Multi-objective Trajectory Optimization Method for Industrial Robots Based on Improved Particle Swarm Optimization Algorithm

Abstract

The present invention belongs to the technical field related to industrial robot control, and discloses a multi-objective trajectory optimization method for industrial robots based on an improved particle swarm algorithm. The method includes the following steps: (1) Convert the path point constraints in the working space to the joint space for unified representation and use the fifth-order non-uniform B-spline curve for trajectory planning to obtain the fifth-order non-uniform B-spline trajectory equation under velocity and acceleration constraints; (2) Implement multi-objective trajectory optimization through the improved particle swarm algorithm: Take the time, energy, average pulsation, and average change rate of joint torque of the robot to be optimized as the objective function of trajectory optimization, use the Logistic chaotic mapping for population initialization and inertia weight allocation, and find the optimal solution based on the Pareto dominance relationship; (3) Use the extreme performance metric method and the SSM comprehensive performance metric method to select the optimal trajectory that meets the requirements of different application scenarios. The trajectory planning of the present invention has better effects.

Description

Technical Field

[0001] The present invention belongs to the technical field related to industrial robot control, and more specifically, relates to a multi-objective trajectory optimization method for industrial robots based on an improved particle swarm optimization algorithm. Background Technique

[0002] Generally, a robot can achieve basic operations through trajectory planning, but it is difficult to ensure high efficiency, smoothness, and low energy consumption during task execution. Therefore, it is of great significance to further optimize the running trajectory of the robot on the basis of trajectory planning. The goal of trajectory optimization is to minimize or maximize one or more performance indicators related to the robot operation process. The main performance indicators usually concerned are: execution time, energy consumption, maximum power, driving torque, etc. To optimize the above performance indicators, scholars have proposed different trajectory optimization strategies, which can be specifically divided into single-objective trajectory optimization and multi-objective trajectory optimization.

[0003] The goal of single-objective trajectory optimization is to minimize or maximize a certain performance indicator of the robot during the trajectory planning process. Some application scenarios are more concerned about production volume. A shorter task execution time can improve the production efficiency of the robot, so as to increase the production volume within the same task execution time. The trajectory planning problem of a single objective is relatively simple, but it is difficult to guarantee the performance of other objectives. The multi-objective trajectory planning method can achieve the performance balance between different objectives of the industrial robot and can better meet the performance requirements of the industrial robot in different application scenarios. Multi-objective trajectory optimization is to construct multiple objective functions during the trajectory planning process to minimize or maximize multiple performance indicators of the robot. A better trajectory optimization method can ensure that the robot runs with lower energy, shorter time, and lower joint pulsation under the conditions of meeting constraints such as position, speed, and acceleration, so as to achieve the goal of reducing energy consumption during task execution and improving operation efficiency. Summary of the Invention

[0004] Aiming at the above defects or improvement requirements of the prior art, the present invention provides a multi-objective trajectory optimization method for industrial robots based on an improved particle swarm optimization algorithm, which realizes the multi-objective trajectory optimization of industrial robots in different application scenarios and has the advantages of wide applicability and good optimization performance.

[0005] To achieve the above object, according to one aspect of the present invention, a multi-objective trajectory optimization method for industrial robots based on an improved particle swarm optimization algorithm is provided. The optimization method includes the following steps:

[0006] (1) Convert the workspace path point constraints to the joint space for unified representation and use a fifth-order non-uniform B-spline curve for trajectory planning to obtain a fifth-order non-uniform B-spline trajectory equation under speed and acceleration constraints;

[0007] (2) Implement multi-objective trajectory optimization by improving the particle swarm algorithm: Take the time, energy, average pulsation, and average change rate of joint torque of the robot to be optimized as the objective function of trajectory optimization. Use the Logistic chaotic map for population initialization and inertia weight allocation, and find the optimal solution based on the Pareto dominance relationship;

[0008] (3) Adopt the extreme performance metric method and the SSM comprehensive performance metric method to select the optimal trajectory that meets the requirements of different application scenarios.

[0009] Furthermore, in step (1), parameterize the path points through the function buffering method, and at the same time configure the attitude of the path points through the Slerp interpolation method. After completing the attitude configuration of each path point, input the workspace path points into the inverse solution function for solution, and finally obtain the joint space path points.

