Industrial robot trajectory planning method considering operation time and smoothness

Abstract

The invention relates to an industrial robot trajectory planning method considering operation time and smoothness, and belongs to the technical field related to robot machining. Aiming at the problem that the existing industrial robot trajectory planning only considers the correlation between single-target trajectory planning and lacks multi-target trajectory planning, the method comprises the following steps: obtaining a joint angle sequence of each joint at a machining cutter point based on a tail end space pose matrix of a robot, and carrying out initial running time distribution on the joint angle sequence to obtain a joint angle sequence; a quintic B spline is used to interpolate each joint angle, a smooth trajectory line before optimization is constructed, a traditional particle swarm algorithm is improved through fuzzy logic, the improved particle swarm algorithm is used to carry out trajectory planning optimization with comprehensive consideration of processing time and smoothness on a robot, the quintic B spline is used to interpolate each joint angle, and a smooth trajectory line before optimization is constructed. And constructing an optimized smooth trajectory. According to the method, machining time and smoothness are comprehensively considered, high-performance operation of the robot is guaranteed, and machining quality is improved while mechanical abrasion is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field related to robot processing, and in particular, to an industrial robot trajectory planning method considering operation time and smoothness. Background Art

[0002] In the manufacturing field, industrial robots, with advantages such as a large working space, high stability, and good repeatability accuracy, have expanded their application fields from the automotive manufacturing field to various fields such as aerospace and shipbuilding. In particular, their application prospects in processing directions with higher precision requirements such as grinding, polishing, and milling are very broad.

[0003] When using a robot to perform grinding work on a workpiece, its processing time and smoothness problems affect the efficiency and accuracy of the processing operation. When performing a specified task, we expect the running trajectory of the robot to be smooth and continuous. On the one hand, the industrial robot trajectory planning oriented to time optimization can obtain high working efficiency, which can not only shorten the production cycle but also reduce production costs to a certain extent; on the other hand, the industrial robot trajectory planning oriented to smoothness can ensure the stability and accuracy of processing, and thus obtain better processing surface quality. At the same time, it can also avoid problems such as mechanical wear and shortened lifespan caused by excessive impact.

[0004] The time of trajectory planning can reflect the working efficiency of machinery, etc., and is also related to the production efficiency of enterprises. At present, taking the robot running time as the optimization goal is the focus of in-depth research by most scholars. Most trajectory planning optimizations are only for single objectives, and there are not many studies considering time and smoothness comprehensively, and the correlation between multi-objective trajectory planning has not been concerned. Therefore, it is of great significance for this field to research and develop a high-precision technology that ensures the continuity of the kinematic performance index of the robot and at the same time, a trajectory planning method that takes into account the processing time and smoothness of the robot. Summary of the Invention

[0005] In order to solve the deficiencies existing in the above-mentioned prior art, the present invention aims to provide an industrial robot trajectory planning method considering operation time and smoothness. This method combines smooth interpolation with optimized simulation to achieve higher-order smooth trajectory generation, provide sufficient control degrees of freedom and be compatible with optimization algorithms, and is applicable to high-precision processing operations under the efficient operation of industrial robots, so as to better solve the problems existing in the background art part.

[0006] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0007] An industrial robot trajectory planning method considering operation time and smoothness, comprising the following steps:

[0008] S1: Based on the end - effector spatial pose matrix of the robot, obtain the joint - angle sequence at the machining tool - point position for each joint, and perform initialization operation - time allocation for the joint - angle sequence.

[0009] S2: Use quintic B - spline to interpolate each joint angle and construct a smooth trajectory line before optimization.

[0010] S3: Improve the traditional particle - swarm algorithm through fuzzy logic to obtain an improved particle - swarm algorithm, and use the improved particle - swarm algorithm to optimize the trajectory planning of the robot by comprehensively considering machining time and smoothness.

[0011] S4: Use quintic B - spline to interpolate the joint angles of the trajectory planning obtained in step S3, and construct a smooth trajectory line after optimization.

[0012] As a further preferred solution of the above - mentioned scheme: In step S2, to construct the smooth trajectory line before optimization, quintic B - spline is used to interpolate each joint angle in the joint space, and the specific steps are as follows:

[0013] S21: Construct a high - order B - spline basis function, and its expression is as follows:

[0014]

[0015] In the formula, N i,k (u) is the high - order B - spline basis function, u is the knot in the knot vector, i is the number of knots, k is the order of the polynomial, and when k takes the value of 6, it represents the quintic B - spline basis function.

