Mobile robot obstacle avoidance and repetitive motion method based on variable parameter dynamic learning network

Abstract

The invention discloses a mobile robot obstacle avoidance and repetitive motion method based on a variable parameter dynamic learning network, and the method comprises the following steps: 1), building a robot inverse kinematics equation on a speed layer through a tail end track main task; 2) establishing a periodic circulation repetitive motion constraint of the mobile redundancy robot, and introducing an equality obstacle avoidance constraint based on a critical distance; 3) setting the repetitive motion and obstacle avoidance sub-problem of the comprehensive robot as a dynamically weighted target function, and solving a time-varying matrix equation of the target function through a variable parameter dynamic learning network; and (4) the inverse kinematics equation and the constraint of the robot are set as a quadratic programming problem, the problem is solved by converting the problem into a time-varying matrix equation through a Lagrange function, and the optimal solution of the mobile redundancy mechanical arm in the inverse kinematics problem is obtained. According to the method, high-precision path tracking and high-efficiency obstacle avoidance are realized through relaxation constrained repetitive motion control and obstacle avoidance constraint, and the calculation efficiency and stability are improved by adopting a variable-parameter dynamic learning network for solving.

Description

Technical Field

[0001] The present invention belongs to the field of robot motion control, and particularly relates to a method for obstacle avoidance and repetitive motion of a mobile robot based on a variable-parameter dynamic learning network. Background Art

[0002] With the continuous development of robot technology, redundant robots have gradually become an indispensable important tool in various fields. These robots have high flexibility and adaptability and can complete more complex tasks without increasing the hardware complexity. However, due to the redundant characteristics, robots can not only complete the main tasks but also perform additional tasks at the same time. For this reason, redundant robots need to face some unique challenges when completing complex tasks. Especially when performing tasks in a complex environment, how to perform effective path planning and obstacle avoidance has become a key problem to be solved urgently.

[0003] In an actual industrial production line, in the face of a complex environment, it is usually required that a mobile redundant robot move an object from one point to another point. This task requires the robot to have the ability of repetitive motion and obstacle avoidance.

[0004] For redundant robots, without considering repetitive motion, the inverse kinematics solution may be infinite, which will lead to multiple possibilities of the end effector posture after one task cycle. Therefore, the final posture after completing the task cycle may not completely coincide with the initial state, which may lead to joint angle deviation and even position error of the end effector. In addition, with the iteration of the working cycle, the error will accumulate continuously and even lead to task failure. Therefore, it is particularly urgent to design an effective repetitive motion scheme for redundant robots. To solve the aforementioned non-repetitive problem, some constraint optimization schemes based on the velocity layer have been designed. However, due to the limitation of the feasible region of the constraint, it is difficult to complete the main task and other additional subtasks at the same time. Therefore, researchers designed a more relaxed repetitive motion scheme (A New Performance Index for the Repetitive Motion of Mobile Manipulators Lin Xiao and Yunong Zhang, Membe,; IEEE), which transformed the original rotation angle constraint into a constraint of its trigonometric function value. Although this relaxed constraint scheme expands the range of feasible solutions to a certain extent, it does not consider the obstacle avoidance problem that often occurs in practice. Therefore, how to design an efficient relaxed constraint and combine it with an obstacle avoidance scheme has become a key problem.

