Industrial robot trajectory planning method considering operation time and smoothness

Abstract

The application discloses an industrial robot trajectory planning method considering operation time and smoothness, and belongs to the technical field of robot machining. In view of the problem that existing industrial robot trajectory planning only considers a single target and lacks correlation between multi-target trajectory planning, the method comprises the following steps: obtaining joint angle sequences of each joint at machining tool point positions based on a spatial pose matrix of the end of the robot, performing initialization operation time distribution on the joint angle sequences, using a quintic B-spline to interpolate each joint angle, constructing a smooth trajectory line before optimization, improving a traditional particle swarm algorithm through fuzzy logic, using the improved particle swarm algorithm to perform trajectory planning optimization of the robot considering machining time and smoothness, using a quintic B-spline to interpolate each joint angle, and constructing a smooth trajectory line after optimization. The method comprehensively considers machining time and smoothness, guarantees high-performance operation of the robot, reduces mechanical wear, and improves machining quality.

Description

Technical Field

[0001] This invention relates to the field of robot processing technology, and in particular to an industrial robot trajectory planning method that takes into account operation time and smoothness. Background Technology

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

[0003] When using robots to grind workpieces, the processing time and smoothness affect the efficiency and accuracy of the operation. When performing a specified task, we expect the robot's trajectory to be smooth and continuous. On the one hand, time-optimized industrial robot trajectory planning can achieve high work efficiency, which can not only shorten the production cycle but also reduce production costs to a certain extent. On the other hand, smoothness-oriented industrial robot trajectory planning can ensure the stability and accuracy of processing, thereby obtaining better surface quality, while also avoiding problems such as mechanical wear and shortened lifespan caused by excessive impact.

[0004] The time required for trajectory planning reflects the efficiency of machinery and is related to the production efficiency of enterprises. Currently, most scholars focus on optimizing robot running time as the primary research objective. However, most trajectory planning optimizations only address single objectives, with limited research considering both time and smoothness, and neglecting the correlation between multi-objective trajectory planning. Therefore, developing a high-precision technique that ensures continuous robot kinematic performance while simultaneously considering robot processing time and smoothness is of great significance to this field. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, this invention aims to provide an industrial robot trajectory planning method that considers operation time and smoothness. This method combines smooth interpolation with optimization simulation to achieve higher-order smooth trajectory generation, provide sufficient control degrees of freedom and be compatible with optimization algorithms. It is suitable for high-precision machining operations under the efficient operation of industrial robots, thereby better solving the problems existing in the background technology.

[0006] To achieve the above technical objectives, the present invention adopts the following technical solution:

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

[0008] S1: Based on the robot's end-effector spatial pose matrix, obtain the joint angle sequence of each joint at the machining tool point, and initialize the running time allocation for the joint angle sequence;

[0009] S2: Use quintic B-splines to interpolate the joint angles and construct a smooth trajectory line before optimization;

[0010] S3: Improve the traditional particle swarm optimization algorithm by fuzzy logic to obtain an improved particle swarm optimization algorithm. Use the improved particle swarm optimization algorithm to optimize the trajectory planning of the robot by taking into account both processing time and smoothness.

[0011] S4: Use quintic B-splines to interpolate the joint angles of the trajectory planning obtained in step S3 to construct an optimized smooth trajectory line.

[0012] As a further preferred option of the above scheme: In step S2, the smooth trajectory line before optimization is constructed by interpolating the joint angles of each joint in the joint space using a fifth-order B-spline. The specific steps are as follows:

[0013] S21: Construct higher-order B-spline basis functions, the expressions of which are as follows:

[0014]

[0015] In the formula, For higher-order B-spline basis functions, Let i be a node in the node vector, and i be the number of nodes. Let be the order of the polynomial, and A value of 6 indicates a quintic B-spline basis function;

[0016] S22: Set the relevant boundary conditions for the smooth trajectory line, and construct control points based on the relevant boundary conditions. The system equations are expressed as follows:

[0017]

[0018] In the formula, matrix A consists of higher-order B-spline basis functions and boundary conditions, and vector e consists of data points and boundary conditions;

[0019] S23: An angle curve is constructed using quintic B-spline basis functions and control points. Its expression is:

[0020]

[0021] In the formula, For fifth-order B-spline basis functions, For control points;

[0022] S24: Solve for the first and second derivatives of the angle curves to obtain the velocity and acceleration curves, whose expressions are as follows:

[0023]

[0024]

[0025] In the formula, For the velocity curve, It is an angle curve.