[0010] Furthermore, the formula used for parameter optimization of the path points is:

[0011]

[0012]

[0013] where P j is the j-th path point on the path, i = 1~f, c0 = 0.

[0014] Furthermore, the Slerp interpolation method is used to configure the attitude of the end of the robotic arm in the trajectory, and the formula used is:

[0015]

[0016] ω = ||q0·q f ||

[0017] where, R pq is the p-th row and q-th column of the attitude matrix. After conversion, the R s0 and R sf of the robot correspond to q0 and q f respectively.

[0018] Furthermore, the optimal evaluation indicators of the multi-objective trajectory planning based on the improved particle swarm include the efficiency, energy consumption, stability, and average change rate of joint torque of the robot. The objective functions of the above evaluation indicators are:

[0019]

[0020]

[0021]

[0022]

[0023] Among them, F1, F2, F3, and F4 are the average change rates of the efficiency, energy consumption, stability, and joint torque of the robot respectively; n + 1 represents the number of path points; t0 and t n represent the moments corresponding to the starting point and the ending point of the robot respectively; τ i represents the torque of joint i; v i represents the angular velocity of joint i; d t represents the control period of the robot; J i represents the pulsation of joint i.

[0024] Furthermore, the constraint relationships of each joint are:

[0025]

[0026] Among them, u1 to u4 represent the safety factors of torque τ, velocity v, acceleration a, and jerk J respectively.

[0027] Furthermore, the improved particle swarm optimization algorithm uses the Pareto dominance relationship to evaluate the superiority and inferiority of different particles, and finds a set of Pareto optimal solution sets according to the dominance relationship to make each sub-objective function F i (x), x ∈ X approach the optimal state.

[0028] Furthermore, the algorithm function expressions for initializing the particle positions and velocities using the Logistic chaotic map are:

[0029]

[0030] When updating the particle velocity and position, the Logistic algorithm is added to the linear weight, and the update formula for ω is:

[0031]

[0032] Among them, t max is the total number of iterations; ω max and ω min are the maximum and minimum inertia weights respectively.

[0033] Furthermore, the SSM performance measurement method is used to characterize the diversity of solutions, and the corresponding calculation formula is:

[0034]

[0035] Among them, M represents the number of solutions on the Pareto front; d i is the Euclidean distance between adjacent solutions on the front; For all d i is the average value; d f and d l are the Euclidean distances between the boundary solution and the extreme value, respectively.

[0036] Furthermore, a fuzzy membership function is used to evaluate the fitness values in the optimal trajectory solution set, and the corresponding fitness factor is calculated through the fuzzy membership function. The calculation formula used is:

[0037]

[0038] where F i (j) represents the i-th objective function value corresponding to the j-th solution on the Pareto front; F i max and F i min represent the maximum and minimum values of the i-th objective function on the Pareto front; λ i can only represent the i-th objective. To complete the comprehensive evaluation of the total time, energy, average pulsation, and average torque change rate of the robot, the comprehensive fitness factor evaluation formula for all objective functions is:

[0039]

[0040] where λ syn is the comprehensive fitness factor.

[0041] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the multi-objective trajectory optimization method for industrial robots provided by the present invention mainly has the following beneficial effects:

[0042] 1. The present invention uses the function buffering method and the slerp interpolation method to obtain the parameters and end postures of each interpolation point on the path points. Through the function buffering method, the path points are parameterized and the Slerp interpolation method is used to realize the posture configuration of the path points. The posture change amplitude near the starting point and the ending point is small, while the posture change amplitude far from the starting point and the ending point is large, and the acceleration and deceleration effects can be better realized. The continuous path motion trajectory constructed by the quintic B-spline curve has continuous speed at the path connection, good local support, and the constraints can be adjusted according to needs, and the effect of trajectory planning is better.

[0043] 2. The present invention realizes multi-objective trajectory optimization through the modified particle swarm algorithm, takes optimizing the time, energy, average pulsation, and average change rate of joint torque of the robot as the objective functions of trajectory optimization, finds the optimal solution based on the Pareto dominance relationship, and uses the Logistic chaotic mapping for population initialization and inertia weight allocation. The optimal trajectory solution set obtained by this method has small pulsation changes, short time consumption, and high working efficiency.