[0005] Regarding the obstacle avoidance problem of redundant manipulators, some effective solutions have been proposed (Real-Time Obstacle Avoidance for Fast Mobile Robots Article in lEEE Transactions on Systems Man and cybernetics. October 1989 DO:33.1103021.44311 5ource:EE Xplore)(Novel Method of Obstacle Avoidance Planning for Redundant Sliding Manipulators JINGUO LIU(Senior Member, IEEE), YUCHUANG TONG(Student Member, IEEE) ZHAOJIE JU(Senior Member IEEE), AND YUWANG LIU(Member EEe)). For example, a real-time obstacle avoidance method applicable to mobile robots can enable the robot to move towards the target direction while avoiding obstacles. In addition, based on the known trajectory of the end effector, a weighted additional offset speed based on the gradient projection method is designed. This method ensures the smooth obstacle avoidance of the manipulator while avoiding severe jitter. However, most of these methods use the pseudo-inverse method to solve the inverse kinematic equation, which usually requires a large number of matrix operations, resulting in a time-consuming solution process. By specifying the escape velocity at the critical point, the researchers proposed a QP-based obstacle avoidance scheme. However, restricted by inequality constraints, the number of feasible solutions is small, and sometimes this scheme will conflict with other additional subtasks (such as repetitive motion). Summary of the Invention

[0006] The object of the present invention is to propose a control method for a mobile redundant manipulator based on a variable-parameter dynamic learning network, which is mainly used to solve the path planning, obstacle avoidance, and repetitive motion problems of mobile redundant robots when performing tasks in complex environments. This technology can be widely applied in fields such as industrial automation, aerospace, logistics distribution, and medical robots. By combining hybrid obstacle avoidance and repetitive motion constraints, a dynamic weighted objective function is constructed to achieve efficient motion planning and control of redundant robots in complex environments. This method uses a variable-parameter dynamic learning network to solve the kinematic problem, thus showing good performance in terms of real-time performance, accuracy, and robustness.

[0007] A method for obstacle avoidance and repetitive motion of a mobile robot based on a variable-parameter dynamic learning network includes the following steps:

[0008] 1) Establish the inverse kinematic equation of the robot on the velocity layer through the main task of the end trajectory;

[0009] 2) Establish the periodic cyclic repetitive motion constraint of the mobile redundant robot, and introduce the equality obstacle avoidance constraint based on the critical distance;

[0010] 3) Set the comprehensive robot repetitive motion and obstacle avoidance sub-problems as a dynamically weighted objective function, and solve the time-varying matrix equation of the objective function through a variable-parameter dynamic learning network;

[0011] 4) Set the robot inverse kinematics equation in step 1) and the constraints in step 2) as a quadratic programming problem and convert it into a time-varying matrix equation solution problem through the Lagrangian function, and obtain the optimal solution of the inverse kinematics problem of the mobile redundant manipulator, so as to control the motion of the mobile redundant manipulator.

[0012] Furthermore, in step 1), the robot inverse kinematics equation is the kinematics equation of the mobile redundant manipulator:

[0013] r = r p + τg(θ) = p(ψ, α, θ);

[0014] Where r is the expected end trajectory of the manipulator, r p is the position vector of the mobile platform, g(·) is a non-linear equation about the manipulator joint angle, τ represents the coordinate transformation matrix, ψ, α, θ respectively represent the Mecanum wheel rotation angle, the mobile platform rotation angle and the manipulator joint angle value of the mobile redundant manipulator, and p(ψ, α, θ) represents a function of the Mecanum wheel rotation angle, the mobile platform rotation angle and the manipulator joint angle value of the mobile redundant manipulator; Differentiating both sides of the kinematics equation of the mobile redundant manipulator gives the inverse kinematics equation on the velocity layer, and adding position feedback gives:

[0015]

[0016] Where K is the Jacobian matrix of the manipulator, and are the derivatives of the angles of each part of the mobile redundant manipulator and the end trajectory with respect to time respectively, and ε represents the control factor, which is used to control the accuracy of position feedback.

