Space robot optimal trajectory planning method based on improved genetic particle swarm algorithm

Abstract

This invention discloses an optimal trajectory planning method for space robots based on an improved genetic particle swarm optimization algorithm. This method, applied to the optimal trajectory planning of space robots, includes: establishing the kinematic and dynamic equations of the space robot; defining the objective function for optimal trajectory optimization; parameterizing the joint angles of the space robot using sine functions; finding the optimal parameters using an improved genetic particle swarm optimization hybrid algorithm; and solving for the optimal trajectory of the robot using the obtained optimal parameters. The trajectory planning method of this invention minimizes the interference from the base on the space robot. Simultaneously, it uses time and energy consumption as planning objectives, thereby improving the time efficiency and energy utilization efficiency of the robot in completing tasks. This method has advantages such as fast convergence speed and ease of finding the optimal solution, and can provide satisfactory trajectories for space robots.

Description

Technical Field

[0001] This invention relates to the field of trajectory planning for space robots, and in particular to an optimal trajectory planning method for space robots based on an improved genetic particle swarm optimization algorithm. Background Technology

[0002] Space robots are highly complex intelligent operating systems whose applications are rapidly impacting and changing traditional models of space transportation, space station construction and maintenance, on-orbit maintenance, retrieval and repair of faulty spacecraft, and the conduct of on-orbit scientific experiments. Due to the dynamic coupling between the spacecraft base and the robotic arm, the movement of the robotic arm system generates reaction forces and torques on the base, causing disturbances and changes in the base's attitude. These disturbances to the spacecraft base, in turn, affect the stability and control precision of the robotic arm system. Therefore, employing appropriate trajectory planning methods to select a trajectory with minimal base interference is a crucial step in reducing disturbances to the base.

[0003] The paper (Xia HW, Zhai YB, Ma GC, et al. Path planning of space manipulator based on chaos particle swarm optimization algorithm[J]. Journal of Chinese Inertial Technology, 2014, 32(10): 2152-2157.) proposes a trajectory planning method for minimizing base perturbation of space robots. This method uses a chaotic particle swarm optimization algorithm, but it does not consider the position of the base.

[0004] The literature (Wang MM, Luo JJ, Walter U. Trajectory planning of free-floating space robot using Particle Swarm Optimization (PSO)[J]. Acta Astronautica, 2015, 112: 77-88.) designs a trajectory planning method for a multi-degree-of-freedom redundant space robot and considers the nonholonomic characteristics of the robot. The method adopts a particle swarm optimization algorithm, but does not consider minimizing the pose perturbation of the base.

[0005] The paper (Wei XP, Zhang JX, Zhou DS, et al. Optimal path planning for minimizing base disturbance of space robot[J]. International Journal of Advanced Robotic Systems, 2016, 13(2): 41.) proposes a method for planning the trajectory of space robot with minimum base disturbance. This method uses an improved chaotic particle swarm optimization algorithm, but does not consider the other effects of the reaction on the base. Summary of the Invention

[0006] The purpose of this invention is to provide an optimal trajectory planning method for space robots based on an improved genetic particle swarm optimization algorithm. The method considers the robot's motion trajectory from the aspects of motion time, energy consumption, and base stability, and establishes an optimization objective function. The improved genetic particle swarm optimization algorithm is used to find the optimal parameters, and finally the optimal trajectory of the robot's motion is obtained.

[0007] The technical solution to achieve the objective of this invention is as follows: Firstly, this invention provides a method for optimal trajectory planning of a space robot based on an improved genetic particle swarm optimization algorithm, comprising the following steps:

[0008] Step 1: Establish the kinematic and dynamic equations of the space robot;

[0009] Step 2: Define the optimization objective function to minimize base disturbance;

[0010] Step 3: Parameterize the joint angles of the space robot using sine functions;

[0011] Step 4: Use the improved genetic particle swarm optimization algorithm to find the optimal parameters;

[0012] Step 5: Solve for the optimal trajectory of the robot using the obtained optimal parameters.

[0013] In a second aspect, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in the first aspect.

[0014] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0015] Compared with the prior art, the significant advantages of this invention are:

[0016] (1) To address the problems of standard particle swarm optimization algorithm struggling to find the optimal solution and easily getting trapped in local optima, an improved genetic adaptive weighted particle swarm optimization algorithm (HGAIPSO) is proposed to optimize unknown parameters. This algorithm has advantages such as fast convergence speed and ease of finding the optimal solution.

