A motion control optimization method for a rehabilitation walking wheelchair

Abstract

A rehabilitation walking wheelchair motion control optimization method proposed in the present invention belongs to the field of PID control optimization, and the specific steps are: step one: converting the rehabilitation walking wheelchair motion control problem into a mathematical model to be optimized; step two: establishing a PID control model of the rehabilitation walking wheelchair motion control system; step three: establishing an improved gradient algorithm-based mathematical model to verify the performance of the improved gradient algorithm-based PID controller; the improved gradient algorithm includes: D1, using chaotic mapping to initialize the population position; D2, introducing Gaussian mutation strategy to improve the population position update formula; step four: using the improved gradient algorithm-based optimization rehabilitation walking wheelchair speed PID controller to obtain the optimal control parameters Kp, Ki, Kd; step five: inputting the obtained optimal control parameters into the PID control model of the rehabilitation walking wheelchair motion control system to achieve optimal robust control of the rehabilitation walking wheelchair.

Description

Technical Field

[0001] The invention belongs to the field of PID control optimization, and in particular relates to a method for optimizing motion control of a rehabilitation walking-assisting wheelchair. Background Art

[0002] The rehabilitation walking wheelchair is an assistive device designed for elderly people with limited mobility, disabled people and patients in rehabilitation. With the aging of the population and the increase in chronic diseases, many people need long-term rehabilitation care and walking assistance. Although traditional wheelchairs provide mobility support, they cannot effectively help users with gait training and rehabilitation. The rehabilitation walking wheelchair fills this gap by combining wheelchairs and walking assistance functions. It not only provides mobility convenience, but also provides effective support during the rehabilitation process. With the advancement of modern technology, the intelligent control system monitors the user's status and environmental changes in real time, making the rehabilitation walking wheelchair more intelligent and adaptable, and can make real-time adjustments according to the user's needs to promote rehabilitation effects. The rehabilitation walking wheelchair helps users gradually restore their walking ability through the built-in walking assistance function, enabling them to carry out daily activities independently, reduce their dependence on others, significantly improve the user's independence, and promote the rehabilitation process. These advantages make the rehabilitation walking wheelchair an important tool for improving the quality of life and rehabilitation effects.

[0003] The PID control method is usually used for the motion control of rehabilitation wheelchairs. The motor is controlled by PID, and then the motor drives the wheelchair wheels to rotate, thus realizing the speed control of the rehabilitation wheelchair. PID control is a control algorithm widely used in control systems. Its control performance is highly dependent on the setting of parameters (proportional, integral, differential). Inappropriate parameter settings may lead to over-adjustment or under-adjustment, affecting the control effect. Secondly, PID control assumes that the system model is linear, but the actual response of people with walking disabilities to rehabilitation wheelchairs is often nonlinear, which leads to the control system being unable to accurately adapt to the actual needs of users in some cases.

[0004] Gradient-Based Optimizer (GBO) is a new meta-heuristic optimization algorithm that uses Newton's method to determine the search direction to explore the search domain and update the location of the solution in the search domain based on the gradient information. Gradient-Based Optimizer relies on parameter settings to a certain extent and lacks differentiated treatment of individual exploration and utilization behaviors, which can easily lead to local optimal traps and premature convergence in the search process. Summary of the invention

[0005] The purpose of the present invention is to solve the problems of low performance and difficult parameter adjustment brought about by the traditional PID control of the rehabilitation walking wheelchair motion control, and to improve the performance and robustness of the rehabilitation walking wheelchair motion control system by improving the control parameters Kp, Ki, and Kd of the rehabilitation walking wheelchair speed PID controller based on the gradient algorithm.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for optimizing the motion control of a rehabilitation walking wheelchair, comprising the following specific steps:

[0008] Step 1: Convert the rehabilitation wheelchair motion control problem into a mathematical model to be optimized.

[0009] Step 2: Establish the PID control model of the rehabilitation wheelchair motion control system.