[0017] Furthermore, the periodic cyclic repetitive motion constraint of the mobile redundant robot in step 2) is:

[0018]

[0019] r p is the position vector of the mobile platform, α, θ respectively represent the mobile platform rotation angle and the manipulator joint angle value of the mobile redundant manipulator, and r p (0), α(0), θ(0) respectively represent their initial state values; In addition respectively represent the first derivatives of the robotic arm joint angle, the mobile platform position, and the rotation angle, ε θ 、 ε α respectively represent the control factors for the constraints of each variable, which are used to control the convergence rate;

[0020] And it is further simplified to matrix representation as

[0021]

[0022] where is the derivative of the angles of each part of the mobile redundant manipulator, represents the square value of the two-norm, J E 、 respectively represent the Jacobian matrix for controlling the repetitive motion of the robot and the repetitive motion expressions of each variable:

[0023]

[0024] where, J M =[J(γ), -sinαJ T T , I is the identity matrix, J T is the Jacobian matrix of the rotation angle of the mobile platform, J(γ) is the Jacobian matrix of the position of the mobile platform, and γ is the linear velocity of the Mecanum wheels of the mobile platform;

[0025] where the constraint on the rotation angle is the constraint on the value of its cosine function:

[0026]

[0027] where ε α respectively represent the derivative of the rotation angle of the mobile platform and the convergence speed control factor; α, α(0) respectively represent the rotation angle of the mobile platform and its initial state value;

[0028] The equality obstacle avoidance constraint based on the critical distance is:

[0029]

[0030] where, L represents the distance vector between the robot and the obstacle, ||·|| 2 represents the vector two-norm, l 1 is the critical distance value, and the control factors ε o and κ are used to adjust the degree of obstacle avoidance.

[0031] It can also be simplified and expressed as:

[0032] ​

[0033] Among them is the derivative of the angles of each part of the mobile redundant manipulator, represents the square value of the two-norm, J C 、 respectively represent the Jacobian matrix for controlling the robot to avoid obstacles and the repetitive motion expressions of each variable:

[0034]

[0035] Among them, J F is the position derivative of the mobile platform.

[0036] Furthermore, the dynamic weighted objective function in step 3) is the dynamic sum of obstacle avoidance and repetitive motion constraints:

[0037]

[0038] Among them is the derivative of the angles of each part of the mobile redundant manipulator, J C 、 respectively represent the Jacobian matrix for controlling the robot to avoid obstacles and the repetitive motion expressions of each variable, J E 、 respectively represent the Jacobian matrix for controlling the repetitive motion of the robot and the repetitive motion expressions of each variable, ξ is the dynamic weighting factor used to balance the weights of obstacle avoidance and repetitive motion, ζ is the control factor, and the critical distance l 2 is used to control the start of the obstacle avoidance task.

[0039] Furthermore, the mathematical expression of the dynamic weighting factor ξ is:

[0040]

[0041] where tanh(·) represents the hyperbolic tangent function, l 2 represents the critical distance value at which the mobile redundant robot starts to avoid obstacles, ζ is the control factor, and L represents the distance vector between the robot and the obstacle.

[0042] Furthermore, in step 4), the optimization problem of the obstacle avoidance and repetitive motion sub-problems in step 3) is formulated as a standard convex quadratic programming problem, that is: Subject to And introducing the Lagrange multiplier λ to obtain the Lagrangian function:

[0043]

[0044] Among them, is the derivative of the angles of each part of the mobile redundant manipulator, is the Lagrangian function, K(t) is the Jacobian matrix of the robotic arm, and λ(t) is the Lagrange multiplier. That is is the derivative of the angles of each part of the mobile redundant robotic arm;

[0045]

[0046] where t represents time. is the derivative of the end trajectory with respect to time, ε represents the control factor, ξ is the dynamic weighting factor used to balance the weights of obstacle avoidance and repetitive motion, and J C 、 respectively represent the Jacobian matrix for controlling the obstacle avoidance of the robot and the repetitive motion expressions of each variable, and J E 、 respectively represent the Jacobian matrix for controlling the repetitive motion of the robot and the repetitive motion expressions of each variable. ψ, α, and θ respectively represent the Mecanum wheel rotation angle, the mobile platform rotation angle, and the robotic arm joint angle value of the mobile redundant robotic arm. r is the desired end trajectory of the robotic arm, and p(ψ,α,θ) represents a function of the Mecanum wheel rotation angle, the mobile platform rotation angle, and the robotic arm joint angle value of the mobile redundant robotic arm.

