CN118596155A - A mobile redundant mechanical arm trajectory tracking control method and system - Google Patents

Abstract

The present application provides a trajectory tracking control method and system for a mobile redundant robotic arm, which relates to the field of redundant robotic arms. The method includes: designing a kinematic model of a mobile redundant robotic arm; designing a posture model prediction trajectory tracking control strategy based on the kinematic model; designing a finite-time convergence neural dynamics model, solving the posture model prediction trajectory tracking control strategy through the finite-time convergence neural dynamics model, obtaining the joint speed and joint angle values of the redundant robotic arm, and realizing finite-time control of the mobile redundant robotic arm. According to the established kinematic model, a posture model prediction trajectory tracking control strategy is designed and constructed, which introduces three-level joint constraints and considers the synchronous control of the position and posture of the end effector. The posture model prediction trajectory tracking control strategy is solved through the finite-time convergence neural dynamics model, thereby realizing finite-time control of the system.

Description

A mobile redundant mechanical arm trajectory tracking control method and system

Technical Field

The present application relates to the field of redundant robotic arms, and in particular to a trajectory tracking control method and system for a mobile redundant robotic arm.

Background Art

Over the past few decades, robots have been applied in various fields, such as factory workshops, service industries, and medical fields. Due to their mobility, agility, and flexibility, mobile redundant manipulators have played an increasingly important role in transportation, rescue, and military operations. Modern innovations in robotics and control theory, coupled with increasingly powerful computer systems, have prompted the academic community to shift its research focus to mobile manipulators. Industrial robots are used to perform various tasks, such as moving, assembling, and transporting objects. Most industrial redundant manipulators have redundant joints because the additional degrees of freedom can meet additional design goals, such as obstacle avoidance, joint angle constraints, and torque minimization. Mobile redundant manipulators consist of a mobile base and redundant manipulators, combining the advantages of both and being able to work in more complex environments. Among them, trajectory tracking control is an important control direction for mobile redundant manipulators, and many researchers have conducted extensive research in these areas. Therefore, studying the trajectory tracking control scheme of mobile redundant manipulators is not only of great theoretical significance, but also of great engineering application value.

For mobile redundant manipulator systems, the flexible operation of redundant manipulators is crucial, so the synchronous tracking of the position and posture of the end effector is particularly important. There are various trajectory tracking schemes for redundant manipulators. Some scholars have proposed a synchronous repetitive motion planning and control scheme at the joint acceleration level, which solves the joint angle drift phenomenon that occurs in the trajectory tracking process of two redundant manipulators, and proves the effectiveness and accuracy of the scheme through position and velocity error feedback. In addition to simultaneously tracking the position and posture of the end effector, redundant manipulators must also ensure operational safety when performing dexterous tasks. Therefore, it is necessary to incorporate the joint constraints of joint angle, joint velocity and joint acceleration into the control scheme. However, most trajectory tracking schemes for redundant manipulators, such as the commonly used minimum velocity norm (MVN) method and minimum acceleration norm (MAN) method, have limitations in handling multi-level joint constraints. MVN and MAN can handle different levels of joint constraints through conversion technology. However, the former can only introduce joint angle and joint velocity constraints at the velocity level, while the latter can introduce three-level joint constraints (position, velocity and acceleration) at the acceleration level, and the existing constraint conversion technology may narrow the feasible domain of decision variables and affect the flexibility of the system.

In addition, the interference caused by the motion of the mobile base is a factor that needs to be considered. Some scholars have studied the modeling and control of the aerostat manipulator. The simulation results show that if the motion of the aircraft is not taken into account, the end effector cannot fully track the trajectory. Model predictive control (MPC) is a powerful tool for dealing with system uncertainty and interference. It can predict the future state of the system based on the model, thereby compensating for the interference caused by the motion of the mobile base. However, given the rolling optimization characteristics of MPC, it has some disadvantages, such as increased computational complexity and the existence of local optimal solutions. Therefore, it is crucial to solve the optimization problem of the robot efficiently and accurately. Neural dynamics (ND) is effective in solving robot optimization problems. Some scholars have proposed a force-position control method for robot manipulators based on projected recursive neural networks, which successfully converted the force control in the neural network framework into a force-position control method.