[0010] Step 3: Use Matlab software to establish an improved mathematical model based on the gradient algorithm to verify the performance of the improved gradient algorithm to optimize the PID controller; the improved gradient algorithm includes:

[0011] D1, using chaotic mapping to initialize population positions;

[0012] D2. During the algorithm development phase, the Gaussian mutation strategy is introduced to improve the population position update formula; the details are as follows.

[0013] Step 1: In the initialization stage of the algorithm, the chaotic map is used to initialize the population position. The improved formula for initializing the population position is:

[0014] (2);

[0015] (3);

[0016] In the formula, is the initial position of the nth individual in the population, Search for a lower bound for the algorithm, To search for the upper bound of the algorithm, rand(0,1) is a random number between 0 and 1. is the i-th variable value of the generated chaotic sequence, is the i+1th variable value of the generated chaotic sequence, and a is the chaotic factor;

[0017] Step 2. In the algorithm development stage, the Gaussian mutation strategy is introduced to improve the population position update formula: when rand(0,1)<0.5, execute equations (6)-(8) and (4); when rand(0,1) is other values, execute equations (6)-(8) and (5);

[0018] (4);

[0019] (5);

[0020] (6);

[0021] (7);

[0022] (8);

[0023] In the formula, is the new position of the nth population individual in the next iteration, is the current iteration position of the nth population individual, is a random number between -1 and 1. is a parameter that controls the decay speed of the standard deviation, m is the current iteration number, u1, u2 and u3 are all random numbers between 0 and 1, is the best individual position of the population in the current iteration, and and are the current positions of random individuals in the population, is a random number from a normal distribution with mean 0 and standard deviation 1. is the balance factor, and are all positions created at random points under the current gradient, is the sine function parameter, To adjust the parameters of the search process, and The values ​​are 1.2 and 0.2 respectively, M is the maximum number of iterations, and the meanings of other parameters are the same as in Step 1.

[0024] Step 4: Use the improved gradient-based algorithm to optimize the rehabilitation wheelchair speed PID controller and obtain the optimal control parameters Kp, Ki, and Kd.

[0025] Step 5: Input the obtained optimal control parameters Kp, Ki, and Kd into the PID control model of the rehabilitation walking wheelchair motion control system to obtain the optimal effect of PID control of the rehabilitation walking wheelchair motion control system.

[0026] Furthermore, in step 1, the mathematical model to be optimized is:

[0027] (1);

[0028] In the formula, J is the fitness value, T is the total control time, t is the tth second control time, is the expected speed value in the motion control system of the rehabilitation wheelchair, is the actual speed value at the tth second in the rehabilitation wheelchair motion control system, is the weight coefficient.

[0029] Furthermore, the mathematical model formula to be optimized uses the square error function. The square error function is more sensitive to larger errors by squaring the errors, which makes it prioritize reducing larger prediction errors during the optimization process, helping to improve the accuracy of the algorithm.

[0030] Furthermore, in the step 2, a PID control model of the rehabilitation walking wheelchair motion control system is established, and the model includes an input module, an error calculation module, an improved gradient algorithm module, a speed PID controller module, a speed detection module, a motor module, and a wheelchair wheel module; the expected speed value is input from the input module, and is input into the error calculation module together with the actual speed value detected by the speed detection module to obtain a speed error value by subtraction; the speed PID controller module receives the speed error value, and uses the PID parameters optimized by the improved gradient algorithm module to calculate and obtain a reference speed value, thereby controlling the motor to drive the wheelchair wheels to rotate, thereby realizing the control of the speed of the rehabilitation walking wheelchair.

[0031] Furthermore, in the step 3, in the algorithm initialization phase, the chaotic map is used to initialize the population position. The sequence generated by the chaotic map usually has good randomness and complexity, which can effectively maintain the diversity of the population. In addition, the chaotic map has initial value sensitivity and ergodicity, which makes the initial population more evenly distributed in the search space and covers the entire search space. This helps to avoid the algorithm from falling into a local optimal solution and enhances the global search capability.