[0047] Furthermore, in step 3), by setting the following two partial differential equations equal to 0:

[0048]

[0049] and further simplifying to the following matrix equation: A(t)y(t) = G(t), where

[0050] Furthermore, the matrix equation further transforms the matrix equation into an error function whose form is:

[0051]

[0052] Thus, a variable-parameter dynamic learning network solver can be further used for solving.

[0053] Furthermore, in step 4), a variable-parameter dynamic learning network solver is used for solving to obtain the optimal solution y of the matrix equation * That is, first construct the following neurodynamics equation:

[0054]

[0055] and further expand it to:

[0056]

[0057] where \(t\) represents time, \(\gamma(t)\) is a constant representing the convergence rate of the neural network, \(\exp(\cdot)\) represents the natural logarithm, and \(\Phi(\cdot)\) represents the activation function of the neural network, which respectively represent the first-order derivatives of \(y(t)\), \(A(t)\), and \(G(t)\). Then, by solving this neural dynamics equation, the optimal solution \(y\) can be obtained. * .

[0058] Furthermore, the optimal solution \(y\) obtained by the variable-parameter dynamic learning network solver * , from the first \(n\) terms of \(y\) * , the optimal solution of the quadratic programming problem is obtained, which is the optimal solution \(\theta\) of the joint angles of the mobile redundant manipulator, * the optimal value \(\alpha\) of the rotation angle of the mobile platform * and the optimal value \(\psi\) of the rotation angle of the Mecanum wheel. * .

[0059] Compared with the existing repeated motion planning schemes for mobile redundant manipulators, the present invention has the following advantages:

[0060] 1. Compared with the strong constraint repeated motion scheme, by proposing a periodic repetition constraint, the present invention has a larger inverse kinematics solution space and can consider various sub-task constraint conditions, enabling the robot to handle multiple sub-tasks simultaneously;

[0061] 2. Compared with the traditional pseudo-inverse-based method, the present invention solves the non-repeated motion and obstacle avoidance problems of the mobile redundant manipulator through a quadratic programming scheme, avoiding lengthy matrix operations and having good real-time performance;

[0062] 3. Compared with the classical recursive neural network solver, the present invention uses a variable-parameter dynamic learning network solver, which has a faster convergence speed, higher calculation accuracy, better robustness, and can handle various challenges in dynamic environments;

[0063] 4. Compared with the numerical method solver, the present invention belongs to a neural network solver, has a fast calculation speed, higher efficiency, and can handle complex obstacle avoidance and task execution problems in real time.

[0064] To overcome the above deficiencies, the present invention proposes a hybrid obstacle avoidance and repeated motion scheme, which combines relaxed repeated motion constraints and an obstacle avoidance scheme with equality constraints, and uses the QP method to achieve more precise control of the mobile redundant robot. The hybrid obstacle avoidance and repeated motion scheme is an effective method for motion generation in multi-task situations. When solving this scheme, the corresponding motion generation of the mobile redundant robot is realized.

[0065] To solve the proposed control scheme, some neurodynamics methods can be adopted. With the continuous development of neurodynamics methods, inspired by the design process of fixed-parameter convergent difference neural networks, researchers have proposed a variable-parameter dynamic learning network method to address the problem of increased computation time caused by the expansion of the computational scale. Considering its fast convergence, high robustness, and accuracy, the present invention uses the variable-parameter dynamic learning network method for solution.

