Homogeneous modular robot topology adaptive control method

Abstract

The embodiment of the application provides a homogeneous modular robot topology adaptive control method, realizes optimal control of the modular robot under external interference, and comprises the following steps: obtaining a homogeneous modular robot topology mathematical representation and a module unit three-dimensional model, then obtaining a dynamic equation, a state update equation, a cost function, a value function and an action value function, then calculating first-order partial derivatives, second-order partial derivatives and second-order mixed partial derivatives of the homogeneous modular robot state update equation, the value function and the action value function with respect to contained variables, and then obtaining an optimal controller and a nonlinear disturbance observer, designing a homogeneous modular robot distributed optimal control method integrated with the nonlinear disturbance observer, and obtaining a homogeneous modular robot topology adaptive controller integrated with the nonlinear disturbance observer. According to the technical scheme provided by the embodiment of the application, optimal control of the modular robot under any topology can be realized.

Description

TECHNICAL FIELD

[0001] The application relates to a homogeneous modular robot topology adaptive control method and belongs to the field of robot control. BACKGROUND

[0002] With the further promotion of industrial automation, the application of robots in various fields is gradually popularized. Robots with single performance and fixed structure will be difficult to adapt to tasks with various loads and diverse demands. The concept of modular robots was proposed in 1988. Such robots are generally composed of multiple identical modules (homogeneous) or different modules (heterogeneous). By changing the number and relative position of the modules, the robot can be reconstructed into a new configuration to obtain new functions, adapt to changing working environments, and meet diverse task requirements. Therefore, research on modular robots can promote the further development of the robot field in China.

[0003] Compared with heterogeneous modular robots, homogeneous modular robots can replace each other, have strong module expansion and universality, and can carry out related work such as design, manufacturing, assembly and maintenance in batches, and have high usability. Therefore, the application scenarios of homogeneous modular robots are more extensive. In the actual application process of robots, the robots are affected by external interference, limited energy and other factors, and the topology structure of the modular robots is not fixed in the application process. Therefore, it is of important theoretical research value to carry out optimal control research on homogeneous modular robots. SUMMARY

[0004] Therefore, the application provides a homogeneous modular robot topology adaptive control method to realize optimal control of the homogeneous modular robot.

[0005] The application embodiment provides a homogeneous modular robot topology adaptive control method, which comprises the following steps:

[0006] Obtaining a homogeneous modular robot topology mathematical representation and a module unit three-dimensional model;

[0007] Obtaining a homogeneous modular robot dynamics equation according to the homogeneous modular robot topology mathematical representation and the module unit three-dimensional model;

[0008] Obtaining a homogeneous modular robot state update equation according to the homogeneous modular robot dynamics equation;

[0009] Obtaining first-order partial derivatives, second-order partial derivatives and second-order mixed partial derivatives of the homogeneous modular robot state update equation with respect to the contained variables according to the homogeneous modular robot state update equation;

[0010] Obtaining a homogeneous modular robot cost function according to the homogeneous modular robot state update equation;

[0011] obtaining the homogeneous modular robot value function according to the homogeneous modular robot cost function;

[0012] obtaining the homogeneous modular robot action value function according to the homogeneous modular robot cost function and the homogeneous modular robot value function;

[0013] obtaining the first-order partial derivative, the second-order partial derivative and the second-order mixed partial derivative of the homogeneous modular robot value function with respect to the variables contained in the homogeneous modular robot value function according to the homogeneous modular robot value function;

[0014] obtaining the first-order partial derivative, the second-order partial derivative and the second-order mixed partial derivative of the homogeneous modular robot action value function with respect to the variables contained in the homogeneous modular robot action value function according to the homogeneous modular robot action value function;

[0015] obtaining the homogeneous modular robot optimal controller according to the first-order partial derivative, the second-order partial derivative and the second-order mixed partial derivative of the homogeneous modular robot state update equation with respect to the variables contained in the homogeneous modular robot state update equation, the first-order partial derivative, the second-order partial derivative and the second-order mixed partial derivative of the homogeneous modular robot value function with respect to the variables contained in the homogeneous modular robot value function, and the first-order partial derivative, the second-order partial derivative and the second-order mixed partial derivative of the homogeneous modular robot action value function with respect to the variables contained in the homogeneous modular robot action value function;

[0016] obtaining the homogeneous modular robot nonlinear disturbance observer according to the homogeneous modular robot dynamics equation;

[0017] obtaining the homogeneous modular robot topology structure adaptive controller integrated with the nonlinear disturbance observer according to the homogeneous modular robot topology structure mathematical representation, the module unit three-dimensional model, the homogeneous modular robot optimal controller and the homogeneous modular robot nonlinear disturbance observer.

