Chaotic particle swarm optimization trajectory method based on constrained base space manipulator

Abstract

The invention discloses a chaos particle swarm optimization trajectory method based on a constrained base space manipulator, which comprises the following steps of: deducing a kinematic model of a constrained base through a finite momentum conservation principle according to the constraint of the base of the space manipulator; a singular solving problem caused by dynamic singularity is avoided by using a damping least square method; combining trapezoidal speed planning with a trigonometric function, and parameterizing trajectory planning of the end mechanism of the constrained base space manipulator; in consideration of an error introduced by a damping reduction least square method, reduction of base attitude disturbance and reduction of motion time as optimization objectives, a chaos particle swarm optimization algorithm is adopted to plan a trajectory of the end mechanism of the constrained base space manipulator. According to the method, singular avoidance planning can be carried out on the tail end mechanism track of the constrained base space manipulator, and an optimization target is selected according to specific requirements.

Description

Technical Field

[0001] The invention belongs to the field of space manipulator path planning, and in particular relates to a chaotic particle swarm optimization trajectory method based on a constrained base space manipulator. Background Art

[0002] With the rapid development of space technology and the increasing frequency of human space activities, space control tasks are increasing. As one of the key equipment for autonomous and intelligent space control, space manipulators are changing the way humans conduct space exploration activities such as manned spaceflight and deep space exploration.

[0003] Taking into account the strong coupling effect, singularity, nonlinearity and time-varying characteristics of the space manipulator system, these factors have brought major challenges to the accurate modeling and path planning of the space manipulator. Therefore, it is necessary to design a chaotic particle swarm optimization trajectory method based on a constrained base space manipulator. Under the condition of meeting the requirements of high degree of freedom, high tracking accuracy, small substrate attitude disturbance and fast response speed, a trajectory of the end mechanism of the space manipulator can be generated, and the mission requirements can be reasonably planned to achieve the goal that the space robot can replace humans to work in the harsh space environment, reduce costs and improve the efficiency of space exploration. Summary of the invention

[0004] Purpose of the invention: To provide a chaotic particle swarm optimization trajectory method based on a constrained base space robot, to achieve singularity avoidance planning of the end mechanism trajectory of the constrained base space robot, and to select the optimization target according to specific needs.

[0005] Technical solution: To achieve the above-mentioned invention object, the present invention adopts the following technical solution:

[0006] A chaotic particle swarm optimization trajectory method for a space manipulator based on a constrained base comprises the following steps: according to the constraints imposed on the base of the space manipulator, a kinematic model of the constrained base is derived through the principle of conservation of finite momentum; the damped least square method is used to avoid the singularity problem caused by dynamic singularity; the trajectory planning of the end mechanism of the space manipulator based on the constrained base is parameterized by combining trapezoidal velocity planning with trigonometric functions; and the trajectory of the end mechanism of the space manipulator based on the constrained base is planned by using a chaotic particle swarm optimization algorithm, taking into account the reduction of the error introduced by the damped least square method, the reduction of the base attitude disturbance, and the reduction of the motion time as optimization goals.

[0007] Optionally, obtain the generalized kinematic model of the space manipulator in, are the linear velocity and angular velocity of the end mechanism, is the linear velocity and angular velocity of the base, J s is the Jacobian matrix representing the motion of the partially constrained base, J mis the Jacobian matrix representing the motion of the robot link, is the angular velocity of each joint of the manipulator, and n is the joint number. According to the constraints on the base of the space manipulator, the kinematic model of the constrained base space manipulator is derived through the principle of finite momentum conservation. Among them, J float is the generalized Jacobian matrix of the partially constrained base space manipulator, and the linear velocity and angular velocity of the constrained base are [v 0x v 0y 0 0 0 ω 0z ] T .

[0008] Optionally, the damped least squares method is used to avoid the singularity problem caused by dynamic singularity and obtain the inverse kinematics model of the constrained base space manipulator after introducing the damping coefficient. in, is the linear velocity and angular velocity of the end mechanism, λ is the introduced damping coefficient, where the damping coefficient λ is adaptively adjusted according to the following formula: in, is the estimated value of the minimum singular value, ε is the threshold for judging whether it is singular, and λ 0 is the maximum damping value in the neighborhood of the singular point.