[0066] In summary, the present invention aims to achieve coordinated control of repetitive motion and obstacle avoidance by designing a relaxation constraint and a dynamic weighting factor optimization method, thereby improving the accuracy of path tracking and the stability of system operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 FIG. is a flowchart of a method for obstacle avoidance and repetitive motion of a mobile robot based on a variable-parameter dynamic learning network in an embodiment;

[0068] Figure 2 FIG. is a schematic diagram of a mobile redundant manipulator performing non-repetitive motion in an embodiment;

[0069] Figure 3 FIG. is a schematic diagram for comparing repetitive motion of a mobile redundant manipulator in an embodiment;

[0070] Figure 4 FIG. is a schematic diagram of a redundant manipulator performing an obstacle avoidance task in an embodiment;

[0071] Figure 5 FIG. is a schematic diagram of a redundant manipulator performing an obstacle avoidance task without adopting the solution of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] To make the technical solution of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings.

[0073] Figure 1 As shown, the process of the method for repetitive motion and obstacle avoidance of a mobile robot based on a variable-parameter dynamic learning network in this embodiment mainly consists of three parts: problem posing, problem transformation, and problem solving. First, by designing the main task of the end trajectory, the inverse kinematics equation of the robot is established at the velocity layer; at the same time, the sub-problems of robot repetitive motion and obstacle avoidance are considered and expressed as a dynamically weighted objective function; and the objective function is combined with the robot inverse kinematics equation and further expressed as a quadratic programming problem and transformed into a time-varying matrix equation through the Lagrangian function; then the matrix equation is solved by a variable-parameter dynamic learning network, specifically including the following steps:

[0074] First, consider the inverse kinematics equation of a single manipulator,

[0075] g(θ) = r (1);

[0076] where \(r\) is the desired end - effector trajectory of the robotic arm, \(\theta\) is the joint angle of the robotic arm, and \(g(\cdot)\) is a non - linear equation regarding the joint angles of the robotic arm. Equation (1) represents finding the positions of each joint of the robotic arm at corresponding moments from the known end - effector positions. However, due to the non - linearity of the equation, the solution of the equation is not unique. Therefore, we consider the problem at the velocity - linearization level. Taking the derivative of both sides of the equation with respect to time, we get,

[0077]

[0078] where \(J(\theta)\) is the Jacobian matrix of the robotic arm, and are the derivatives of the joint angles and the end - effector trajectory of the robotic arm with respect to time respectively.

[0079] Then, by further considering the equation of the mobile redundant robotic arm, the forward kinematic equation of the entire mobile redundant robotic arm can be obtained as,

[0080] \(r = r\) p +\(\tau g(\theta)=p(\psi,\alpha,\theta)\ (3)\)

[0081] where \(r\) is the desired end - effector trajectory of the robotic arm, \(r\) p is the position vector of the mobile platform, \(g(\cdot)\) is a non - linear equation regarding the joint angles of the robotic arm, \(\tau\) represents the coordinate transformation matrix, \(\psi\), \(\alpha\), \(\theta\) represent the Mecanum wheel rotation angle, the rotation angle of the mobile platform, and the joint angle values of the robotic arm of the mobile redundant robotic arm respectively, and finally it is uniformly simplified and represented by the \(p(\cdot)\) function.

[0082] Similarly, linearized to the velocity - layer representation and adding position feedback, we can get,

[0083]

[0084] where \(K\) is the Jacobian matrix of the robotic arm, and are the derivatives of the angles of each part of the mobile redundant robotic arm and the end - effector trajectory with respect to time respectively, and \(\varepsilon\) represents the control factor used to control the accuracy of position feedback.

[0085] Considering the constraints on the joint angles, the position and rotation angle of the mobile platform of the robot to achieve repeated motion, that is,

[0086]

[0087] \(r\) p is the position vector of the mobile platform, \(\alpha\), \(\theta\) represent the rotation angle of the mobile platform and the joint angle values of the robotic arm of the mobile redundant robotic arm respectively, and \(r\) p (0), \(\alpha(0)\), \(\theta(0)\) represent their initial state values; in addition respectively represent the first-order derivatives of the robotic arm joint angles, the mobile platform position, and the rotation angle, ε θ 、 ε α respectively represent the control factors for the constraints of each variable, and are used to control the convergence rate.