[0032] Furthermore, in step 3, the Gaussian mutation strategy is introduced in the algorithm development phase to improve the population position update formula. Gaussian mutation can introduce small random perturbations in the local area of ​​the solution, which helps to refine the search, further explore the neighborhood of the current solution, and increase the possibility of finding a better solution. In addition, by introducing Gaussian mutation, the population can be prevented from converging to the local optimal solution too early, maintaining the diversity of the population.

[0033] Furthermore, in step 4, the improved gradient-based algorithm is used to optimize the rehabilitation walking wheelchair speed PID controller, and the specific steps are:

[0034] S1. The mathematical model of the rehabilitation wheelchair motion control system is used as the objective function of the improved gradient-based algorithm, wherein the objective function is used as the fitness function;

[0035] S2. Simulate the working conditions of the rehabilitation wheelchair motion control system and design transfer functions to describe the dynamic characteristics of the system;

[0036] S3, giving an input of a rehabilitation walking wheelchair motion control system, the input being a desired speed value of the wheelchair wheels in the control system;

[0037] S4, Initialization Improvement Gradient-based Algorithm Population Size np, Problem Dimension d, Algorithm Search Upper Bound , algorithm searches for lower bounds , maximum number of iterations M;

[0038] S5, encoding the rehabilitation wheelchair speed PID controller parameters Kp, Ki, Kd as a solution based on the gradient algorithm search space, and as the algorithm iterates, the position of the algorithm population individual is the solution of the rehabilitation wheelchair speed PID controller parameters;

[0039] S6. Calculate the individual fitness values ​​of the current iteration population according to the fitness function, record the minimum fitness value, and compare it with the optimal fitness value of the population in the previous iteration, and retain the optimal fitness value;

[0040] S7, establishing an improved mathematical model of position update strategy based on gradient algorithm, and using the mathematical model to update the position of individuals in the population, that is, updating the Kp, Ki, and Kd parameters of the speed PID controller of the rehabilitation walking wheelchair;

[0041] S8. If the updated position of the individual in the population is better than the position updated in the previous iteration, the current optimal solution is retained;

[0042] S9. Determine whether the current number of iterations reaches the maximum number of iterations. If so, exit the loop, output the global optimal solution, and assign it to the rehabilitation wheelchair speed PID controller as the three parameters Kp, Ki, and Kd. Otherwise, return to execute S3.

[0043] Furthermore, in S2, the working condition of the rehabilitation walking wheelchair motion control system is simulated, and a transfer function is designed to describe the dynamic characteristics of the system; the transfer function expression is:

[0044] ;

[0045] Where s is a complex frequency variable.

[0046] Furthermore, in S5, the rehabilitation wheelchair speed PID controller parameters Kp, Ki, Kd are encoded as a solution based on the gradient algorithm search space, and the encoding vector is:

[0047] ;

[0048] In the formula, x is the encoding vector, , and They are respectively the proportional parameter, integral parameter and differential parameter of the speed PID controller of the rehabilitation walking wheelchair.

[0049] Furthermore, in S7, an improved mathematical model of the position update strategy based on the gradient algorithm is established, and the specific steps are as follows:

[0050] S71, algorithm initialization stage, using chaotic mapping to initialize the population position, and establishing the initialization population position mathematical model according to formulas (2)-(3);

[0051] S72, algorithm exploration stage, establishing a population position mathematical model according to formulas (9)-(10);

[0052] (9);

[0053] (10);

[0054] In the formula, is the new position of the nth population individual in the next iteration, and are all random numbers between 0 and 1. and and are all positions created at random points under the current gradient, is the current iteration position of the nth population individual, is the balance factor;

[0055] S73. During the algorithm development phase, the Gaussian mutation strategy is introduced to improve the population position update formula: when rand(0,1)<0.5, the population position mathematical model is established according to formulas (6)-(8) and (4); when rand(0,1) is other values, the population position mathematical model is established according to formulas (6)-(8) and (5).