[0016] S22: Set the relevant boundary conditions of the smooth trajectory line, and construct a system equation of the control point P i The expression of this system equation is:

[0017] A·P i = e

[0018] In the formula, the matrix A is composed of the high - order B - spline basis function and the boundary conditions, and the vector e is composed of the data points and the boundary conditions.

[0019] S23: Construct an angle curve through the quintic B - spline basis function and the control point, and its expression is:

[0020]

[0021] In the formula, N i,6 (u) is the quintic B - spline basis function, and P i is the control point.

[0022] S24: Solve the first - order derivative and the second - order derivative of the angle curve respectively to obtain the velocity curve and the acceleration curve, and their expressions are as follows:

[0023]

[0024] Wherein, V(u) is the velocity curve and A(u) is the angle curve.

[0025] Based on the above technical solution, further, in step S22, the relevant boundary conditions of the smooth trajectory line include angle boundary conditions, velocity boundary conditions, and acceleration boundary conditions, where:

[0026] The angle boundary condition is set as:

[0027]

[0028] The velocity boundary condition is set as:

[0029]

[0030] The acceleration boundary condition is set as:

[0031]

[0032] Wherein, S(u s ) and S(u e ) respectively represent the starting angle and the ending angle of the joint, P s , P e respectively represent the angle values of the set starting point and ending point of the trajectory, V(u s ) and V(u e ) respectively represent the velocities of the joint at the starting point and the ending point of the trajectory, A(u s ) and A(u e ) respectively represent the accelerations of the joint at the starting point and the ending point of the trajectory.

[0033] As a further preferred solution of the above solution: In step S3, the relevant parameters of the traditional particle swarm optimization algorithm are dynamically adjusted by fuzzy logic to improve the traditional particle swarm optimization algorithm. The specific steps are as follows:

[0034] S31: Initialize the parameters in the traditional particle swarm optimization algorithm, and set the expressions for position limit and velocity limit as follows:

[0035]

[0036] Wherein, rand represents a random number uniformly distributed in the interval [0,1], x i represents the initial position of the i-th particle, x min represents the lower bound of the position in the search space, x max represents the upper bound of the position in the search space, v i represents the initial velocity of the i-th particle, vmin represents the minimum velocity v that restricts the movement of particles max represents the maximum velocity that restricts the movement of particles;

[0037] S32: Define the diversity of the particle swarm, which is calculated by the average of the standard deviations of the particles in all dimensions;

[0038]

[0039] In the formula, P diversity is the diversity of the particle swarm, D is the total number of dimensions of the particles, d is the dimension index of the particle, that is, the d-th dimension of the particle, and σ d is the standard deviation of all particles in the d-th dimension;

[0040] S33: Define a fuzzy control system, and use the fuzzy control system to dynamically adjust the parameters in the traditional particle swarm algorithm.

[0041] Based on the above technical solution, further, in step S32, when defining the diversity of the particle swarm, for each spatial dimension d, the standard deviation is calculated using the positions of all particles in the particle swarm in this dimension and the mean value of all particles in this dimension. The calculation formula is as follows:

[0042]

[0043] In the formula, x id is the position of all particles in the spatial dimension d, μ d is the mean value of the positions of all particles in the spatial dimension d, and N is the number of particles.

[0044] Based on the above technical solution, further, in step S33, the steps of dynamically adjusting the parameters of the particle swarm using the fuzzy control system include:

[0045] S331: Take the iteration number P iteration and the particle swarm diversity P diversity as the input variables of the fuzzy control system, and the inertia weight and learning factors as the output variables of the fuzzy control system, and establish a fuzzy control function. Its expression is:

[0046] (w, c1, c2) = Function-One(P iteration , P diversity )

[0047] In the formula, the distribution interval of P iteration is [1, MaxIter], MaxIter is the maximum number of iterations, the distribution interval of P diversity is [0, 1], w is the inertia weight, and c1 and c2 are the first learning factor and the second learning factor respectively;

[0048] S332: Add membership functions and fuzzy rules to the fuzzy control function, thereby dynamically adjusting the inertia weight, the first learning factor, and the second learning factor;

