Manipulator Trajectory Planning Method and System Based on Improved Great White Shark Optimization Algorithm

Abstract

The robotic arm trajectory planning method and system based on the improved white shark optimization algorithm disclosed by the present invention include: obtaining the joint angles of each interpolation point in the robotic arm joints; obtaining the joint motion trajectory according to the joint angles of each interpolation point and the polynomial interpolation trajectory model; wherein, with the goal of minimizing the sum of all interpolation times, each interpolation time in the polynomial interpolation trajectory model is determined by the improved white shark optimization algorithm. By optimizing the interpolation time through the improved white shark optimization algorithm, the joint motion trajectory is finally obtained. When the robotic arm joints move according to this joint motion trajectory, the motion time is the shortest.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm trajectory planning, and particularly to a robotic arm trajectory planning method and system based on an improved white shark optimization algorithm. Background Art

[0002] The statements in this part merely provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] In the control of exoskeleton robots, trajectory planning is an important basic research. By setting path time information, the kinematic parameters of the robotic arm between each path point can be planned, thereby improving the motion accuracy and stability of the robotic arm. When using polynomial interpolation trajectory planning, as the interpolation order increases, the computational amount increases sharply, which may lead to the "Runge phenomenon", resulting in the non-convergence and oscillation of the curve fitted by the robotic arm trajectory planning, poor fitting performance, and unsatisfactory interpolation effect. Optimizing the robotic arm trajectory can effectively solve problems such as low efficiency, high energy consumption, and large impact of the robotic arm. Due to the high coupling and non-linear characteristics of the exoskeleton robotic arm trajectory optimization problem, it is difficult for many current trajectory optimization methods to obtain its optimal solution or sub-optimal solution. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a robotic arm trajectory planning method and system based on an improved white shark optimization algorithm. By optimizing the time in the polynomial interpolation trajectory model through the improved white shark optimization algorithm, the joint motion trajectory is obtained. When the robotic arm joints move according to this motion trajectory, the motion time is the shortest.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] In the first aspect, a robotic arm trajectory planning method based on an improved white shark optimization algorithm is proposed, including:

[0007] Obtaining the joint angles of each interpolation point in the robotic arm joints;

[0008] Obtaining the joint motion trajectory according to the joint angles of each interpolation point and the polynomial interpolation trajectory model;

[0009] Among them, with the goal of minimizing the sum of all interpolation times, each interpolation time in the polynomial interpolation trajectory model is determined by the improved white shark optimization algorithm.

[0010] In the second aspect, a robotic arm trajectory planning system based on an improved white shark optimization algorithm is proposed, including:

[0011] A joint angle acquisition module for obtaining the joint angles of each interpolation point in the robotic arm joints;

[0012] The optimal joint angle determination module is used to obtain the joint motion trajectory according to the joint angles of each interpolation point and the polynomial interpolation trajectory model; wherein, with the goal of minimizing the sum of all interpolation times, the improved great white shark optimization algorithm is used to determine each interpolation time in the polynomial interpolation trajectory model.

[0013] In a third aspect, an electronic device is proposed, including a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the steps of the robotic arm trajectory planning method using the improved great white shark optimization algorithm are completed.

[0014] In a fourth aspect, a computer-readable storage medium is proposed, which is used to store computer instructions. When the computer instructions are executed by the processor, the steps of the robotic arm trajectory planning method using the improved great white shark optimization algorithm are completed.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0016] 1. The present invention optimizes the time in the polynomial interpolation trajectory model through the improved great white shark optimization algorithm to obtain the joint motion trajectory. When the robotic arm joints move according to this motion trajectory, the motion time is the shortest, and it can move from the initial point to the target point more quickly and smoothly, thus effectively shortening the running time of the robotic arm.

[0017] Advantages of additional aspects of the present invention will be partly given in the following description, partly will become obvious from the following description, or be understood through the practice of the present invention. Description of the Drawings

[0018] The specification drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application.