[0018] In the above method, the homogeneous modular robot dynamics equation is obtained according to the homogeneous modular robot topology structure mathematical representation and the module unit three-dimensional model, and the homogeneous modular robot dynamics equation comprises:

[0019] for a homogeneous modular robot topology structure containing n topo_module modules, the mathematical representation is

[0020]

[0021] wherein, n topo_module represents the number of modules contained in the homogeneous modular robot topology structure; m i (i=1, 2,..., n topo_module ) represents the number of each module in the homogeneous modular robot topology structure; the matrix B is called the grounding relationship matrix, ba i (i=1, 2,..., ntopo_module ba = 0 means module m i is not grounded as a base when in use, ba i ≠ 0 means module m i is grounded as a base when in use, ba i ≠ 0 means module m i is grounded as a base when in use, ba ij (i = 1, 2,..., n topo_module ; j = 1, 2,..., n topo_module ) ∈ {1,..., n surf_con} means the interface number of module m i connected to module m j , when i = j, c ij = 0 (i = 1, 2,..., n topo_module ; j = 1, 2,..., n topo_module ), n surf_con means the number of face interfaces of a single module; matrix O is called the connection orientation relationship matrix of the homogeneous modular robot, co ij (i = 1, 2,..., n topo_module ; j = 1, 2,..., n topo_module ) means the connection orientation relationship of module m i and module m j , when i = j, co ij = 0 (i = 1, 2,..., n topo_module ; j = 1, 2,..., n topo_module );

[0022] The dynamics model of a homogeneous modular robot containing m module units and n degrees of freedom is

[0023]

[0024] wherein, represents an inertia force matrix; | represents the Coriolis force and centrifugal force terms received by each joint during the motion of the homogeneous modular robot; represents the gravity term received by the homogeneous modular robot during the motion; in turn represents the joint angle, joint angular velocity, joint angular acceleration, and driving torque.

[0025] In the above method, the homogeneous modular robot state update equation is obtained according to the homogeneous modular robot dynamics equation, comprising:

[0026] According to the homogeneous modular robot dynamics equation, it can be obtained that:

[0027]

[0028] wherein, represents an inertia force matrix; represents a Coriolis force, centrifugal force term received by each joint during the motion of the homogeneous modular robot; represents a gravity term received during the motion of the homogeneous modular robot; represent a joint angle, joint angular velocity, joint angular acceleration, driving torque in turn, and n represents the number of degrees of freedom in the homogeneous modular robot;

[0029] Let be a system state quantity, and be a system input quantity, so that:

[0030]

[0031] After arrangement, it can be obtained that:

[0032]

[0033] wherein, is composed of elements in M -1 (x), C(x), G(x);

[0034] The state update equation of the homogeneous modular robot is obtained as:

[0035]

[0036] wherein, t , x| t+1 represent the system state quantity at time t, the system state quantity at time t+1 respectively, u| t represents the system input quantity at time t, and ε represents a time interval, which is set according to the task requirement.

[0037] In the above method, the cost function of the homogeneous modular robot is obtained according to the state update equation of the homogeneous modular robot, which comprises:

[0038] The cost function at a certain state of the system is designed as:

[0039]

[0040] wherein, t , u| t represent the system state quantity, the system input quantity at time t, x| t,d represents the expected system state quantity at time t, e=x| t -x| t,d represents the system state quantity error at time t, and ug | t,d This represents the joint driving torque corresponding to the gravity compensation force at time t under the desired system state. The weight matrix represents the error term and torque term of the system state variables. It is a positive definite matrix and is set according to the task requirements. n represents the number of degrees of freedom in the homogeneous modular robot.