[0017] (2) The robot’s motion trajectory is comprehensively considered from the aspects of motion time, energy consumption and base stability, and an optimization objective function is established; so that the planned trajectory can reduce the impact of motion time and energy consumption while ensuring base stability. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the overall process of the trajectory planning method of the present invention.

[0019] Figure 2 This is a schematic diagram of a space robot model.

[0020] Figure 3 These are the specific parameters for the space robot.

[0021] Figure 4 Flowchart for improving the genetic adaptive weighted particle swarm optimization algorithm.

[0022] Figure 5 A comparison diagram of the base stability before and after optimization.

[0023] Figure 6 This is the trajectory diagram of the joint angles obtained from the planning.

[0024] Figure 7 The diagram shows the joint angular velocity trajectory obtained from the planning.

[0025] Figure 8 The diagram shows the joint angular acceleration trajectory obtained from the planning. Detailed Implementation

[0026] The trajectory planning method of this invention minimizes interference from the base on the space robot. Simultaneously, it uses time and energy consumption as planning objectives, thereby improving the robot's time efficiency and energy utilization efficiency in completing tasks. It also considers speed and acceleration limitations. The smaller the range of joint angles, speeds, and accelerations, the less energy is required to drive the joints, and the easier the space robot is to control. This method has advantages such as fast convergence speed and ease of finding the optimal solution, providing satisfactory trajectories for space robots.

[0027] To illustrate the technical solution and objectives of this invention, the invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0028] Combination Figure 1The present invention discloses an optimal trajectory planning method for space robots based on an improved genetic particle swarm optimization algorithm, comprising the following steps:

[0029] Step 1: Establish a model of the space robot system, such as... Figure 2 As shown:

[0030] 1.1 Kinematics

[0031] For a space robot with 6 degrees of freedom, its kinematic equations can be expressed as:

[0032]

[0033] Among them, v e and ω e These represent the velocity and angular velocity of the end effector, respectively; v0 and ω0 represent the velocity and angular velocity of the base; J b ∈R 6×6 J represents the Jacobian matrix of the base. m ∈R 6×n The Jacobian matrix represents the robotic arm system. This represents the generalized velocity of each joint of the robotic arm.

[0034] 1.2 Dynamics

[0035] Assuming that all external forces and torques acting on the space robot system, except for joint driving torques, are zero, then the dynamics of the space robot can be expressed as:

[0036]

[0037] Where H(q) represents the inertia matrix of the system; is the nonlinear term in the system; μ represents the driving torque applied to each joint of the robotic arm.

[0038] Step 2: Define the optimization objective function that minimizes time, energy, and base disturbance;

[0039] 2.1 Define the time-optimal objective function:

[0040]

[0041] This represents the time from the initial time t0 to the final time t. f The time of movement between;

[0042] 2.2 Define the objective function for minimizing energy consumption:

[0043]

[0044] This represents the time from the initial time t0 to the final time t of the motion. fThe energy consumption generated by applying active control u(t) to the robot;

[0045] 2.3 Define the objective function for minimizing base disturbance:

[0046]

[0047] f=ω1J p +ω2J N (6)

[0048] J p =||p b ||2+||q b ||2 (7)

[0049] J N =||F0||2+||N0||2 (8)

[0050] In the formula, q b and p b Let F0 and N0 represent the attitude angle and position of the base, respectively; let F0 and N0 represent the reaction force and reaction torque generated by the robotic arm on the base, respectively; and let f represent the objective function J for base posture optimization. p And the reaction force optimization objective function J N The comprehensive index, and the weighting coefficients ω1 and ω2, can be determined according to the accuracy requirements of the planning. This invention defines the objective function J3≤1 as meaning the objective function already meets the required accuracy.

[0051] In summary, the following objective function for optimal trajectory optimization is defined:

[0052] J = aJ1 + bJ2 + cJ3 (9)

[0053] Where a, b, and c are the coefficients of time, energy, and base stability performance indicators, respectively.

