Method for solving inverse kinematics of redundant degree of freedom robot based on harvester beetle optimization algorithm

Abstract

The application discloses a method for solving inverse kinematics of a redundant degree of freedom robot based on a dung beetle optimization algorithm, and the method comprises the following steps: a forward kinematics model of the redundant degree of freedom robot is established by using a D-H method; an evaluation standard for solving inverse kinematics of the robot is formulated; the dung beetle optimization algorithm is improved; and the inverse kinematics evaluation index of the robot is taken as an optimization target, and the improved dung beetle optimization algorithm is used to solve the inverse kinematics of the redundant degree of freedom robot. The method for solving inverse kinematics of the redundant degree of freedom robot based on the dung beetle optimization algorithm solves the defects that the convergence speed of a traditional intelligent algorithm is not fast enough, the traditional intelligent algorithm is prone to falling into a local extremum, the speed is slow, and the accuracy is not high when solving inverse kinematics of the redundant degree of freedom robot.

Description

Technical Field

[0001] This invention belongs to the field of robot motion solution technology, specifically involving a method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm. Background Technology

[0002] With the widespread application of redundant degree-of-freedom robots in industrial production lines, the extra degrees of freedom of redundant robotic arms are used to achieve additional tasks such as obstacle avoidance, singularity avoidance, joint limit avoidance, joint torque optimization, and increased maneuverability. To better control the position of redundant degree-of-freedom robots, it is necessary to quickly solve the inverse kinematics of redundant degree-of-freedom robots.

[0003] Currently, the main methods for solving the inverse kinematics of redundant degree-of-freedom robots include geometric analytical methods, pseudo-inverse methods, and intelligent algorithms. Geometric analytical methods require specific configurations, pseudo-inverse methods suffer from cumulative errors, and traditional intelligent algorithms, while unaffected by the robot's structure and possessing versatility, suffer from slow convergence speeds and susceptibility to local extrema. To improve the solution speed and accuracy of inverse kinematics of redundant degree-of-freedom robots and simplify the solution difficulty, it is necessary to propose a method for solving the inverse kinematics of redundant degree-of-freedom robots. Summary of the Invention

[0004] The purpose of this invention is to provide a method for solving the inverse kinematics of a redundant degree-of-freedom robot based on the dung beetle optimization algorithm. This method solves the problems of slow convergence speed, easy getting trapped in local extrema, slow speed, and low accuracy of traditional intelligent algorithms when solving the inverse kinematics of redundant degree-of-freedom robots.

[0005] The technical solution adopted in this invention is a method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm, and is implemented according to the following steps:

[0006] Step 1: Use the DH method to establish a forward kinematic model of the redundant degree-of-freedom robot;

[0007] Step 2: Develop evaluation criteria for solving robot inverse kinematics;

[0008] Step 3: Improve the dung beetle optimization algorithm;

[0009] Step 4: Using the evaluation criteria of solving the robot's inverse kinematics in Step 2 as the optimization objective, use the improved dung beetle optimization algorithm from Step 3 to solve the inverse kinematics of the robot with redundant degrees of freedom.

[0010] The invention is further characterized in that,

[0011] Step 1: Multiply the transformation matrices of each joint of the robot sequentially according to the DH method to obtain the transformation matrix of the robot's end effector relative to the base coordinates, and construct a positive kinematic model.

[0012]

[0013] In the formula, m is the m-th link of the robot. The transformation matrix of the m-th link Let be the transformation matrix of the robot's end effector relative to the base coordinates, and D be the total number of degrees of freedom. When D ≥ 7, the robot is a redundant degree-of-freedom robot.

[0014] Step 2 is as follows:

[0015] In order to calculate the error between the robot's actual pose and the target pose, a fitness function is constructed by weighting the robot's approach vector and position vector.

[0016] f = η||p d -p c ||+β||a d -a c || (2)

[0017] In the formula, p d It is the target pose, p c It is the actual pose, a d and a c These are the target approach vector and the actual approach vector, respectively, and η and β are the weighting coefficients, respectively.

[0018] The inverse kinematics of the redundant robotic arm has an infinite number of solutions, while equation (3) only obtains one set of point-to-point solutions each time; in order to find a smooth and continuous motion trajectory in spatial motion, the fitness function is constructed using equation (4) for solution:

[0019]

[0020] f2=min(f+γf1) (4)

[0021] Let θ be the initial joint angle of the k-th joint. k γ is the current joint angle of the k-th joint, f1 is the minimum change in joint motion, and γ is the weighting coefficient.