[0019] Figure 1 It is a flowchart of the method disclosed in Embodiment 1;

[0020] Figure 2 It is a schematic diagram of the 3-5-3 piecewise polynomial disclosed in Embodiment 1;

[0021] Figure 3 It is a flowchart of the improved great white shark optimization algorithm disclosed in Embodiment 1;

[0022] Figure 4 It is the end trajectory of the robotic arm in three-dimensional space disclosed in Embodiment 1;

[0023] Figure 5 It is the end motion curve of the robotic arm disclosed in Embodiment 1;

[0024] Figure 6The joint motion curves disclosed in Embodiment 1. Detailed implementation manners

[0025] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0026] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further descriptions of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0027] Embodiment 1

[0028] In this embodiment, a manipulator trajectory planning method based on an improved white shark optimization algorithm is disclosed. As Figure 1 shown, it includes:

[0029] S1: Obtain the joint angles of each interpolation point in the manipulator joints.

[0030] In this embodiment, it is set that the manipulator joints have four interpolation points, and the four interpolation points include an initial point, a target point, and two process points between the initial point and the target point.

[0031] Inverse kinematics solution is performed on the positions of each interpolation point to obtain the joint angles of each interpolation point.

[0032] S2: Obtain the joint motion trajectory according to the joint angles of each interpolation point and the polynomial interpolation trajectory model; wherein, with the goal of minimizing the sum of all interpolation times, each interpolation time in the polynomial interpolation trajectory model is determined by an improved white shark optimization algorithm.

[0033] Preferably, a 3-5-3 piecewise polynomial interpolation method is used to construct the polynomial interpolation trajectory model.

[0034] In this embodiment, a 3-5-3 piecewise polynomial algorithm is used to construct a motion trajectory between 4 interpolation points of each joint of the manipulator to obtain a polynomial interpolation trajectory model.

[0035] As Figure 2 shown, for the first segment (0 - t1), a cubic interpolation polynomial is used for the manipulator trajectory planning; for the second segment (t1 - t2), a quintic interpolation polynomial is used for the manipulator trajectory planning, and for the third segment (t2 - t3), a cubic interpolation polynomial is used for the manipulator trajectory planning.

[0036] The expression of the polynomial interpolation trajectory model is as follows:

[0037] The cubic interpolation polynomial of the first segment is:

[0038]

[0039] The fifth-degree interpolation polynomial of the second segment is:

[0040]

[0041] The third-degree interpolation polynomial of the third segment is:

[0042]

[0043] where θ is the joint angle, is the joint angular velocity, is the joint angular acceleration, t is the time, and a j are the polynomial coefficients.

[0044] The joint angles of the four interpolation points of the joint are X j1 , X j2 , X j3 , X j4 , and the motion trajectory of the robotic arm at the interpolation points is continuous. Its coefficient matrix is:

[0045]

[0046] The matrix composed of polynomial coefficients is:

[0047] a = [a j13 a j12 a j11 a j10 a j25 a j24 a j23 a j22 a j21 a j20 a j33 a j32 a j31 a j30 T (1 - 5)

[0048] The expression of the joint angle is:

[0049] B = [0 0 0 0 0 0 X j4 0 0 X j1 0 0 X j3 [[ID=8O]] X j2 T (1 - 6)

[0050] From a = A -1 ·B, the polynomial coefficients of the polynomial interpolation trajectory model can be obtained, and then the specific expression of the polynomial interpolation trajectory model can be obtained, and finally the joint motion trajectory can be obtained.

[0051] ​​To minimize the time for the joint to move from the starting point to the target point along the joint motion trajectory, that is, to minimize the sum of all interpolation times, the improved white shark optimization algorithm is used to optimize each interpolation time to obtain the final interpolation time.

[0052] The process of determining the interpolation time through the improved white shark optimization algorithm is as follows:

[0053] Regarding each interpolation time as a shark individual, a shark swarm is constructed, and the tolerance and the maximum number of stagnations are set. An objective function is constructed with the goal of minimizing the sum of all interpolation times. The objective function is used as the fitness function of the white shark optimization algorithm for iterative calculation. During each iteration, the global best position vector of the white shark is determined according to the current position of the white shark. When the change amount of the global best position vector of the white shark is less than the tolerance for consecutive maximum stagnation times, the iteration stops, and the final interpolation time is obtained.