[0009] Optionally, the trajectory planning of the end mechanism of the constrained base space manipulator is parameterized by combining trapezoidal velocity planning and trigonometric functions, and the velocity planning function of the end mechanism is obtained as in, is the normalized linear velocity and angular velocity of the end mechanism, τ=t / T f is the normalized time parameter, T f is the motion time, A, ξ, η are parameters to be confirmed, which are determined according to the optimization results, and f(τ) is the trapezoidal speed planning function, which is expressed in the form of

[0010] Optionally, the optimization objectives are as follows: 1) Reduce the error introduced by the damped least squares method, and calculate the difference between the position of the end mechanism at the termination time and the position of the trajectory planning || X ef -X ed || as one of the objective functions, where X ef is the position of the end mechanism at the end time, X ed is the position of the trajectory planning at the termination time. Set one of the objective functions as: Among them, K a is the weight coefficient, representing the proportion of the trajectory tracking error; 2) reduce the base attitude disturbance, the maximum change of the base attitude relative to the initial moment is |Δα| max , set one of the corresponding objective functions as: Among them, K b is the weight coefficient, representing the proportion of the base attitude disturbance; 3) Reduce the movement time, and set the objective function corresponding to the movement time as Among them, K i is the weight coefficient, representing the proportion of motion time; the trajectory planning problem of the constrained base space manipulator is reconstructed into the following optimization problem: The optimization problem is solved by using the chaotic particle swarm optimization algorithm. M particles are randomly generated as the initial population, and their positions and velocities are then generated. The initial number of iterations k is set. iter =0; calculate the fitness of M particles; update the historical optimal position P of each particle best , the global optimal position P Gbest And the corresponding fitness value G best ; Using P Gbest Generate a chaotic sequence and perform a chaotic optimization search, where the chaotic optimization search consists of the following three steps: 1) First, set the global optimal position P Gbest =[P G1 , P G2 ,…,P Gm ] is mapped to the domain of the Logistic equation (0, 1), where m means that the particle has m unknown parameters. The mapped sequence can be obtained Among them, a i , b i Represents the upper and lower limits of the value of the particle's ith parameter; 2) Generate N groups of chaotic sequences Z using the Logistic equation Ni =[z 1i z 2i … z Ni ], the chaotic sequence generates N new particles, where the position of each particle is mapped to the solution space by the sequence, and the mapping method is P gji =a i +(b i -a i ) ji , j = 1, 2, ... N, then the position of each particle is P gj =[P gj1 P gj2 … P gjm ]; 3) Substitute these N particles into the objective function to calculate their respective fitness values, and obtain the optimal position of the N particles as P Nbest , the fitness value is G Nbest , if G Nbest <G best , then use P Nbest Instead of P Gbest, and randomly replace a particle in the current population; update the speed and position of each particle according to the PSO standard formula: Among them, x i , v i Represent the position and velocity of each particle, ω is the inertia factor, c 1 , c 2 is the learning factor, r 1 , r 2 is a random number uniformly distributed in [0, 1]; until K iter Reaching the maximum number of iterations or G best Satisfy the set optimal fitness value, find the global minimum fitness value and the corresponding global optimal position, and obtain a planning trajectory of the end mechanism of the constrained base space manipulator that meets the target requirements.

[0011] Beneficial effects: The present invention provides a chaotic particle swarm optimization trajectory method for a constrained base space robot, establishes a kinematic model of a partially constrained base space robot, plans the trajectory of the end effector by combining trapezoidal programming with trigonometric functions, and uses the minimum damping variance method to solve the dynamic singularity problem. When considering the objective function, factors such as the posture disturbance of the base and the movement duration of the robot are added, and the solution is solved by a chaotic particle swarm optimization algorithm to achieve reasonable planning of the trajectory of the end mechanism of the space robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a schematic diagram of the process of the present invention;

[0013] Figure 2 It is a schematic diagram of a partially constrained base space manipulator model of the present invention;

[0014] Figure 3 It is a schematic diagram of the chaotic particle swarm optimization algorithm of the present invention; DETAILED DESCRIPTION

[0015] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0016] like Figure 1 As shown, the process of the present invention is as follows: according to the constraints on the base of the space robot, the kinematic model of the constrained base is derived through the principle of conservation of finite momentum; the damped least squares method is used to avoid the problem of solving singularities caused by dynamic singularities; the trajectory planning of the end mechanism of the space robot of the constrained base is parameterized by combining trapezoidal velocity planning and trigonometric functions; considering reducing the error introduced by the damped least squares method, reducing the base posture disturbance, and reducing the movement time as optimization goals, the chaotic particle swarm optimization algorithm is used to plan the trajectory of the end mechanism of the space robot of the constrained base.