[0022] The specific process of step 3 is as follows:

[0023] Step 3.1: Add Tent chaos mapping;

[0024] Step 3.2: Calculate the initial fitness values ​​of all dung beetles and determine the current optimal dung beetle position;

[0025] Step 3.3: Introduce a sinusoidal strategy to update the local optimal position of the common dung beetle;

[0026] Step 3.4: Update the local optimal positions of other Dung Beetle characters.

[0027] Step 3.5: Calculate the current global optimal position of the dung beetle colony, compare the current global optimal position with the previous generation's global optimal position, and if the fitness value of the current global optimal position is better than that of the previous generation, then update the optimal position of the dung beetle colony to the current global optimal position.

[0028] Step 3.6: If the maximum number of iterations T is not reached, repeat steps 3.3 to 3.5 until the end.

[0029] Step 3.1 Expand the search range of the initial population solution space according to equation (5);

[0030]

[0031] In the formula, X n The sequence is generated by the nth iteration, where ω is the chaos parameter and is not 0.5.

[0032] A random array sequence X0 is generated between (0, 1), where n is 0. Then, according to equation (5), an iterative calculation is performed to generate a new sequence. When n reaches the maximum number of iterations, the generated sequence is used as the initial distribution of dung beetle individuals.

[0033] The specific process of step 3.3 is as follows:

[0034]

[0035] In the formula, t represents the current iteration number. This represents the position of the i-th dung beetle in the t-th iteration; ω t For inertial weights, k∈(0,0.2] represents the deflection coefficient, and b is a constant value between (0,1); This indicates the worst position in the current population. To simulate changes in light intensity, alpha simulates natural factors that cause dung beetles to deviate from their original direction. Let r1 be the component of the optimal individual position variable in the t-th iteration; r2 is a nonlinear decreasing function; r3 is a random number in the interval [0, 2π]; δ is a random constant between (0, 1); and ST is a random number between 0.5 and 1.

[0036] The nonlinear decreasing function r1 is:

[0037]

[0038] In the formula, ω min and ω max Represents ω t The minimum and maximum values ​​of T max This represents the maximum number of iterations.

[0039]

[0040] For a regular dung beetle, when δ < ST, it indicates that the dung beetle has a designated target and is in the global exploration phase; otherwise, it means that the dung beetle has no designated target and needs to search and move using a sine function.

[0041] In step 3.4, the position of the egg ball is updated for the female dung beetle using formula (9);

[0042] B j (t+1)=X * +b1×(B j (t)-Lb * )+b2×(B j (t)-Ub * (9)

[0043] Among them, B j (t) represents the position information of the j-th egg in the t-th iteration, where b1 and b2 are two independent random vectors of size 1×D, and D is the dimension of the optimization problem, where X * Lb represents the current local optimum. * and Ub * These represent the lower and upper boundaries of the spawning area, respectively.

[0044] For dung beetles to update their foraging locations;

[0045]

[0046] Where c1 is a random number following a normal distribution, i.e., c1 ~ N(0,1), c2 is a 1×D random vector belonging to the interval (0,1), and X l The optimal local position for the current population of dung beetles; using Lb l and Ub l The lower and upper bounds of the dung beetle's foraging range were defined.

[0047] Update the location of the dung beetle thief;

[0048]

[0049] Where g represents a random vector of size 1×D that follows a normal distribution, and S represents a constant value.

[0050] The specific process of step 4 is as follows:

[0051] Step 4.1: Determine the angle range of each joint of the robot and initialize the parameters, including the number of dung beetles, the ratio between dung beetles of different roles, and the maximum number of iterations or threshold.

[0052] Step 4.2: Generate an initial population within the joint range using the Tent chaotic sequence;

[0053] Step 4.3: Calculate the fitness value of each dung beetle.

[0054] Step 4.4: Iteratively generate new solutions using the improved dung beetle optimization algorithm, update the positions of ordinary dung beetles, egg balls, small dung beetles, and thieving dung beetles, perform boundary checks on each dung beetle, and recalculate and compare the fitness value of each dung beetle and the population average fitness value after each optimization iteration to update the angles of each joint of the robot.