[0054] 2.4 For the joint angles q∈R of the space robot 6 and its speed and acceleration Impose constraints. Plan the motion of the space robot's joints to satisfy the following constraints:

[0055]

[0056]

[0057] In the formula, i = 1, ..., 6, q i0 Let q be the initial state of the i-th joint angle at time t0; if For the i-th joint angle at t f The final state at time q; i_minLet q represent the minimum value of the i-th joint angle. i_max This represents the maximum value of the i-th joint angle. The limit velocity of the joint angle. This represents the limiting acceleration at the joint angle.

[0058] Evaluation functions for joint angular velocity and angular acceleration Defined as follows

[0059]

[0060]

[0061] In the formula, and These represent the out-of-limit indicators for the angular velocity and angular acceleration of each joint of the robotic arm; and These represent the limiting angular velocity and limiting angular acceleration of each joint, respectively. and These represent the values ​​in [t0, t] respectively. f Within a given time interval, the maximum velocity and maximum acceleration of the i-th joint.

[0062] 2.5. Combining equation (9), the objective function under the condition of limited joint angular velocity and angular acceleration is defined as follows:

[0063]

[0064] In the formula, The weighting coefficients for the joint angular velocity constraints; These are the weighting coefficients for the joint angular acceleration constraints.

[0065] Step 3 uses sine functions to parameterize the joint angles of the space robot, specifically:

[0066] The joint angles are parameterized using a sine polynomial function. The function formula is shown below:

[0067] q i (t)=Δ i1 sin(α i7 t 7 +α i6 t 6 +α i5 t 5 +α i4 t 4 +α i3 t 3 +α i2 t 2 +α i1 t+α i0 )+Δ i2 (15)

[0068] In the formula, i=1,...,6,α i0 ~α i7 These are called polynomial coefficients, representing the joint angle parameters of the six joints, combined with the constraints of equation (11).

[0069]

[0070] Differentiating equation (15) with respect to time t, we obtain the expression for the joint angular velocity as follows:

[0071]

[0072] Differentiating equation (17) again with respect to time t, we can obtain the joint angular acceleration from the following equation.

[0073]

[0074] Substituting equations (8)-(11) into equations (15)-(18) and rearranging, we can obtain the parameters of the polynomial as follows:

[0075]

[0076] α i1 =0, α i2 =0 (20)

[0077]

[0078]

[0079]

[0080] After parameterization with a seventh-order sine polynomial function, each joint has only the variable α. i6 and α i7 It cannot be determined; they are functions of joint angles, velocities, and accelerations. Define vectors.

[0081]

[0082] Once α is determined, the joint trajectory of the space robot is uniquely determined.

[0083] Step 4: An improved genetic particle swarm optimization algorithm is used to find the optimal parameters, combining two improved search algorithms. This algorithm utilizes the selection operator of the genetic algorithm and the velocity and position update mechanism of the PSO algorithm, while introducing particle swarm optimization and mutation operators to improve optimization efficiency. Specifically, the algorithm first uses the selection operator of the genetic algorithm to sort the fitness values ​​in descending order, retaining a subset of individuals with higher fitness values ​​while maintaining population diversity and improving convergence speed. Then, an adaptive weighted particle swarm optimization algorithm is used to update the velocity and position of individuals, employing non-linear dynamic inertia weights, i.e., the inertia weights automatically change with the objective function value of the particles, increasing the maturity of individuals. For the crossover operator, a survival-of-the-fittest strategy is adopted, emphasizing competition between individuals. Finally, the mutation operator is introduced using particle swarm optimization to mutate individuals that have completed the crossover operation, increasing population diversity. Figure 4 As shown, the specific steps include:

[0084] 4.1. Initialize the relevant parameters of the population and calculate the fitness function value according to equation (14). If the set optimal requirements are met, proceed to step 4.8; otherwise, continue to step 4.2.