Through the above analysis, the research on trajectory tracking control of mobile redundant manipulator system still faces many challenges. First, how to not reduce the feasible domain of decision variables when introducing triple joint constraints is a problem that needs to be solved. Secondly, for mobile redundant manipulators, how to achieve synchronous control of the end effector position and posture is a problem that needs to be solved. Finally, how to achieve finite time control of mobile redundant manipulators is also a problem that needs to be solved.

Summary of the invention

The purpose of the present invention is to provide a trajectory tracking control method and system for a mobile redundant robotic arm in order to solve the problem that the end effector position and posture are difficult to be synchronously controlled in the existing mobile redundant robotic arm system, and the constraint transformation technology will reduce the feasible domain of decision variables.

The above-mentioned purpose of the present application is achieved through the following technical solutions:

S1: Design the kinematic model of the mobile redundant manipulator;

S2: Based on the kinematic model, design a posture model prediction trajectory tracking control strategy;

S3: Design a finite-time convergence neural dynamics model, solve the posture model through the finite-time convergence neural dynamics model to predict the trajectory tracking control strategy, obtain the joint speed and joint angle values of the redundant robotic arm, and realize the finite-time control of the mobile redundant robotic arm.

Optionally, step S1 includes:

The mobile redundant robotic arm system comprises: a mobile base and a redundant robotic arm; mathematical modeling is performed on the mobile base and the redundant robotic arm;

make represents the coordinates of the end effector of the redundant manipulator, where and They represent the position and attitude relative to the inertial reference system, respectively. The attitude is expressed in Euler angles. represents the coordinates of the end effector in the three-dimensional coordinate system, Represents the rotation vector around the X, Y, and Z axes;

The state variables of the mobile redundant manipulator system are defined as ,in Contains the location of the mobile base and posture ,and represents the joint angle vector of the redundant manipulator, represents the field of real numbers; it has the following formula:

(1)

in, represents the velocity of the mobile base in the fixed coordinate system, and represents the Jacobian matrix of the moving base; Indicates the linear speed of the base;

The generalized velocity of the end effector is defined as ,in and represent the linear velocity and angular velocity of the end effector, respectively;

The position and orientation of the end effector relative to the inertial reference frame are determined by the forward kinematics of the entire mobile redundant manipulator system and are expressed as:

(2)

in, represents the positive kinematic function;

For the entire mobile redundant robotic arm system, there are:

(3)

in, represents the speed of the mobile base and the joint speed of the redundant robot, and is the geometric Jacobian matrix; Indicates the speed of the moving base; Indicates the joint velocity of the redundant robot arm.

Optionally, the posture model prediction trajectory tracking control strategy is as follows:

(4)

in, Indicate desired position and posture; represents the positive kinematic function; represents the joint angle of the mobile redundant manipulator at the i-th moment; represents the joint angular velocity of the mobile redundant manipulator at the i-th moment; represents the joint angular acceleration of the mobile redundant manipulator at the i-th moment; is the matrix The weighted norm, is the weight matrix of the tracking error, is the weight matrix of joint velocities, is the weight matrix of joint acceleration increments, represents the increment of joint velocity, represents the number of joints in the robot, represents the prediction space, represents the forecast control interval; , , denote the minimum constraints on joint angle, velocity and acceleration respectively, and , , is the corresponding maximum constraint.

Optionally, the steps of solving the posture model prediction trajectory tracking control strategy include:

Construct the following matrix to simplify formula (4):

in, Indicates the sampling time; Indicates the position and posture of the end effector of the mobile redundant robot arm at the current moment; Indicates the angular velocity of the mobile redundant manipulator at the last moment; Indicates the joint angle of the mobile redundant robot arm at the current moment; Indicates The joint angular acceleration of the system at each moment; Indicates The joint angular velocity of the system at all times; Indicates the position and posture of the end effector of the robot arm at the Nth moment; represents the expected position and posture of the end effector of the robot at the Nth moment; Represents the desired position and posture of the robot end effector;

The design formula is as follows:

in , ; ; , ; ; represents the identity matrix; Indicates vectorized operation on variables;

By omitting The irrelevant constant term is used to simplify the cost function (4) and transform it into the OP optimization problem as follows:

(7)

in , express The transpose of and ,have:

exist At this moment, the first element in the solution of equation (7) Used to calculate joint velocity delta.

