A six-axis robot trajectory planning method based on particle swarm optimization algorithm

Abstract

The application provides a six-axis mechanical arm trajectory planning method based on a particle swarm optimization algorithm, and comprises the following steps: S1, a particle swarm optimization algorithm is used for trajectory planning of a six-degree-of-freedom serial robot arm, including that an end mechanical arm of the robot starts to move from a starting point, whether there is an obstacle is checked in the process of moving to a target, and if there is an obstacle, the particle swarm optimization algorithm is used; when the best trajectory of the particle in the search motion space is searched, a local best value and a global best value are determined to ensure that the target moves to the best trajectory in the best particle tracking; S2, a five-order polynomial is used for trajectory planning of a joint space, so that the end effector of the serial robot moves from the starting point to the target point without vibration, and all joints of the robot arm are completed at the same time. The application can determine the position of the robot at each point when moving from the starting point to the target according to user requirements for such a high complexity system as the six-degree-of-freedom mechanical arm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of industrial robots, and particularly relates to a six-axis mechanical arm trajectory planning method based on a particle swarm optimization algorithm. BACKGROUND

[0002] Nowadays, with the rapid development of industrial automation, robot systems have become an integral part of production systems and daily life. In the era of intelligent manufacturing, controlled operation of robots plays a key role in various tasks and stages, including improving production efficiency, achieving high-precision error-free assembly, and achieving and barrier-free transportation. This ensures the optimal use of time, while also increasing the potential of work. Robot manipulators are usually composed of a set of rigid arms connected by rotating or prismatic joints. These rigid arms can be programmed and self-controlled on three or more axes in order to move various objects from one point to another.

[0003] Today, mechanical arms are widely used in many fields, but this has also raised the problem of trajectory control, which requires proper trajectory planning. The goal of trajectory planning is to move the mechanical arm from the starting point to the predetermined end point in a smooth and controllable manner, while avoiding vibrations and ensuring that no collision with any obstacles occurs. This is particularly crucial in the workspace, as there are usually multiple possible paths between the starting point and the end point, and one of the tasks of trajectory planning is to determine the path with the shortest distance.

[0004] Currently, in the industry, there is no mature trajectory planning scheme for high-complexity systems such as six-degree-of-freedom mechanical arms, especially one that can determine the position of the robot at each point when moving from the starting point to the target according to user requirements. SUMMARY

[0005] The present application aims to at least solve one of the aforementioned technical defects.

[0006] To this end, the present application aims to propose a six-axis mechanical arm trajectory planning method based on a particle swarm optimization algorithm, which can determine the position of the robot at each point when moving from the starting point to the target according to user requirements for high-complexity systems such as six-degree-of-freedom mechanical arms.

[0007] To achieve the above-mentioned purpose, the embodiments of the present application provide a six-axis mechanical arm trajectory planning method based on a particle swarm optimization algorithm, comprising the following steps:

[0008] Step S1, a particle swarm optimization algorithm is used for trajectory planning of a six-degree-of-freedom serial robot arm, including: the end mechanical arm of the robot starts to move from a starting point, and checks whether there is an obstacle in the process of moving to a target, and if there is an obstacle, a particle swarm optimization algorithm is used; when searching for the best trajectory of the particles in the motion space, the local best value and the global best value are determined to ensure that the target moves to the best trajectory in the best particle tracking, and the particle swarm optimization algorithm includes:

[0009] Step S11, a starting group, speed and position are created;

[0010] Step S12, the fitness value of all particles in the group is calculated;

[0011] Step S13, in each generation, all particles are compared with the best particle of the previous generation, and if the fitness value is better, the replacement is performed;

[0012] Step S14, all local best values are compared, and the best one is selected as the global best value;

[0013] Step S15, the speed and position values are updated;

[0014] Step S16, steps S12 to S15 are repeatedly executed, and when the stop condition is met, the particle swarm algorithm is stopped, and the result is displayed;

[0015] Step S2, a five-order polynomial is used for trajectory planning in the joint space, so that the end effector of the serial robot moves from the starting point to the target point without vibration, and all joints of the robot arm are completed at the same time.