[0085] 4.2 Sort all individuals in descending order of fitness value; and remove the 1 / 4 of individuals whose fitness value is least in line with expectations;

[0086] 4.3. Copy the middle third of the remaining individuals from the three equal parts, and keep the other two parts for the next iteration to form a new population;

[0087] 4.4. Perform the adaptive weighted particle swarm optimization (IPSO) evolution process and update the velocity and position of the individual according to equations (25), (26) and (27);

[0088] v ij (t+1)=ωv ij (t)+c1r1[p ij -x ij (t)]+c2r2[p gj -x ij (t)] (25)

[0089] x ij (t+1)=x ij (t)+v ij (t+1) (26)

[0090]

[0091] In the formula, v ij (t), x ij (t) represents the current velocity and position of the individual; vij (t+1),x ij (t+1) represents the updated velocity and position of the individual; j = 1,...,d; d is the dimension of the search space; ω represents the inertia weight, whose value changes with the current fitness function value F; c1 and c2 are called acceleration coefficients; r1 and r2 represent two independent uniformly distributed random variables, ranging from (0,1); p ij p represents the optimal value of the particle itself. gj This is called the optimal value for the entire population; maxT represents the maximum value of the population; ω min ω max This represents the minimum and maximum values ​​of ω. f min f max f avg Let f represent the minimum, maximum, and average values ​​of f, respectively.

[0092] 4.5. Two individuals are grouped together. Two groups are selected, and the two individuals with higher fitness values ​​in the two groups are crossover and mutation operations according to equations (28) and (29).

[0093]

[0094]

[0095] In the formula: θ∈(0,1); x 1new x 2new Represents the two individuals after the update; x 1 x 2 The two best individuals from the previous generation; x j The ωth best individual of the previous generation g Each component, ω g c3 and c4 are inertial weights, c3 and c4 are acceleration coefficients, and r3 and r4 represent two independent uniformly distributed random variables with a range of (0,1).

[0096] 4.6 Update the speed and position of the remaining two individuals again;

[0097] 4.7 Merge the mutated individuals and the particles that undergo IPSO evolution again to form a new population;

[0098] 4.8. If the requirements are met, output the optimal solution α = (α... 16 ,α 17 ,…,α i6 ,α i7 ) and its fitness function value F min (α).

[0099] Step 5 uses the optimal parameters obtained in Step 4 to solve for the robot's trajectory with minimum base disturbance, specifically:

[0100] The optimal solution α = (α) obtained in step 4 16 ,α 17 ,…,α i6 ,α i7 Substitute these equations (15)-(18) into step 3 to obtain the trajectory of the space robot.

[0101] Example

[0102] To verify the effectiveness of this invention, a 6-DOF space robot (specific parameters as follows) was used. Figure 3 Taking as an example, we can perform trajectory planning on it.

[0103] Step 1: Establish a space robot system model

[0104] 1.1 Kinematics

[0105] For a space robot with 6 degrees of freedom, its kinematic equations can be expressed as:

[0106]

[0107] Among them, v e and ω e These represent the velocity and angular velocity of the end effector, respectively; v0 and ω0 represent the velocity and angular velocity of the base; J b ∈R 6×6 J represents the Jacobian matrix of the base. m ∈R 6×n The Jacobian matrix represents the robotic arm system. This represents the generalized velocity of each joint of the robotic arm.

[0108] 1.2 Dynamics

[0109] Assuming that all external forces and torques acting on the space robot system, except for joint driving torques, are zero, then the dynamics of the space robot can be expressed as:

[0110]

[0111] Where H(q) represents the system's inertia matrix; is the nonlinear term in the system; μ represents the driving torque applied to each joint of the robotic arm.

[0112] Step 2: Define the optimization objective function that minimizes time, energy, and base disturbance;

[0113] Let the initial joint angle and the desired joint angle of the space robot be q respectively. i0 =[45° 20° 15° 55° 35°60°] and q if= [15° 10° 5° 25° 25° 30°]. The range of joint angle values ​​is set as follows:

[0114]

[0115] The range of joint angular velocity is shown in the following formula:

[0116]

[0117] The range of joint angular acceleration is as follows:

[0118]

[0119] 2.1 Define the time-optimal objective function:

[0120]

[0121] 2.2 Define the objective function for minimizing energy consumption:

[0122]

[0123] 2.3 Define the objective function for minimizing base disturbance:

[0124]

[0125] f=ω1J p +ω2J N (9)

[0126] J p =||p b ||2+||q b ||2 (10)

[0127] J N =||F0||2+||N0||2 (11)

[0128] In the formula, q b and p b The attitude angle and position of the base are respectively represented by F0 and N0, which represent the reaction force and reaction torque generated by the robotic arm on the base, respectively. The magnitudes of the coefficients ω1 and ω2 can be determined according to the planned accuracy requirements. In this invention, the objective function J3≤1 is defined as the objective function meeting the required accuracy.

