A robot trajectory planning method based on improved blowfish algorithm

Abstract

The present invention discloses a robot trajectory planning method based on an improved blowfish algorithm, selects 4-3-4 mixed polynomials for robot trajectory planning, and proposes an improved blowfish optimization algorithm. First, a chaotic initialization strategy is introduced to increase the diversity of the blowfish population; secondly, an adaptive coefficient is added so that as the iteration proceeds, the current particle approaches the optimized particle more and more closely; finally, any particle is replaced by the average position of particles that are better than the current position, and particle information is fully utilized to improve the global search capability. The algorithm is used to perform the robot's time optimal trajectory planning, and the results are applied to the actual robot platform, which has better optimization capability and convergence speed in trajectory planning problems.

Description

Technical Field

[0001] The invention relates to the technical field of robot control, in particular to a robot trajectory planning method based on an improved blowfish algorithm. Background Art

[0002] With the development of society, robots are increasingly used in production and life. Six-degree-of-freedom robotic arms are widely used in industrial production for loading and unloading, palletizing, grinding, painting and other scenes due to their excellent flexibility. Path planning is the basis of robot kinematics research. The terminal trajectory planning of industrial robots directly determines whether the robots can successfully complete the scheduled tasks.

[0003] The trajectory planning of robots is a highly complex nonlinear control problem with constraints. In practical applications, trajectory planning can be divided into workspace trajectory planning and joint space trajectory planning according to different description methods. The trajectory planning of the workspace can be converted into the trajectory planning of the joint space through inverse kinematic transformation. Common joint space trajectory planning methods include cubic polynomial interpolation, 3-5-3 mixed polynomial interpolation, 4-3-4 mixed polynomial interpolation, B-spline curve, etc. Among them, the B-spline curve has excellent smoothing performance, but the curve cannot traverse all control points; the piecewise polynomial takes into account the smoothness of the curve and the simplification of calculation, and has become a widely used trajectory planning method.

[0004] Trajectory planning optimization is one of the current research hotspots. According to different optimization objectives, trajectory planning can be divided into time optimization, energy optimization, operation stability optimization and multi-objective optimization. At present, many intelligent optimization algorithms are used to solve trajectory optimization problems. The pufferfish optimization algorithm (POA) is a bionic meta-inspired intelligent optimization algorithm that simulates the defense mechanism of pufferfish against predators in nature. It has the advantage of no need to control parameters and shows good exploration and development capabilities in the search space. However, it still has shortcomings in global search capabilities, and there is no report on its application to robot path planning. Summary of the invention

[0005] The object of the present invention is to provide a robot trajectory planning method based on an improved blowfish algorithm to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: a robot trajectory planning method based on an improved blowfish algorithm, the method comprising:

[0007] S1: According to the coordinates of the robot's starting point, middle point and end point, the positions of each joint at the starting point and end point are obtained through inverse kinematics, and the motion trajectory of each joint is represented by a 4-3-4 piecewise polynomial interpolation function;

[0008] S2: Constrain the 4-3-4 piecewise polynomial interpolation function to obtain the coefficients of the 4-3-4 piecewise polynomial interpolation function, derive the position, velocity, acceleration and jerk of each joint, complete the trajectory planning, and obtain the motion path;

[0009] S3: Calculate the optimal motion time of each joint in the motion path based on the improved Blowfish algorithm, including:

[0010] S31: Set the relevant parameters of the Blowfish algorithm and set the movement time of each joint , , As a pufferfish individual, a chaotic initialization strategy is used to initialize the particle population, enhance the overall search ability of the population, and calculate the fitness value of each particle;

[0011] S32: In the global search phase, through the predator attack mechanism and the introduction of adaptive parameters, the average position of all particles is used to replace the set of all particles in the current population that are better than the i-th particle to guide the movement of the current particle, update the position of each pufferfish individual, and use particles with better fitness values ​​to replace the current particle;

[0012] S33: In the local search phase, the position of each pufferfish individual is fine-tuned through the pufferfish's defense mechanism, and particles with better fitness values ​​are used to replace the current particles;

[0013] S34: Repeat steps S32 to S33 until the termination condition is met and output the optimal running time , and ;

[0014] S4: The optimal motion time is brought into the 4-3-4 piecewise polynomial interpolation function of each joint to obtain the position, velocity, acceleration and jerk of each joint, which are used for robot motion control, complete trajectory optimization, and obtain the optimized motion path.