[0026] Based on the above technical solution, further, in step S22, the relevant boundary conditions of the smooth trajectory line include angular boundary conditions, velocity boundary conditions, and acceleration boundary conditions, wherein:

[0027] The angular boundary conditions are set as follows:

[0028]

[0029] The velocity boundary conditions are set as follows:

[0030]

[0031] The acceleration boundary conditions are set as follows:

[0032]

[0033] In the formula, , These represent the starting and ending angles of the joint, respectively. , These represent the angle values ​​of the set starting and ending points of the trajectory, respectively. , These represent the velocities of the joint at the start and end points of the trajectory, respectively. , These represent the accelerations of the joint at the start and end points of the trajectory, respectively.

[0034] As a further preferred option of the above scheme: 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:

[0035] S31: Initialize the parameters for the traditional particle swarm optimization algorithm, setting the expressions for position and velocity limits as follows:

[0036]

[0037] In the formula, Let x represent a uniformly distributed random number within the interval [0,1]. i Indicates the initial position of the i-th particle, xmin The lower bound of the location in the search space, x max Represents the upper bound of the location in the search space, v i Represents the initial velocity of the i-th particle, v min Indicates the minimum speed that limits particle movement, v max Indicates the maximum speed at which a particle can move;

[0038] S32: Define particle swarm diversity, which is calculated by the average of the standard deviations of particles across all dimensions.

[0039]

[0040] In the formula, For particle swarm diversity, Let be the total number of dimensions of the particle, and d be the dimension index of the particle, i.e., the d-th dimension of the particle. For all particles in the first Standard deviation in dimensions;

[0041] S33: Define a fuzzy control system to dynamically adjust the parameters in the traditional particle swarm optimization algorithm.

[0042] Based on the above technical solution, further, in step S32, when defining particle swarm diversity, for each spatial dimension d, the standard deviation is calculated using the positions of all particles in the particle swarm in that dimension and the mean of all particles in that dimension. The calculation formula is as follows:

[0043]

[0044]

[0045] In the formula, Let be the positions of all particles in the spatial dimension d. Let d be the mean of all particle positions along the spatial dimension d, and N be the number of particles.

[0046] Based on the above technical solution, further, in step S33, the step of dynamically adjusting the parameters of the particle swarm using a fuzzy control system includes:

[0047] S331: Number of iterations and particle swarm diversity As input variables of the fuzzy control system, inertia weight and learning factor are used as output variables. A fuzzy control function is established, and its expression is:

[0048]

[0049] In the formula, The distribution interval is [1, MaxIter], where MaxIter is the maximum number of iterations. The distribution interval is [0,1], w is the inertia weight, and c1 and c2 are the first learning factor and the second learning factor, respectively.

[0050] 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;

[0051] S333: Evaluate the adjusted inertia weights, the first learning factor, and the second learning factor to update the individual optimality and swarm optimality of the particle swarm, with the following expressions:

[0052]

[0053]

[0054] In the formula, For the individual's optimal, For the group optimal, x i This represents the current position of the i-th particle;

[0055] S334: Update the velocity and position of the particles based on the individual optimal and swarm optimal results, as expressed below:

[0056]

[0057]

[0058] In the formula, , , These are the inertia weights and learning factors dynamically adjusted using fuzzy logic. and The value of t is a random number in the range [0,1], and the value of t is 1. Let be the current velocity of the i-th particle in the d-th dimension. Let be the current position of the i-th particle in the d-th dimension. Let be the optimal position of the i-th particle in the d-th dimension. This represents the globally optimal position in the d-th dimension.

[0059] As a further preferred option of the above scheme: In step S3, the step of using the improved particle swarm optimization algorithm to optimize the trajectory planning of the robot, taking into account both processing time and smoothness, includes:

[0060] (1) Define the optimization objectives for processing time and smoothness, and their calculation formulas are as follows:

[0061]

[0062]

[0063] In the formula, For processing time, This represents the time required for each segment of the processing trajectory. For smoothness, The value of the joint acceleration;

[0064] (2) Weighted processing optimizes the objective to generate a comprehensive evaluation index, and uses a fuzzy evaluation function to evaluate the fitness;

[0065]

[0066]

[0067] In the formula, As a comprehensive evaluation indicator, and It is a weighting coefficient, and ,

[0068] (3) Establish the constraints and objective function for trajectory planning optimization that comprehensively consider processing time and smoothness, and their expressions are as follows:

[0069]

[0070] In the formula, and These represent the robot's maximum speed and maximum acceleration, respectively.