[0055] Step 4.5: Determine if the output conditions are met. If they are met, output the result; otherwise, repeat step 4.4.

[0056] The beneficial effects of this invention are as follows: This invention provides a method for solving the inverse kinematics of a redundant degree-of-freedom robot based on the dung beetle optimization algorithm. The dung beetle optimization algorithm improves global exploration capabilities, reduces the possibility of getting trapped in local optima, and enhances the accuracy of the solution. This invention applies the improved dung beetle optimization algorithm to the solution of the inverse kinematics of a redundant degree-of-freedom robot, solving the problems of slow speed and low accuracy in solving the inverse kinematics of a redundant degree-of-freedom robot, enhancing the versatility of the solution, and meeting the requirements for speed and accuracy in robot control. Attached Figure Description

[0057] Figure 1 This is a flowchart of the method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm of the present invention.

[0058] Figure 2 These are the fitness change curves of the improved dung beetle optimization algorithm (I-DBO), the original dung beetle optimization algorithm (DBO), and three other algorithms (ALO, WOA, GWO) of this invention. Detailed Implementation

[0059] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0060] Example 1

[0061] This invention relates to a method for solving the inverse kinematics of a robot with redundant degrees of freedom based on a dung beetle optimization algorithm, which is implemented according to the following steps:

[0062] Step 1: Use the DH method to establish a forward kinematic model of the redundant degree-of-freedom robot;

[0063] Step 2: Develop evaluation criteria for solving the robot's inverse kinematics.

[0064] Step 3: Improve the dung beetle optimization algorithm;

[0065] Step 4: Using the evaluation criteria of solving the robot's inverse kinematics in Step 2 as the optimization objective, use the improved dung beetle optimization algorithm from Step 3 to solve the inverse kinematics of the robot with redundant degrees of freedom.

[0066] Example 2

[0067] This invention relates to a method for solving the inverse kinematics of a robot with redundant degrees of freedom based on a dung beetle optimization algorithm, such as... Figure 1 As shown, please follow these steps:

[0068] Step 1: Establish a forward kinematic model of the redundant degree-of-freedom robot using the DH method;

[0069] Step 1: Multiply the transformation matrices of each joint of the robot sequentially according to the DH method to obtain the transformation matrix of the robot's end effector relative to the base coordinates, and construct a positive kinematic model.

[0070]

[0071] In the formula, m is the m-th link of the robot. The transformation matrix of the m-th link Let D be the transformation matrix of the robot's end effector relative to the base coordinates, and D be the total number of degrees of freedom. When D ≥ 7, the robot is a redundant degree-of-freedom robot.

[0072] Step 2: Develop evaluation metrics for solving robot inverse kinematics;

[0073] Step 2 is as follows:

[0074] To determine the error between the robot's actual pose and the target pose, a fitness function is constructed by weighting the robot's approach vector and position vector.

[0075] f = η||p d -p c ||+β||a d -a c || (2)

[0076] In the formula, p d It is the target pose, p c It is the actual pose, a d and a c Let be the target approach vector and the actual approach vector, respectively, and η and β be the weighting coefficients, respectively.

[0077] The inverse kinematics of the redundant robotic arm has an infinite number of solutions, while equation (3) only obtains one set of point-to-point solutions each time; in order to find a smooth and continuous motion trajectory in spatial motion, equation (4) is used to construct a fitness function for solution:

[0078]

[0079] f2=min(f+γf1) (4)

[0080] Let θ be the initial joint angle of the k-th joint. k γ is the current joint angle of the k-th joint, f1 is the minimum change in joint motion, and γ is the weighting coefficient.

[0081] Step 3: Improve the dung beetle optimization algorithm;

[0082] The specific process of step 3 is as follows:

[0083] Step 3.1: Add the Tent chaotic mapping and expand the search range of the initial population solution space according to equation (5);

[0084]

[0085] In the formula, X n The sequence is generated by the nth iteration, where ω is the chaos parameter and is not 0.5.

[0086] A random array sequence X0 is generated between (0, 1), where n is 0. Then, according to equation (5), an iterative calculation is performed to generate a new sequence. When n reaches the maximum number of iterations, the generated sequence is used as the initial distribution of dung beetle individuals to improve its uniformity and randomness.