[0016] Further, in the step S14, for each particle, the local best value is found from the current generation, and the number of optimal groups is equal to the number of particles, and the global best value is selected from the local best values of the current generation.

[0017] Further, for the fitness function calculation of the problem composed of multi-dimensional parameters, the particle matrix composed of n particles is as follows

[0018]

[0019] In the above particle matrix, particle i, x i = [x i1 , x i2 ,..., x iD ],

[0020] The position of particle i is given, P bset = [p i1 , p i2 ,..., p iD ].

[0021] The global best value Gbest is unique for all particles in each iteration, and

[0022] G bset = [p1, p2,..., p D ]

[0023] The velocity of the particle is expressed as:

[0024] Further, in the step S1, the joint angles of the robot are determined using a library function, the joint angles including: the start and end angles of each joint;

[0025] A quintic polynomial is created according to the maximum and minimum constraints determined by the joint angles; a smooth and continuous trajectory is estimated for the end-effector from the start point to the end point; wherein the quintic polynomial is used to describe the motion trajectory of the end-effector between two points.

[0026] Further, the path traveled by the robot manipulator is estimated by determining a linear equation for each joint angle, the goal being to obtain a linear equation that gives the shortest distance and avoids obstacles that can exist.

[0027] Further, in the step S1, the objective function for each particle position is evaluated to determine the best function value and the best position, wherein the objective function is used to minimize the trajectory time and the total distance according to the speed, acceleration and vibration limit parameters.

[0028] Further, a new velocity is selected according to the current velocity, the individual best position of the particle and the best position of its neighbors.

[0029] Further, the particle position, velocity and neighbors are iteratively updated, wherein the new position of the iterative update is the old position plus the velocity, and the velocity is modified to keep the particle within the boundary.

[0030] Further, a target function is created by calculating the distance between all points drawn by the end-effector and the target point as follows:

[0031]

[0032] wherein Q is the target coordinate and P represents the position coordinate created when the robot moves to the target point.

[0033] The six-axis robot trajectory planning method based on the particle swarm optimization algorithm according to the embodiment of the present application introduces a quintic polynomial into the PSO algorithm, maximally reduces the vibration that may occur in the movement of the robot, and provides the best continuity. The trajectory planning is performed in the joint space by using the quintic polynomial and the PSO algorithm, and the simulation effect is outstanding by considering the technical information of the 6-axis robot. According to the simulation result, it is concluded that the end robot avoids obstacles from the best path to reach the end point under the constraint condition. The present application can be applied to a high complexity system such as a six-degree-of-freedom robot, and the position of the robot at each point when moving from the starting point to the target can be determined according to the user demand.

[0034] Additional aspects and advantages of the present application will be set forth in part in the description that follows, and in part will become apparent to those having ordinary skill in the art upon examination of the following or can be learned from practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0035] The above and / or additional aspects and advantages of the present application will become apparent and be readily appreciated from the description of the embodiments, taken in conjunction with the following drawings in which:

[0036] Figure 1 A flow chart of the six-axis robot trajectory planning method based on the particle swarm optimization algorithm according to the embodiment of the present application;

[0037] Figure 2 A schematic diagram of the six-axis robot trajectory planning method based on the particle swarm optimization algorithm according to the embodiment of the present application;

[0038] Figure 3 A schematic diagram of the simulation model of the robot according to the embodiment of the present application;

[0039] Figure 4 A schematic diagram of the robot trajectory created according to the embodiment of the present application;

[0040] Figure 5 A schematic diagram of the angle-time graph of the nonlinear motion obtained from the quintic polynomial equation according to the embodiment of the present application. DETAILED DESCRIPTION

[0041] Embodiments of the present application are described in detail below with reference to the attached drawings, which show by way of example, embodiments in which the same or similar elements have the same or similar reference numbers. The embodiments described below are examples intended to explain the present application, and are not to be understood as limiting the present application.

[0042] First, some technical terms related to the present application are described below.