[0017] Obtaining a generalized kinematic model for a space manipulator in, are the linear velocity and angular velocity of the end mechanism, is the linear velocity and angular velocity of the base, J s is the Jacobian matrix representing the motion of the partially constrained base, J m is the Jacobian matrix representing the motion of the robot link, is the angular velocity of each joint of the robot arm, and n is the joint number. Figure 2 As shown in the figure, the base of the constrained base space manipulator can only move in the x and y axis directions and rotate around the z axis, that is, v 0z =0,ω 0x =0,ω 0y = 0, where the subscripts of x, y, and z represent the components of the vector on the corresponding axis. According to the constraints on the base of the constrained base space manipulator, the principle of conservation of finite momentum can be used to obtain Among them, m i is the mass of each joint and base, v i is the velocity of the center of mass of each joint and the center of mass of the base, P is the linear momentum, L is the angular momentum, I i is the inertia tensor of each joint and the base, ω i is the angular velocity of the center of mass of each joint and the center of mass of the base, r i is the vector from the origin of the inertial coordinate system to the center of mass of each joint and the center of mass of the base. Then the kinematic model of the space manipulator constrained by the base can be derived. Among them, J float is the generalized Jacobian matrix of the partially constrained base space manipulator, and the linear velocity and angular velocity of the constrained base are [v 0x v 0y 0 0 0 ω 0z ] T .

[0018] Kinematic model of a space manipulator with a constrained base Its inverse kinematics model can be obtained in, + J float For J float The pseudo-reversal, is the linear velocity and angular velocity of the end mechanism. In the process of using the pseudo-inverse of the generalized Jacobian matrix to solve the inverse kinematics, the generalized Jacobian matrix may still be singular. Therefore, the damped least squares method is used to avoid the singularity problem caused by the dynamic singularity, and the inverse kinematics model of the constrained base space manipulator is obtained after the damping coefficient is introduced. in, is the linear velocity and angular velocity of the end mechanism, λ is the introduced damping coefficient, where the damping coefficient λ is adaptively adjusted according to the following formula: in, is the estimated value of the minimum singular value, ε is the threshold for judging whether it is singular, and λ 0 is the maximum damping value in the neighborhood of the singular point.

[0019] The trajectory of the end mechanism of the partially constrained base space manipulator in the Cartesian space is planned so that the end mechanism can move from an initial position x e0 Move to a given end position x ed , and ensure that the motion state can be maintained continuously and smoothly during the motion process. The trajectory planning of the end mechanism of the constrained base space manipulator is parameterized by combining trapezoidal velocity planning and trigonometric functions. Assuming that the end mechanism moves on a straight line formed by the initial and terminal positions, the velocity planning function of the end mechanism can be obtained as in, is the normalized linear velocity and angular velocity of the end mechanism, τ=t / T f is the normalized time parameter, T f is the motion time, A, ξ, η are parameters to be confirmed, which are determined according to the optimization results, and f(τ) is the trapezoidal speed planning function, which is expressed in the form of Considering the smoothness of the trajectory at the start and end times, the start and end times of the velocity planning function should meet the following conditions:

[0020] Consider the following three optimization objectives: 1) Reduce the error introduced by the damped least squares method, and calculate the difference between the position of the end mechanism at the termination time and the position of the trajectory planning || X ef -X ed || as one of the objective functions, where X ef is the position of the end mechanism at the end time, X ed is the position of the trajectory planning at the termination time. Set one of the objective functions as: Among them, K a is the weight coefficient, representing the proportion of the trajectory tracking error; 2) reduce the base attitude disturbance, the maximum change of the base attitude relative to the initial moment is |Δα| max , set one of the corresponding objective functions as: Among them, K b is the weight coefficient, representing the proportion of the base attitude disturbance: 3) Reduce the movement time and set the objective function corresponding to the movement time as Among them, K i is the weight coefficient, representing the proportion of motion time; the trajectory planning problem of the constrained base space manipulator is reconstructed into the following optimization problem: The optimization problem is solved by using the chaotic particle swarm optimization algorithm. The whole process is as follows: Figure 3As shown, M particles are randomly generated as the initial population, and their positions and velocities are then generated. The initial number of iterations k is set. iter =0; calculate the fitness of M particles; update the historical optimal position P of each particle best , the global optimal position P Gbest And the corresponding fitness value G best ; Using P Gbest With the Logistic equation z n+1 =uz n (1-z n ), n=0, 1, 2, ... to generate chaotic sequences, where u is the parameter of the chaotic mapping. When u=4 and the initial value z 0 ∈(0, 1), the sequence generated is completely in a chaotic state, and then a chaotic optimization search is performed, wherein the chaotic optimization search is the following three steps: 1) First, the global optimal position P Gbest =[P G1 , P G2 ,…,P Gm ] is mapped to the domain of the Logistic equation (0, 1), where m means that the particle has m unknown parameters. The mapped sequence can be obtained Among them, a i , b i Represents the upper and lower limits of the value of the particle's ith parameter; 2) Generate N groups of chaotic sequences Z using the Logistic equation Ni =[z 1i z 2i … z Ni ], the chaotic sequence generates N new particles, where the position of each particle is mapped to the solution space by the sequence, and the mapping method is P gji =a i +(b i -a i ) ji , j = 1, 2, ... N, then the position of each particle is P gj =[P gj1 P gj2 …P gjm ]; 3) Substitute these N particles into the objective function to calculate their respective fitness values, and obtain the optimal position of the N particles as P Nbest , the fitness value is G Nbest , if G Nbest <G best , then use P Nbest Instead of P Gbest , and randomly replace a particle in the current population; update the speed and position of each particle according to the PSO standard formula: Among them, x i , vi Represent the position and velocity of each particle, ω is the inertia factor, c 1 , c 2 is the learning factor, r 1 , r 2 is a random number uniformly distributed in [0, 1]; until k iter Reaching the maximum number of iterations or G best Satisfy the set optimal fitness value, find the global minimum fitness value and the corresponding global optimal position, and obtain a planning trajectory of the end mechanism of the constrained base space manipulator that meets the target requirements.

Claims

1. A chaotic particle swarm optimization trajectory method based on a constrained base space manipulator, characterized in that: According to the constraints on the base of the space manipulator, the kinematic model of the constrained base is derived through the principle of conservation of finite momentum. The damped least squares method is used to avoid the problem of solving singularities caused by dynamic singularities. The trajectory planning of the end mechanism of the space manipulator of the constrained base is parameterized by combining trapezoidal velocity planning with trigonometric functions. Considering reducing the error introduced by the damped least squares method, reducing the base attitude disturbance, and reducing the motion time as optimization goals, the chaotic particle swarm optimization algorithm is used to plan the trajectory of the end mechanism of the space manipulator of the constrained base.

2. The method for optimizing trajectory of a space robot based on a constrained base according to claim 1 is characterized in that: Obtaining a generalized kinematic model for a space manipulator in, are the linear velocity and angular velocity of the end mechanism, is the linear velocity and angular velocity of the base, J s is the Jacobian matrix representing the motion of the partially constrained base, J m is the Jacobian matrix representing the motion of the robot link, is the angular velocity of each joint of the manipulator, and n is the joint number. According to the constraints on the base of the space manipulator, the kinematic model of the constrained base space manipulator is derived through the principle of finite momentum conservation. Among them, J float is the generalized Jacobian matrix of the partially constrained base space manipulator, and the linear velocity and angular velocity of the constrained base are [v 0x v 0y 0 0 0 ω 0z ] T .

3. The method for optimizing trajectory of a space robot based on a constrained base according to claim 1 is characterized in that: The damped least squares method is used to avoid the singularity problem caused by dynamic singularity, and the inverse kinematics model of the constrained base space manipulator is obtained after the damping coefficient is introduced. in, is the linear velocity and angular velocity of the end mechanism, λ is the introduced damping coefficient, where the damping coefficient λ is adaptively adjusted according to the following formula: in, is the estimated value of the minimum singular value, ε is the threshold for judging whether it is singular, and λ0 is the maximum damping value in the neighborhood of the singular point.