[0015] Further, in step S1, Indicates joints No. The angle of the point, Indicates the serial number of the joint, Represents the serial number of the path point. The expression of the 4-3-4 piecewise polynomial interpolation function is:

[0016]

[0017] In the formula, Indicates The joint Segment polynomial trajectory; Indicates The first, second and third trajectories of the joint The coefficients of the polynomial function, Indicates time, , , Represents the time taken by three-segment polynomials.

[0018] Furthermore, in step S2, the constraint condition of the 4-3-4 piecewise polynomial interpolation function is that when the robot passes through the starting point and the end point, the speed and acceleration are both zero, that is: , , at the connection of the 4-3-4 piecewise polynomial interpolation function (i.e. and ), the position, velocity and acceleration of the joint are continuous, and at the midpoint, , According to the above constraints, we get the equation system of 4-3-4 piecewise polynomial interpolation function coefficients:

[0019]

[0020]

[0021] In the formula,

[0022] Through equations and preset time parameters , and , solve for the coefficients of the 4-3-4 piecewise polynomial interpolation function:

[0023]

[0024] In the formula,

[0025]

[0026] Furthermore, in step S2, when the robot's motion time is constrained, the time parameter , and The optimized objective function is:

[0027]

[0028] And considering the constraints of the position, velocity, and acceleration of the robot joints when the robot moves, the constraints are:

[0029]

[0030] In the formula, Indicates The joint Segment track, , , and Indicates The limit values ​​of joint position, velocity, and acceleration.

[0031] Furthermore, the step S3 includes:

[0032] Furthermore, in step S31, For puffer particles, the chaotic sequence is constructed using Logistic mapping: ; Initialize the position of the population,

[0033] In the formula, Indicates i The first j Quantity, The position of the pufferfish is represented by ,in , represents the population size, represents the dimension of the particle, is the value generated by the chaotic sequence, ub j and lb j Represents the particle j The upper and lower bounds of the dimension components.

[0034] Furthermore, in step S31, the fitness function Calculate the fitness value of each particle.

[0035] Furthermore, in step S32, an adaptive parameter is introduced ω, set up is the best in the current population. i The set of all particles of particles, using the average position of all particles replace Guide the movement of the current particle and update the i The position of each particle is updated as follows:

[0036]

[0037] In the formula, Indicates i The particle j Quantity, =0.9-0.8×t / T, represents a random number between [0,1], represents a randomly selected number from the set {1,2}, represents the updated particle position, is its j-th dimension component, is its fitness value.

[0038] Furthermore, in step S33, the updating formula of the pufferfish defense mechanism is:

[0039]

[0040] In the formula, represents the updated particle position, represents its fitness value, Indicates its j Dimensional component, represents a random number between [0,1], , Respectively represent the particle j The upper and lower limits of the dimension components, t Indicates the current loop number.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows: when the robot performs sequential movements such as picking, assembling, and placing, the present invention needs to meet the constraints of speed and acceleration, ensure smooth movement of the starting and ending segments and fast movement of the middle segment, and select 4-3-4 mixed polynomials for trajectory planning. In view of the defects of the pufferfish algorithm, an improved pufferfish optimization algorithm is proposed. First, a chaotic initialization strategy is introduced to increase the diversity of the pufferfish population; secondly, an adaptive coefficient is added so that as the iteration proceeds, the current particle approaches the optimized particle more and more closely; finally, by using the average position of particles that are better than the current position to replace any particle, the particle information is fully utilized to improve the global search capability. The algorithm is used to perform the time optimal trajectory planning of the robot, and the results are applied to the actual robot platform, which has better optimization capability and convergence speed in trajectory planning problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A step diagram of a robot trajectory planning method based on an improved blowfish algorithm of the present invention;