[0129] In summary, the following objective function for optimal trajectory optimization is defined:

[0130] J = aJ1 + bJ2 + cJ3 (12)

[0131] Where a, b, and c are the coefficients of time, energy, and base stability performance indicators, respectively.

[0132] 2.4 For the joint angles q∈R of the space robot 6 and its speed and acceleration Impose constraints. Plan the motion of the space robot's joints to satisfy the following constraints:

[0133]

[0134]

[0135] In the formula, i = 1, ..., 6, q i0 Let q be the initial state of the i-th joint angle at time t0; if For the i-th joint angle at t f The final state at time q; i_min Let q represent the minimum value of the i-th joint angle. i_max This represents the maximum value of the i-th joint angle. The limit velocity of the joint angle. This represents the limiting acceleration at the joint angle.

[0136] The evaluation functions for joint angular velocity and angular acceleration are defined as follows:

[0137]

[0138]

[0139] In the formula, and They represent the values ​​in [t0, t] respectively. f Within a given time interval, the maximum velocity and maximum acceleration of the i-th joint.

[0140] 2.5. Combining equation (12), the objective function under the condition of limited joint angular velocity and angular acceleration is defined as follows:

[0141]

[0142] In the formula, The weighting coefficients for the joint angular velocity constraints; These are the weighting coefficients for the joint angular acceleration constraints.

[0143] Step 3 uses sine functions to parameterize the joint angles of the space robot, specifically:

[0144] The joint angles are parameterized using a sine polynomial function. The function formula is shown below:

[0145] q i (t)=Δ i1 sin(α i7 t7 +α i6 t 6 +α i5 t 5 +α i4 t 4 +α i3 t 3 +α i2 t 2 +α i1 t+α i0 )+Δ i2 (18)

[0146] In the formula, i=1,...,6,α i0 ~α i7 These are called polynomial coefficients, representing the joint angle parameters of the six joints, combined with the constraints of equation (14).

[0147]

[0148] Differentiating equation (18) with respect to time t, we obtain the expression for the joint angular velocity as follows:

[0149]

[0150] Differentiating equation (20) again with respect to time t, we can obtain the joint angular acceleration from the following equation.

[0151]

[0152] Substituting equations (13) and (14) into equations (18)-(20), and rearranging, we can obtain the parameters of the polynomial as follows:

[0153]

[0154] α i1 =0, α i2 =0 (23)

[0155]

[0156]

[0157]

[0158] After parameterization with a seventh-order sine polynomial function, each joint has only the variable α. i6 and α i7 It cannot be determined; they are functions of joint angles, velocities, and accelerations. Define vectors.

[0159]

[0160] Once α is determined, the joint trajectory of the space robot is uniquely determined.

[0161] Step 4 uses an improved genetic particle swarm optimization algorithm to find the optimal parameters (e.g., ...). Figure 4 As shown), the specific steps include:

[0162] 4.1. Initialize the relevant parameters of the population and calculate the fitness function value according to equation (17). If the set optimal requirements are met, proceed to step 4.8; otherwise, continue to step 4.2.

[0163] 4.2 Sort all individuals in descending order of fitness value; and remove the 1 / 4 of individuals whose fitness value is least in line with expectations;

[0164] 4.3. Copy the middle third of the remaining individuals from the three equal parts, and keep the other two parts for the next iteration to form a new population;

[0165] 4.4. Perform an adaptive weighted particle swarm optimization (IPSO) evolution process, updating the individual velocity v according to equations (25), (26), and (27). ij With position x ij ;

[0166] v ij (t+1)=ωv ij (t)+c1r1[p ij -x ij (t)]+c2r2[p gj -x ij (t)] (28)

[0167] x ij (t+1)=x ij (t)+v ij (t+1) (29)

[0168]

[0169] In the formula, v ij (t), x ij (t) represents the current velocity and position of the individual; v ij (t+1),x ij (t+1) represents the updated velocity and position of the individual; j = 1, ..., d; d is the dimension of the search space; ω represents the inertia weight, whose value changes with the current fitness function value F; c1 and c2 are called acceleration coefficients; r1 and r2 represent two independent uniformly distributed random variables, ranging from (0, 1); p ij p represents the optimal value of the particle itself. gjThis is called the optimal value for the entire population; maxT represents the maximum value of the population; ω min ω max This represents the minimum and maximum values ​​of ω. F min F max F avg Let F represent the minimum, maximum, and average values, respectively.