[0044] 3. The present invention adopts the extreme performance measurement method and the SSM comprehensive performance measurement method to select the optimal solution according to the actual application scenario. The obtained result has good optimization effect and good environmental adaptability. This method can significantly improve the operating efficiency and stability of the robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flowchart of a multi-objective trajectory optimization method for an industrial robot based on an improved particle swarm algorithm provided by an embodiment of the present invention;

[0046] Figure 2 is a flow chart of trajectory optimization of an improved particle swarm algorithm provided by an embodiment of the present invention;

[0047] Figure 3 It is a flow chart of selecting the optimal trajectory using the limit metric method provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0049] The present invention provides an industrial robot multi-objective trajectory optimization method based on an improved particle swarm algorithm, and the optimization method mainly comprises the following steps:

[0050] Step 1: Convert the workspace path point constraints to the joint space for unified representation and use the 5th-order non-uniform B-spline curve for trajectory planning to obtain the 5th-order non-uniform B-spline trajectory equation under velocity and acceleration constraints.

[0051] Among them, the robot workspace path point constraints are transformed into the joint space through inverse solution and Jacobian matrix pseudo-inverse to uniformly represent the end position and velocity, and on this basis, the path point is parameterized using the function buffer method. This method converts the posture matrix R of the robot's starting path point P0 into s0 , End path point P f The posture matrix R sf According to the parameter s i Divide it and then assign it to each path point in turn. The calculation formula is:

[0052]

[0053]

[0054] Where P jis the j-th path point on the path.

[0055] The path point parameters also include the posture of the end of the robotic arm. The rotation matrix is converted into a quaternion for representation, and then the Slerp interpolation method is used to perform weighted averaging on the parameters of the quaternion, so that the postures of each path point are always on the quaternion sector surface corresponding to the start point posture and the end point posture. Through the following formula:

[0056] q = ω + x i + y j + z k

[0057] The posture matrices of each path point of the robot are converted into quaternions for description, and the description formula is as follows:

[0058]

[0059]

[0060] Among them, R pq is the p-th row and q-th column of the posture matrix. After conversion, the R s0 and R sf of the robot correspond to q0 and q f respectively.

[0061] Next, the Slerp interpolation method is used to configure it, and the relevant formula is as follows:

[0062]

[0063] ω = ||q0 · q f ||

[0064] Finally, the quaternion q i corresponding to each path point is converted into a posture matrix, and the conversion formula is as follows:

[0065]

[0066] After completing the posture configuration of each path point, the workspace path points are input into the inverse solution function for solution, and finally the joint space path points are obtained.

[0067] Taking the 5th-degree non-uniform B-spline curve as the basic trajectory of the robot trajectory planning, the 5th-degree non-uniform B-spline trajectory equation with velocity and acceleration constraints is derived, and the calculation method of the B-spline curve is as follows:

[0068]

[0069] Among them, d j ∈R A , (j = 0~n) is the j-th control vertex of the curve, and the R ADenote A dimensions, for example, each joint of a six-degree-of-freedom robot is 1 dimension; u i ∈U{u0, u1, u2, …, u m} represents nodes. To ensure that the curve passes through the starting and ending points of the path, the nodes need to meet the requirement of multiplicity, that is, u0 = u1 = u2 = … = u k 、u n+k =u n+k+1 =u n+k+2 =…=u n+2k , so the node vector becomes U = {u0, u1, u2, …, u n+2k}; u is a parameter for controlling the curve shape; P(u) ∈ R N represents the point on the curve corresponding to u, that is, the point on the robot joint space trajectory; m + 1 represents the number of nodes; k represents the degree of the curve; n + 1 represents the number of control vertices, and there is an equality constraint relationship of m = n + k + 1 among m, n, and k; N j，k (u) represents the jth basis function of a k-degree curve, which generates points on the curve by weighted summation of all control vertices. The definition methods include difference quotient definition, blossoming definition, and de Boor Cox-de Boor methods, etc. The calculation formula is as follows:

[0070]

[0071]

[0072] Considering that there are constraints on the velocities and accelerations of each joint of the robot, in order to solve for the velocities and accelerations, it is also necessary to obtain the derivative vector of the points on the curve with respect to the parameter u, and its expression form is as follows:

[0073]

[0074] Among them, r represents the order of the derivative; represents the basis function corresponding to the rth derivative of the curve, and its expression form is as follows:

[0075]