[0043] Trajectory planning for robotic arms can be approached in two ways: joint space and Cartesian space. When trajectory planning in Cartesian space, the robotic arm achieves linear motion between its start and target positions. On the defined linear path, the position and velocity of the robotic arm at the intermediate points in the near distance need to be determined. In trajectory planning in joint space, the motion of the end-effector occurs at certain time intervals between the start and target points, and is usually described using a cubic or higher order polynomial. By using a polynomial function, it is possible to ensure that the joint position, velocity, and acceleration parameters are continuous, resulting in a smooth joint trajectory. This approach helps to ensure that the robotic arm remains stable and precise during motion.

[0044] Particle swarm optimization (PSO) is a stochastic optimization technique inspired by the behavior of bird and fish swarms. PSO is used to solve multi-dimensional and parameterized nonlinear optimization problems, simulating the random behavior of group animals such as birds and fish when searching for food and ensuring safety. These animals communicate with each other to reach the target in the shortest path and adjust their own speed. The PSO algorithm starts from a set of random solutions and searches for the optimal solution through iterative updates. In PSO, possible solutions are called particles, which move in the problem space based on the current best particle. Unlike traditional optimization techniques, PSO does not require derivative information. PSO models social interactions between particles within a group. In the PSO algorithm, each solution particle is referred to as a particle in the swarm and uses its own experience to adjust its position to approach the best position in the group. In summary, the PSO algorithm finds the optimal solution based on the update of particles relative to the best position in the group.

[0045] Determining the intermediate points between the start and end points, as well as the velocity of the robotic arm, depends on the acceleration and distance parameters, which become more complex when considering the degrees of freedom of the robotic arm. As research in the field of robotics continues to advance, a variety of heuristic optimization methods have been developed to effectively solve this difficult problem. In research, the PSO algorithm is widely used because it allows for the latest multi-information exchange, thereby reducing computational burden. With the help of the PSO algorithm, robots can more efficiently plan trajectories, avoid obstacles, and reach target locations in the fastest, shortest, and most convenient way.

[0046] The present application provides a six-axis robot trajectory planning method based on particle swarm optimization algorithm, using PSO algorithm to provide five-order polynomial interpolation and continuity of trajectory control. The robot is simulated by MATLAB programming language. Various obstacles such as circles and rectangles are placed in the simulation, and the trajectory formed by the robot in the presence of these obstacles is checked according to the number of iterations and RNG parameters. The present application can determine the position of the robot at each point when moving from the starting point to the target according to the user's needs for such a high complexity system as a six-degree-of-freedom robot. Therefore, time optimization is achieved by selecting the shortest path between two points.

[0047] As Figure 1 shown, the six-axis robot trajectory planning method based on particle swarm optimization algorithm of the present application embodiment comprises the following steps:

[0048] Step S1, using particle swarm optimization algorithm to plan the trajectory of six-degree-of-freedom serial robot arm, including: the end of the robot arm moves from the starting point, checks whether there are obstacles in the process of moving to the target, if there are obstacles, uses particle swarm optimization algorithm; when searching for the best trajectory of particles in the motion space, determine the local best value and the global best value to ensure that the target moves to the best trajectory in the best particle tracking. As Figure 2 shown, the particle swarm optimization algorithm comprises:

[0049] Step S11, creating the starting swarm, speed and position.

[0050] Specifically, the starting swarm is created with randomly generated starting position and speed.

[0051] Step S12, calculating the fitness value of all particles in the swarm.

[0052] Step S13, comparing all particles with the best particle of the previous generation in each generation, and replacing if the fitness value is better.

[0053] Step S14, comparing all local best values pbest, and selecting the best as the global best value gbest.

[0054] For each particle, find the local best value from the current generation, and the number of best values in the swarm is equal to the number of particles, and the global best value is selected from the local best values of the current generation.

[0055] Step S15, updating the speed and position values.

[0056] Step S16, repeating steps S12 to S15, stopping the particle swarm algorithm when the stop condition is met, and displaying the results.