[0056] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0057] The present invention proposes a method for optimizing the motion control of a rehabilitation walking wheelchair, which controls the motor by using a PID control method, and then the motor drives the wheelchair wheels to rotate. By using a chaotic map to initialize the population position in the algorithm initialization stage, and introducing a Gaussian mutation strategy to improve the gradient-based algorithm in the algorithm development stage, the global search capability and accuracy of the algorithm are improved. The improved gradient-based algorithm is used to optimize the speed PID controller of the rehabilitation walking wheelchair to obtain the optimal control parameters Kp, Ki, and Kd. The obtained optimal control parameters Kp, Ki, and Kd are input into the PID control model of the rehabilitation walking wheelchair motion control system to achieve optimal robust control of the rehabilitation walking wheelchair. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Flowchart of steps for optimizing the motion control of a rehabilitation walking wheelchair.

[0059] Figure 2 This is the PID control model diagram of the rehabilitation walking wheelchair motion control system.

[0060] Figure 3 Flowchart of steps for optimizing the speed PID controller of a rehabilitation walking wheelchair using the improved gradient-based algorithm.

[0061] Figure 4 Comparison chart of the best fitness function values ​​between the basic gradient-based algorithm and the improved gradient-based algorithm.

[0062] Figure 5 A comparison chart of the effects of optimizing PID control parameters based on the basic gradient algorithm and the improved gradient algorithm. DETAILED DESCRIPTION

[0063] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] See also Figure 1-Figure 5 , the present invention provides a technical solution:

[0065] A method for optimizing motion control of a rehabilitation walking wheelchair, such as Figure 1 As shown, the specific steps are:

[0066] Step 1: Convert the rehabilitation wheelchair motion control problem into a mathematical model to be optimized. The mathematical model to be optimized is:

[0067] (1);

[0068] In the formula, J is the fitness value, T is the total control time, t is the tth second control time, is the expected speed value in the motion control system of the rehabilitation wheelchair, is the actual speed value at the tth second in the rehabilitation wheelchair motion control system, is the weight coefficient.

[0069] Step 2: Establish the PID control model of the rehabilitation wheelchair motion control system, such as Figure 2As shown, the model includes an input module, an error calculation module, an improved gradient algorithm module, a speed PID controller module, a speed detection module, a motor module, and a wheelchair wheel module; the expected speed value is input from the input module, and is input together with the actual speed value detected by the speed detection module into the error calculation module for subtraction to obtain a speed error value; the speed PID controller module receives the speed error value, and uses the PID parameters optimized by the improved gradient algorithm module to calculate and obtain a reference speed value, thereby controlling the motor to drive the wheelchair wheels to rotate, thereby realizing the speed control of the rehabilitation walking wheelchair.

[0070] Step 3: Use Matlab software to establish an improved mathematical model based on the gradient algorithm to verify the performance of the improved gradient algorithm to optimize the PID controller; the improved gradient algorithm includes:

[0071] D1, using chaotic mapping to initialize population positions;

[0072] D2. During the algorithm development phase, the Gaussian mutation strategy is introduced to improve the population position update formula; the details are as follows.

[0073] Step 1: In the initialization stage of the algorithm, the chaotic map is used to initialize the population position. The improved formula for initializing the population position is:

[0074] (2);

[0075] (3);

[0076] In the formula, is the initial position of the nth individual in the population, Search for a lower bound for the algorithm, To search for the upper bound of the algorithm, rand(0,1) is a random number between 0 and 1. is the i-th variable value of the generated chaotic sequence, is the i+1th variable value of the generated chaotic sequence, and a is the chaotic factor;

[0077] Step 2. In the algorithm development stage, the Gaussian mutation strategy is introduced to improve the population position update formula: when rand(0,1)<0.5, execute equations (6)-(8) and (4); when rand(0,1) is other values, execute equations (6)-(8) and (5);

[0078] (4);

[0079] (5);

[0080] (6);

[0081] (7);

[0082] (8);

[0083] In the formula, is the new position of the nth population individual in the next iteration, is the current iteration position of the nth population individual, is a random number between -1 and 1. is a parameter that controls the decay speed of the standard deviation, m is the current iteration number, u1, u2 and u3 are all random numbers between 0 and 1, is the best individual position of the population in the current iteration, and and are the current positions of random individuals in the population, is a random number from a normal distribution with mean 0 and standard deviation 1. is the balance factor, and are all positions created at random points under the current gradient, is the sine function parameter, To adjust the parameters of the search process, and The values ​​are 1.2 and 0.2 respectively, M is the maximum number of iterations, and the meanings of other parameters are the same as in Step 1.