[0071] Compared with the prior art, the present invention can produce the following beneficial effects:

[0072] 1. The method of this invention incorporates a smoothness index into the time optimization research of robot trajectory planning, which improves robot processing efficiency while ensuring high-performance operation of the robot. This not only reduces mechanical wear but also improves processing quality.

[0073] 2. The method of this invention overcomes the premature convergence problem of traditional particle swarm optimization (PSO) when facing complex trajectory planning and optimization problems. By using a fuzzy control system, the inertia weight and learning factor are dynamically adjusted according to the current iteration number and particle swarm diversity, so that the improved PSO algorithm maintains a high search and optimization capability, and improves the overall convergence speed and the quality of the optimized solution. Attached Figure Description

[0074] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0075] Figure 1 A flowchart of an industrial robot trajectory planning method considering operation time and smoothness provided by the present invention;

[0076] Figure 2 The diagrams show the angles, velocities, and accelerations of each joint of the robot before optimization, where: (a) represents the angle diagram of each joint before optimization, (b) represents the velocity diagram of each joint before optimization, and (c) represents the acceleration diagram of each joint before optimization.

[0077] Figure 3 The diagram shows the target iterative convergence graph for robot trajectory planning under the improved particle swarm optimization algorithm of this invention, where: (a) represents the iterative convergence graph of robot joint 1 fitness, (b) represents the iterative convergence graph of robot joint 2 fitness, (c) represents the iterative convergence graph of robot joint 3 fitness, (d) represents the iterative convergence graph of robot joint 4 fitness, (e) represents the iterative convergence graph of robot joint 5 fitness, and (f) represents the iterative convergence graph of robot joint 6 fitness.

[0078] Figure 4 The diagrams show the optimized angles, velocities, and accelerations of each joint of the robot according to the present invention, wherein: (a) represents the optimized angle diagram of each joint, (b) represents the optimized velocity diagram of each joint, and (c) represents the optimized acceleration diagram of each joint. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0080] Reference Figures 1-4 This invention provides an industrial robot trajectory planning method that considers operation time and smoothness, comprising the following steps:

[0081] S1: Based on the robot's end-effector spatial pose matrix, obtain the joint angle sequence of each joint at the machining tool point, and initialize the running time allocation for the joint angle sequence;

[0082] In this step, inverse kinematics is used to solve the joint angle sequence of each joint at the machining tool position, for a given robot end-effector spatial pose. By performing inverse kinematics solutions, the angles of each machining tool point in joint space can be obtained. This shows the joint angle sequence for each joint. There are a total of One joint angle, of which The number of robot joints, This represents the number of machining tool points.

[0083] Initialize the runtime allocation for the joint angle sequence and allocate the robot machining time sequence. To initialize, first set the time for the first processing point. Configure the settings, typically set to 0 seconds, and specify the time for each of the other processing points. ( Calculate according to the following recursive formula:

[0084]

[0085] in, This is the time interval constant for each segment of the processing trajectory, which can be set according to actual needs.

[0086] S2: Use quintic B-splines to interpolate the joint angles and construct a smooth trajectory line before optimization;

[0087] First, the node vector is initialized by setting the first and last nodes to 0 and 1 respectively, and the intermediate nodes are calculated recursively according to the following formula:

[0088]

[0089] In the formula, Let be the vector of the i-th node, where i is the number of nodes. It is a two-dimensional matrix, composed of the initialization time allocation sequence and the joint angle sequence mentioned above. This represents the total length between data points.

[0090] Next, for the zeroth-order B-spline basis function The calculation formula is as follows:

[0091] (3)

[0092] In the formula, It is a trajectory parameterized variable used to describe the position of the curve at different interpolation points.