[0041] Starting with the initial system state x0, in the system input sequence U = {u| c ,u|1,...,u| N-1 Under the influence of}, the total cost of the entire motion process is:

[0042]

[0043] Where N represents the number of steps taken.

[0044] In the above method, obtaining the optimal controller for the homogeneous modular robot based on the first-order partial derivatives, second-order partial derivatives, and mixed second-order partial derivatives of the state update equation of the homogeneous modular robot with respect to the variables, the first-order partial derivatives, second-order partial derivatives, and mixed second-order partial derivatives of the value function of the homogeneous modular robot with respect to the variables, and the first-order partial derivatives, second-order partial derivatives, and mixed second-order partial derivatives of the action value function of the homogeneous modular robot with respect to the variables includes:

[0045] The optimal controller for a homogeneous modular robot is:

[0046]

[0047] in, This represents the second-order partial derivative of the action-value function with respect to the system input in u| i Take the value at that location. This represents the second-order mixed partial derivative of the action-value function with respect to the system input and system state variables in x| i 、u| i Take the value at that location. The first-order partial derivative of the action-value function with respect to the system input is expressed in u| i The value at Δx| i Δu| represents the difference between the system state variables at time i in two consecutive calculations during the optimal control calculation process. i It represents the difference between the system input at time i in two adjacent calculations during the optimal control calculation process.

[0048] As can be seen from the above technical solutions, the embodiments of the present invention have the following beneficial effects:

[0049] In the technical scheme of the embodiment of the present application, the mathematical representation of the homogeneous modular robot topology structure and the three-dimensional model of the module unit are obtained, and then the homogeneous modular robot dynamics equation, the state update equation, the cost function, the value function and the action value function are obtained, and then the first-order partial derivative, the second-order partial derivative and the second-order mixed partial derivative of the homogeneous modular robot state update equation, the value function and the action value function with respect to the contained variables are calculated, and then the optimal controller and the nonlinear disturbance observer are obtained, and the homogeneous modular robot distributed optimal control method integrated with the nonlinear disturbance observer is designed, and the homogeneous modular robot distributed optimal controller integrated with the nonlinear disturbance observer is obtained. According to the technical scheme provided by the embodiment of the present application, the optimal control of the homogeneous modular robot can be realized. Combined with the characteristics of the homogeneous modular robot and based on the three-dimensional model of the module unit, the optimal control of the modular robot under any topology structure is realized, and the control basis for the application of the modular robot is provided. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical scheme of the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative and laborious work.

[0051] Figure 1 is a flowchart of the homogeneous modular robot topology structure adaptive control method provided by the embodiment of the present application;

[0052] Figure 2 is a three-dimensional model of the module unit in the embodiment of the present application;

[0053] Figure 3 is a target function convergence curve of the homogeneous modular robot in the embodiment of the present application;

[0054] Figure 4 is an optimization rate curve of the target function of the homogeneous modular robot in the embodiment of the present application;

[0055] Figure 5 is the end trajectory tracking situation of the homogeneous modular robot in the embodiment of the present application. DETAILED DESCRIPTION

[0056] In order to better understand the technical scheme of the present application, the embodiments of the present application will be described in detail below with reference to the drawings.

[0057] It should be clear that the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0058] The embodiment of the application provides a homogeneous modular robot topology adaptive control method, please refer to Figure 1 , which is a flowchart of the homogeneous modular robot topology adaptive control method provided by the embodiment of the application and integrated with a nonlinear disturbance observer, as Figure 1 shown, the method comprises the following steps:

[0059] Step 101, obtaining a homogeneous modular robot topology mathematical representation and a module unit three-dimensional model.

[0060] Specifically, the module unit three-dimensional model is as shown in Figure 2 , 1 represents a two-hemisphere shell connecting plane; 2 and 18 represent two hemispherical shells; 3, 6, 11 and 15 represent positioning devices on the male interface; 4 and 14 represent torque output shafts of motor modules of the active interface; 5 and 12 represent motor module bodies on the active interface; 7, 10, 13 and 20 represent mechanical structural components on the interface; 8, 9, 19 and 21 represent positioning grooves on the female interface matched with the positioning devices; 16 represents a motor module body at the center of the module unit; and 17 represents a motor module torque output shaft at the center of the module unit.