Optionally, the step of solving the posture model prediction trajectory tracking control strategy also includes:

Design a slack variable , , and introduce a penalty factor to transform the OP optimization problem (7) into an unconstrained OP optimization problem containing slack variables, the formula is as follows:

(8)

in is a penalty factor; is the expression of the Euler-Lagrange equation.

Optionally, the step of solving the posture model prediction trajectory tracking control strategy also includes:

Formula (8) is a convex optimization OP optimization problem, so there must be a solution that satisfies the following conditions:

(9)

in and is the global optimal solution; represents a global optimal solution; represents the gradient operator of the Euler-Lagrange equation L on the direction variable z; It represents the Euler-Lagrange equation L in the direction variable Gradient operator on ;

Define the function:

have:

, ,

when When it approaches zero, the solution of equation (10) is obtained;

The error function is made by using the neural dynamics formula with activation function Approaches zero, as follows:

in represents the rate of change of the error function; is an indicator related to the convergence speed, and is an odd function and monotonically increasing The activation function composed of It is expressed as:

in express No. elements, is a custom parameter. and are all positive numbers, and we have:

in express The kth power of the absolute value;

Therefore, the solution formula of formula (10) is as follows:

According to formula (11), we can get time The solution to obtain The value of The first element in Used to update the joint velocity and determine the joint angle value at the next moment.

A mobile redundant mechanical arm trajectory tracking control system, the system comprising: a computer, a mobile base, a redundant mechanical arm, and a display screen;

The mobile base, redundant mechanical arms and display screen are all connected to a computer;

The computer is used to obtain the operation data of the mobile base and the redundant mechanical arm;

The computer is also used to design a kinematic model for a mobile redundant robotic arm;

The computer is also used to design a posture model prediction trajectory tracking control strategy based on a kinematic model;

The computer is also used to design a finite-time convergent neural dynamics model;

The computer is also used to solve the posture model prediction trajectory tracking control strategy through the finite time convergence neural dynamics model and operation data, and obtain the joint speed and joint angle values of the redundant manipulator;

The computer is also used to realize limited time control of the mobile redundant manipulator through joint speed and joint angle values;

The display screen is used for visually displaying the three-dimensional state model of the mobile redundant mechanical arm in real time.

A computer-readable storage medium stores instructions. When the instructions are executed, a mobile redundant manipulator trajectory tracking control method is executed.

The beneficial effects of the technical solution provided by this application are:

Considering the trajectory tracking control of the redundant manipulator in the mobile redundant manipulator, the mobile base is independently controlled, and the movement of the mobile base is regarded as a disturbance to the redundant manipulator system. The posture model predicts the trajectory tracking control strategy, which takes into account the three-level constraints of the position and posture of the end effector, the joint velocity and the joint acceleration, and can realize the synchronous control of the position and posture of the end effector. The designed finite-time convergence neural dynamics model can converge within a finite time, so as to obtain the solution of the posture model predictive trajectory tracking control strategy and realize the finite-time control of the mobile redundant manipulator. The technical solution of the present application can not only realize the synchronous trajectory tracking control of the position and posture of the mobile redundant manipulator, but also can simultaneously handle the three-level joint constraints of the redundant manipulator and realize the finite-time control of the system.

BRIEF DESCRIPTION OF THE DRAWINGS

The present application will be further described below with reference to the accompanying drawings and embodiments, in which:

FIG1 is a step diagram of a trajectory tracking control method for a mobile redundant robotic arm in an embodiment of the present application;

FIG2 is a kinematic analysis diagram of a mobile redundant mechanical arm in a mobile redundant mechanical arm trajectory tracking control method in an embodiment of the present application;

3 is a diagram of the tracking trajectory of a mobile redundant mechanical arm in a mobile redundant mechanical arm trajectory tracking control method in an embodiment of the present application;

FIG4 is a diagram of a three-dimensional desired trajectory and an actual trajectory of a mobile redundant manipulator trajectory tracking control method according to an embodiment of the present application;

5 is a two-dimensional diagram of actual trajectory and expected trajectory of the mobile redundant manipulator trajectory tracking control method in an embodiment of the present application;

6 is a position error diagram of the end effector of the mobile redundant manipulator trajectory tracking control method in an embodiment of the present application;