[0076] During the process of the controller sending instructions to the robot, generally a reference input signal is sent to the robot at a fixed period. Therefore, during the trajectory planning process, the sampling points on the trajectory should also be sampled at equal intervals. To ensure equal-interval sampling, the parameter u is given corresponding physical meaning and is equivalent to the time nodes T = {t0, t1, …, t nNormalization of}, the result of T normalization will affect the shape of the entire motion trajectory. To avoid the phenomenon of curve knotting, the cumulative chord length method with better effect is used to normalize the time nodes of the trajectory. The expression forms of each node on the curve after processing are as follows:

[0077] u0 = u1 = … = u k = 0

[0078]

[0079] u n+k = u n+k+1 = … = u n+2k = 1

[0080] Among them, t j+1 - t j represents the time interval between adjacent path points. To ensure that the trajectory passes through each path point, it is necessary to calculate the control points d of the B-spline curve by back-calculating through the path point P. The relevant equations for path point constraints are as follows:

[0081]

[0082] According to the constraint relationship between the degree of the fifth-order B-spline curve, the number of nodes, and the number of control points, the following constraint equations are added at the starting point and the ending point of the curve:

[0083]

[0084]

[0085] After organizing it into matrix form, it is:

[0086]

[0087] Among them, v1, v2, a1, a2 are the velocities and accelerations at the starting point and the ending point of the trajectory, and the matrix coefficient C (n-k+1)×(n+1) The expanded expression is as follows:

[0088]

[0089] Substituting the constraints at the starting point and the ending point, the expressions of the parameters in the matrix coefficient C can be obtained as follows:

[0090] c1 = -k / (u k+1 - u1) / t n , c2 = k / (u k+1 - u1) / t n

[0091] c6 = -k / (u n+2k-1 - u n+k-1 ) / tn , c7 = k / (u n+2k-1 - u n+k-1 ) / t n

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] Step 2. Implement multi - objective trajectory optimization through an improved particle swarm algorithm: Take the time, energy, average pulsation, and average change rate of joint torque of the robot to be optimized as the objective function of trajectory optimization. Use Logistic chaotic mapping for population initialization and inertia weight assignment, and find the optimal solution based on the Pareto dominance relationship.

[0099] Specifically, implementing multi - objective trajectory optimization through an improved particle swarm algorithm includes the construction of a multi - objective optimization model, initialization, and update of particle positions and velocities. The optimal evaluation indexes for multi - objective trajectory planning based on the improved particle swarm include the efficiency, energy consumption, stability, and average change rate of joint torque of the robot. The objective functions of the above evaluation indexes are shown as follows:

[0100]

[0101]

[0102]

[0103]

[0104] Among them, F1, F2, F3, and F4 are the efficiency, energy consumption, stability, and average change rate of joint torque of the robot respectively; n + 1 represents the number of path points; t0 and t n represent the moments corresponding to the starting point and the ending point of the robot respectively; τ i represents the torque of joint i; v i represents the angular velocity of joint i; d t represents the control period of the robot; J i represents the pulsation of joint i.

[0105] During the process of trajectory optimization, it should also be ensured that the robot is always in a safe state throughout the entire working process, so that the positions, velocities, accelerations, jerks, and torques of all joints of the robot simultaneously satisfy the constraint conditions. Finally, the constraint relationships of each joint are as follows:

[0106]

[0107] Among them, u1 to u4 respectively represent the safety factors of torque τ, velocity v, acceleration a, and jerk J.

[0108] The improved particle swarm optimization algorithm uses the Pareto dominance relationship to evaluate the superiority and inferiority of different particles, and finds a set of Pareto optimal solutions according to the dominance relationship to make each sub-objective function F i (x), x ∈ X approach the optimal state.

[0109] When the size of the entire population is N and the time interval parameter between adjacent path points is Δt = {t1 - t0, t2 - t1,..., t n - t n-1}, the states of each particle in the population and the state of the population are as follows:

[0110] Description of the position of each particle:

[0111] Y i =[y i1 , y i2 ,..., y i(n-1) T

[0112] Description of the velocity of each particle:

[0113] V i =[v i1 , v i2 ,..., v i(n-1) T

[0114] Description of the historical best position of each particle:

[0115] p best =[p i1 , p i2 ,..., p i(n-1) T

[0116] Description of the best position of the population:

[0117] g best =[g1, g2,..., g n-1 T

[0118] ​​​​Velocity update formula for each particle:

[0119] v ij (t + 1) = ωv ij (t) + c1r1(t)[p ij (t) - x ij (t)] + c2r2(t)[p gj (t) - x ij (t)]

[0120] Position update formula for each particle:

[0121] x ij (t + 1) = x ij (t) + v ij (t + 1)

[0122] where i represents the i-th particle; j represents the j-th dimension; t is the iteration number; ω represents the inertia weight; c1 and c2 represent the individual learning factor and the population learning factor respectively, r1 and r2 randomly take values in the range [0, 1]; v ij 、x ij 、p ij respectively represent the velocity, position and historical best position of the i-th particle in the j-dimensional space; p gj represents the best position of the population in the j-dimensional space.

[0123] In the optimization process of the improved particle swarm algorithm, a crossover and mutation mechanism is introduced, and the Logistic chaotic mapping is used to replace the random algorithm for population initialization and the Logistic chaotic mapping is used to replace the linear inertia weight allocation strategy for particle velocity update. Among them, the algorithm function expressions for initializing the particle position and velocity using the Logistic chaotic mapping are as follows:

[0124]

[0125] The formulas for calculating the velocity and position of each particle using the Logistics algorithm are as follows:

[0126] Y(i) = ΔT min +β(t)·(ΔT max -ΔT min )

[0127] V(i) = V min +β(t)·(V max -V min )

[0128] where ΔT min 、ΔT max are respectively the minimum and maximum time limits between each joint path point, V min 、Vmax They are the minimum and maximum speed limits for each joint respectively.

[0129] Due to the mutual exclusion relationship among the four objectives of time, energy, average pulsation, and the average torque change rate of the robot, during the sorting process, the Pareto dominance relationship is first used to judge the global dominance status of each particle, and p is updated according to the dominance relationship best . Then, store those particles without a dominance relationship in the rep archive; next, take 0.1 times the total number of particles as the number G of grids n , and according to the maximum and minimum fitness values of each particle in the four objectives in the rep archive, divide each objective fitness value into G n parts to form a four-dimensional hyper-grid body; during the sorting process, according to the density of particles in each grid, use the roulette wheel algorithm to select g best .

[0130] When updating the particle velocity and position, add the Logistic algorithm to the linear weight. The update formula of ω is as follows:

[0131]

[0132] Among them, t max is the total number of iterations; ω max , ω min are the maximum and minimum inertia weights respectively.

[0133] Step 3: Use the extreme performance metric method and the SSM comprehensive performance metric method to select the optimal trajectory that meets the requirements of different application scenarios.

[0134] To achieve the optimal selection of solutions in different scenarios, the extreme performance metric method and the SSM comprehensive performance metric method are used to select the optimal solution according to the actual application scenario. When a certain performance index of the robot receives more attention, the extreme performance metric method can quickly sort the trajectory parameter set; when all performance indexes of the robot are relatively concerned and an optimal solution with comprehensive performance is required, the comprehensive performance metric method characterizes the diversity of solutions, and the optimal solution can be selected by comparing the sizes of the fitness factors.

[0135] The calculation formula of the SSM performance metric method is as follows:

[0136]

[0137] Among them, M represents the number of solutions on the Pareto front; d i is the Euclidean distance between adjacent solutions on the front, is the average value of all d i ; d f and dl is the Euclidean distance between the boundary solution and the extreme value.

[0138] The fitness values in the optimal trajectory solution set are evaluated using a fuzzy membership function, and the corresponding fitness factors are calculated through the fuzzy membership function. The calculation formula is as follows:

[0139]

[0140] where F i(j) represents the i-th objective function value corresponding to the j-th solution on the Pareto front; F i max and F i min represent the maximum and minimum values of the i-th objective function on the Pareto front. λ i can only represent the i-th objective. To complete the comprehensive evaluation of the total time, energy, average pulsation, and the average torque change rate of the robot, the comprehensive fitness factor evaluation formula for all objective functions is as follows:

[0141]

[0142] where λ syn is the comprehensive fitness factor.

[0143] The following uses specific embodiments to further elaborate on the present invention.