[0049] S333: Evaluate the adjusted inertia weight, the first learning factor, and the second learning factor, and update the individual optimum and the global optimum of the particle swarm. Their expressions are as follows:

[0050]

[0051]

[0052] In the formula, p best is the individual optimum, g best is the global optimum, and x i is the current position of the i-th particle;

[0053] S334: Update the velocity and position of the particle according to the individual optimum and the global optimum results of the particle swarm. Their expressions are as follows:

[0054]

[0055] In the formula, are the inertia weight and the learning factors dynamically adjusted by fuzzy logic; r1 and r2 are random numbers within [0, 1], and t takes the value of 1. is the current velocity of the i-th particle in the d-th dimension, is the current position of the i-th particle in the d-th dimension, is the individual optimum position of the i-th particle in the d-th dimension, is the global optimum position in the d-th dimension.

[0056] As a further preferred solution of the above solution: In step S3, the steps of using the improved particle swarm algorithm to optimize the trajectory planning by comprehensively considering the processing time and smoothness of the robot include:

[0057] (1) Define the optimization objectives of the processing time and smoothness. Their calculation formulas are as follows:

[0058]

[0059] In the formula, t total is the processing time, t i is the time required for each section of the processing trajectory, s process is the smoothness, and j i is the value of the joint acceleration;

[0060] (2) Perform weighted processing on the optimization objectives to generate a comprehensive evaluation index, and use the fuzzy evaluation function to evaluate the fitness;

[0061] C index = w time ·t total + w jerk ·s process

[0062] fitness = Function - Two(C index )

[0063] In the formula, C index is the comprehensive evaluation index, w time and w jerk are the weight coefficients, and w time + w jerk = 1,

[0064] (3) Establish the constraint conditions and objective function for the trajectory planning optimization considering processing time and smoothness, and their expressions are as follows:

[0065]

[0066] In the formula, maxV and maxA are the maximum speed and maximum acceleration of the robot operation respectively.

[0067] Compared with the prior art, the present invention can produce the following beneficial effects:

[0068] 1. The method of the present invention adds a smoothness index to the time optimization research work of robot trajectory planning, improves the processing efficiency of the robot while ensuring the high-performance operation of the robot, which can not only reduce mechanical wear but also improve the processing quality.

[0069] 2. The method of the present invention overcomes the premature convergence problem existing in the traditional particle swarm optimization algorithm when facing complex trajectory planning optimization problems. Through the fuzzy control system, the inertia weight and learning factor are dynamically adjusted according to the current iteration number of the particle swarm and the diversity of the particle swarm, so that the improved particle swarm optimization algorithm maintains a high search and optimization ability, and improves the overall convergence speed and the quality of the optimization solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art.

[0071] Figure 1 It is a flowchart of an industrial robot trajectory planning method considering operation time and smoothness provided by the present invention;

[0072] Figure 2These are the graphs of the angles, speeds, and accelerations of each joint of the robot of the present invention before optimization, where: (a) represents the graph of the angles of each joint of the robot before optimization, (b) represents the graph of the speeds of each joint of the robot before optimization, and (c) represents the graph of the accelerations of each joint of the robot before optimization;

[0073] Figure 3 This is the target iterative convergence graph of the robot trajectory planning under the improved particle swarm algorithm of the present invention, where: (a) represents the fitness iterative convergence graph of joint one of the robot, (b) represents the fitness iterative convergence graph of joint two of the robot, (c) represents the fitness iterative convergence graph of joint three of the robot, (d) represents the fitness iterative convergence graph of joint four of the robot, (e) represents the fitness iterative convergence graph of joint five of the robot, and (f) represents the fitness iterative convergence graph of joint six of the robot;

[0074] Figure 4 These are the graphs of the angles, speeds, and accelerations of each joint of the robot of the present invention after optimization, where: (a) represents the graph of the angles of each joint of the robot after optimization, (b) represents the graph of the speeds of each joint of the robot after optimization, and (c) represents the graph of the accelerations of each joint of the robot after optimization. Detailed implementation manners

[0075] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention.