[0043] Figure 2 The optimal motion time step diagram of each joint in the motion path is calculated based on the improved blowfish algorithm of the present invention;

[0044] Figure 3 This is a flow chart of a robot trajectory planning method based on an improved blowfish algorithm of the present invention;

[0045] Figure 4This is a comparison chart of the convergence curves of the IPOA algorithm and the other five optimization algorithms on nine functions;

[0046] Figure 5 This is the coordinate system diagram of the QX6 robot and joints;

[0047] Figure 6 Iterative curve diagram of IPOA algorithm and other five optimization algorithms in robot trajectory planning optimization;

[0048] Figure 7 It is the position, velocity and acceleration curve of each joint of the robot;

[0049] Figure 8 This is the motion process diagram of the robot after optimization. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] This embodiment provides a robot trajectory planning method based on an improved blowfish algorithm, such as Figure 1 As shown, the method comprises the following steps:

[0052] S1: According to the coordinates of the robot's starting point, middle point and end point, the positions of each joint at the starting point and end point are obtained through inverse kinematics, and the motion trajectory of each joint is represented by a 4-3-4 piecewise polynomial interpolation function;

[0053] S2: Constrain the 4-3-4 piecewise polynomial interpolation function to obtain the coefficients of the 4-3-4 piecewise polynomial interpolation function, derive the position, velocity, acceleration and jerk of each joint, complete the trajectory planning, and obtain the motion path;

[0054] S3: Calculate the optimal movement time of each joint in the motion path based on the improved Blowfish algorithm;

[0055] S4: The optimal motion time is brought into the 4-3-4 piecewise polynomial interpolation function of each joint to obtain the position, velocity, acceleration and jerk of each joint, which are used for robot motion control, complete trajectory optimization, and obtain the optimized motion path.

[0056] The starting point of the robot in the Cartesian coordinate system is known , midpoint , and end point , the positions of each joint at the starting point and the end point are obtained through inverse kinematics, and the robot's working trajectory is divided into three segments. Indicates joints No. The angle of the point, Indicates the serial number of the joint, Represents the serial number of the path point. The motion trajectory of the joint is represented by a 4-3-4 piecewise polynomial interpolation function, and its expression is:

[0057] (1)

[0058] In the formula, Indicates The joint Segment polynomial trajectory; Indicates The first, second and third trajectories of the joint The coefficients of the polynomial function, Indicates time, , , Represents the time taken by three-segment polynomials.

[0059] During the robot operation, the robot passes the starting point and end point When , the velocity and acceleration are both zero, and the positions of the starting point and the end point are the positions of the 4-3-4 piecewise polynomial at the corresponding time, that is: , , at the connection of the 4-3-4 piecewise polynomial interpolation function (i.e. and ), the position, velocity and acceleration of the joint are continuous, and at the midpoint, , According to the above constraints, we get the equation set of 4-3-4 piecewise polynomial interpolation function coefficients:

[0060] (2)

[0061] (3)

[0062] In the formula,

[0063]

[0064] (4)

[0065] In the formula,

[0066]

[0067] Known time parameters , and , the coefficients of the 4-3-4 piecewise polynomial interpolation function can be solved by formula (4). The position, velocity, acceleration and jerk of each joint can be derived by the solved coefficients and formula (1). Among them, the position curve of the joint is given by the 4-3-4 piecewise polynomial interpolation function, the velocity is the derivative of the position with respect to time, the acceleration is the derivative of the velocity with respect to time, and the jerk is the derivative of the acceleration with respect to time. In this way, the position, velocity, acceleration and jerk curves of each joint and each time period can be calculated, the trajectory planning is completed, and the motion path is obtained for the motion control of the robot to ensure that the robot can move smoothly along the planned path.