7 is a diagram of joint angles of a robot arm in a mobile redundant robot arm trajectory tracking control method according to an embodiment of the present application;

8 is a diagram of joint speeds of a robot arm in a mobile redundant robot arm trajectory tracking control method according to an embodiment of the present application;

9 is a joint torque diagram of the trajectory tracking control method of the mobile redundant manipulator in an embodiment of the present application;

10 is a rotation vector diagram of actual and desired postures of a mobile redundant manipulator trajectory tracking control method according to an embodiment of the present application;

11 is a rotation vector error diagram of the posture of the mobile redundant manipulator trajectory tracking control method in an embodiment of the present application;

12 is a diagram showing a position error of the end effector in the X direction of the mobile redundant manipulator trajectory tracking control method according to an embodiment of the present application;

13 is a diagram showing a position error of the end effector in the Y direction of the mobile redundant manipulator trajectory tracking control method according to an embodiment of the present application;

14 is a diagram showing a position error of the end effector in the Z direction of the mobile redundant manipulator trajectory tracking control method according to an embodiment of the present application;

15 is a diagram of a rotation vector error around the X-axis of the end effector of the mobile redundant manipulator trajectory tracking control method in an embodiment of the present application;

16 is a diagram of a rotation vector error around the Y axis of the end effector of the mobile redundant manipulator trajectory tracking control method in an embodiment of the present application;

FIG. 17 is a diagram of the rotation vector error around the Z-axis of the end effector of the mobile redundant robot arm trajectory tracking control method in an embodiment of the present application.

DETAILED DESCRIPTION

In order to have a clearer understanding of the technical features, purposes and effects of the present application, the specific implementation methods of the present application are now described in detail with reference to the accompanying drawings.

An embodiment of the present application provides a trajectory tracking control method for a mobile redundant robotic arm.

Please refer to FIG. 1 , which is a step diagram of a mobile redundant robot arm trajectory tracking control method in an embodiment of the present application, including:

S1: Design the kinematic model of the mobile redundant manipulator;

Step S1 includes:

The mobile redundant robotic arm system comprises: a mobile base and a redundant robotic arm; mathematical modeling is performed on the mobile base and the redundant robotic arm;

make represents the coordinates of the end effector of the redundant manipulator, where and They represent the position and attitude relative to the inertial reference system, respectively. The attitude is expressed in Euler angles. represents the coordinates of the end effector in the three-dimensional coordinate system, Represents the rotation vector around the X, Y, and Z axes;

The state variables of the mobile redundant manipulator system are defined as ,in Contains the location of the mobile base and posture ,and represents the joint angle vector of the redundant manipulator, represents the field of real numbers; it has the following formula:

(1)

in, represents the velocity of the mobile base in the fixed coordinate system, and represents the Jacobian matrix of the moving base; Indicates the linear speed of the base;

The generalized velocity of the end effector is defined as ,in and represent the linear velocity and angular velocity of the end effector, respectively;

The position and orientation of the end effector relative to the inertial reference frame are determined by the forward kinematics of the entire mobile redundant manipulator system and are expressed as:

(2)

in, represents the positive kinematic function;

For the entire mobile redundant robotic arm system, there are:

(3)

in, represents the speed of the mobile base and the joint speed of the redundant robot, and is the geometric Jacobian matrix; Indicates the speed of the moving base; Indicates the joint velocity of the redundant robot arm.

Specifically, the mobile redundant robotic arm is explained as a combination of a mobile base and a redundant robotic arm. As shown in FIG2 , in order to analyze the structure of the mobile redundant robotic arm, mathematical models are respectively performed on the mobile base and the redundant robotic arm.

S2: Based on the kinematic model, design a posture model prediction trajectory tracking control strategy;

The posture model predicts the trajectory tracking control strategy as follows:

(4)

in, Indicate desired position and posture; represents the positive kinematic function; represents the joint angle of the mobile redundant manipulator at the i-th moment; represents the joint angular velocity of the mobile redundant manipulator at the i-th moment; represents the joint angular acceleration of the mobile redundant manipulator at the i-th moment; is the matrix The weighted norm, is the weight matrix of the tracking error, is the weight matrix of joint velocities, is the weight matrix of joint acceleration increments, represents the increment of joint velocity, represents the number of joints in the robot, represents the prediction space, represents the forecast control interval; , , denote the minimum constraints on joint angle, velocity and acceleration respectively, and , , is the corresponding maximum constraint.