[0076] Refer to Figures 1-4 , the present invention provides an industrial robot trajectory planning method considering operation time and smoothness, including the following steps:

[0077] S1: Based on the end-effector spatial pose matrix of the robot, obtain the joint angle sequence at the machining tool point positions of each joint, and perform initialization operation time allocation on the joint angle sequence;

[0078] In this step, inverse kinematics is used to solve the joint angle sequence at the machining tool point positions of each joint. For a given end-effector spatial pose T target perform inverse kinematics solution, and through the solution, the angles θ of each machining tool point position in the joint space can be obtained i,n , it can be seen that there are n joint angles in each joint angle sequence θ i where i is the number of robot joints and n is the number of machining tool point positions.

[0079] For the joint angle sequence, perform initialization operation time allocation on the robot machining time allocation sequence t initializedInitialize. First, set the time t1 of the first processing point, usually set to 0 seconds, and the time t of the remaining processing points p (p ∈ [1, n]) is calculated according to the following recurrence formula:

[0080] t p = t p-1 + C interval

[0081] where C interval is the time interval constant for each segment of the processing trajectory and can be set according to actual requirements.

[0082] S2: Use quintic B-spline to interpolate each joint angle to construct a smooth trajectory line before optimization;

[0083] First, perform initialization processing on the knot vector. Set the first and last knots to 0 and 1 respectively, and calculate the middle knots recursively according to the following formula:

[0084]

[0085] In the formula, u(i) is the i-th knot vector, i is the number of knots, X is a two-dimensional matrix composed of the initialization time allocation sequence and each joint angle sequence in the previous text, and L is the total length between data points.

[0086] Next, for the zero-order B-spline basis function N i,0 (u), its calculation formula is as follows:

[0087]

[0088] In the formula, u is the trajectory parameterization variable used to describe the position of the curve at different interpolation points.

[0089] Based on the zero-order B-spline basis function N i,0 (u), recursively calculate the higher-order B-spline basis function N i,k (u), and its formula is as follows:

[0090]

[0091] In the formula, N i,k (u) is the higher-order B-spline basis function, k is the order of the polynomial. In the present invention, the quintic B-spline basis function is adopted, so k takes the value of 6;

[0092] Furthermore, set the relevant boundary conditions of the smooth trajectory line to ensure the smoothness of the constructed smooth trajectory line, which is mainly divided into the boundary condition settings of the angle curve, velocity curve, and acceleration curve, where:

[0093] The angle boundary condition is set as:

[0094]

[0095] The velocity boundary condition is set as:

[0096]

[0097] The acceleration boundary condition is set as:

[0098]

[0099] In the formula, S(u s ), S(u e ) represent the starting angle and the ending angle of the joint respectively, P s , P e represent the angular values of the set starting point and ending point of the trajectory respectively, V(u s ), V(u e ) represent the velocities of the joint at the starting point and ending point of the trajectory respectively, A(u s ), A(u e ) represent the accelerations of the joint at the starting point and ending point of the trajectory respectively.

[0100] Then, based on the relevant boundary conditions, a system equation of the control point P i on the smooth trajectory line is constructed, and the expression of this system equation is:

[0101] A·P i =e

[0102] In the formula, the matrix A is composed of high-order B-spline basis functions and boundary conditions, and the vector e is composed of data points and boundary conditions; the control point P i is solved according to the constructed system equation, and the following result is obtained:

[0103] P i =A -1 ·e

[0104] Since the quintic B-spline interpolation curve is a linear combination of weighted basis functions and all control points, the quintic B-spline basis function N i,6 (u) and the control point P i solved above are used to construct the following angle curve:

[0105]

[0106] Finally, based on the angle curve, a velocity curve v(u) and an acceleration curve A(u) are constructed, where:

[0107] The velocity curve V(u) is the first derivative of the angle curve S(u), and the calculation formula is as follows:

[0108]

[0109] The acceleration curve A(u) is the second derivative of the angle curve S(u), and the calculation formula is as follows:

[0110]

[0111] Refer to Figure 2 As shown, the angle, velocity, and acceleration curves before optimization of each joint generated by the interpolation of the quintic B-spline of the present invention are shown.