[0088] And it is further simplified and represented in matrix form as

[0089]

[0090] where is the derivative of the angles of each part of the mobile redundant robotic arm represents the square value of the two-norm, J E 、 respectively represent the Jacobian matrix for controlling the repetitive motion of the robot and the repetitive motion expressions of each variable;

[0091] Then, by introducing the equality obstacle avoidance constraint based on the critical distance, that is,

[0092]

[0093] where L represents the distance vector between the robot and the obstacle, ||·|| 2 represents the vector two-norm, l 1 is the critical distance value, and the control factor ε o and the control factor k are used to adjust the degree of obstacle avoidance.

[0094] Similarly, it is simplified and expressed as

[0095]

[0096] where J C 、 respectively represent the Jacobian matrix for controlling the obstacle avoidance of the robot and the repetitive motion design expressions of each variable:

[0097]

[0098] As an embodiment, the method of quadratic programming is used to solve the problems of obstacle avoidance and non-repetitive motion of the mobile redundant robotic arm, and the following unified quadratic programming problem is designed

[0099]

[0100] where K is the Jacobian matrix of the robotic arm is the derivative of the angles of each part of the mobile redundant robotic arm t represents time;

[0101] Since the above problem is a time-varying quadratic programming problem, the Lagrangian function is constructed as follows:

[0102]

[0103] where λ(t) is the Lagrange multiplier, is the derivative of each variable of the robot, and K(t) is the Jacobian matrix of the manipulator. Taking the partial derivative of equation (10) gives:

[0104]

[0105] The system of equations (11) can be expressed as the following matrix equation:

[0106] A(t)y(t) = G(t) (12)

[0107] where,

[0108] To solve the matrix equation (12), an error function in the following form is defined to facilitate the subsequent construction and solution of the neural dynamics equation:

[0109]

[0110] As an embodiment, through the method of neural dynamics, the error converges to zero in the following manner:

[0111]

[0112] where η is a parameter for adjusting the convergence rate. Substituting equation (13) into equation (14) gives the variable-parameter convergence differential neural network solver, that is:

[0113]

[0114] where γ is a constant representing the convergence rate of the neural network, Φ(·) represents the activation function of the neural network, respectively represent the first-order derivatives of A(t), G(t), and y(t), and exp(·) represents the natural logarithm.

[0115] From equation (15), the optimal solution y of the matrix equation (12) can be obtained * , and its first n terms are the optimal solution of the quadratic programming (9), which is the optimal solution θ of the joint angles of the mobile redundant manipulator * , the optimal value α of the rotation angle of the mobile platform * and the optimal value ψ of the rotation angle of the Mecanum wheel * .

[0116] The effectiveness comparison of the solution of the present invention is as follows Figures 2 to 5 as shown Figure 2 , Figure 3 shows the comparison between the redundant manipulator adopting the solution of the present invention and the redundant manipulator not adopting the solution of the present invention in the repetitive motion task. It can be seen that after the manipulator adopting the solution of the present invention completes the task cycle, the posture of the end effector is consistent with the initial state, ensuring the precise execution of the task, while the manipulator not adopting this solution has an end posture deviation and cannot ensure repeatability. Figure 4 , Figure 5 shows the comparison between the redundant manipulator adopting the solution of the present invention and the redundant manipulator not adopting the solution in the obstacle avoidance task. In a complex environment, the manipulator adopting the solution of the present invention can successfully avoid obstacles and complete the task, while the manipulator not adopting this solution fails to avoid obstacles successfully, resulting in the failure of the task.

[0117] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principle and practical application of the present invention, so that those skilled in the art can well understand and utilize the present invention.