[0093] Based on zero-order B-spline basis function Recursively derive higher-order B-spline basis functions The formula is as follows:

[0094]

[0095] In the formula, For higher-order B-spline basis functions, The order of the polynomial is given by the fifth-order B-spline basis function used in this invention. The value is 6;

[0096] Furthermore, boundary conditions are set for the smooth trajectory to ensure its smoothness. This mainly involves setting boundary conditions for angle curves, velocity curves, and acceleration curves, among which:

[0097] The angular boundary conditions are set as follows:

[0098]

[0099] The velocity boundary conditions are set as follows:

[0100]

[0101] The acceleration boundary conditions are set as follows:

[0102]

[0103] In the formula, , These represent the starting and ending angles of the joint, respectively. , These represent the angle values ​​of the set starting and ending points of the trajectory, respectively. , These represent the velocities of the joint at the start and end points of the trajectory, respectively. , These represent the accelerations of the joint at the start and end points of the trajectory, respectively.

[0104] Then, control points are constructed on the smooth trajectory line based on relevant boundary conditions. The system equations are expressed as follows:

[0105]

[0106] In the formula, matrix A consists of high-order B-spline basis functions and boundary conditions, and vector e consists of data points and boundary conditions; the control points are solved based on the constructed system equations. The following results were obtained:

[0107]

[0108] Since the fifth-order B-spline interpolation curve is a linear combination of the weighted basis functions and all control points, the fifth-order B-spline basis functions obtained through the above solution... and control points Construct the angle curve of the following formula:

[0109]

[0110] Finally, a velocity curve is constructed based on the angle curve. Acceleration curve ,in:

[0111] velocity curve It is an angle curve The first derivative of is calculated using the following formula:

[0112]

[0113] acceleration curve It is an angle curve The second derivative is calculated using the following formula:

[0114]

[0115] See Figure 2 As shown, these are the angle, velocity, and acceleration curves of each joint before optimization, generated by interpolation using quintic B-splines in this invention.

[0116] S3: Improve the traditional particle swarm optimization algorithm by fuzzy logic to obtain an improved particle swarm optimization algorithm. Use the improved particle swarm optimization algorithm to optimize the trajectory planning of the robot by taking into account both processing time and smoothness.

[0117] First, the parameters of the traditional particle swarm optimization algorithm are initialized. This includes initializing the population position and velocity, setting position and velocity constraints, and then initializing the historical best fitness and position of individuals and the population. The expressions for the position and velocity constraints are as follows:

[0118]

[0119] In the formula, Let x represent a uniformly distributed random number within the interval [0,1]. i Indicates the initial position of the i-th particle, x min The lower bound of the location in the search space, x max Represents the upper bound of the location in the search space, v i Represents the initial velocity of the i-th particle, v min Indicates the minimum speed that limits particle movement, v max Indicates the maximum speed at which a particle can move;

[0120] Furthermore, particle swarm diversity is defined. For each spatial dimension, the standard deviation is calculated using the positions of all particles in the swarm in that dimension and the mean of all particles in that dimension. The calculation formula is as follows:

[0121]

[0122]

[0123] In the formula, For all particles in the first Standard deviation in dimensions Let be the positions of all particles in the spatial dimension d. Let d be the mean of all particle positions along the spatial dimension d, and N be the number of particles.

[0124] Particle swarm diversity is calculated by averaging the standard deviations of particles across all dimensions, using the following formula:

[0125]

[0126] In the formula, For particle swarm diversity, The total dimension of the particle.

[0127] Furthermore, a fuzzy system is defined, and the relevant parameters of the particle swarm are dynamically adjusted, specifically including the following steps:

[0128] First, add the relevant variables; set the iteration count. and particle swarm diversity As input variables of the fuzzy control system, the inertia weight and learning factor are output variables of the fuzzy control system. After adjustment by the fuzzy system, the output is used to establish the fuzzy control function, the expression of which is:

[0129]

[0130] In the formula, The distribution interval is [1, MaxIter], where MaxIter is the maximum number of iterations. The distribution interval is [0,1], w is the inertia weight, and c1 and c2 are the first learning factor and the second learning factor, respectively.

[0131] 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. A set of fuzzy rules is formulated to adjust the inertia weights and learning factors. In this invention, a fuzzy rule matrix is ​​used to represent this. Here, it is assumed that… There are 2 fuzzy sets. There are 3 fuzzy sets, so the matrix size is 2*3. The fuzzy rule matrix is ​​shown in the following formula:

[0132]

[0133] In the formula, the elements in the matrix Corresponding input variables No. Fuzzy set No. When dealing with fuzzy sets, output the fuzzy set corresponding to the variable.