[0054] Specifically, during each iteration, the fitness value of each white shark is calculated according to the current position of the white shark; according to the fitness value of the white shark, the current global best position vector of the white shark is determined; according to the current global best position vector of the white shark, the updated position of the white shark is determined; the current position of the white shark is updated through the updated position of the white shark to determine the updated position of the white shark; the updated position of the white shark is used as the current position of the white shark in the next iteration process.

[0055] In this embodiment, when determining the interpolation time through the improved white shark optimization algorithm, in addition to constructing an objective function with the goal of minimizing the sum of all interpolation times, the joint angles, angular velocities, and angular accelerations of the outer limb manipulator are also restricted to satisfy the joint angle constraint, angular velocity constraint, and angular acceleration constraint, respectively.

[0056] Based on the constructed polynomial interpolation trajectory model, the objective function with the goal of minimizing the sum of all interpolation times is:

[0057]

[0058] where f(t) is the objective function, and t j1 、t j2 、t j3 are the three interpolation times of the polynomial interpolation trajectory model.

[0059] The joint angles, angular velocities, and angular accelerations of the outer limb manipulator satisfy the joint angle constraint, angular velocity constraint, and angular acceleration constraint, respectively, as follows:

[0060]

[0061] where q j (t), and respectively represent the joint angle, angular velocity, and angular acceleration of the jth joint. A jmax , V jmax , W jmax respectively represent the joint angle limit value, angular velocity limit value, and angular acceleration limit value.

[0062] With the goal of the shortest movement time and subject to joint angle constraints, angular velocity constraints, and angular acceleration constraints, the optimal movement trajectory of the robotic arm joints is determined through an improved white shark optimization algorithm.

[0063] In this embodiment, a tolerance Δ tol is introduced into the improved white shark optimization algorithm, which is used to represent the precision value that the fitness function needs to reach. During the iteration process of the white shark optimization algorithm, after obtaining the current global best position vector of the white shark each time, the change amount Δ between it and the global best position vector of the white shark fit in the previous iteration is calculated to check whether the precision requirement is met. Δ fit is defined as in Equation (1-9):

[0064]

[0065] Judge the relative magnitudes of Δ fit and Δ tol . If the former is smaller, then stagnates. At each iteration, detect whether stagnates. To optimize the performance of the algorithm, when the improved algorithm meets any of the following conditions, the search ends:

[0066] (1) If it stagnates for C stop consecutive iterations , the program exits the search. Among them, C stop is defined as the maximum number of stagnant times.

[0067] (2) When the maximum number of iterations is reached, the program exits the search.

[0068] The main steps to determine the interpolation time for each segment through the improved white shark optimization algorithm (WSO) are as shown in Figure 3 and include:

[0069] Step 1: Initialize the parameters of the improved white shark optimization algorithm, including: the dimension Dim of the population, the number N of white sharks, and the maximum number of iterations Iter max .

[0070] Step 2: Initialize the position w of the white shark, and each white shark position corresponds to a segment of interpolation time.

[0071] Step 3: Initialize the velocity ν of the white shark.

[0072] Step 4: According to the current position of the great white sharks, solve the objective function to obtain the fitness value of each great white shark. At the same time, according to the current position of the great white sharks, determine the joint angles, joint angular velocities, and joint angular accelerations, and then judge whether the joint angles, joint angular velocities, and joint angular accelerations meet the constraint conditions. Obtain the fitness values of the great white sharks that meet the constraint conditions, and select the current position of the great white shark with the smallest global fitness value as the current global best position vector.

[0073] When performing the first iteration, the current position of the great white sharks is the initial position of the great white sharks.

[0074] Determine the updated position of the great white sharks according to the current global best position vector of the great white sharks; update the current position of the great white sharks through the updated position of the great white sharks to determine the updated position of the great white sharks.