[0112] S3: Improve the traditional particle swarm optimization algorithm through fuzzy logic to obtain an improved particle swarm optimization algorithm, and use the improved particle swarm optimization algorithm to optimize the trajectory planning of the robot by comprehensively considering the processing time and smoothness;

[0113] First, initialize the parameters of the traditional particle swarm optimization algorithm; first initialize the population position and population velocity, set the position limit and velocity limit, and then initialize the historical best fitness and position of individuals and groups. Among them, the expressions of the position limit and velocity limit are as follows:

[0114]

[0115] In the formula, rand represents a random number uniformly distributed in the interval [0,1], x i represents the initial position of the i-th particle, x min represents the lower bound of the position in the search space, x max represents the upper bound of the position in the search space, v i represents the initial velocity of the i-th particle, v min represents the lowest velocity that restricts the movement of the particle, v max represents the highest velocity that restricts the movement of the particle;

[0116] Furthermore, define the diversity of the particle swarm. For each spatial dimension, use the positions of all particles in the particle swarm in this dimension and the mean value of all particles in this dimension to calculate the standard deviation σ d , and the calculation formula is as follows:

[0117]

[0118] In the formula, σ d is the standard deviation of all particles in the d-th dimension, x id is the position of all particles in the spatial dimension d, μ d is the mean value of the positions of all particles in the spatial dimension d, and N is the number of particles.

[0119] Calculate the particle swarm diversity through the average value of the standard deviations of all-dimensional particles, and the calculation formula is as follows:

[0120]

[0121] Wherein, P diversity is the diversity of the particle swarm, and D is the total number of dimensions of the particles.

[0122] Furthermore, a fuzzy system is defined to dynamically adjust the relevant parameters of the particle swarm, which specifically includes the following steps:

[0123] First, relevant variables are added; the iteration number P iteration and the particle swarm diversity P diversity are used as the input variables of the fuzzy control system, and the inertia weight and learning factors are used as the output variables of the fuzzy control system, and are output after being adjusted by the fuzzy system, and a fuzzy control function is established, and its expression is:

[0124] (w, c1, c2) = Function-One(P iteration , P diversity )

[0125] Wherein, the distribution interval of P iteration is [1, MaxIter], MaxIter is the maximum number of iterations, the distribution interval of P diversity is [0, 1], w is the inertia weight, and c1 and c2 are the first learning factor and the second learning factor respectively;

[0126] Secondly, membership functions are defined for the fuzzy control function and fuzzy rules are added. Appropriate membership function types are used to capture the characteristics of each variable at different stages, and a set of fuzzy rules are formulated to adjust the inertia weight and learning factors. In the present invention, a fuzzy rule matrix is used to embody this. Here, it is assumed that P iteration has 2 fuzzy sets, and P diversity has 3 fuzzy sets. Therefore, the matrix size is 2*3, and the fuzzy rule matrix is shown in the following formula:

[0127]

[0128] Wherein, the element R pq in the matrix corresponds to the fuzzy set corresponding to the output variable when the input variable P iteration is in the i-th type of fuzzy set and P diversity is in the j-th type of fuzzy set.

[0129] Finally, the inertia weight w, the first learning factor c1, and the second learning factor c2 adjusted by the fuzzy control system are evaluated. After evaluation, the individual and group optima of the particle swarm are updated, and their expressions are respectively:

[0130]

[0131] Wherein, p best is the individual optimum, gbest is the group optimum, and x i is the current position of the i-th particle;

[0132] According to the individual optimum and group optimum results of the particle swarm, update the velocity and position of the particle, and its expression is as follows:

[0133]

[0134] In the formula, is the inertia weight and learning factor dynamically adjusted by fuzzy logic; r1 and r2 are random numbers within [0, 1], and t takes the value of 1. is the current velocity of the i-th particle in the d-th dimension, is the current position of the i-th particle in the d-th dimension, is the individual optimum position of the i-th particle in the d-th dimension, is the global optimum position in the d-th dimension.

[0135] Refer to Figure 3 As shown, this is the iterative convergence diagram of each joint of the optimization target using the improved particle swarm algorithm in the present invention.