[0134] Finally, the inertial weight w and the first and second learning factors c1 and c2, adjusted by the fuzzy control system, are evaluated. After evaluation, the individual and swarm optima of the particle swarm are updated, with the following expressions:

[0135]

[0136]

[0137] In the formula, For the individual's optimal, For the group optimal, x i This represents the current position of the i-th particle;

[0138] Based on the individual optimality and swarm optimality results of the particle swarm, the velocity and position of the particles are updated, and the expression is as follows:

[0139]

[0140]

[0141] In the formula, , , These are the inertia weights and learning factors dynamically adjusted using fuzzy logic. and The value of t is a random number in the range [0,1], and the value of t is 1. Let be the current velocity of the i-th particle in the d-th dimension. Let be the current position of the i-th particle in the d-th dimension. Let be the optimal position of the i-th particle in the d-th dimension. This represents the globally optimal position in the d-th dimension.

[0142] See Figure 3 The figure shown is an iterative convergence diagram of each joint of the target optimization using the improved particle swarm optimization algorithm of this invention.

[0143] An improved particle swarm optimization algorithm is used to optimize the robot's trajectory planning. The optimization process comprehensively considers processing time and smoothness, as follows:

[0144] First, we define the optimization objectives for processing time and smoothness, and the calculation formulas for processing time and smoothness are as follows:

[0145]

[0146]

[0147] In the formula, For processing time, This represents the time required for each segment of the processing trajectory. For smoothness, The value of the joint acceleration;

[0148] Next, the optimization objective is weighted. To better adjust the impact of processing time and smoothness on the optimization result, a comprehensive evaluation index is generated using weighted methods. Its expression is as follows:

[0149]

[0150] In the formula, As a comprehensive evaluation indicator, and It is a weighting coefficient, and .

[0151] Furthermore, the fitness is evaluated using a fuzzy evaluation function, which is shown below;

[0152]

[0153] Finally, the constraints and objective function for trajectory planning optimization, which comprehensively consider processing time and smoothness, are established, and their expressions are as follows:

[0154]

[0155] In the formula, and These represent the robot's maximum speed and maximum acceleration, respectively.

[0156] S4: Use quintic B-splines to interpolate the joint angles of the trajectory planning obtained in step S3 to construct an optimized smooth trajectory line.

[0157] In this step, the optimized time parameters and joint angle sequences are used as input, and a new kinematic trajectory is generated using the fifth-order B-spline interpolation method. The generated trajectory achieves time optimization while satisfying the speed and acceleration constraints in kinematics, and ensures smooth trajectory transition, thereby improving the efficiency and accuracy of robot motion. Finally, a fast and smooth industrial robot motion trajectory is created to improve the efficiency and accuracy of robot processing.

[0158] See Figure 4 As shown, the angle, velocity, and acceleration curves of each joint are optimized and generated by interpolation using quintic B-splines according to this invention.

[0159] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this 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, Includes the following steps: S1: Based on the robot's end-effector spatial pose matrix, obtain the joint angle sequence of each joint at the machining tool point, and initialize the running time allocation for the joint angle sequence; S2: Use quintic B-splines to interpolate the joint angles and construct a smooth trajectory line before optimization; S3: Improve the traditional particle swarm optimization algorithm by fuzzy logic to obtain an improved particle swarm optimization algorithm. Use the improved particle swarm optimization algorithm to optimize the trajectory planning of the robot by taking into account both processing time and smoothness. The traditional particle swarm optimization (PSO) algorithm is improved by dynamically adjusting relevant parameters using fuzzy logic. The specific steps are as follows: S31: Initialize the parameters for the traditional particle swarm optimization algorithm, setting the expressions for position and velocity limits as follows: ； In the formula, Let x represent a uniformly distributed random number within the interval [0,1]. i Indicates the initial position of the i-th particle, x min x represents the lower bound of a position in the search space. max v represents the upper bound of a position in the search space. i Let v represent the initial velocity of the i-th particle. min v represents the minimum speed at which a particle can move. max Indicates the maximum speed at which a particle can move; S32: Define particle swarm diversity, which is calculated by the average of the standard deviations of particles across all dimensions. ； In the formula, For particle swarm diversity, Let be the total number of dimensions of the particle, and d be the dimension index of the particle, i.e., the d-th dimension of the particle. For all particles in the first Standard deviation in dimensions; S33: Define a fuzzy control system to dynamically adjust the parameters in the traditional particle swarm optimization algorithm. The steps for trajectory planning optimization of a robot that comprehensively considers processing time and smoothness using an improved particle swarm optimization algorithm include: (1) Define the optimization objectives for processing time and smoothness, and their calculation formulas are as follows: ； ； In the formula, For processing time, This represents the time required for each segment of the processing trajectory. For smoothness, The value of the joint acceleration; (2) Weighted processing optimizes the objective to generate a comprehensive evaluation index, and uses a fuzzy evaluation function to evaluate the fitness; ； ； In the formula, As a comprehensive evaluation indicator, and It is a weighting coefficient, and , (3) Establish the constraints and objective function for trajectory planning optimization that comprehensively consider processing time and smoothness, and their expressions are as follows: ； In the formula, and These are the robot's maximum speed and maximum acceleration, respectively. S4: Use quintic B-splines to interpolate the joint angles of the trajectory planning obtained in step S3 to construct an optimized smooth trajectory line.