[0075] Step 5: Judge whether the updated position of the great white sharks meets the constraint conditions. Take the updated position of the great white sharks that meets the constraint conditions as the current position of the great white sharks in the next iteration process. According to the updated position of the great white sharks, calculate the fitness value of each updated great white shark, and find the current global best position vector of the great white sharks. Compare the minimum value of the current great white shark fitness value with the minimum value of the objective function obtained in Step 4. If the former is smaller, then replace the minimum value of the objective function obtained in Step 4 with the minimum value of the fitness value obtained in this iteration.

[0076] When the current global best position of the great white sharks stagnates or the maximum number of iterations is reached, stop the iteration and output the optimal solution, which is the final interpolation time.

[0077] When the best position of the great white sharks does not meet the stagnation conditions, return to Step 4.

[0078] Each iteration process of the improved great white shark optimization algorithm includes four stages:

[0079] (1) Quickly approaching the prey

[0080] When the great white shark moves towards the prey, it determines the position of the prey according to the fluctuations of the ocean waves, and then quickly approaches the prey in a undulating motion. This motion can be defined using mathematical equations:

[0081]

[0082] where, i = 1, 2,... n represents a group of n great white sharks, represents the new velocity vector of the i-th great white shark in the (m + 1)-th iteration, is defined as the current velocity vector of the i-th great white shark in the m-th iteration, represents the global best position vector obtained by all great white sharks in the m-th iteration so far, represents the current position vector of the i-th white shark in the m-th iteration, represents the i-th best position vector known to the group, i represents the i-th index vector of the white shark reaching the best position, c1 and c2 are two random numbers uniformly generated in the range [0,1], h1 and h2 represent the control and right is the force affecting the white shark, and μ is the contraction factor proposed in WSO, which is used to analyze the convergence behavior of the great white shark.

[0083]

[0084] Here, rand(1,n) is a random number vector uniformly distributed in the range [0,1].

[0085]

[0086]

[0087] Among them, m and M represent the current number of iterations and the maximum number of iterations respectively, h min and h max They represent the initial speed and slave speed for achieving good movement of the white shark, with values of 0.5 and 1.5 respectively.

[0088]

[0089] Here, τ represents the acceleration coefficient, and its value is 4.125.

[0090] (2) Surround the best prey

[0091] White sharks move randomly in search of prey, similar to the behavior of a school of fish looking for food. The following formula models the behavior of a white shark moving towards its prey:

[0092]

[0093] in refers to the new position vector of the i-th white shark in the m+1-th iteration, is a negation operator, a and b are one-dimensional binary vectors, defined as in Equations (1-16) and (1-17). l and u represent the lower and upper limits of the search space, respectively. w0 represents a logical vector, defined as in Equation (1-18); f represents the frequency of the white shark's wave motion, defined as in Equation (1-19); rand is a random number in the range [0,1]; and mv represents the intensity of the white shark's hearing and smell when approaching its prey. The value of mv affects the white shark's search strategy. Smaller values cause it to conduct a local search, while larger values cause it to conduct a global search, defined as in Equation (1-20).

[0094]

[0095]

[0096]

[0097] Among them, is the bitwise exclusive OR operation.

[0098]

[0099] Among them, f min and f max respectively represent the minimum and maximum frequencies of the wave motion, with values of 0.07 and 0.75 respectively.

[0100]

[0101] Among them, the constants a0 and a1 are used to control the exploration and exploitation behaviors, with values of 6.25 and 100 respectively.

[0102] (3) Approach the optimal position

[0103] When the great white shark discovers the prey and starts to surround it, it will approach the optimal attacking position to better hunt the prey:

[0104]

[0105] Among them, represents the updated position of the i-th great white shark relative to the prey position. sgn(d2 - 0.5) takes 1 or -1 to change the search direction. The variables d1, d2, and d3 are random numbers in the range [0, 1]. is the distance between the prey and the great white shark, defined as in Equation (1 - 22). The parameter s n is used to represent the olfactory and visual intensities of other great white sharks when a great white shark is tracking and approaching the optimal prey, defined as in Equation (1 - 23).

[0106]

[0107] Among them, rand is a random number in the range [0, 1].

[0108]

[0109] Among them, the constant a2 is used to control the exploration and exploitation behaviors, with a value of 0.0005. When the optimal great white shark approaches the prey, the great white shark will update its position according to the optimal position.