[0068] The optimization goal of this embodiment is to shorten the running time of the robot as much as possible while satisfying the constraints. Therefore, the time parameter , and The optimized objective function is:

[0069] (5)

[0070] When the robot moves, the constraints that should be met are:

[0071] (6)

[0072] In the formula, Indicates The joint Segment track, , , and Indicates The limit values ​​of joint position, velocity, and acceleration.

[0073] Through these constraints, it can be ensured that the robot can move within a safe range when planning the trajectory, while meeting the continuity and smoothness requirements of kinematics. This embodiment uses an improved blowfish optimization algorithm to optimize the time parameters and effectively control the movement of the robot, making it efficient and stable when performing tasks.

[0074] The following introduces the original blowfish optimization algorithm:

[0075] The Pufferfish Optimization Algorithm (POA) simulates the attack of predators on pufferfish and the defense mechanism of pufferfish against predators, aiming to establish a meta-heuristic algorithm through this biological behavior. Each pufferfish in the population represents a candidate solution, and the predator attack and the pufferfish's defense work together to ultimately achieve the search for the global optimal solution. POA has the advantages of no control parameters, excellent global search capabilities, and fast convergence. The specific optimization steps are as follows:

[0076] (1) Population initialization: Randomly initialize the position of the population, as shown in formula (7):

[0077] (7)

[0078] In the formula, Indicates i The first j Quantity, The position of the pufferfish is represented by ,in . represents the population size, represents the dimension of the particle, r represents a random variable uniformly distributed on [0,1], ub j and lb j Represents the particle j The upper and lower bounds of the dimension components;

[0079] Fitness function

[0080] (2) Predator attacks pufferfish: The predator discovers the pufferfish and moves towards it, causing the pufferfish population particles to change, thereby improving the algorithm's global search capability. In the population, particles with better fitness function values ​​are used to replace the current particles. is the set of all particles in the current population that are better than the i-th particle, from which a particle is randomly selected , used to update the position of the i-th particle, the update formula is as follows:

[0081] (8)

[0082] (9)

[0083] (10)

[0084] In the formula, Indicates i The particle j Quantity, represents a random number between [0,1], represents a randomly selected number from the set {1,2}, represents the updated particle position, is its j-th dimension component, is its fitness value;

[0085] Calculate the fitness function of the new particle. If the new particle is better than the original particle, replace the original particle with the new particle.

[0086] (3) Pufferfish’s defense mechanism against predators: When a pufferfish finds a predator, it launches an attack defense, which causes a slight change in the particle population. This step enhances the algorithm’s local search capability. The update mechanism formula is as follows:

[0087] (11)

[0088] (12)

[0089] In the formula, represents the updated particle position, represents its fitness value, Indicates its j Dimensional component, represents a random number between [0,1], , Respectively represent the particle j The upper and lower limits of the dimension components, t Indicates the current number of loops;

[0090] Calculate the fitness function of the new particle. If the new particle is better than the original particle, replace the original particle with the new particle.

[0091] Through analysis, it is found that POA performs well in global optimization and convergence speed, but still has some shortcomings in finding the global optimal value. To this end, this embodiment improves the Blowfish optimization algorithm and provides an improved Blowfish optimization algorithm, denoted as IPOA, and calculates the optimal motion time of each joint in the motion path based on the improved Blowfish algorithm, such as Figure 2 As shown, the following steps are included:

[0092] S31: Set the relevant parameters of the Blowfish algorithm and set the movement time of each joint , , As a pufferfish individual, a chaotic initialization strategy is used to initialize the particle population, enhance the overall search ability of the population, and calculate the fitness value of each particle;

[0093] S32: In the global search phase, through the predator attack mechanism and the introduction of adaptive parameters, the average position of all particles is used to replace the set of all particles in the current population that are better than the i-th particle to guide the movement of the current particle, update the position of each pufferfish individual, and use particles with better fitness values ​​to replace the current particle;

[0094] S33: In the local search phase, the position of each pufferfish individual is fine-tuned through the pufferfish's defense mechanism, and particles with better fitness values ​​are used to replace the current particles;

[0095] S34: Repeat steps S32 to S33 until the termination condition is met and output the optimal running time , and .