[0144] Aiming at the problems of low accuracy and efficiency in multi-objective robot trajectory optimization, this embodiment provides a multi-objective trajectory optimization method based on an improved particle swarm algorithm. The overall idea is to convert the workspace path point constraints into the joint space for unified representation and use the fifth-order non-uniform B-spline curve for trajectory planning to obtain the fifth-order non-uniform B-spline trajectory equation under velocity and acceleration constraints; then propose calculation methods for different performance indicators, design a cost function for calculating different performance indicators, and propose a multi-objective trajectory optimization method for an improved particle swarm algorithm; use the extreme performance metric method and the SSM comprehensive performance metric method to select the optimal trajectory that meets different application scenarios.

[0145] Without loss of generality, the following embodiments will take the improvement of the trajectory tracking accuracy of the UNIVERSAL ROBOTS 10 robot (hereinafter referred to as "UR10") as an example to further explain the technical solution of the present invention.

[0146] Embodiment 1

[0147] A multi-objective trajectory optimization method based on an improved particle swarm algorithm, as Figure 1 shown, includes:

[0148] The function buffer method is adopted to transform the path point constraints in the working space into the joint space for unified representation; the 5th-order non-uniform B-spline curve is used for trajectory planning; calculation methods for different performance indexes are proposed; a cost function for calculating different performance indexes is designed; a multi-objective trajectory optimization method for improving the particle swarm algorithm is proposed; the extreme performance metric method and the SSM comprehensive performance metric method are used to select the optimal trajectory that meets different application scenarios.

[0149] Optionally, in this embodiment, in the robot working space, 8 points are randomly selected as the path points in the working space, and then the joint angles corresponding to each path point are calculated through inverse kinematics to obtain the path points of each joint of the robot.

[0150] Taking the above path points as the input of the particle swarm algorithm, after 100 iterations, the Pareto front corresponding to the total time, energy, and average pulsation is obtained.

[0151] When single performance of the trajectory is concerned, the extreme metric method can be used to quickly obtain the optimal trajectory. When the efficiency of the robot is concerned, the particle with the optimal time can be selected as the result of parameter optimization through the time axis; when the energy consumption of the robot is concerned, the particle with the optimal energy can be selected as the result of parameter optimization through the energy axis; when the smoothness of the robot is concerned, the particle with the optimal energy can be selected as the result of parameter optimization through the pulsation axis.

[0152] When the comprehensive performance of the trajectory is concerned, the following formula is used:

[0153]

[0154] Calculate the diversity of the optimal trajectory set on the Pareto front, and measure the performance of the solution set to obtain the value of SSM. In order to further screen out the optimal solution according to the above method, a fuzzy membership function is used to evaluate the fitness value in the optimal trajectory solution set, and the corresponding fitness factor is calculated through the fuzzy membership function. The calculation method is as follows:

[0155]

[0156] In order to complete the comprehensive evaluation of the total time, energy, average pulsation, and the average torque change rate of the robot, the following formula is used:

[0157]

[0158] Calculate the comprehensive fitness factors of all particles on the front by calculating the comprehensive fitness factors of all objective functions, and the optimal solution can be selected by comparing the sizes of the comprehensive fitness factors.

[0159] Due to different performance concerns, the selection of particles on the Pareto front is usually different. To avoid repeated experiments, the trajectory with the optimal comprehensive fitness is selected for the experiment. Substitute the above control points into the equation of the fifth-degree non-uniform B-spline curve to obtain the trajectory curves of each joint. Substitute the obtained discrete joint data points into the forward kinematics equation to obtain the end trajectory of the robot.

[0160] Subsequently, the calculated data is brought into the experiment, and the main process is as follows:

[0161] Find the particle with the optimal comprehensive fitness, and save the angles, angular velocities, and angular accelerations corresponding to each joint as a trajectory file in MATLAB for easy reading of the trajectory file for data during the subsequent control process; use the teach pendant to complete the initialization of the robot and return the robot to zero; read the trajectory file and store it in an array, and use the linear interpolation command to move the robot to the starting point of the optimal trajectory; according to the control period of 0.01 s, loop to send the data points on the trajectory to the robot to make the robot run according to the optimal trajectory, and at the same time record the speed, acceleration, and jerk information of each joint during the robot's operation in real time.

[0162] In other types of robots, such as ABB, KUKA, Huashu, etc., the specific implementation of the multi-objective trajectory optimization method based on the improved particle swarm algorithm provided by the present invention is similar to the compensation method of the UR10 robot, and will not be listed one by one here.