[0110] (4) School behavior

[0111] To mathematically simulate the behavior of a white shark group, the first two best solutions are retained, and these two best positions are used to update the positions of other white sharks. Specifically, the current position of the white shark is added to the updated position of the white shark and then multiplied by a random number of 2 times to obtain the updated position of the white shark.

[0112]

[0113] The joint motion trajectory obtained in this embodiment is sent to the robotic arm controller, and the controller sends instructions to the robotic arm to make the robotic arm start moving according to the joint motion trajectory; the robotic arm feeds back joint information to the controller in real time, and the controller determines whether the expected joint angle is reached. If it reaches, it continues to execute the next position instruction. If it does not reach, it makes adjustments.

[0114] In specific implementation, the parameters of the improved white shark optimization algorithm are preferably set as follows: the population size N of the white shark = 30; the maximum number of iterations Iter max = 500; the population dimension Dim = 3; the initial optimal fitness gBest = 50; the maximum frequency and minimum frequency of the wave motion are f max = 0.75 and f min = 0.07; the acceleration coefficient τ = 4.11; the initial velocity and subordinate velocity required for the white shark to obtain good motion are h min = 0.5 and h max = 1.5; the initial value of the counter is set to C = 0; the maximum count value C stop = 30; the function change tolerance Δ tol = 0.001.

[0115] To avoid unnecessary damage caused by the robotic arm running too fast, the maximum angular velocity of each joint of the robotic arm is set to 1.396 rad / s, and the maximum angular acceleration is 1.396 rad / s 2 , the starting point and ending point of the robotic arm are (0, -0.215, 1.008) and (0.1, -0.4, 0.4) respectively, and the two interpolation points are (-0.034, -0.219, 1.006) and (0.068, -0.435, 0.441). Using the trajectory planning method disclosed in this embodiment, the joint motion trajectory is obtained. Among them, Figure 4 The joint motion trajectory of the end of the robotic arm in three-dimensional space is shown. It can be seen that the position change of the end of the robotic arm during the motion is accurate; Figure 5 The position change of the end of the robotic arm during the entire joint motion trajectory is shown. It can be seen that the path between each interpolation point of the robotic arm is very smooth; Figure 6 The motion curves of each joint of the robotic arm during the entire motion process are shown. The change of the joint variables of each joint can be observed, and the change curve is continuous and stable.

[0116] Through analysis, the trajectory optimization based on the improved great white shark optimization algorithm satisfies the kinematic constraints of the manipulator, such as joint angles, joint angular velocities, and joint angular accelerations. During the entire motion process, the manipulator does not exhibit adverse jitter, and the joint angular velocities and angular accelerations do not experience sudden changes, and the manipulator operates smoothly. The time taken for the optimized manipulator to complete the motion is 9.82 s. Compared with the 15 s required for the manipulator to complete the motion without optimization, the efficiency is increased by 34.5%. This indicates that optimizing the manipulator trajectory through the improved great white shark optimization algorithm enables the manipulator to perform actual tasks, achieving the expected experimental results.

[0117] Example 2

[0118] In this embodiment, a manipulator trajectory planning system based on the improved great white shark optimization algorithm is disclosed, including:

[0119] A joint angle acquisition module for acquiring the joint angles of each interpolation point in the manipulator joints;

[0120] An optimal joint angle determination module for obtaining the joint motion trajectory according to the joint angles of each interpolation point and the polynomial interpolation trajectory model; wherein, with the goal of minimizing the sum of all interpolation times, each interpolation time in the polynomial interpolation trajectory model is determined by the improved great white shark optimization algorithm.

[0121] Example 3

[0122] In this embodiment, an electronic device is disclosed, including a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the steps of the manipulator trajectory planning method of the improved great white shark optimization algorithm disclosed in Example 1 are completed.

[0123] Example 4

[0124] In this embodiment, a computer-readable storage medium is disclosed for storing computer instructions. When the computer instructions are executed by the processor, the steps of the manipulator trajectory planning method of the improved great white shark optimization algorithm disclosed in Example 1 are completed.