[0087] Step 3.2: Calculate the initial fitness values ​​of all dung beetles and determine the current optimal dung beetle position;

[0088] Step 3.3: Introduce a sinusoidal strategy to update the local optimal position of the common dung beetle;

[0089]

[0090] In the formula, t represents the current iteration number. This represents the position of the i-th dung beetle in the t-th iteration; ω t For inertial weights, k∈(0,0.2] represents the deflection coefficient, and b is a constant value between (0,1); This indicates the worst position in the current population. To simulate changes in light intensity, alpha simulates natural factors that cause dung beetles to deviate from their original direction. Let r1 be the component of the optimal individual position variable in the t-th iteration, r2 be a random number in the interval [0, 2π], r3 be a random number in the interval [-2, 2], δ be a random constant between (0, 1), and ST be a random number between 0.5 and 1.

[0091] The nonlinear decreasing function r1 is:

[0092]

[0093] In the formula, ω min and ω max Represents ω t The minimum and maximum values ​​of T max Maximum number of iterations

[0094]

[0095] For a regular dung beetle, when δ < ST, it indicates that the dung beetle has a designated target and is in the global exploration phase; otherwise, it means that the dung beetle has no designated target and needs to search and move using a sine function.

[0096] Step 3.4: Update the local optimal position of other dung beetles. For female dung beetles, update the position of the egg ball using formula (9).

[0097]

[0098] Among them, B j (t) represents the position information of the j-th egg in the t-th iteration, where b1 and b2 are two independent random vectors of size 1×D, and D is the dimension of the optimization problem, where X * Lb represents the current local optimum. * and Ub * These represent the lower and upper boundaries of the spawning area, respectively.

[0099] For dung beetles to update their foraging locations;

[0100]

[0101] Where c1 is a random number following a normal distribution, i.e., c1 ~ N(0,1), c2 is a 1×D random vector belonging to the interval (0,1), and X l This represents the local optimum position for the current population of dung beetles. Using Lb... l and Ub l The lower and upper bounds of the dung beetle's foraging range were defined.

[0102] Update the location of the dung beetle thief;

[0103]

[0104] Where g represents a random vector of size 1×D that follows a normal distribution, and S represents a constant value.

[0105] Step 3.5: Calculate the current global optimal position of the dung beetle colony, compare the current global optimal position with the previous generation's global optimal position, and if the fitness value of the current global optimal position is better than that of the previous generation, then update the optimal position of the dung beetle colony to the current global optimal position.

[0106] Step 3.6: If the maximum number of iterations T is not reached, repeat steps 3.3 to 3.5 until the end.

[0107] Step 4: Using the robot inverse kinematics solution evaluation index as the optimization objective, use the improved dung beetle optimization algorithm to solve the inverse kinematics solution of the redundant degrees of freedom of the robot.

[0108] The specific process of step 4 is as follows:

[0109] Step 4.1: Determine the angle range of each joint of the robot and initialize the parameters, including the number of dung beetles, the ratio between dung beetles of different roles, and the maximum number of iterations or threshold.

[0110] Step 4.2: Generate an initial population within the joint range using the Tent chaotic sequence;

[0111] Step 4.3: Calculate the fitness value of each dung beetle.

[0112] Step 4.4: Iteratively generate new solutions using the improved dung beetle optimization algorithm, update the positions of ordinary dung beetles, egg balls, small dung beetles, and thieving dung beetles, perform boundary checks on each dung beetle, and recalculate and compare the fitness value of each dung beetle and the population average fitness value after each optimization iteration to update the angles of each joint of the robot.

[0113] Step 4.5: Determine if the output conditions are met. If they are met, output the result; otherwise, repeat step 4.4.

[0114] Example 3

[0115] This invention relates to a method for solving the inverse kinematics of a robot with redundant degrees of freedom based on a dung beetle optimization algorithm, which is implemented according to the following steps:

[0116] Step 1: Use the DH method to establish a forward kinematic model of the redundant degree-of-freedom robot;

[0117] Step 2: Develop evaluation criteria for solving robot inverse kinematics;

[0118] Step 3: Improve the dung beetle optimization algorithm;

[0119] Step 4: Using the evaluation criteria for solving the robot's inverse kinematics as the optimization objective, the improved dung beetle optimization algorithm is used to solve the inverse kinematics of the robot with redundant degrees of freedom.