Claims

1. A mobile robot obstacle avoidance and repeated motion method based on a variable parameter dynamic learning network, characterized in that: The steps include: 1) Establish the robot inverse kinematics equation on the velocity layer through the terminal trajectory main task; 2) Establish the periodic repetitive motion constraints of the mobile redundant robot and introduce the equation obstacle avoidance constraints based on the critical distance; 3) The problem of comprehensive robot repetitive motion and obstacle avoidance is set as a dynamically weighted objective function, and the time-varying matrix equation of the objective function is solved through a variable parameter dynamic learning network; 4) The robot inverse kinematics equation of step 1) and the constraints of step 2) are set as a quadratic programming problem and converted into a time-varying matrix equation through Lagrangian function to solve the problem, and the optimal solution of the inverse kinematics problem of the mobile redundant manipulator is obtained, thereby controlling the movement of the mobile redundant manipulator.

2. The mobile robot obstacle avoidance and repeated motion method based on a variable parameter dynamic learning network according to claim 1, characterized in that: In step 1), the inverse kinematics equation of the robot is the kinematics equation of the mobile redundant manipulator: r=r p +τg(θ)=p(ψ,α,θ); Where r is the desired end trajectory of the robot arm, r p is the position vector of the mobile platform, g(·) is the nonlinear equation about the joint angle of the manipulator, τ represents the coordinate transformation matrix, ψ, α, θ represent the Mecanum wheel rotation angle of the mobile redundant manipulator, the rotation angle of the mobile platform and the joint angle value of the manipulator, respectively, and p(ψ, α, θ) represents the function of the Mecanum wheel rotation angle, the rotation angle of the mobile platform and the joint angle value of the manipulator. The inverse kinematics equation on the velocity layer is obtained by differentiating both sides of the kinematic equation of the mobile redundant manipulator, and the position feedback is added to obtain: Where K is the Jacobian matrix of the robot arm, and are the time derivatives of the angles of each part of the mobile redundant manipulator and the end trajectory, and ε represents the control factor, which is used to control the accuracy of position feedback.

3. The mobile robot obstacle avoidance and repeated motion method based on variable parameter dynamic learning network according to claim 1 is characterized in that: The periodic repetitive motion constraints of the mobile redundant robot in step 2) are: r p is the position vector of the mobile platform, α and θ represent the rotation angle of the mobile platform and the joint angle of the mobile redundant manipulator, respectively, and r p (0), α(0), and θ(0) represent their initial state values ​​respectively; also Represent the first-order derivatives of the robot arm joint angle, mobile platform position and rotation angle, ε θ , ε α Represent the control factors of each variable constraint, which are used to control the convergence rate; And further simplified into a matrix representation as, in is the derivative of the angle of each part of the mobile redundant manipulator, represents the square value of the second norm, J E , They represent the Jacobian matrix used to control the repetitive motion of the robot and the repetitive motion expressions of each variable: Among them, J M =[J(γ),-sinαJ T ] T , I is the identity matrix, J T is the Jacobian matrix of the mobile platform rotation angle, J(γ) is the Jacobian matrix of the mobile platform position, and γ is the linear velocity of the Mecanum wheel of the mobile platform; The constraint on the rotation angle is the constraint on the value of the cosine function: in ε α They represent the derivative of the mobile platform rotation angle and the convergence speed control factor respectively; α and α(0) represent the mobile platform rotation angle and its initial state value respectively; The equality obstacle avoidance constraint based on critical distance is: Among them, L represents the distance vector between the robot and the obstacle, ||·‖2 represents the vector norm, l1 is the critical distance value, and the control factor ε o and k are used to adjust the degree of obstacle avoidance; the simplified expression is: in is the derivative of the angle of each part of the mobile redundant manipulator, represents the square value of the second norm, J C , They represent the Jacobian matrix used to control the robot's obstacle avoidance and the repeated motion expressions of each variable: Among them, J F is the position derivative of the mobile platform.