[0170] 4.5. Two individuals are grouped together. Two groups are selected, and the two individuals with higher fitness values ​​in the two groups are crossover and mutation operations according to equations (31) and (32).

[0171]

[0172]

[0173] In the formula: θ∈(0,1); x 1new x 2new Represents the two individuals after the update; x 1 x 2 The two best individuals from the previous generation; x j The ωth best individual of the previous generation g Each component, ω g c3 and c4 are inertial weights, c3 and c4 are acceleration coefficients, and r3 and r4 represent two independent uniformly distributed random variables with a range of (0,1).

[0174] 4.6 Update the speed and position of the remaining two individuals again;

[0175] 4.7 Merge the mutated individuals and the particles that undergo IPSO evolution again to form a new population;

[0176] 4.8. If the requirements are met, output the optimal solution α = (α... 16 ,α 17 ,…,α i6 ,α i7 ) and its fitness function value F min (α).

[0177] Step 5 uses the optimal parameters obtained in Step 4 to solve for the robot's optimal trajectory, specifically:

[0178] The optimal solution α = (α) obtained in step 4 16 ,α 17 ,…,α i6 ,α i7 Substituting these equations into steps 3 (18)-(20) yields the motion trajectory of the space robot. Figure 5The comparison of base stability before and after optimization shows that the trajectory optimized by this invention can significantly reduce the impact of base disturbances on system stability. Figure 6 , 7 Figure 8 shows the planned joint angle trajectory, joint angular velocity trajectory, and joint angular acceleration trajectory. The obtained trajectory curves can all meet the set expectations, while taking into account the motion time and energy consumption. Moreover, the trajectory curves are relatively smooth, which meets the actual engineering application requirements.

[0179] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimal trajectory planning of a space robot based on an improved genetic particle swarm optimization algorithm, characterized in that, Includes the following steps: Step 1: Establish the kinematic and dynamic equations of the space robot; Step 2: Define the objective function for optimizing the optimal trajectory: J = aJ1 + bJ2 + cJ3 (1) Where a, b, and c are the performance coefficients for time, energy, and base stability, respectively; The time-optimal objective function J1 is: This represents the time from the initial time t0 to the final time t. f The time of movement between; The objective function for minimizing energy consumption is J2: This represents the time from the initial time t0 to the final time t of the motion. f The energy consumption generated by applying active control u(t) to the robot; Objective function J3 for minimizing base disturbance: f=ω1J p +ω2J N (5) J p =||p b ||2+||q b ||2 (6) J N =||F0||2+||N0||2 (7) In the formula, q b and p b Let F0 and N0 represent the attitude angle and position of the base, respectively; let F0 and N0 represent the reaction force and reaction torque generated by the robotic arm on the base, respectively; and let f represent the objective function J for base posture optimization. p And the reaction force optimization objective function J N The comprehensive index, where ω1 and ω2 are weighting coefficients; Step 3: Parameterize the joint angles of the space robot using sine functions; Step 4: Use the improved genetic particle swarm optimization algorithm to find the optimal parameters; Step 5: Solve for the optimal trajectory of the robot using the obtained optimal parameters.

2. The method according to claim 1, characterized in that, In step 2, the evaluation functions for joint angular velocity and angular acceleration are... Defined as follows In the formula, and These represent the out-of-limit indicators for the angular velocity and angular acceleration of each joint of the robotic arm, respectively. and These represent the limiting angular velocity and limiting angular acceleration of each joint, respectively. and These represent the values ​​in [t0, t] respectively. f Within a given time interval, the maximum velocity and maximum acceleration of the i-th joint; Combining equation (1), the objective function under the condition of limited joint angular velocity and angular acceleration is defined as follows: In the formula, These are the weighting coefficients for the joint angular velocity constraints. These are the weighting coefficients for the joint angular acceleration constraints.