[0136] Use the improved particle swarm algorithm to optimize the trajectory planning of the robot. During the optimization process, comprehensively consider the processing time and smoothness. The process is as follows:

[0137] First, define the optimization objectives of processing time and smoothness. The calculation formulas for processing time and smoothness are respectively:

[0138]

[0139] In the formula, t total is the processing time, t i is the time required for each section of the processing trajectory, s process is the smoothness, and j i is the value of the joint acceleration;

[0140] Next, perform weighted processing on the optimization objectives. In order to better adjust the influence of processing time and smoothness on the optimization results, a comprehensive evaluation index C index is weighted and generated, and its expression is as follows:

[0141] C index = w time ·t total + w jerk ·s process

[0142] In the formula, C index is the comprehensive evaluation index, w time and w jerk are weight coefficients, and wtime +w jerk = 1. Further, a fuzzy evaluation function is used to evaluate the fitness, and the fuzzy evaluation function is as follows;

[0143] fitness = Function-Two(C index )

[0144] Finally, the constraint conditions and objective function for optimizing the trajectory planning by comprehensively considering the processing time and smoothness are established, and their expressions are as follows:

[0145]

[0146] In the formula, maxV and maxA are the maximum speed and maximum acceleration of the robot operation respectively.

[0147] S4: Use quintic B-spline to interpolate the joint angles of the trajectory planning obtained in step S3 to construct an optimized smooth trajectory line.

[0148] In this step, the time parameters and joint angle sequences optimized above are used as inputs, and the quintic B-spline interpolation method is used to generate a new kinematic trajectory. The generated trajectory is time-optimal on the basis of satisfying the speed and acceleration limits kinematically, and at the same time ensures the smooth transition of the trajectory, thereby improving the efficiency and accuracy of the robot movement. Finally, a fast and smooth industrial robot movement trajectory is created to improve the efficiency and accuracy of robot processing.

[0149] Refer to Figure 4 As shown, the optimized angle, speed, and acceleration curves of each joint generated by the present invention using quintic B-spline interpolation.

[0150] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art of this industry should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. An industrial robot trajectory planning method considering operation time and smoothness, characterized in that It includes the following steps: S1: Based on the end - effector spatial pose matrix of the robot, obtain the joint angle sequence at the machining tool point of each joint, and perform initialization operation time allocation on the joint angle sequence; S2: Use quintic B - spline to interpolate each joint angle, and construct a smooth trajectory line before optimization; S3: Improve the traditional particle swarm optimization algorithm through fuzzy logic to obtain an improved particle swarm optimization algorithm, and use the improved particle swarm optimization algorithm to optimize the trajectory planning of the robot by comprehensively considering machining time and smoothness; S4: Use quintic B - spline to interpolate the joint angles of the trajectory planning obtained in step S3, and construct a smooth trajectory line after optimization.

2. The industrial robot trajectory planning method considering operation time and smoothness according to claim 1, wherein In step S2, to construct the smooth trajectory line before optimization, quintic B - spline is used to interpolate each joint angle in the joint space. The specific steps are as follows: S21: Construct a high - order B - spline basis function, and its expression is as follows: where N i,k (u) is a high-order B-spline basis function, u is a knot in the knot vector, i is the basis function index, k is the order of the polynomial, and k taking the value of 6 represents a fifth-order B-spline basis function; S22: Set the relevant boundary conditions of the smooth trajectory line, and construct the control point P i based on the relevant boundary conditions. The expression of the system equation of this system equation is: A·P i = e In the formula, matrix A is composed of high - order B - spline basis functions and derivative information, and vector e is composed of the target position values corresponding to the data points and the target derivative values corresponding to the boundary conditions; S23: Construct an angle curve through the quintic B - spline basis function and control points, and its expression is: where N i,6 (u) is the quintic B-spline basis function, and P i is the control point; S24: Solve the first - order derivative and second - order derivative of the angle curve respectively to obtain the velocity curve and acceleration curve, and their expressions are as follows: In the formula, V(u) is the velocity curve, and A(u) is the acceleration curve.

3. An industrial robot trajectory planning method considering operation time and smoothness according to claim 2, characterized in that, In step S22, the relevant boundary conditions of the smooth trajectory line include angle boundary conditions, velocity boundary conditions, and acceleration boundary conditions, where: The angle boundary conditions are set as: The velocity boundary conditions are set as: The acceleration boundary conditions are set as: where, S(u s ) and S(u e ) respectively represent the starting angle and the ending angle of the joint, P s and P e respectively represent the angular values of the set starting point and the ending point of the trajectory, V(u s ) and V(u e ) respectively represent the velocities of the joint at the starting point and the ending point of the trajectory, and A(u s ) and A(u e ) respectively represent the accelerations of the joint at the starting point and the ending point of the trajectory.