[0096] Specifically, Figure 3 As shown, input variable dimension D and variable value range , constraints and object functions, set the population size N, the maximum number of iterations T，

[0097] by The random initialization may lead to uneven initialization distribution of the population particles, thus affecting the algorithm effect. Chaotic mapping has the characteristics of ergodicity, non-repetitiveness and dynamics, which can enhance the overall search ability of the population. This embodiment uses Logistic mapping to construct a chaotic sequence:

[0098] (13)

[0099] Using the values ​​in the chaotic sequence to replace the random variable r in formula (7), we get:

[0100]

[0101] Initialize the particle population according to the above formula and calculate the fitness value of each particle;

[0102] In the global search phase, the predator attack mechanism is used and adaptive parameters are introduced ω , as the number of iterations increases, the parameter ω Gradually decrease to ensure that the particle is closer to the optimized particle, thereby enhancing the algorithm's early global search ability and later convergence ability. The average position of all particles is used replace , guide the movement of the current particle, make full use of the information of all particles to improve performance, update the position of the i-th particle, and the update formula is as follows:

[0103] (8)

[0104] (14)

[0105] (10)

[0106] In the formula, =0.9-0.8×t / T.

[0107] The new particle position update formula makes full use of the information of all optimized particles, effectively simulating the process of particles avoiding natural enemies and group movement in the pufferfish population, thereby improving the global search ability of the algorithm and avoiding falling into local optimality; using particles with better fitness values ​​to replace the current particles;

[0108] In the local search phase, the position of each pufferfish is fine-tuned through the pufferfish's defense mechanism. The update formula of the pufferfish defense mechanism is:

[0109] (11)

[0110] (12)

[0111] After that, the current particle is replaced by a particle with a better fitness value;

[0112] Repeat the above steps until the termination condition is met and output the optimal running time , and .

[0113] Will output the optimal running time , and The 4-3-4 piecewise polynomial interpolation function of each joint is introduced to obtain the position, velocity, acceleration and jerk of each joint, which are used for robot motion control, complete trajectory optimization, and obtain the optimized motion path.

[0114] Test Example 1: Standard Test Function Test

[0115] The performance of IPOA algorithm is compared through simulation experiments: the experiment is carried out on a computer with a main frequency of 2.40GHz, 16GB memory, Corei5-1135G7CPU, 64-bit Windows10 operating system, and MATLAB R2022b software platform. In order to make an effective comparison, five classic optimization algorithms are selected, including the blowfish algorithm (POA), zebra algorithm (ZOA), particle swarm algorithm (PSO), whale algorithm (WOA) and grey wolf algorithm (GWO), and the parameter settings of all algorithms are consistent with those in the literature.

[0116] Nine standard test functions were selected in the experiment, of which F1~F5 are unimodal functions and F6~F9 are multimodal functions. Each algorithm was run 30 times independently on each test function, and each run was performed for 1000 iterations. The detailed information of the test functions is shown in Table 1.

[0117] Table 1 Overview of standard test functions

[0118]

[0119] In each experiment, the mean value, standard deviation and other performance indicators of each algorithm are recorded to evaluate the performance of different algorithms on different functions. The results are shown in Table 2.

[0120] Table 2 Comparison of optimization results of test functions of algorithms

[0121]

[0122] It can be seen that on the unimodal functions F1~F5, the average value and standard deviation of IPOA are significantly better than those of other algorithms, which shows that IPOA has higher accuracy and better stability when searching for the optimal solution. On the multimodal functions F7~F9, the average values ​​and standard deviations of IPOA, POA, and ZOA are similar, all of which are better than other algorithms. Specifically, on the multimodal function F6, although the average value of IPOA is slightly inferior to that of the whale algorithm (WOA), its standard deviation shows a clear advantage, indicating that IPOA has a greater advantage in the stability of the results. Combining these results, it can be judged that the performance of IPOA is better than that of POA and other comparison algorithms, showing its advantages in optimization accuracy and convergence ability.