[0120] Using a robot with redundant degrees of freedom (DOF) based on the parameters in Table 1 as the research object, the desired pose of the robotic arm's end effector was set to (100, 200, 300, 90°, 60°, 45°). To compare the convergence accuracy, convergence speed, performance stability, and other parameters of the algorithms, the standard DBO algorithm, GWO algorithm, ALO algorithm, WOA algorithm, and the improved I-DBO algorithm were used for comparative analysis. For all algorithms, the population size was 50, the dimension was 7, and the maximum number of iterations was 500.

[0121] Table 1 Robot DH Parameter Table

[0122]

[0123] To reduce the influence of random factors, each of the five algorithms solves the problem independently 10 times, and the optimal solution from the 10 sets is compared. The iterative process of the five algorithms for the optimal solution is as follows: Figure 2 As shown.

[0124] from Figure 2 The results show that the WOA and ALO algorithms converge to relatively large values, making them prone to getting trapped in local optima and prematurely convergent. The GWO algorithm converges relatively quickly, but its fluctuations are large, indicating instability and high convergence values. In contrast, the DBO and I-DBO algorithms converge to lower levels, escaping local optima. Moreover, the I-DBO algorithm not only achieves the best convergence performance but also has the fastest convergence speed compared to the DBO and other algorithms.

[0125] To further compare the inverse kinematics solution capability of this invention on a redundant degree-of-freedom robot, 50 points were randomly selected in the workspace, and Equation (4) was used as the optimization objective function of the algorithm, with 300 iterations and 50 particles. The best fitness, mean fitness, worst fitness, and optimization success rate (SR) of each algorithm are shown in Table 2.

[0126] Table 2 Comparison of the inverse kinematics optimization performance of five algorithms

[0127] GWO 1.0081 2.3908 10.9703 100％ WOA 8.0010 11.3092 17.0299 100％ ALO 20.044 23.1099 27.9087 98％ DBO <![CDATA[6.0961×10 -14 ]]> <![CDATA[2.1637×10 -13 ]]> <![CDATA[7.7714×10 -12 ]]> 100％ I-DBO <![CDATA[2.3328×10 -14 ]]> <![CDATA[4.5985×10 -14 ]]> <![CDATA[4.2311×10 -12 ]]> 100％

[0128] As shown in Table 2, except for the ALO algorithm, all the other algorithms completed the optimization, but the I-DBO algorithm has a faster convergence speed and higher convergence accuracy.

[0129] The specific data results demonstrate the effectiveness and universality of the algorithm.

[0130] This invention presents a method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm. Its advantages include: employing the dung beetle optimization algorithm to solve the inverse kinematics; using Tent chaotic mapping in the population initialization stage to generate a highly diverse initial population to improve the diversity of initial solutions; compared to the original dung beetle optimization algorithm, expanding the search range of the initial population solution space improves global search capability; and incorporating an improved sine algorithm enhances the dung beetle's global exploration and local exploitation capabilities, expanding its search range, improving global exploration capability, and reducing the possibility of getting trapped in local optima.

Claims

1. A method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm, characterized in that, The specific steps are as follows: Step 1: Use the DH method to establish a forward kinematic model of the redundant degree-of-freedom robot; Step 2: Develop evaluation criteria for solving robot inverse kinematics; Step 3: Improve the dung beetle optimization algorithm; Step 4: Using the evaluation criteria of solving the robot inverse kinematics in Step 2 as the optimization objective, use the improved dung beetle optimization algorithm from Step 3 to solve the inverse kinematics of the robot with redundant degrees of freedom. The specific process of step 2 is as follows: In order to calculate the error between the robot's actual pose and the target pose, a fitness function is constructed by weighting the robot's approach vector and position vector. （2） In the formula, It is the target pose. It is the actual pose. and These are the target approach vector and the actual approach vector, respectively. and These are the weighting coefficients; The inverse kinematics of the redundant robotic arm has an infinite number of solutions, while equation (3) only obtains one set of point-to-point solutions each time; in order to find a smooth and continuous motion trajectory in spatial motion, equation (4) is used to construct a fitness function for solving: The total degrees of freedom, For the first Initial joint angles of each joint For the first The current joint angle of each joint. γ represents the minimum change in joint movement, and γ is the weighting coefficient. The specific process of step 3 is as follows: Step 3.1: Add Tent chaos mapping; Step 3.2: Calculate the initial fitness values ​​of all dung beetles and determine the current optimal dung beetle position; Step 3.3: Introduce a sinusoidal strategy to update the local optimal position of the common dung beetle; Step 3.4: Update the local optimal positions of other Dung Beetle characters. Step 3.5: Calculate the current global optimal position of the dung beetle colony, compare the current global optimal position with the previous generation's global optimal position, and if the fitness value of the current global optimal position is better than that of the previous generation, then update the optimal position of the dung beetle colony to the current global optimal position. Step 3.6, if the maximum number of iterations has not been reached. Then repeat steps 3.3 to 3.5 in a loop until the end.