[0061] The homogeneous modular robot topology mathematical representation is

[0062] M=[1,3,2,4]

[0063] BA=[2,0,0,0]

[0064]

[0065] Step 102, obtaining a homogeneous modular robot dynamics equation according to the homogeneous modular robot topology mathematical representation and the module unit three-dimensional model.

[0066] Specifically, the dynamics model of a homogeneous modular robot containing m module units and n degrees of freedom is

[0067]

[0068] wherein, represents an inertia force matrix; represents a Coriolis force and a centrifugal force term received by each joint of the homogeneous modular robot in a motion process of the homogeneous modular robot; represents a gravity term received by the homogeneous modular robot in the motion process of the homogeneous modular robot; represents joint angles, joint angular velocities, joint angular accelerations and driving torques in sequence.

[0069] Step 103, obtaining a homogeneous modular robot state update equation according to a homogeneous modular robot dynamics equation.

[0070] Specifically, according to the homogeneous modular robot dynamics equation, the following can be obtained:

[0071]

[0072] wherein, represents an inertia force matrix; represents a Coriolis force and a centrifugal force term received by each joint of the homogeneous modular robot during movement; represents a gravity term received by the homogeneous modular robot during movement; represents a joint angle, a joint angular velocity, a joint angular acceleration, and a driving torque in turn, and n represents a degree of freedom number in the homogeneous modular robot;

[0073] Let be a system state quantity, and let be a system input quantity, and the following can be obtained:

[0074]

[0075] After arrangement, the following can be obtained:

[0076]

[0077] wherein, ψ(x) is composed of elements in M -1 (x), C(x), and G(x);

[0078] The homogeneous modular robot state update equation is obtained as follows:

[0079]

[0080] wherein, x| t and x| t+1 represent system state quantities at time t and time t+1 respectively, u| t represents a system input quantity at time t, and ε represents a time interval, which is set to 10 -3 seconds according to task requirements.

[0081] Step 104, obtaining first-order partial derivatives, second-order partial derivatives, and second-order mixed partial derivatives of the homogeneous modular robot state update equation with respect to variables contained in the homogeneous modular robot state update equation.

[0082] Specifically, using Taylor's formula, a second-order Taylor polynomial expansion is performed on the state update equation near (x| i , u| i ), and linearization can be obtained as follows:

[0083]

[0084] The first-order partial derivative of the function Θ with respect to x is

[0085]

[0086] The first-order partial derivative of the function Θ with respect to u is

[0087]

[0088] The fourth, fifth and sixth terms in the linearization of the state update equation near (x| i , u| i ) are

[0089]

[0090] where I 2n is a 2n x 2n identity matrix, is a 4n 2 x 4n 2 exchange matrix, denotes the Kronecker product, and are the second-order partial derivatives of the function Θ with respect to x and u, respectively, and the second-order mixed partial derivatives, in gradient form, are denoted by xx Θ, and uu Θ, and xu Θ, and ux Θ, respectively, and xu T Θ = ∇ ux Θ.

[0091] Step 105, obtaining the cost function of the homogeneous modular robot according to the state update equation of the homogeneous modular robot.

[0092] Specifically, the cost function of the system in a certain state is designed as:

[0093]

[0094] where x| t , u| t represent the system state quantity and the system input quantity at time t, x| t,d represents the expected system state quantity at time t, e = x| t -x| t,d represents the system state quantity error at time t, u g | t,d represents the joint driving torque corresponding to the compensation of gravity at time t under the expected system state, represents the weight matrix corresponding to the system state quantity error term and the torque term, which is a positive definite matrix, and is set according to the task requirements, The diagonal elements are 10, and the rest are 0, The diagonal elements are 1, and the rest are 0;

[0095] Take the initial state of the system x|0 as the starting point, and under the action of the system input sequence U={u|0, u|1,…, u| N-1 The total cost during the entire movement process is:

[0096]

[0097] Where N represents the number of steps.

[0098] Step 106, obtaining the homogeneous modular robot value function according to the homogeneous modular robot cost function.

[0099] Step 107, obtaining the homogeneous modular robot action value function according to the homogeneous modular robot cost function and the homogeneous modular robot value function.