[0084] Step 4: Use the improved gradient-based algorithm to optimize the rehabilitation wheelchair speed PID controller to obtain the optimal control parameters Kp, Ki, and Kd, as shown in Figure 3 As shown, the specific steps are:

[0085] S1. The mathematical model of the rehabilitation wheelchair motion control system is used as the objective function of the improved gradient-based algorithm, wherein the objective function is used as the fitness function;

[0086] S2. Simulate the working conditions of the rehabilitation wheelchair motion control system and design transfer functions to describe the dynamic characteristics of the system;

[0087] S3, giving an input of a rehabilitation walking wheelchair motion control system, the input being a desired speed value of the wheelchair wheels in the control system;

[0088] S4, Initialization Improvement Gradient-based Algorithm Population Size np, Problem Dimension d, Algorithm Search Upper Bound , algorithm searches for lower bounds , maximum number of iterations M;

[0089] S5, encoding the rehabilitation wheelchair speed PID controller parameters Kp, Ki, Kd as a solution based on the gradient algorithm search space, and as the algorithm iterates, the position of the algorithm population individual is the solution of the rehabilitation wheelchair speed PID controller parameters;

[0090] S6. Calculate the individual fitness values ​​of the current iteration population according to the fitness function, record the minimum fitness value, and compare it with the optimal fitness value of the population in the previous iteration, and retain the optimal fitness value;

[0091] S7, establishing an improved mathematical model of position update strategy based on gradient algorithm, and using the mathematical model to update the position of individuals in the population, that is, updating the Kp, Ki, and Kd parameters of the speed PID controller of the rehabilitation walking wheelchair;

[0092] S8. If the updated position of the individual in the population is better than the position updated in the previous iteration, the current optimal solution is retained;

[0093] S9. Determine whether the current number of iterations reaches the maximum number of iterations. If so, exit the loop, output the global optimal solution, and assign it to the rehabilitation wheelchair speed PID controller as the three parameters Kp, Ki, and Kd. Otherwise, return to execute S3.

[0094] Furthermore, in S2, the working condition of the rehabilitation walking wheelchair motion control system is simulated, and a transfer function is designed to describe the dynamic characteristics of the system; the transfer function expression is:

[0095] ;

[0096] Where s is a complex frequency variable.

[0097] Furthermore, in S5, the rehabilitation wheelchair speed PID controller parameters Kp, Ki, Kd are encoded as a solution based on the gradient algorithm search space, and the encoding vector is:

[0098] ;

[0099] Where x is the encoding vector, , and They are respectively the proportional parameter, integral parameter and differential parameter of the speed PID controller of the rehabilitation walking wheelchair.

[0100] Furthermore, in S7, an improved mathematical model of the position update strategy based on the gradient algorithm is established, and the specific steps are as follows:

[0101] S71, algorithm initialization stage, using chaotic mapping to initialize the population position, and establishing the initialization population position mathematical model according to formulas (2)-(3);

[0102] S72, algorithm exploration stage, establishing a population position mathematical model according to formulas (9)-(10);

[0103] (9);

[0104] (10);

[0105] In the formula, is the new position of the nth population individual in the next iteration, and are all random numbers between 0 and 1. and and are all positions created at random points under the current gradient, is the current iteration position of the nth population individual, is the balance factor;

[0106] S73. During the algorithm development phase, the Gaussian mutation strategy is introduced to improve the population position update formula: when rand(0,1)<0.5, the population position mathematical model is established according to formulas (6)-(8) and (4); when rand(0,1) is other values, the population position mathematical model is established according to formulas (6)-(8) and (5).

[0107] Step 5: Input the obtained optimal control parameters Kp, Ki, and Kd into the PID control model of the rehabilitation walking wheelchair motion control system to obtain the optimal effect of PID control of the rehabilitation walking wheelchair motion control system.