[0057] The fitness function calculation for a problem consisting of D parameters is given by a matrix of n particles as follows:

[0058]

[0059] In the above matrix, particle i, x i = [x i1 , x i2 , Ix iD ] gives the position of particle i that gives the best fitness value previously, P bset = [p i1 , p i2 ,..., p iD ].

[0060] The global best value gbest is unique for all particles in each iteration and G bset = [p1, p2,..., p D ]. The velocity of a particle (which is the amount of change in its position in each dimension) is represented as:

[0061] Step S2, the trajectory planning of the joint space is carried out by using a five-order polynomial, so that the end effector of the serial robot moves from the starting point to the target point without vibration, and all the joints of the robot arm are completed at the same time.

[0062] The detailed process of the six-axis robot trajectory planning method based on the particle swarm optimization algorithm of the embodiment of the application is described below.

[0063] The particle swarm optimization (PSO) algorithm is the main method for trajectory planning of a six-degree-of-freedom serial robot arm. By using the PSO algorithm, the starting point reaches the target point in the best time, so that the position, velocity and acceleration parameters of each joint are more sensitive.

[0064] The trajectory planning of the joint space is carried out by using a five-order polynomial, so that the end effector of the serial robot moves from the starting point to the target point without vibration, and all the joints of the robot arm are completed at the same time. Using forward kinematics and joint angles, the initial and final positions of the end manipulator are studied in Cartesian space without and with obstacles.

[0065] In the flowchart created by the PSO algorithm, the end manipulator starts moving from the starting point, and checks whether there are obstacles in the process of moving towards the target. When there are obstacles, the PSO algorithm is adopted. When searching for the best trajectory of the particle in the motion space, the Pbest and Gbest values are determined to ensure that the target moves to the best trajectory in the best particle tracking.

[0066] The flowchart of the particle swarm algorithm is as follows:

[0067] (1) Evaluate the objective function for each particle position, determine the best (lowest) function value and the best position.

[0068] (2) Choose a new velocity based on the current velocity, the individual best position of the particle and the best position of its neighbors.

[0069] (3) Then iteratively update the particle position (new position is old position plus velocity), velocity and neighbors, modifying the velocity to keep the particle within the bounds.

[0070] (4) Iteration continues until the algorithm reaches a stopping criterion.

[0071] In the embodiment of the present invention, a simulation model of the robot was created using the Robotic Toolbox library on MATLAB program, as shown in Figure 3 .

[0072] By using the library functions, the start and end angles of each joint of the robot were determined. Forward kinematics can obtain the position and rotation information of the robot end function at the start and end points in the Cartesian space using joint angles.

[0073] Trajectory planning of the robot includes point-to-point (PTP) and continuous path-CP two methods: PTP method only specifies the start and end points, CP method also specifies the intermediate points between two points. This study adopts PTP method, using five polynomial algorithm in MATLAB to perform joint space interpolation every 2s. The created trajectory is shown in Figure 4 .

[0074] The quintic polynomial determined by the maximum and minimum constraints created according to the joint angle; the trajectory of the end manipulator from the start point to the end point is estimated to be smooth and continuous. Quintic polynomial is used to describe the motion trajectory of the end manipulator between two points. Figure 5 The angle-time graph of

[0075] The path traveled by the robot manipulator is estimated by determining the linear equation for each joint angle. The goal is to obtain a linear equation that gives the shortest distance and avoids possible obstacles. The PSO algorithm searches for the best linear or nonlinear equation of the trajectory. The obtained equation can be from a linear equation to a multidimensional polynomial. This result indicates that the joint angle can be moved from the start point to the target point using a simple linear equation or a nonlinear polynomial equation.

[0076] The purpose of using the quintic polynomial is to minimize the vibration that can occur during the movement of the robot arm and to ensure the best continuity. All joints belong to the robot. The objective function is used to minimize the trajectory time and total distance according to the speed, acceleration and vibration limit parameters. The objective function created by calculating the distance between all points drawn by the tip of the robot arm to the target point is shown in the formula:

[0077]

[0078] Where: Q is the target coordinate. P represents the position coordinates created when the robot moves to the target point.