4. The mobile robot obstacle avoidance and repeated motion method based on variable parameter dynamic learning network according to claim 1 is characterized in that: The dynamic weighted objective function in step 3) is the dynamic sum of obstacle avoidance and repeated motion constraints: in is the derivative of the angle of each part of the mobile redundant manipulator, J C , They represent the Jacobian matrix used to control the robot to avoid obstacles and the repeated motion expressions of each variable, J E , They represent the Jacobian matrix used to control the repetitive motion of the robot and the repetitive motion expression of each variable respectively. ξ is the dynamic weighting factor used to balance the weights of obstacle avoidance and repetitive motion. ζ is the control factor. The critical distance l2 is used to control the start of the obstacle avoidance task.

5. The mobile robot obstacle avoidance and repeated motion method based on variable parameter dynamic learning network according to claim 4 is characterized in that: The mathematical expression of the dynamic weighting factor ξ is: Where tanh(·) represents the hyperbolic tangent function, l2 represents the critical distance value at which the mobile redundant robot starts to avoid obstacles, ζ is the control factor, and L represents the distance vector between the robot and the obstacle.

6. The mobile robot obstacle avoidance and repeated motion method based on variable parameter dynamic learning network according to claim 1, characterized in that: In step 4), the optimization problem of the obstacle avoidance and repeated motion sub-problems in step 3) is expressed as a standard convex quadratic programming problem, namely: Constrained to And introduce the Lagrange multiplier λ to get the Lagrange function: in, is the derivative of the angle of each part of the mobile redundant manipulator, is the Lagrangian function, K(t) is the Jacobian matrix of the robot, λ(t) is the Lagrangian multiplier, Right now is the derivative of the angle of each part of the mobile redundant manipulator; Where t represents time, is the time derivative of the terminal trajectory, ε represents the control factor, ξ is the dynamic weighting factor used to balance the weights of obstacle avoidance and repeated motion, J C , They represent the Jacobian matrix used to control the robot to avoid obstacles and the repeated motion expressions of each variable, J E , Respectively represent the Jacobian matrix used to control the repetitive motion of the robot and the repetitive motion expression of each variable, ψ, α, θ represent the Mecanum wheel rotation angle, mobile platform rotation angle and robot arm joint angle value of the mobile redundant manipulator, r is the expected end trajectory of the manipulator, and p(ψ, α, θ) represents the function of the Mecanum wheel rotation angle, mobile platform rotation angle and robot arm joint angle value of the mobile redundant manipulator.

7. The mobile robot obstacle avoidance and repeated motion method based on a variable parameter dynamic learning network according to claim 6, characterized in that: In step 3), by setting the following two partial differential equations equal to 0: And further simplified to the following matrix equation: A(t)y(t)=g(t), where 8. The mobile robot obstacle avoidance and repeated motion method based on variable parameter dynamic learning network according to claim 7 is characterized in that: The matrix equation further transforms the matrix equation into an error function Its form is: Therefore, the problem can be further solved using a variable parameter dynamic learning network solver.

9. The mobile robot obstacle avoidance and repeated motion method based on a variable parameter dynamic learning network according to claim 8, characterized in that: In step 4), the variable parameter dynamic learning network solver is used to solve the optimal solution y of the matrix equation * That is, first construct the following neural dynamics equation: And further expanded to: Where t represents time, γ(t) is a constant representing the convergence rate of the neural network, exp(·) represents the natural logarithm, and Φ(·) represents the activation function of the neural network. They represent the first-order derivatives of y(t), A(t), and G(t) respectively, and then the optimal solution is obtained by solving the neurodynamic equation.

10. The mobile robot obstacle avoidance and repeated motion method based on variable parameter dynamic learning network according to claim 7, characterized in that: The optimal solution y obtained by the variable parameter dynamic learning network solver * , by y * The first n items of get the optimal solution of the quadratic programming problem, which is the optimal solution of the joint angle of the mobile redundant manipulator θ * , optimal value of mobile platform rotation angle α * And the optimal value of the Mecanum wheel rotation angle.

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