[0123] Figure 4 The convergence curves of the six algorithms are shown, with the horizontal axis representing the number of iterations and the vertical axis representing the function fitness value. Figure 4 It can be clearly seen that IPOA has better convergence performance than other algorithms. In the convergence curves of functions F1~F4 and F5~F9, POA shows excellent exploration ability and convergence speed. In the multi-peak function F6, although IPOA's performance failed to surpass WOA, its performance was still better than other comparison algorithms. These convergence curves further verify that IPOA can not only quickly find the optimal solution during the optimization process, but also maintain a high stability during the iteration process. This provides strong support for its effectiveness in practical applications.

[0124] Test Example 2: Trajectory Planning Test

[0125] The feasibility of IPOA algorithm was verified by using QIXING QX6 robot. Figure 5 In the left figure, there are six joints, such as Figure 5The right figure shows the position coordinates of each joint. Each DH matrix is ​​shown in Table 3. The Matlab RTB toolbox is used to model and perform forward and inverse kinematics calculations to provide support for trajectory planning. The maximum speed of the robot's joints is 3.15 rad / s and the maximum acceleration is 15 rad / s 2 ,These parameters will be used for subsequent trajectory planning and motion control.

[0126] Table 3 Robot DH parameter table

[0127]

[0128] In the table, d is the i-1 Axis to X i The distance along the Z axis i-1 The direction is positive; a is from Z i-1 Axis to Z i The distance along X i The direction of the axis is positive; Alpha is from Z i-1 Axis to Z i The corner of X i The positive rotation of the shaft is positive; is the rotation range of the joint angle; off is when the robot is in the position shown in the figure The angle value of the

[0129] Four target points are set in the robot workspace. The Cartesian coordinates and corresponding joint angles of each target point are shown in Table 4.

[0130] Table 4 Cartesian space path points and joint angles

[0131]

[0132] When optimizing the trajectory planning problem, speed and acceleration constraints are set. The objective function used is designed to minimize the total time the robot takes to move while satisfying all kinematic constraints. To this end, a variety of different algorithms are used for comparison, with a particle population of 30 for each algorithm and a maximum number of iterations set to 100. The value range of each particle is [ ,2], where Δqi is the angle change of the joint, is the maximum speed. This setting ensures that the particles can search within a reasonable range during the entire optimization process, so as to find the optimal solution more effectively. After calculation, the optimal time of joints 1 to 6 is shown in Table 5. As can be seen from Table 5, the time planning results of IPOA are better than those of other algorithms. The running times of the six joints are 1.4833s, 2.4329s, 1.9819s, 1.8037s, 1.6617s, and 2.0312s respectively. These results show that through the IPOA algorithm, the robot can complete the predetermined trajectory in less time, significantly improving the motion efficiency.

[0133] Table 5 Optimal time planning results for each joint of the robot

[0134]

[0135] Table 6 Optimization time of joints

[0136]

[0137] In the iterative process of the optimization algorithm, Figure 6 As shown in Figure 2, the convergence of each algorithm is plotted as an iteration curve. Figure 6 It can be seen that IPOA reaches convergence in about 50 generations, and its convergence speed and accuracy are significantly better than other algorithms. In terms of convergence speed, the IPOA algorithm drops rapidly in the early iteration and remains stable in subsequent iterations, showing a faster convergence characteristic. In terms of convergence accuracy, compared with other algorithms, IPOA has higher convergence accuracy and can more easily jump out of the local optimal solution, improving the ability of global optimization.

[0138] The IPOA optimization algorithm calculated the optimal time periods t1, t2, and t3 of each joint, as shown in Table 6. The maximum values ​​of the three time periods of each joint are 0.8731s, 0.9744s, and 0.8455s. Compared with the initial values, these optimized times are reduced by 56.3%, 51.3%, and 57.7%, respectively. In the end, the total optimized time is 2.6930s, which is 55.12% less than the initial value. This result shows that the IPOA algorithm performs well in optimizing joint motion time, which not only significantly improves motion efficiency, but also provides support for the flexibility and response speed of the robot in practical applications.