S3: Design a finite-time convergence neural dynamics model, solve the posture model prediction trajectory tracking control strategy through the finite-time convergence neural dynamics model, obtain the joint speed and joint angle values of the redundant robotic arm, and realize the finite-time control of the mobile redundant robotic arm.

The steps of solving the posture model prediction trajectory tracking control strategy include:

Construct the following matrix to simplify formula (4):

in, Indicates the sampling time; Indicates the position and posture of the end effector of the mobile redundant robot arm at the current moment; Indicates the angular velocity of the mobile redundant manipulator at the last moment; Indicates the joint angle of the mobile redundant robot arm at the current moment; Indicates The joint angular acceleration of the system at each moment; Indicates The joint angular velocity of the system at all times; Indicates the position and posture of the end effector of the robot arm at the Nth moment; represents the expected position and posture of the end effector of the robot at the Nth moment; Represents the desired position and posture of the robot end effector;

The design formula is as follows:

in , ; ; , ; ; represents the identity matrix; Indicates vectorized operation on variables;

By omitting The irrelevant constant term is used to simplify the cost function (4) and transform it into the OP optimization problem as follows:

(7)

in , express The transpose of and ,have:

exist At this moment, the first element in the solution of equation (7) Used to calculate joint velocity delta.

The step of solving the posture model prediction trajectory tracking control strategy also includes:

Design a slack variable , , and introduce a penalty factor to transform the OP optimization problem (7) into an unconstrained OP optimization problem containing slack variables, the formula is as follows:

(8)

in is a penalty factor; is the expression of the Euler-Lagrange equation.

The step of solving the posture model prediction trajectory tracking control strategy also includes:

Formula (8) is a convex optimization OP optimization problem, so there must be a solution that satisfies the following conditions:

(9)

in and is the global optimal solution; represents a global optimal solution; represents the gradient operator of the Euler-Lagrange equation L on the direction variable z; It represents the Euler-Lagrange equation L in the direction variable Gradient operator on ;

Define the function:

have:

, ,

when When it approaches zero, the solution of equation (10) is obtained;

The error function is made by using the neural dynamics formula with activation function Approaches zero, as follows:

in represents the rate of change of the error function; is an indicator related to the convergence speed, and is an odd function and monotonically increasing The activation function composed of It is expressed as:

in express No. elements, is a custom parameter. and are all positive numbers, and we have:

in express The kth power of the absolute value;

Therefore, the solution formula of formula (10) is as follows:

According to formula (11), we can get time The solution to obtain The value of The first element in Used to update the joint velocity and determine the joint angle value at the next moment.

A mobile redundant mechanical arm trajectory tracking control system, the system comprising: a computer, a mobile base, a redundant mechanical arm, and a display screen;

The mobile base, redundant mechanical arms and display screen are all connected to a computer;

The computer is used to obtain the operation data of the mobile base and the redundant mechanical arm;

The computer is also used to design a kinematic model for a mobile redundant robotic arm;

The computer is also used to design a posture model prediction trajectory tracking control strategy based on a kinematic model;

The computer is also used to design a finite-time convergent neural dynamics model;

The computer is also used to solve the posture model prediction trajectory tracking control strategy through the finite time convergence neural dynamics model and operation data, and obtain the joint speed and joint angle values of the redundant manipulator;

The computer is also used to realize limited time control of the mobile redundant manipulator through joint speed and joint angle values;

The display screen is used for visually displaying the three-dimensional state model of the mobile redundant mechanical arm in real time.

To verify the effectiveness of the proposed method, a base with six degrees of freedom and a redundant manipulator with seven degrees of freedom are combined into a mobile redundant manipulator system in a simulation environment. The specific experimental process includes: when the base moves, the redundant manipulator end effector needs to track a circular trajectory in a fixed coordinate system. Figure 3 shows the mobile redundant manipulator tracking a circular trajectory.

In the simulation, the parameters related to POMPTC and finite-time convergent neural dynamics are set as follows: , , s, , , , , , , , , The initial joint angle is set to rad.