[0100] Step 108, obtaining the first-order partial derivative, second-order partial derivative and second-order mixed partial derivative of the homogeneous modular robot value function with respect to the contained variables according to the homogeneous modular robot value function.

[0101] Step 109, obtaining the first-order partial derivative, second-order partial derivative and second-order mixed partial derivative of the homogeneous modular robot action value function with respect to the contained variables according to the homogeneous modular robot action value function.

[0102] Step 110, obtaining the homogeneous modular robot optimal controller according to the first-order partial derivative, second-order partial derivative and second-order mixed partial derivative of the homogeneous modular robot state update equation with respect to the contained variables, the first-order partial derivative, second-order partial derivative and second-order mixed partial derivative of the homogeneous modular robot value function with respect to the contained variables, and the first-order partial derivative, second-order partial derivative and second-order mixed partial derivative of the homogeneous modular robot action value function with respect to the contained variables.

[0103] Specifically, the homogeneous modular robot optimal controller is:

[0104]

[0105] Where, represents the second-order partial derivative of the action value function with respect to the system input at u| i , represents the second-order mixed partial derivative of the action value function with respect to the system input and system state at x| i , u| i , represents the first-order partial derivative of the action value function with respect to the system input at u| i , Δx| iΔu| represents the difference between the system state variables at time i in two consecutive calculations during the optimal control calculation process. i It represents the difference between the system input at time i in two adjacent calculations during the optimal control calculation process.

[0106] Step 111: Obtain the nonlinear disturbance observer of the homogeneous modular robot based on the dynamic equations of the homogeneous modular robot.

[0107] Specifically, the nonlinear disturbance observer of module unit i is

[0108]

[0109] in, This represents the gain matrix of the interference observer. Indicates the module unit interference term τ di Estimated value M represents the dynamic equation of the module unit. i (θ i ), G i (θ i The nominal parameter of θ i , These represent the joint angle, joint angular velocity, and joint angular acceleration in the module unit, respectively.

[0110] Introducing auxiliary state variables in

[0111] The nonlinear state observer for a homogeneous modular robot is

[0112]

[0113] Step 112: Based on the mathematical representation of the topology of the homogeneous modular robot, the three-dimensional model of the module unit, the optimal controller of the homogeneous modular robot, and the nonlinear disturbance observer of the homogeneous modular robot, design a distributed optimal control method for the homogeneous modular robot that incorporates the nonlinear disturbance observer, and obtain an adaptive controller for the topology of the homogeneous modular robot that incorporates the nonlinear disturbance observer.

[0114] Specifically, the homogeneous modular robot topology adaptive controller incorporating a nonlinear disturbance observer is...

[0115]

[0116] The initial state of each module unit is thetalist ini =[10°,10°,10°] T Its corresponding terminal expected state is EEF end= [-0.4658m, 0.0414m, -0.2289m, -159.1376°, -32.3454°, -108.1587°] T The above method provided by the embodiment of the application is simulated.

[0117] The trajectory tracking of the homogeneous modular robot is performed using the topology adaptive control of the homogeneous modular robot integrated with the nonlinear disturbance observer, and the convergence curve of the objective function of the homogeneous modular robot in the optimal control optimization process is as shown in Figure 3 The optimization rate curve of the objective function of the homogeneous modular robot is as shown in Figure 4 According to Figure 3 and Figure 4 It can be seen that, with the progress of the iteration process, the overall cost calculated by the objective function value of the homogeneous modular robot presents a convergence trend, and the optimization rate of the objective function also presents a convergence trend. When the iteration is performed to the 86th generation, the objective change amount of the homogeneous modular robot is 8.2979*10 -6 , and the objective function value of the homogeneous modular robot is 0.0854. Using the control sequence after the iteration convergence as the system input, the end trajectory tracking of the homogeneous modular robot is as shown in Figure 5 , wherein Figure 5 (a) is a comparison diagram of the three-dimensional trajectory of the end, Figure 5 (b) is a comparison diagram of the actual position and the expected position of the end, Figure 5 (c) is a comparison diagram of the end position error at the beginning of the iteration and the convergence, Figure 5 (d) is the motion trajectory of each joint, Figure 5 (e) is the driving torque of each joint. Through comparison, it can be concluded that: after the iteration convergence, the tracking error of the end of the modular robot is reduced by 10 -1 orders of magnitude from 10 -3 , and the tracking accuracy is obviously improved, thereby proving the correctness and effectiveness of the topology adaptive control method of the homogeneous modular robot integrated with the nonlinear disturbance observer.

