular robot.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the multi-modular robot optimal coordination control method described in any one of claims 1 to 8 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the multi-modular robot optimal coordination control method described in any one of claims 1 to 8 is implemented.

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