Figures 4-11 are the simulation results of trajectory tracking control of mobile redundant manipulators. Figure 4 shows the three-dimensional desired trajectory and actual trajectory. Figure 5 shows the two-dimensional actual trajectory and desired trajectory. Figure 6 shows the position error of the end effector. Figure 7 shows the joint angle of the manipulator. Figure 8 shows the joint velocity of the manipulator. Figure 9 shows the joint torque. Figure 10 shows the rotation vector of the actual and desired posture. Figure 11 shows the rotation vector error of the posture.

Simulation results of trajectory tracking of mobile redundant manipulator based on trajectory tracking control strategy predicted by posture model. It can be seen from the figure that the position and direction tracking errors converge quickly to within 0.01 meters and 0.01 radians respectively, and all joint angles, velocities and torques (and accelerations that can be regarded as accelerations through conversion) are kept within the limit range. Therefore, the proposed method is effective and has high control accuracy.

To further verify the superiority of the proposed method, a comparative experiment was conducted between the proposed method and the PD method. The specific experimental process is as follows: based on the two control methods, the mobile redundant robot end effector tracks a circular trajectory, and then the control effects of the two methods are compared to analyze their errors in position and attitude.

As shown in Figures 12 to 17, the experimental results of the proposed method and PD control are compared, where the blue dotted line represents the proposed method and the red solid line represents the PD method. Figures 12, 13, and 14 represent the position errors of the end effector in the X, Y, and Z directions, respectively, and Figures 15, 16, and 17 represent the rotation vector errors of the end effector, respectively. It can be seen that the highest errors of the proposed method are all smaller than the highest errors of the PD method. Therefore, the method proposed in this paper is superior to the PD control method and has certain advantages.

The present application also discloses a computer-readable storage medium, which stores a plurality of instructions, and the instructions are suitable for a processor to load to execute the above-mentioned mobile redundant robot arm trajectory tracking control method.

The above are only exemplary embodiments of the present disclosure and cannot be used to limit the scope of the present disclosure. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the disclosure of the specification and the truth of practice, those skilled in the art will easily think of other embodiments of the present disclosure.

This application is intended to cover any variation, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the art not described in the present disclosure. The description and examples are to be regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

Claims (8)