[0118] The technical scheme of the embodiment of the application has the following beneficial effects:

[0119] In the technical scheme of the embodiment of the present application, the homogeneous modular robot topology structure mathematical representation and the module unit three-dimensional model are obtained, then the homogeneous modular robot dynamics equation, the state updating equation, the cost function, the value function and the action value function are obtained, then the first-order partial derivative, the second-order partial derivative and the second-order mixed partial derivative of the state updating equation, the value function and the action value function of the homogeneous modular robot to the contained variables are calculated, and then the optimal controller and the nonlinear disturbance observer of the homogeneous modular robot are obtained, the homogeneous modular robot distributed optimal control method integrated with the nonlinear disturbance observer is designed, and the homogeneous modular robot distributed optimal controller integrated with the nonlinear disturbance observer is obtained. According to the technical scheme provided by the embodiment of the present application, the optimal control of the homogeneous modular robot can be realized. In combination with the characteristics of the homogeneous modular robot, the optimal control of the modular robot under any topology structure is realized based on the module unit three-dimensional model, and the control basis for the application of the modular robot is provided.

[0120] The above merely describes preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

[0121] The contents not described in detail in the specification of the present application are the known technology of the person skilled in the art.

Claims

1. An adaptive control method for the topology of a homogeneous modular robot incorporating a nonlinear disturbance observer, characterized in that, The method includes: Obtain mathematical representations of the topological structure of homogeneous modular robots and three-dimensional models of modular units; Based on the mathematical representation of the topological structure of the homogeneous modular robot and the three-dimensional model of the modular unit, the dynamic equation of the homogeneous modular robot is obtained; Based on the dynamic equations of the homogeneous modular robot, the state update equations of the homogeneous modular robot are obtained; Based on the state update equation of the homogeneous modular robot, the first-order partial derivative, second-order partial derivative, and second-order mixed partial derivative of the state update equation of the homogeneous modular robot with respect to the variables are obtained. Based on the state update equation of the homogeneous modular robot, the cost function of the homogeneous modular robot is obtained; Based on the cost function of the homogeneous modular robot, the value function of the homogeneous modular robot is obtained; Based on the cost function and value function of the homogeneous modular robot, the motion value function of the homogeneous modular robot is obtained. Based on the value function of a homogeneous modular robot, the first-order partial derivative, second-order partial derivative, and second-order mixed partial derivative of the value function of the homogeneous modular robot with respect to the variables are obtained; Based on the motion value function of a homogeneous modular robot, the first-order partial derivative, second-order partial derivative, and second-order mixed partial derivative of the motion value function of the homogeneous modular robot with respect to the variables are obtained; Based on the first-order partial derivatives, second-order partial derivatives, and mixed second-order partial derivatives of the state update equation of the homogeneous modular robot with respect to the variables, the first-order partial derivatives, second-order partial derivatives, and mixed second-order partial derivatives of the value function of the homogeneous modular robot with respect to the variables, and the first-order partial derivatives, second-order partial derivatives, and mixed second-order partial derivatives of the action value function of the homogeneous modular robot with respect to the variables, the optimal controller of the homogeneous modular robot is obtained. Based on the dynamic equations of a homogeneous modular robot, a nonlinear disturbance observer for the homogeneous modular robot is obtained; Based on the mathematical representation of the topology of a homogeneous modular robot, the three-dimensional model of the modular unit, the optimal controller of the homogeneous modular robot, and the nonlinear disturbance observer of the homogeneous modular robot, a distributed optimal control method for the homogeneous modular robot incorporating the nonlinear disturbance observer is designed, and an adaptive controller for the topology of the homogeneous modular robot incorporating the nonlinear disturbance observer is obtained.