4. The method for optimizing trajectory of a space robot based on a constrained base according to claim 1 is characterized in that: By combining trapezoidal velocity planning and trigonometric functions, the trajectory planning of the end mechanism of the constrained base space manipulator is parameterized, and the velocity planning function of the end mechanism is obtained as follows: in, is the normalized linear velocity and angular velocity of the end mechanism, τ=t / T f is the normalized time parameter, T f is the motion time, A, ξ, η are parameters to be confirmed, which are determined according to the optimization results, and f(τ) is the trapezoidal speed planning function, which is expressed in the form of 5. The method for optimizing trajectory of a space robot based on a constrained base according to claim 1 is characterized in that: Consider the following three optimization objectives: 1) Reduce the error introduced by the damped least squares method, and calculate the difference between the position of the end mechanism at the termination time and the position of the trajectory planning || X ef -X ed || as one of the objective functions, where X ef is the position of the end mechanism at the end time, X ed is the position of the trajectory planning at the termination time. Set one of the objective functions as: Among them, K a is the weight coefficient, representing the proportion of the trajectory tracking error; 2) reduce the base attitude disturbance, the maximum change of the base attitude relative to the initial moment is |Δα| max , set one of the corresponding objective functions as: Among them, K b is the weight coefficient, representing the proportion of the base attitude disturbance; 3) Reduce the movement time, and set the objective function corresponding to the movement time as Among them, K t is the weight coefficient, representing the proportion of motion time; the trajectory planning problem of the constrained base space manipulator is reconstructed into the following optimization problem: The optimization problem is solved by using the chaotic particle swarm optimization algorithm. M particles are randomly generated as the initial population, and their positions and velocities are then generated. The initial number of iterations k is set. iter =0; calculate the fitness of M particles; update the historical optimal position P of each particle best , the global optimal position P Gbest And the corresponding fitness value G best ; Using P Gbest Generate a chaotic sequence and perform a chaotic optimization search, where the chaotic optimization search consists of the following three steps: 1) First, set the global optimal position P Gbest =[P G1 , P G2 ,…,P Gm ] is mapped to the domain of the Logistic equation (0, 1), where m means that the particle has m unknown parameters. The mapped sequence can be obtained Among them, a i , b i Represents the upper and lower limits of the value of the particle's ith parameter; 2) Generate N groups of chaotic sequences Z using the Logistic equation Ni =[z 1i z 2i … z Ni ], the chaotic sequence generates N new particles, where the position of each particle is mapped to the solution space by the sequence, and the mapping method is P gji =a i +(b i -a i ) ji , j = 1, 2, ... N, then the position of each particle is P gj =[P gj1 P gj2 … P gjm ]; 3) Substitute these N particles into the objective function to calculate their respective fitness values, and obtain the optimal position of the N particles as P Nbest , the fitness value is G Nbest , if G Nbest <G best , then use P Nbest Instead of P Gbest , and randomly replace a particle in the current population; update the speed and position of each particle according to the PSO standard formula: Among them, x i , v i Represent the position and speed of each particle respectively, ω is the inertia factor, c1, c2 are learning factors, r1, r2 are random numbers uniformly distributed in [0, 1]; until k iter Reaching the maximum number of iterations or G best Satisfy the set optimal fitness value, find the global minimum fitness value and the corresponding global optimal position, and obtain a planning trajectory of the end mechanism of the constrained base space manipulator that meets the target requirements.

6. A chaotic particle swarm optimization trajectory method based on a constrained base space manipulator as claimed in any one of claims 1 to 5, characterized in that: The following steps are included: (1) According to the constraints on the base of the space manipulator, the kinematic model of the constrained base is derived through the principle of conservation of finite momentum; (2) Using the damped least squares method to avoid the singular problem caused by dynamic singularity; (3) Using a combination of trapezoidal velocity planning and trigonometric functions, the trajectory planning of the end-of-arm mechanism in the constrained base space is parameterized; (4) Considering the optimization goals of reducing the error introduced by the damped least squares method, reducing the base attitude disturbance, and reducing the movement time, the chaotic particle swarm optimization algorithm is used to plan the trajectory of the end mechanism of the constrained base space robot.

7. The method for optimizing trajectory of a space robot based on a constrained base according to claim 6, characterized in that: Step (1) comprises the following steps: (1a) Obtaining the generalized kinematic model of the space manipulator in, are the linear velocity and angular velocity of the end mechanism, is the linear velocity and angular velocity of the base, J s is the Jacobian matrix representing the motion of the partially constrained base, J m is the Jacobian matrix representing the motion of the robot link, is the angular velocity of each joint of the robot arm, and n is the joint number. (1b) According to the constraints on the base of the space manipulator, the kinematic model of the constrained base space manipulator is derived through the principle of finite momentum conservation. Among them, J float is the generalized Jacobian matrix of the partially constrained base space manipulator, and the linear velocity and angular velocity of the constrained base are [v 0x v 0y 0 0 0 ω 0z ] T .