1. A mobile redundant robot arm trajectory tracking control method, characterized in that the method comprises the following steps: S1: Design the kinematic model of the mobile redundant manipulator; S2: Based on the kinematic model, design a posture model prediction trajectory tracking control strategy; S3: Design a finite-time convergence neural dynamics model, solve the posture model prediction trajectory tracking control strategy through the finite-time convergence neural dynamics model, obtain the joint speed and joint angle values of the redundant robotic arm, and realize the finite-time control of the mobile redundant robotic arm. 2. A mobile redundant robot arm trajectory tracking control method as claimed in claim 1, characterized in that step S1 comprises: The mobile redundant robotic arm system comprises: a mobile base and a redundant robotic arm; mathematical modeling is performed on the mobile base and the redundant robotic arm; make represents the coordinates of the end effector of the redundant manipulator, where and They represent the position and attitude relative to the inertial reference system, respectively. The attitude is expressed in Euler angles. represents the coordinates of the end effector in the three-dimensional coordinate system, Represents the rotation vector around the X, Y, and Z axes; The state variables of the mobile redundant manipulator system are defined as ,in Contains the location of the mobile base and posture ,and represents the joint angle vector of the redundant manipulator, represents the field of real numbers; it has the following formula: (1) in, represents the velocity of the mobile base in the fixed coordinate system, and represents the Jacobian matrix of the moving base; Indicates the linear speed of the base; The generalized velocity of the end effector is defined as ,in and represent the linear velocity and angular velocity of the end effector, respectively; The position and orientation of the end effector relative to the inertial reference frame are determined by the forward kinematics of the entire mobile redundant manipulator system and are expressed as: (2) in, represents the positive kinematic function; For the entire mobile redundant robotic arm system, there are: (3) in, represents the speed of the mobile base and the joint speed of the redundant robot, and is the geometric Jacobian matrix; Indicates the speed of the moving base; Indicates the joint velocity of the redundant robot arm. 3. A mobile redundant manipulator trajectory tracking control method according to claim 2, characterized in that the posture model predicts the trajectory tracking control strategy as follows: (4) in, Indicate desired position and posture; represents the positive kinematic function; represents the joint angle of the mobile redundant manipulator at the i-th moment; represents the joint angular velocity of the mobile redundant manipulator at the i-th moment; represents the joint angular acceleration of the mobile redundant manipulator at the i-th moment; is the matrix The weighted norm, is the weight matrix of the tracking error, is the weight matrix of joint velocities, is the weight matrix of joint acceleration increments, represents the increment of joint velocity, represents the number of joints in the robot, represents the prediction space, represents the forecast control interval; , , denote the minimum constraints on joint angle, velocity and acceleration respectively, and , , is the corresponding maximum constraint. 4. A mobile redundant manipulator trajectory tracking control method according to claim 3, characterized in that the step of solving the posture model prediction trajectory tracking control strategy comprises: Construct the following matrix to simplify formula (4): in, Indicates the sampling time; Indicates the position and posture of the end effector of the mobile redundant robot arm at the current moment; Indicates the angular velocity of the mobile redundant manipulator at the last moment; Indicates the joint angle of the mobile redundant robot arm at the current moment; Indicates The joint angular acceleration of the system at each moment; Indicates The joint angular velocity of the system at all times; Indicates the position and posture of the end effector of the robot arm at the Nth moment; represents the expected position and posture of the end effector of the robot at the Nth moment; Represents the desired position and posture of the robot end effector; The design formula is as follows: in , ; ; , ; ; represents the identity matrix; Indicates vectorized operation on variables; By omitting The irrelevant constant term is used to simplify the cost function (4) and transform it into the OP optimization problem as follows: (7) in , express The transpose of and ,have: exist At this moment, the first element in the solution of equation (7) Used to calculate joint velocity delta. 5. A mobile redundant manipulator trajectory tracking control method according to claim 4, characterized in that the step of solving the posture model prediction trajectory tracking control strategy further comprises: Design a slack variable , , and introduce a penalty factor to transform the OP optimization problem (7) into an unconstrained OP optimization problem containing slack variables, the formula is as follows: (8) in is a penalty factor; is the expression of the Euler-Lagrange equation. 6. A mobile redundant manipulator trajectory tracking control method according to claim 5, characterized in that the step of solving the posture model prediction trajectory tracking control strategy further comprises: Formula (8) is a convex optimization OP optimization problem, so there must be a solution that satisfies the following conditions: (9) in and is the global optimal solution; represents a global optimal solution; represents the gradient operator of the Euler-Lagrange equation L on the direction variable z; It represents the Euler-Lagrange equation L in the direction variable Gradient operator on ; Define the function: have: , , when When it approaches zero, the solution of equation (10) is obtained; The error function is made by using the neural dynamics formula with activation function Approaches zero, as follows: in represents the rate of change of the error function; is an indicator related to the convergence speed, and is an odd function and monotonically increasing The activation function composed of It is expressed as: in express No. elements, is a custom parameter. and are all positive numbers, and we have: in express The kth power of the absolute value; Therefore, the solution formula of formula (10) is as follows: According to formula (11), we can get time The solution to obtain The value of The first element in Used to update the joint velocity and determine the joint angle value at the next moment. 7. A mobile redundant robotic arm trajectory tracking control system, used to implement a mobile redundant robotic arm trajectory tracking control method as described in claims 1-6, characterized in that the system comprises: a computer, a mobile base, a redundant robotic arm, and a display screen; The mobile base, redundant mechanical arms and display screen are all connected to a computer; The computer is used to obtain the operation data of the mobile base and the redundant mechanical arm; The computer is also used to design a kinematic model for a mobile redundant robotic arm; The computer is also used to design a posture model prediction trajectory tracking control strategy based on a kinematic model; The computer is also used to design a finite-time convergent neural dynamics model; The computer is also used to solve the posture model prediction trajectory tracking control strategy through the finite time convergence neural dynamics model and operation data, and obtain the joint speed and joint angle values of the redundant manipulator; The computer is also used to realize limited time control of the mobile redundant manipulator through joint speed and joint angle values; The display screen is used for visually displaying the three-dimensional state model of the mobile redundant mechanical arm in real time. 8. A computer-readable storage medium, characterized in that the computer-readable storage medium stores instructions, and when the instructions are executed by a computer, the method according to any one of claims 1 to 6 is executed.