2. The method according to claim 1, characterized in that, Based on the mathematical representation of the topological structure of the homogeneous modular robot and the three-dimensional model of the modular unit, the dynamic equations of the homogeneous modular robot are obtained, including: For n topo_module The topological structure of a homogeneous modular robot with multiple modules is mathematically represented as follows: Where, n topo_module m represents the number of modules contained in a homogeneous modular robot topology; i This represents the module numbers in the homogeneous modular robot topology; matrix B is called the grounding relation matrix, ba i This indicates whether a module in a homogeneous modular robot topology is grounded as a base during use. i =0 indicates module m i Do not ground during use, ba i ≠0 indicates module m i When using ba i The interface ground serves as the base; matrix C is called the connection relationship matrix of the homogeneous modular robot, c ij ∈{1,...,n surf_con } represents module m i With module m j The interface numbers that are connected, when i = j, c ij =0, n surf_con This represents the number of face interfaces of a single module; matrix O is called the connection orientation matrix of a homogeneous modular robot, co ij Represents module m i With module m j The connection orientation relationship, when i = j, co ij =0; i=1,2,...,n topo_module j = 1, 2, ..., n topo_module ; The dynamic model of a homogeneous modular robot containing m module units and n degrees of freedom is as follows: in, Represents the inertial force matrix; This represents the Coriolis force and centrifugal force terms experienced by each joint during the motion of a homogeneous modular robot. This represents the gravitational force experienced by a homogeneous modular robot during its motion. These represent joint angle, joint angular velocity, joint angular acceleration, and driving torque, respectively.

3. The method according to claim 1, characterized in that, Based on the dynamic equations of the homogeneous modular robot, the state update equations of the homogeneous modular robot are obtained, including: Based on the dynamic equations of a homogeneous modular robot, we can obtain: in, Represents the inertial force matrix; This represents the Coriolis force and centrifugal force terms experienced by each joint during the motion of a homogeneous modular robot. This represents the gravitational force experienced by a homogeneous modular robot during its motion. The joint angle, joint angular velocity, joint angular acceleration, and driving torque are represented in sequence, and n represents the number of degrees of freedom in the homogeneous modular robot. make For system state variables, As the system input, we can obtain: After sorting, we can obtain: in, ψ(x) is derived from M -1 Composed of elements from C(x), G(x); The state update equation for the homogeneous modular robot is obtained as follows: Where, x| t 、x| t+1 Let u| represent the system state variables at time t and time t+1, respectively. t ε represents the system input at time t, and ε represents the time interval, which is set according to task requirements.

4. The method according to claim 1, characterized in that, Based on the state update equation of the homogeneous modular robot, the cost function of the homogeneous modular robot is obtained, including: The cost function of the system in a certain state is designed as follows: Where, x| t u| t x| represents the system state and system input at time t. t,d Let e ​​= x| represent the desired system state variables at time t. t -x| t,d u represents the error of the system state quantity at time t. g | t,d This represents the joint driving torque corresponding to the gravity compensation force at time t under the desired system state. The weight matrix represents the error term and torque term of the system state variables. It is a positive definite matrix and is set according to the task requirements. n represents the number of degrees of freedom in the homogeneous modular robot. Starting with the initial system state x|0, the system input sequence U={u|0,u|1,...,u| N-1 Under the influence of}, the total cost of the entire motion process is: Where N represents the number of steps taken.

5. The method according to claim 1, characterized in that, Based on the first-order, second-order, and mixed second-order partial derivatives of the state update equation of the homogeneous modular robot with respect to the variables, the first-order, second-order, and mixed second-order partial derivatives of the value function of the homogeneous modular robot with respect to the variables, and the first-order, second-order, and mixed second-order partial derivatives of the action value function of the homogeneous modular robot with respect to the variables, the optimal controller for the homogeneous modular robot is obtained, including: The optimal controller for a homogeneous modular robot is: in, This represents the second-order partial derivative of the action-value function with respect to the system input in u| i Take the value at that location. This represents the second-order mixed partial derivative of the action-value function with respect to the system input and system state variables in x| i u| i Take the value at that location. The first-order partial derivative of the action-value function with respect to the system input is expressed in u| i The value at Δx| i Δu| represents the difference between the system state variables at time i in two consecutive calculations during the optimal control calculation process. i It represents the difference between the system input at time i in two adjacent calculations during the optimal control calculation process.

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