3. The method according to claim 2, characterized in that, Step 3 uses sine functions to parameterize the joint angles of the space robot, specifically: The joint angles are parameterized using a sine polynomial function, the formula of which is shown below: q i (t)=Δ i1 sin(a i7 t 7 +a i6 t 6 +a i5 t 5 +a i4 t 4 +a i3 t 3 +a i2 t 2 +a i1 t+a i0 )+Di i2 (15) In the formula, i=1,…,6,α i0 ~α i7 These are called polynomial coefficients, representing the joint angle parameters of the six joints; Differentiating equation (15) with respect to time t, we obtain the expression for the joint angular velocity as follows: Differentiating equation (17) again with respect to time t, the joint angular acceleration can be obtained from the following equation. Substituting equations (8)-(11) into equations (15)-(18), and rearranging, we obtain the parameters of the polynomial as follows: α i1 ＝0，α i2 ＝0 (20) After parameterization with a seventh-order sine polynomial function, each joint has only the variable α. i6 and α i7 It cannot be determined; they are functions of joint angles, velocities, and accelerations; define vectors. Once α is determined, the joint trajectory of the space robot is uniquely determined.

4. The method according to claim 3, characterized in that, Step 4 uses an improved genetic particle swarm optimization algorithm to find the optimal parameters, combining two improved search algorithms. This algorithm first uses the selection operator of the genetic algorithm to sort the fitness values ​​in descending order, retaining a subset of individuals with higher fitness values. Then, it uses an adaptive weighted particle swarm algorithm to update the velocity and position of the individuals, employing non-linear dynamic inertia weights, meaning the inertia weights automatically change with the objective function value of the particles, thus increasing the maturity of the individuals. For the crossover operator, a survival-of-the-fittest strategy is adopted, emphasizing competition between individuals. Finally, a mutation operator is introduced using particle swarm optimization to mutate individuals that have completed the crossover operation.

5. The method according to claim 4, characterized in that, Step 4 specifically includes the following steps: Step 4.1: Initialize the relevant parameters of the population and calculate the fitness function value according to Equation (10). If the set optimal requirements are met, proceed to step 4.8; otherwise, continue to step 4.

2. Step 4.2: Sort all individuals in descending order of fitness value; and remove the 1 / 4 of individuals whose fitness value is least in line with expectations; Step 4.3: Copy the middle third of the remaining individuals from the three equal parts, and keep the other two parts for the next iteration to form a new population; Step 4.4: Execute the adaptive weighted particle swarm evolution process and update the velocity and position of the individual according to equations (25), (26) and (27); v ij (t+1)=ωv ij (t)+c1r1[p ij -x ij (t)]+c2r2[p gj -x ij (t)] (25) x ij (t+1)=x ij (t)+v ij (t+1) (26) In the formula, v ij (t), x ij (t) represents the current velocity and position of the individual; v ij (t+1),x ij (t+1) represents the updated velocity and position of the individual; j = 1,...,d; d is the dimension of the search space; ω represents the inertia weight, whose value changes with the current fitness function value F; c1 and c2 are called acceleration coefficients; r1 and r2 represent two independent uniformly distributed random variables, ranging from (0,1); p ij p represents the optimal value of the particle itself. gj This is called the optimal value for the entire population; maxT represents the maximum value of the population; ω min ω max f represents the minimum and maximum values ​​of ω; min f max f avg Let f represent the minimum, maximum, and average values ​​of f, respectively. Step 4.5: Select two individuals as a group, and perform crossover and mutation operations on the two individuals with higher fitness values ​​in the two groups according to equations (28) and (29); In the formula: θ∈(0,1); x 1new x 2new Represents the two individuals after the update; x 1 x 2 The two best individuals from the previous generation; x j The ωth best individual of the previous generation g Each component, ω g c3 and c4 are inertial weights, c3 and c4 are acceleration coefficients, and r3 and r4 represent two independent uniformly distributed random variables with a range of (0,1). Step 4.6: Update the speed and position of the remaining two individuals again; Step 4.7: Merge the mutated individuals and the particles that undergo IPSO evolution again to form a new population; Step 4.8: If the requirements are met, output the obtained optimal solution α = (α 16 ,α 17 ,…,α i6 ,α i7 ) and its fitness function value F min (α).

6. The method according to claim 5, characterized in that, Step 5 uses the optimal parameters obtained in Step 4 to solve for the robot's trajectory with minimum base disturbance, specifically: The optimal solution α = (α) obtained in step 4 16 ,α 17 ,…,α i6 ,α i7 Substitute these equations (15)-(18) into step 3 to obtain the trajectory of the space robot.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-6.

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