[0139] Substituting t1, t2 and t3 into formula (1), we can obtain the position, velocity and acceleration curves of each joint, as shown in Figure 7 As shown. Figure 7 It can be seen that the maximum and minimum values ​​of velocity are -2.98rad / s and 3.07rad / s respectively, and the maximum and minimum values ​​of acceleration are and 11.74rad / s respectively. 2and -13.88 rad / s 2 , all meet the preset constraints, indicating that the optimized motion planning is within a reasonable range in terms of speed and acceleration. Observing the angle, angular velocity and angular acceleration curves of the joints, it can be seen that the angle and angular velocity curves of the joints show smooth and continuous characteristics, without obvious jumps or mutations. The angular acceleration curves also maintain smoothness, without mutations, and the maximum speed and acceleration of the joints are close to the limit values. It shows that the time optimal trajectory planning method proposed in this application not only effectively meets the motion constraints, but also fully releases the performance of the joint motor. This result means that under the premise of ensuring motion continuity, the robot can achieve higher dynamic performance, thereby improving overall work efficiency and responsiveness.

[0140] The optimized time, position, velocity and acceleration sequence is applied to robot motion control. The experimental results are as follows: Figure 8 The experimental results show that the robot completed all the scheduled actions on time, showing good time control ability; the entire movement process was smooth and vibration-free, indicating that the optimization results effectively reduced the jitter and impact that may occur during the movement; the robot can accurately track the planned trajectory, showing excellent dynamic performance.

[0141] Aiming at the point-to-point trajectory planning problem in the robot joint space, this paper proposes a time-optimal trajectory planning method based on 4-3-4 mixed polynomials and improved blowfish optimization algorithm (IPOA). Firstly, the three-segment trajectory between four path points in the robot joint space is successfully constructed by using the 4-3-4 polynomial interpolation method, and the objective function of the optimization problem is clarified. Secondly, by deeply analyzing the basic principles of the blowfish optimization algorithm, the chaotic initialization, adaptive factors and the mean of the optimized particles are introduced, which significantly improves the contraction ability and convergence speed of the algorithm. Comparative experiments show that the performance of IPOA on the standard test function is better than that of existing optimization algorithms such as POA, PSO, ZOA, GWO and WOA. On the basis of considering the robot joint velocity and acceleration constraints, the time-optimal trajectory planning is implemented. The experimental results show that the initial time is set to 2 seconds, and the total time after optimization is 2.6930 seconds, which is reduced by 56.3%, 51.3%, 57.7% and 55.12% respectively compared with the comparative algorithms. The optimized trajectory shows good speed and acceleration smoothness, and there is no acceleration mutation, which ensures the stable movement of the robot. In the actual robot trajectory planning, after applying the optimization results, the robot successfully completes the predetermined action, and the whole process is smooth and vibration-free, which verifies the effectiveness of the proposed method.

[0142] In summary, IPOA shows excellent accuracy and performance in time-optimal trajectory planning problems. Future research can further explore multi-objective optimization problems, including energy consumption, impact, and torque, to comprehensively improve the performance of the robot and meet diverse application needs.