2. The industrial robot trajectory planning method considering operation time and smoothness according to claim 1, characterized in that, In step S2, the smooth trajectory line before optimization is constructed by interpolating the joint angles in joint space using quintic B-splines. The specific steps are as follows: S21: Construct higher-order B-spline basis functions, the expressions of which are as follows: ； In the formula, For higher-order B-spline basis functions, Let i be a node in the node vector, and let i be the index of the basis function. Let be the order of the polynomial, and A value of 6 indicates a quintic B-spline basis function; S22: Set the relevant boundary conditions for the smooth trajectory line, and construct control points based on the relevant boundary conditions. The system equations are expressed as follows: ； In the formula, matrix A consists of higher-order B-spline basis functions and derivative information, and vector e consists of the target position value corresponding to the data point and the target derivative value corresponding to the boundary condition; S23: An angle curve is constructed using quintic B-spline basis functions and control points. Its expression is: ； In the formula, For fifth-order B-spline basis functions, For control points; S24: Solve for the first and second derivatives of the angle curves to obtain the velocity and acceleration curves, whose expressions are as follows: ； ； In the formula, For the velocity curve, This is the acceleration curve.

3. The industrial robot trajectory planning method considering operation time and smoothness according to claim 2, characterized in that, In step S22, the relevant boundary conditions for the smooth trajectory include angular boundary conditions, velocity boundary conditions, and acceleration boundary conditions, wherein: The angle boundary conditions are set as follows: ； The velocity boundary conditions are set as follows: ； The acceleration boundary conditions are set as follows: ； In the formula, , These represent the starting and ending angles of the joint, respectively. , These represent the angle values ​​of the set starting and ending points of the trajectory, respectively. , These represent the velocities of the joint at the start and end points of the trajectory, respectively. , These represent the accelerations of the joint at the start and end points of the trajectory, respectively.

4. The industrial robot trajectory planning method considering operation time and smoothness according to claim 1, characterized in that, In step S32, when defining particle swarm diversity, for each spatial dimension d, the standard deviation is calculated using the positions of all particles in the swarm along that dimension and the mean of all particles along that dimension. The calculation formula is as follows: ； ； In the formula, Let be the positions of all particles in the spatial dimension d. Let d be the mean of all particle positions along the spatial dimension d, and N be the number of particles.

5. The industrial robot trajectory planning method considering operation time and smoothness according to claim 2, characterized in that, Step S33, the step of dynamically adjusting the parameters of the particle swarm using a fuzzy control system, includes: S331: Number of iterations and particle swarm diversity As input variables of the fuzzy control system, inertia weight and learning factor are used as output variables. A fuzzy control function is established, and its expression is: ； In the formula, The distribution interval is [1, MaxIter], where MaxIter is the maximum number of iterations. The distribution interval is [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 weights, the first learning factor, and the second learning factor to update the individual optimality and swarm optimality of the particle swarm, with the following expressions: ； ； In the formula, For the individual's optimal, For the group optimal, x i This represents the current position of the i-th particle; S334: Update the velocity and position of the particles based on the individual optimal and swarm optimal results, as expressed below: ； ； In the formula, , , These are the inertia weights and learning factors dynamically adjusted using fuzzy logic. and The value of t is a random number in the range [0,1], and the value of t is 1. Let be the current velocity of the i-th particle in the d-th dimension. Let be the current position of the i-th particle in the d-th dimension. Let be the optimal position of the i-th particle in the d-th dimension. This represents the globally optimal position in the d-th dimension.

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