4. An industrial robot trajectory planning method considering operation time and smoothness according to claim 1, characterized in that In step S3, the relevant parameters of the traditional particle swarm optimization algorithm are dynamically adjusted through fuzzy logic to improve the traditional particle swarm optimization algorithm. The specific steps are as follows: S31: Perform initialization processing on the parameters in the traditional particle swarm optimization algorithm, and set the expressions for position limit and velocity limit as follows: where rand represents a random number uniformly distributed in the interval [0, 1], and x i represents the initial position of the i-th particle, and x min represents the lower bound of the position in the search space, and x max represents the upper bound of the position in the search space, and v i represents the initial velocity of the i-th particle, and v min represents the minimum velocity that restricts the movement of the particle, and v max represents the maximum velocity that restricts the movement of the particle; S32: Define the diversity of the particle swarm, and calculate the diversity of the particle swarm through the average value of the standard deviations of all dimensions of the particles; where P diversity is the diversity of the particle swarm, D is the total number of dimensions of the particles, d is the dimension index of the particle, that is, the d-th dimension of the particle, and σ d is the standard deviation of all particles in the d-th dimension; S33: Define a fuzzy control system, and use the fuzzy control system to dynamically adjust the parameters in the traditional particle swarm optimization algorithm.

5. The industrial robot trajectory planning method considering operation time and smoothness according to claim 4, characterized in that In step S32, when defining the diversity of the particle swarm, for each spatial dimension d, calculate the standard deviation using the positions of all particles in the particle swarm in this dimension and the mean value of all particles in this dimension. Its calculation formula is as follows: where \(x\) id is the position of all particles in the spatial dimension \(d\), and \(\mu\) d is the mean value of the positions of all particles in the spatial dimension \(d\), and \(N\) is the number of particles.

6. An industrial robot trajectory planning method considering operation time and smoothness according to claim 4, characterized in that In step S33, the steps of dynamically adjusting the parameters of the particle swarm using the fuzzy control system include: S331: Take the number of iterations P iteration and the particle swarm diversity P diversity as the input variables of the fuzzy control system, and the inertia weight and learning factor as the output variables of the fuzzy control system to establish a fuzzy control function, whose expression is: (w, c1, c2) = Function-One(P iteration , P diversity ) where P iteration is distributed in the range of [1, MaxIter], MaxIter is the maximum number of iterations, and P diversity is distributed in the range of [0, 1], w is the inertia weight, and c1 and c2 are the first learning factor and the second learning factor respectively; S332: Add membership functions and fuzzy rules to the fuzzy control function to dynamically adjust the inertia weight, the first learning factor, and the second learning factor; S333: Evaluate the adjusted inertia weight, the first learning factor, and the second learning factor, and update the individual best and global best of the particle swarm. Their expressions are respectively: where p best is the individual optimum, g best is the global optimum, and x i is the current position of the i-th particle; S334: Update the velocity and position of the particles according to the individual best and global best results of the particle swarm. Their expressions are as follows: wherein, is the inertia weight and learning factor dynamically adjusted by fuzzy logic; r1 and r2 are random numbers within [0, 1], and t takes the value of 1, is the current velocity of the i-th particle in the d-th dimension, is the current position of the i-th particle in the d-th dimension, is the individual optimal position of the i-th particle in the d-th dimension, is the global optimal position in the d-th dimension.

7. A trajectory planning method for an industrial robot considering operation time and smoothness according to claim 1, characterized in that In step S3, the steps of using the improved particle swarm optimization algorithm to optimize the trajectory planning by comprehensively considering the processing time and smoothness of the robot include: (1) Define the optimization objectives of machining time and smoothness, and their calculation formulas are respectively: where t total is the processing time, and t i is the time required for each segment of the processing trajectory, s process is the smoothness, and j i is the value of the joint acceleration; (2) Perform weighted processing on the optimization objectives to generate a comprehensive evaluation index, and use a fuzzy evaluation function to evaluate the fitness; C index = w time · t total + w jerk · s process fitness=Function-Two(C index ) where C index is the comprehensive evaluation index, w time and w jerk are the weight coefficients, and w time + w jerk = 1 (3) Establish the constraint conditions and objective function for trajectory planning optimization that comprehensively consider processing time and smoothness, and their expressions are as follows: In the formula, maxV and maxA are the maximum speed and maximum acceleration of the robot operation respectively.

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