[0163] Those skilled in the art can easily understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An industrial robot multi-objective trajectory optimization method based on an improved particle swarm algorithm, characterized in that, The method includes the following steps: (1) Convert the workspace path point constraints to the joint space for unified representation and use the fifth-order non-uniform B-spline curve for trajectory planning to obtain the fifth-order non-uniform B-spline trajectory equation under velocity and acceleration constraints; (2) Implement multi-objective trajectory optimization through an improved particle swarm algorithm: Take the time, energy, average pulsation, and average change rate of joint torque of the robot to be optimized as the objective function of trajectory optimization, use the Logistic chaotic map for population initialization and inertia weight allocation, and find the optimal solution based on the Pareto dominance relationship; (3) Adopt the extreme performance metric method and the SSM comprehensive performance metric method to select the optimal trajectory that meets the requirements of different application scenarios; In step (1), parameterize the path points through the function buffering method, and at the same time implement the attitude configuration of the path points through the Slerp interpolation method. After completing the attitude configuration of each path point, input the workspace path points into the inverse solution function for solution to finally obtain the joint space path points; The formula used for parameter optimization of the path points is: where P j is the j-th path point on the path, i = 1 to f, and c0 = 0.

2. The industrial robot multi-objective trajectory optimization method based on an improved particle swarm algorithm according to claim 1, characterized in that: The formula used for configuring the end attitude of the manipulator in the trajectory by using the Slerp interpolation method is: ω=||q0·q f ||。 3. The industrial robot multi-objective trajectory optimization method based on an improved particle swarm algorithm according to claim 1, characterized in that: The optimal evaluation indexes of the multi-objective trajectory planning based on the improved particle swarm include the efficiency, energy consumption, stability of the robot, and the average change rate of joint torque. The objective functions of the above evaluation indexes are: Among them, F1, F2, F3, and F4 are the average change rates of the efficiency, energy consumption, stability, and joint torque of the robot respectively; n + 1 represents the number of path points; t0 and t n represent the moments corresponding to the starting point and the ending point of the robot respectively; τ i represents the torque of joint i; v i represents the angular velocity of joint i; d t represents the control period of the robot; J i represents the jerk, which characterizes the pulsation degree of joint i.

4. The industrial robot multi-objective trajectory optimization method based on an improved particle swarm algorithm according to claim 3, characterized in that: The constraint relationships of each joint are: Among them, u1 to u4 respectively represent the safety factors of torque τ, velocity v, acceleration a, and jerk J.

5. The industrial robot multi-objective trajectory optimization method based on an improved particle swarm algorithm according to claim 4, characterized in that: The improved particle swarm optimization algorithm uses the Pareto dominance relationship to evaluate the superiority and inferiority of different particles, and finds a set of Pareto optimal solutions according to the dominance relationship. Make each sub-objective function F i (x), x ∈ X approach the optimal state.

6. The industrial robot multi-objective trajectory optimization method based on an improved particle swarm algorithm according to claim 5, characterized in that: The algorithm function expression for initializing the particle position and velocity using the Logistic chaotic map is: When updating the particle velocity and position, add the Logistic algorithm to the linear weight. The update formula of ω is: where t max is the total number of iterations; ω max , ω min are the maximum and minimum inertia weights, respectively.

7. The industrial robot multi-objective trajectory optimization method based on an improved particle swarm algorithm according to any one of claims 1-6, characterized in that: Use the SSM performance metric method to characterize the diversity of solutions. The corresponding calculation formula is: where M represents the number of solutions on the Pareto front; d i is the Euclidean distance between adjacent solutions on the front; is the average value of all d i ; d f and d l are the Euclidean distances between the boundary solution and the extreme value, respectively.

8. The multi-objective trajectory optimization method for industrial robots based on the improved particle swarm algorithm according to claim 7, characterized in that: Adopt the fuzzy membership function to evaluate the fitness value in the optimal trajectory solution set, and calculate the corresponding fitness factor through the fuzzy membership function. The calculation formula used is: Among them, F i (j) represents the i-th objective function value corresponding to the j-th solution on the Pareto front; F imax and F imin represent the maximum and minimum values of the i-th objective function on the Pareto front; λ i can only represent the i-th objective. In order to complete the comprehensive evaluation of the total time, energy, average pulsation, and average torque change rate of the robot, the comprehensive fitness factor evaluation formula for all objective functions is as follows: Among them, λ syn is the comprehensive fitness factor.

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