8. The method for optimizing trajectory of a space robot based on a constrained base according to claim 6, characterized in that: Step (2) comprises the following steps: (2a) Using the damped least squares method, we can avoid the singularity problem caused by dynamic singularity and obtain the inverse kinematics model of the constrained base space manipulator after introducing the damping coefficient. in, is the linear velocity and angular velocity of the end mechanism, λ is the introduced damping coefficient; (2b) The damping coefficient λ is adaptively adjusted according to the following formula: in, is the estimated value of the minimum singular value, ε is the threshold for judging whether it is singular, and λ0 is the maximum damping value in the neighborhood of the singular point.

9. The method for optimizing trajectory of a space robot based on a constrained base according to claim 6, characterized in that: Step (3) comprises the following steps: (3a) By combining trapezoidal velocity planning and trigonometric functions, the trajectory planning of the end mechanism of the constrained base space manipulator is parameterized, and the velocity planning function of the end mechanism is obtained as follows: in, is the normalized linear velocity and angular velocity of the end mechanism, τ=t / T f is the normalized time parameter, T f is the movement time, A, ξ, η are parameters to be confirmed, which are determined according to the optimization results; (3b)f(τ) is the trapezoidal speed planning function, which is expressed as 10. The method for optimizing trajectory of a space robot based on a constrained base according to claim 6, characterized in that: Step (4) comprises the following steps: (4a) Consider the following three optimization objectives: 1) Reduce the error introduced by the damped least squares method, and calculate the difference between the position of the end mechanism at the end time and the position of the trajectory planning || X ef -X ed || as one of the objective functions, where X ef is the position of the end mechanism at the end time, X ed is the position of the trajectory planning at the termination time. Set one of the objective functions as: Among them, K a is the weight coefficient, representing the proportion of the trajectory tracking error; 2) Reduce the base attitude disturbance. The maximum change of the base attitude relative to the initial moment is |Δα| max , set one of the corresponding objective functions as: Among them, K b is the weight coefficient, representing the proportion of the base attitude disturbance; 3) Reduce the exercise time and set the objective function corresponding to the exercise time as Among them, K t is the weight coefficient, representing the proportion of exercise time; (4b) The trajectory planning problem of the constrained base space manipulator is restructured into the following optimization problem: Using a chaotic particle swarm optimization algorithm to solve the optimization problem; (4c) Randomly generate M particles as the initial population, and then generate their positions and velocities. Set the initial number of iterations k iter =0; (4d) Calculate the fitness of M particles; (4e) Update the historical optimal position P of each particle best , the global optimal position P Gbest And the corresponding fitness value G best ; Using P Gbest Generate a chaotic sequence and perform a chaotic optimization search, where the chaotic optimization search consists of the following three steps: 1) First, the global optimal position P Gbest =[P G1 , P G2 ,…,P Gm ] is mapped to the domain of the Logistic equation (0, 1), where m means that the particle has m unknown parameters. The mapped sequence can be obtained Among them, a i , b i Indicates the upper and lower limits of the value of the i-th parameter of the particle; 2) Generate N groups of chaotic sequences Z using the Logistic equation Ni =[z 1i z 2i … z Ni ], the chaotic sequence generates N new particles, where the position of each particle is mapped to the solution space by the sequence, and the mapping method is P gji =a i +(b i -a i ) ji , j = 1, 2, ... N, then the position of each particle is P gj =[P gj1 P gj2 … P gjm ]; 3) Substitute these N particles into the objective function to calculate their respective fitness values, and obtain the optimal position of the N particles as P Nbest , the fitness value is G Nbest , if G Nbest <G best , then use P Nbest Instead of P Gbest , and randomly replace a particle in the current population; (4f) Update the speed and position of each particle according to the PSO standard formula: Among them, x i , v i Represent the position and velocity of each particle respectively, ω is the inertia factor, c1, c2 are learning factors, r1, r2 are random numbers uniformly distributed in [0, 1]; (4g) until k iter Reaching the maximum number of iterations or G best Satisfy the set optimal fitness value, find the global minimum fitness value and the corresponding global optimal position, and obtain a planning trajectory of the end mechanism of the constrained base space manipulator that meets the target requirements.

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