[0079] The six-axis robot trajectory planning method based on particle swarm optimization algorithm according to the embodiment of the application introduces the quintic polynomial into the PSO algorithm, maximally reduces the vibration that can occur during the movement of the robot arm and provides the best continuity. The trajectory planning is carried out in the joint space by using the quintic polynomial and the PSO algorithm, and the technical information of the 6-axis robot arm is considered, and the simulation effect is outstanding. According to the simulation result, it is concluded that the end robot arm avoids obstacles from the best path under the constraint condition to reach the terminal point. The application can be applied to a high complexity system such as a six-degree-of-freedom robot arm, and the position of the robot at each point when moving from the starting point to the target can be determined according to the user's demand.

[0080] In the description of the present specification, the description referring to the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily mean the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0081] Although the embodiments of the present application have been shown and described above, it is understood that the above-described embodiments are exemplary and are not to be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-described embodiments without departing from the principles and spirit of the present application within the scope of the present application. The scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A trajectory planning method for a six-axis robot based on a particle swarm optimization algorithm, characterized in that, Comprise the following steps: Step S1, using particle swarm optimization algorithm for trajectory planning of six degrees of freedom serial robot arm, including: the end of the robot arm moves from the starting point, in the process of moving to the target, check if there is an obstacle, if there is an obstacle, the particle swarm optimization algorithm is used; when searching for the best trajectory of the particle in the motion space, the local best value and the global best value are determined to ensure that the target moves to the best trajectory in the best particle tracking, the particle swarm optimization algorithm, comprising: Step S11, creating a starting population, speed and position; Step S12, calculating the fitness value of all particles in the population; Step S13, in each generation, all particles are compared with the best particle of the previous generation, and if the fitness value is better, the replacement is carried out; Step S14, compare all local best values, select the best as the global best value; Step S15, update the speed and position value; Step S16, repeat steps S12 to S15, stop the particle swarm algorithm when the stop condition is met, and display the result; For the fitness function calculation of the problem composed of D-dimensional parameters, the particle matrix composed of n particles is as follows: In the above particle matrix, particle i, x i = [x i1 , x i2 , Ix iD ], Position of the particle i that gives the previous best fitness value, P best = [p i1 , p i2 , …, p iD ] ; The global best value Gbest is unique for all particles in each iteration, and G bset = [p1, p2,..., p D ]. The velocity of the particles is denoted by: v i = [v1, v2,..., v iD ] Step S2, using a fifth-order polynomial for trajectory planning in joint space, so that the end effector of the serial robot moves from the starting point to the target point without vibration, and all joints of the robot arm are completed at the same time; The objective function of each particle position is evaluated to determine the best function value and the best position, wherein the objective function is used to minimize the track time and the total distance according to the speed, acceleration and vibration limit parameters; Select a new speed according to the current speed, the individual best position of the particle and the best position of its adjacent particle; Iteratively update the particle position, speed and neighbor, wherein the new position of the iterative update is the old position plus the speed, and the speed is modified to keep the particle within the boundary; Using the library function, the joint angle of the robot is determined, including: the starting and ending angles of each joint; Determine the fifth-order polynomial according to the maximum and minimum constraints created by the joint angle; estimate the smooth and continuous trajectory of the end manipulator from the starting point to the end point; wherein the fifth-order polynomial is used to describe the motion trajectory of the end manipulator between two points; Estimate the path traveled by the robot manipulator by determining the linear equation of each joint angle, the goal being to obtain a linear equation that gives the shortest distance and avoids possible obstacles; By calculating the distance between all points drawn by the tip manipulator and the target point, a target function is created as follows: Wherein Q is the target coordinate, P represents the position coordinate created when the robot moves to the target point.

2. The six-axis robot trajectory planning method based on particle swarm optimization algorithm according to claim 1, wherein, In the step S14, for each particle, the local best value is found from the current generation, and the number of best particles in the population is equal to the number of particles, and the global best value is selected from the local best values of the current generation.

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