[0108] The specific implementation method of the present invention compares the basic gradient algorithm-based PID control and the improved gradient algorithm-based PID control through Matlab simulation modeling. In the test code, the population size np=50 is set, and the algorithm searches for the upper bound. =100, the algorithm searches for the lower bound =0, maximum number of iterations M=30, system input target value=100.

[0109] More specifically, the objective function of formula (1) is used to calculate the fitness value of the basic gradient-based algorithm and the improved gradient-based algorithm in the tuning process, and the comparison is obtained. Figure 4 .like Figure 4As shown in the figure, from the analysis of the overall curve changes, the basic gradient-based algorithm fitness value change characteristics show that the algorithm is prone to fall into the local optimum for a long time, while the improved gradient-based algorithm is trapped in the local optimum for a shorter time during the tuning process, and has a certain ability to jump out of the local optimum. Overall, according to the principle that the smaller the fitness value, the better the performance, it shows that the quality of the solution found by the improved gradient-based algorithm is better; and it can also be seen from the figure that the improved gradient-based algorithm converges faster, indicating that the improved gradient-based algorithm finds solutions faster.

[0110] More specifically, the optimal control parameters Kp, Ki, and Kd are input into the PID control model of the rehabilitation wheelchair motion control system, and the control effect is output to obtain a comparison. Figure 5 .like Figure 5 As shown in the figure, the PID control system based on the improved gradient algorithm has a smaller overshoot and smaller oscillation than the PID control system based on the basic gradient algorithm, and can reach a balanced state in a shorter time. This shows that the PID control system based on the improved gradient algorithm has better stability and stronger robustness than the PID control system based on the basic gradient algorithm.

Claims

1. A method for optimizing the motion control of a rehabilitation walking wheelchair, characterized in that: The specific steps are: Step 1: Convert the rehabilitation wheelchair motion control problem into a mathematical model to be optimized. The mathematical model to be optimized is: （1）； In the formula, J is the fitness value, T is the total control time, t is the tth second control time, is the expected speed value in the motion control system of the rehabilitation wheelchair, is the actual speed value at the tth second in the rehabilitation wheelchair motion control system, is the weight coefficient; Step 2: Establish the PID control model of the rehabilitation wheelchair motion control system; Step 3: Use Matlab software to establish an improved mathematical model based on the gradient algorithm and verify the performance of the improved PID controller based on the gradient algorithm; The improvements are based on the gradient algorithm and include: D1, using chaotic mapping to initialize population positions; D2. In the algorithm development phase, the Gaussian mutation strategy is introduced to improve the population position update formula; Step 4: Use the improved gradient-based algorithm to optimize the rehabilitation wheelchair speed PID controller to obtain the optimal control parameters Kp, Ki, and Kd; Step 5: Input the obtained optimal control parameters Kp, Ki, and Kd into the PID control model of the rehabilitation walking wheelchair motion control system to obtain the optimal effect of PID control of the rehabilitation walking wheelchair motion control system.

2. The method for optimizing the motion control of a rehabilitation walking wheelchair according to claim 1, characterized in that: In the step 2, a PID control model of the rehabilitation walking wheelchair motion control system is established, and the model includes an input module, an error calculation module, an improved gradient-based algorithm module, a speed PID controller module, a speed detection module, a motor module, and a wheelchair wheel module; The expected speed value is input from the input module and input into the error calculation module together with the actual speed value detected by the speed detection module to obtain the speed error value. The speed PID controller module receives the speed error value and uses the improved PID parameters optimized by the gradient algorithm module to calculate the reference speed value, and then controls the motor to drive the wheelchair wheels to rotate, thereby realizing the speed control of the rehabilitation walking wheelchair.