[0143] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A robot trajectory planning method based on an improved blowfish algorithm, characterized in that: The method comprises: S1: According to the coordinates of the robot's starting point, middle point and end point, the positions of each joint at the starting point and end point are obtained through inverse kinematics, and the motion trajectory of each joint is represented by a 4-3-4 piecewise polynomial interpolation function; S2: Constrain the 4-3-4 piecewise polynomial interpolation function to obtain the coefficients of the 4-3-4 piecewise polynomial interpolation function, derive the position, velocity, acceleration and jerk of each joint, complete the trajectory planning, and obtain the motion path; S3: Calculate the optimal motion time of each joint in the motion path based on the improved Blowfish algorithm, including: S31: Set the relevant parameters of the Blowfish algorithm and set the movement time of each joint , , As a pufferfish individual, a chaotic initialization strategy is used to initialize the particle population, enhance the overall search ability of the population, and calculate the fitness value of each particle; S32: In the global search phase, the predator attack mechanism is used and adaptive parameters are introduced ω, set up is the best in the current population. i The set of all particles of particles, using the average position of all particles replace Guide the movement of the current particle and update the i The position of each particle is updated as follows: ； In the formula, For pufferfish particles, is the kth puffer particle, is the fitness value of the kth puffer particle, is the fitness value of the ith puffer particle, Indicates i The particle j Quantity, =0.9-0.8×t / T, represents a random number between [0,1], express The j-th dimension component, represents a randomly selected number from the set {1,2}, represents the updated particle position, is its j-th dimension component, is its fitness value; S33: In the local search phase, the position of each pufferfish individual is fine-tuned through the pufferfish's defense mechanism, and particles with better fitness values ​​are used to replace the current particles; S34: Repeat steps S32 to S33 until the termination condition is met, and output the optimal movement time of each joint , , ; S4: The optimal motion time is brought into the 4-3-4 piecewise polynomial interpolation function of each joint to obtain the position, velocity, acceleration and jerk of each joint, which are used for robot motion control, complete trajectory optimization, and obtain the optimized motion path.

2. The robot trajectory planning method based on the improved blowfish algorithm according to claim 1 is characterized in that: In step S1, Indicates joints No. The angle of the point, Indicates the serial number of the joint, Represents the serial number of the path point. The expression of the 4-3-4 piecewise polynomial interpolation function is: ； In the formula, Indicates The joint Segment polynomial trajectory; Indicates The first, second and third trajectories of the joint The coefficients of the polynomial function, Indicates time, , , Represents the motion time of each joint represented by three-segment polynomial.

3. The robot trajectory planning method based on the improved blowfish algorithm according to claim 2 is characterized in that: In step S2, the constraint condition of the 4-3-4 piecewise polynomial interpolation function is: when the robot passes the starting point and the end point, the speed and acceleration are both zero, that is: , , at the connection of the 4-3-4 piecewise polynomial interpolation function, the position, velocity and acceleration of the joint are continuous, and at the midpoint, it must satisfy , According to the above constraints, we get the equation system of 4-3-4 piecewise polynomial interpolation function coefficients: ； In the formula, ； Through equations and preset time parameters , and , solve for the coefficients of the 4-3-4 piecewise polynomial interpolation function: ； In the formula, 。 4. The robot trajectory planning method based on the improved blowfish algorithm according to claim 3 is characterized in that: In step S2, when the robot's motion time is constrained, the time parameter , and The optimized objective function is: And considering the constraints of the position, velocity, and acceleration of the robot joints when the robot moves, the constraints are: ； In the formula, Indicates The joint Segment track, , , and Indicates The limit values ​​of joint position, velocity, and acceleration.

5. The robot trajectory planning method based on the improved blowfish algorithm according to claim 1, characterized in that: In the step S31, For puffer particles, the chaotic sequence is constructed using Logistic mapping: ; Initialize the position of the population, ; In the formula, Indicates i The first j Quantity, The position of the pufferfish is represented by ,in , represents the population size, represents the dimension of the particle, is the value generated by the chaotic sequence, ub j and lb j Represents the particle j The upper and lower bounds of the dimension components.

6. The robot trajectory planning method based on the improved blowfish algorithm according to claim 1, characterized in that: In step S31, the fitness function ; Calculate the fitness value of each particle.

7. The robot trajectory planning method based on the improved blowfish algorithm according to claim 1, characterized in that: In step S33, the update formula of the pufferfish defense mechanism is: In the formula, For pufferfish particles, Indicates i The particle j Quantity, represents the updated particle position, represents its fitness value, Indicates its j Dimensional component, represents a random number between [0,1], , Respectively represent the particle j The upper and lower limits of the dimension components, t Indicates the current loop number.

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