2. The method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm as described in claim 1, characterized in that, Step 1 specifically involves: Step 1: Multiply the transformation matrices of each joint of the robot sequentially according to the DH method to obtain the transformation matrix of the robot's end effector relative to the base coordinates, and construct a positive kinematic model. （1） In the formula, For the robot One link, No. The transformation matrix of each link. Let be the transformation matrix of the robot's end effector relative to the base coordinates. For the total degrees of freedom, when At that time, the robot is a redundant degree-of-freedom robot.

3. The method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm as described in claim 1, characterized in that, Step 3.1 expands the search range of the initial population solution space according to equation (5); （5） In the formula, For the first The sequence generated by the next iteration. For chaotic parameters, Do not take 0.5; Generate a random array sequence between (0, 1). ,at this time If the value is 0, then iterative calculation is performed according to equation (5) to generate a new sequence. When the maximum number of iterations is reached, the generated sequence is used as the initial distribution of dung beetle individuals in the population.

4. The method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm as described in claim 3, characterized in that, The specific process of step 3.3 is as follows: In the formula, Indicates the current iteration number. This means the first Only one dung beetle in the first The position at the next iteration; For inertial weights, Indicates the deflection coefficient. It is a constant value between (0,1); This indicates the worst position in the current population. Used to simulate changes in light intensity Natural factors were simulated to cause dung beetles to deviate from their original direction. For the first The optimal individual position variable components in the next iteration; It is a non-linear decreasing function. It is a random number in the interval [0, 2π]. It is a random number in the interval [-2, 2]. It is a random constant value between (0,1). It is a random number between 0.5 and 1; Nonlinear decreasing function for: （7） In the formula, and express The minimum and maximum values, This represents the maximum number of iterations. （8） For ordinary dung beetles, when When the time is 0, it indicates that the dung beetle has a designated target and is in the global exploration phase; otherwise, it means that the dung beetle has no designated target and needs to search and move using a sine function.

5. The method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm as described in claim 1, characterized in that, In step 3.4, the position of the egg ball is updated for the female dung beetle using formula (9); （9） in, It is the first The egg sphere in the first Position information for the next iteration. and They are two independent sizes. Let be a random vector, and D be the dimension of the optimization problem. This indicates the current local optimum. and These represent the lower and upper boundaries of the spawning area, respectively; For dung beetles to update their foraging locations; （10） in, For random numbers that follow a normal distribution, i.e. , for The random vectors belonging to the range (0,1) The optimal local position for the current population of dung beetles; using and The lower and upper bounds of the dung beetle's foraging range were defined respectively; For stealing dung beetles to update their location; （11） in, Indicates size is A random vector, which follows a normal distribution. It represents a constant value.

6. The method for solving the inverse kinematics of a robot with redundant degrees of freedom based on the dung beetle optimization algorithm as described in claim 1, characterized in that, The specific process of step 4 is as follows: Step 4.1: Determine the angle range of each joint of the robot and initialize the parameters, including the number of dung beetles, the ratio between dung beetles of different roles, and the maximum number of iterations or threshold. Step 4.2: Generate an initial population within the joint range using the Tent chaotic sequence; Step 4.3: Calculate the fitness value of each dung beetle. Step 4.4: Use the improved dung beetle optimization algorithm to iteratively generate new solutions, update the positions of ordinary dung beetles, egg balls, small dung beetles, and thieving dung beetles, perform boundary determination for each dung beetle, and after each optimization iteration, the fitness value of each dung beetle and the population average fitness value will be recalculated and compared, and the angles of each joint of the robot will be updated. Step 4.5: Determine if the output conditions are met. If they are met, output the result; otherwise, repeat step 4.4.

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