3. The method for optimizing the motion control of a rehabilitation walking wheelchair according to claim 2, characterized in that: In step 3, the specific steps of improving the gradient-based algorithm are: Step 1: In the initialization stage of the algorithm, the chaotic map is used to initialize the population position. The improved formula for initializing the population position is: （2）； （3）； In the formula, is the initial position of the nth individual in the population, Search for a lower bound for the algorithm, To search for the upper bound of the algorithm, rand(0,1) is a random number between 0 and 1. is the i-th variable value of the generated chaotic sequence, is the i+1th variable value of the generated chaotic sequence, and a is the chaotic factor; Step 2. In the algorithm development stage, the Gaussian mutation strategy is introduced to improve the population position update formula: when rand(0,1)<0.5, execute equations (6)-(8) and (4); when rand(0,1) is other values, execute equations (6)-(8) and (5); （4）； （5）； （6）； （7）； （8）； In the formula, is the new position of the nth population individual in the next iteration, is the current iteration position of the nth population individual, is a random number between -1 and 1. is a parameter that controls the decay speed of the standard deviation, m is the current iteration number, u1, u2 and u3 are all random numbers between 0 and 1, is the best individual position of the population in the current iteration, and and are the current positions of random individuals in the population, is a random number from a normal distribution with mean 0 and standard deviation 1. is the balance factor, and are all positions created at random points under the current gradient, is the sine function parameter, To adjust the parameters of the search process, and The values ​​are 1.2 and 0.2 respectively, M is the maximum number of iterations, and the meanings of other parameters are the same as in Step 1.

4. The method for optimizing the motion control of a rehabilitation walking wheelchair according to claim 3, characterized in that: In step 4, the improved gradient-based algorithm is used to optimize the rehabilitation wheelchair speed PID controller, and the specific steps are: S1. The mathematical model of the rehabilitation wheelchair motion control system is used as the objective function of the improved gradient-based algorithm, wherein the objective function is used as the fitness function; S2. Simulate the working conditions of the rehabilitation wheelchair motion control system and design transfer functions to describe the dynamic characteristics of the system; S3, giving an input of a rehabilitation walking wheelchair motion control system, the input being a desired speed value of the wheelchair wheels in the control system; S4, Initialization Improvement Gradient-based Algorithm Population Size np, Problem Dimension d, Algorithm Search Upper Bound , algorithm searches for lower bounds , maximum number of iterations M; S5, encoding the rehabilitation wheelchair speed PID controller parameters Kp, Ki, Kd as a solution based on the gradient algorithm search space, and as the algorithm iterates, the position of the algorithm population individual is the solution of the rehabilitation wheelchair speed PID controller parameters; S6. Calculate the individual fitness values ​​of the current iteration population according to the fitness function, record the minimum fitness value, and compare it with the optimal fitness value of the population in the previous iteration, and retain the optimal fitness value; S7, establishing an improved mathematical model of position update strategy based on gradient algorithm, and using the mathematical model to update the individual positions of the population, that is, updating the Kp, Ki, and Kd parameters of the speed PID controller of the rehabilitation walking wheelchair; S8. If the updated position of the individual in the population is better than the position updated in the previous iteration, the current optimal solution is retained; S9. Determine whether the current number of iterations reaches the maximum number of iterations. If so, exit the loop, output the global optimal solution, and assign it to the rehabilitation wheelchair speed PID controller as the three parameters Kp, Ki, and Kd. Otherwise, return to execute S3.

5. The method for optimizing the motion control of a rehabilitation walking wheelchair according to claim 4, characterized in that: The specific steps to establish the mathematical model of the improved position update strategy based on the gradient algorithm are: S71, algorithm initialization stage, using chaotic mapping to initialize the population position, and establishing the initialization population position mathematical model according to formulas (2)-(3); S72, algorithm exploration stage, establishing a population position mathematical model according to formulas (9)-(10); （9）； （10）； In the formula, is the new position of the nth population individual in the next iteration, and are all random numbers between 0 and 1. and and are all positions created at random points under the current gradient, is the current iteration position of the nth population individual, is the balance factor; S73. During the algorithm development phase, the Gaussian mutation strategy is introduced to improve the population position update formula: when rand(0,1)<0.5, the population position mathematical model is established according to formulas (6)-(8) and (4); when rand(0,1) is other values, the population position mathematical model is established according to formulas (6)-(8) and (5).

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