[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent substitutions can still be made to the specific embodiments of the present invention, and any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A robotic arm trajectory planning method based on an improved white shark optimization algorithm, characterized in that Including: Obtain the joint angles of each interpolation point in the robotic arm joints; Obtain the joint motion trajectory according to the joint angles of each interpolation point and the polynomial interpolation trajectory model; Among them, with the goal of minimizing the sum of all interpolation times, each interpolation time in the polynomial interpolation trajectory model is determined by an improved white shark optimization algorithm; The process of determining the interpolation time by the improved white shark optimization algorithm is as follows: Take each interpolation time as a shark individual, construct a shark swarm, set the tolerance and the maximum number of stagnations, construct an objective function with the goal of minimizing the sum of all interpolation times, use the objective function as the fitness function of the white shark optimization algorithm, and perform iterations of the white shark optimization algorithm. In each iteration process, determine the global best position vector of the white shark according to the current position of the white shark; when the change amount of the global best position vector of the white shark is less than the tolerance for continuously maximum stagnation times, stop the iteration and obtain the final interpolation time.

2. The robotic arm trajectory planning method based on the improved great white shark optimization algorithm according to claim 1, wherein It is set that there are four interpolation points for the joint, and the four interpolation points include the initial point, the target point, and two process points between the initial point and the target point.

3. The robotic arm trajectory planning method based on the improved great white shark optimization algorithm according to claim 1, wherein Adopt the 3-5-3 piecewise polynomial interpolation method to construct the polynomial interpolation trajectory model.

4. The robotic arm trajectory planning method based on the improved great white shark optimization algorithm according to claim 1, characterized in that, When determining the interpolation time by the improved white shark optimization algorithm, in addition to constructing an objective function with the goal of minimizing the sum of all interpolation times, it is also specified that the joint angles, angular velocities, and angular accelerations of the outer limb robotic arm respectively satisfy the joint angle constraint, the angular velocity constraint, and the angular acceleration constraint.

5. The robotic arm trajectory planning method based on the improved great white shark optimization algorithm according to claim 1, wherein In each iteration process, calculate the fitness value of each white shark according to the current position of the white shark; determine the current global best position vector of the white shark according to the fitness value of the white shark; determine the updated position of the white shark according to the current global best position vector of the white shark; update the current position of the white shark through the updated position of the white shark to determine the updated position of the white shark; the updated position of the white shark is used as the current position of the white shark in the next iteration process.

6. The robotic arm trajectory planning method based on the improved great white shark optimization algorithm according to claim 5, characterized in that, Add the current position of the white shark to the updated position of the white shark and then multiply by 2 times a random number to obtain the updated position of the white shark.

7. A robotic arm trajectory planning system based on an improved great white shark optimization algorithm, characterized in that, Including: A joint angle acquisition module for obtaining the joint angles of each interpolation point in the robotic arm joints; An optimal joint angle determination module for obtaining the joint motion trajectory according to the joint angles of each interpolation point and the polynomial interpolation trajectory model; among them, with the goal of minimizing the sum of all interpolation times, each interpolation time in the polynomial interpolation trajectory model is determined by an improved white shark optimization algorithm; The process of determining the interpolation time by the improved white shark optimization algorithm is as follows: Take each interpolation time as a shark individual, construct a shark swarm, set the tolerance and the maximum number of stagnations, construct an objective function with the goal of minimizing the sum of all interpolation times, use the objective function as the fitness function of the white shark optimization algorithm, and perform iterations of the white shark optimization algorithm. In each iteration process, determine the global best position vector of the white shark according to the current position of the white shark; when the change amount of the global best position vector of the white shark is less than the tolerance for continuously maximum stagnation times, stop the iteration and obtain the final interpolation time.

8. An electronic device, characterized in that, It includes a memory, a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps of the robotic arm trajectory planning method of the improved great white shark optimization algorithm described in any one of claims 1-6 are completed.

9. A computer-readable storage medium, characterized in that, For storing computer instructions, when the computer instructions are executed by the processor, the steps of the robotic arm trajectory planning method of the improved great white shark optimization algorithm described in any one of claims 1-6 are completed.

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