A time-optimal based trajectory planning method for robot arm

Abstract

The application discloses a time-optimal-based mechanical arm trajectory planning method, which can make the robot accurately reach a target position in the shortest time while ensuring the smooth continuity of the motion speed and acceleration. The specific measures are as follows: the whale optimization algorithm is combined with the quintic polynomial interpolation method, the whale optimization algorithm is improved to enhance the convergence speed and prevent falling into a local optimal state, and the optimal motion trajectory under the optimal time is ensured, so that the working efficiency of the mechanical arm is improved. The application introduces a segmented attenuation rate and an inertia weight, so that the algorithm has the characteristics of fast convergence, strong global search capability and effective avoidance of falling into a local optimal state. The introduction of the punishment strategy improves the position updating efficiency in the search process. The application has important significance for improving the working efficiency of the robot in tasks such as assembly and stacking.

Description

Technical Field

[0001] This invention relates to the field of robotics research and engineering, specifically to an optimal time trajectory planning method based on the enhanced whale optimization algorithm. Background Technology

[0002] With the advancement of technology, robots have been widely used in various fields such as industry and service in recent years. In particular, robotic arms play a significant role in replacing humans in completing repetitive and tedious labor tasks (such as transporting goods, palletizing, grinding, and polishing). Trajectory planning for robotic arms includes two types: trajectory planning in Cartesian space and trajectory planning in joint space. The former mainly focuses on the continuous motion planning of the robotic arm's end effector and is primarily applied under conditions where the end effector has pose constraints; the latter mainly focuses on the rotation angle planning of each joint of the robotic arm and is primarily applied in motion planning where the end effector's pose is unconstrained. Commonly used planning methods include cubic polynomial interpolation and quintic polynomial interpolation.

[0003] Trajectory planning in joint space, under conditions of ensuring smooth motion and constraints on speed and acceleration, can significantly shorten the robot's runtime if time-optimal planning can be achieved, thus greatly improving robot efficiency. In recent years, with the in-depth research of heuristic optimization algorithms, many algorithms such as particle swarm optimization, genetic algorithms, simulated annealing, and whale algorithms have been applied to trajectory optimization. Genetic algorithms suffer from getting trapped in local optima and slow convergence speed when dealing with optimization problems. Furthermore, the crossover and mutation calculations in genetic algorithms require substantial computational resources, making them unsuitable for deployment in robotic systems. The traditional whale optimization algorithm is based on the behavior of whale groups, simulating their strategies in food searching and mating. It possesses good global search capabilities and is easy to implement. Moreover, this algorithm employs the search strategies of multiple individual whales, enabling multi-directional searches within the search space and exhibiting strong robustness. However, this algorithm also suffers from the problems of easily getting trapped in local optima and slow convergence speed. Summary of the Invention

[0004] To address the above problems, this invention proposes an optimal time trajectory planning method based on an enhanced whale optimization algorithm. This method enables the robot to accurately reach the target position in the shortest time while ensuring smooth and continuous velocity and acceleration. Specifically, it combines the whale optimization algorithm with a fifth-order polynomial interpolation method. By improving and enhancing the whale optimization algorithm, its convergence speed is increased and it is prevented from getting trapped in local optima, ensuring that it can obtain the motion trajectory in the optimal time, thereby improving the working efficiency of the robotic arm.

[0005] First, because the parameters of the traditional whale algorithm are relatively fixed, the robotic arm may get stuck in local optima and have a slow convergence speed when planning joint angles, making it unable to plan the time-optimal angle sequence. To address this problem, this invention proposes a piecewise decay rate and introduces nonlinear weights to improve the algorithm's convergence speed, enhance its global search capability, avoid local optima, and thus find the shortest motion trajectory during planning.

[0006] In the whale optimization algorithm, the parameter 'a' determines the search capability and range of the population, i.e., the range of angles that the robotic arm can choose during planning. In the early stages of the search, a larger parameter 'a' is needed to enhance the algorithm's global search capability and improve the convergence speed; in the later stages of the search, parameter 'a' should be reduced to increase the influence rate of the current best individual in the population. The parameter 'a' in the original algorithm is linearly decreasing, as shown in formula (1), where 't' is the current robotic arm planning iteration number, and T... max The maximum number of iterations for planning the robotic arm. The parameter 'a' used in this invention is expressed in a piecewise manner, and the sigmoid function is introduced to ensure that its convergence region is still [0,2], and its expression is shown in formula (2).

[0007]

[0008]

[0009] As early as the particle swarm optimization algorithm, an inertial weight ω was introduced to adjust its global and local search capabilities. However, the original whale algorithm did not have a corresponding weight coefficient to adjust its position update method. As the search process deepened, it might get stuck in local optima, resulting in the robot arm's planned trajectory being suboptimal. Therefore, this invention introduces the inertial weight ω into the whale algorithm for robot arm trajectory optimization. Its value decreases non-linearly with the increase of the robot arm's planning times. In the early stage of the algorithm search, the weight coefficient is relatively large, and the algorithm has a strong global search capability. As the number of iterations increases, the weight coefficient is relatively small in the later stage of the algorithm search, and the algorithm searches precisely within a certain area, preventing it from getting stuck in local optima, improving search accuracy, and enabling the robot arm to select the optimal trajectory during planning. The expression for the weight ω is shown in formula (3).

[0010]

[0011] Assume the whale's position information (angle sequence in robotic arm trajectory planning) consists of P, and its expression is shown in formula (4), where p i The components representing whale position information within a population are used in robotic arm trajectory optimization. The whale position represents a series of joint angles, p iEach of these represents a specific angle. To improve the efficiency of population position updates during the search process, this invention introduces a penalty strategy on the basis of the original algorithm to penalize the population with low position element update efficiency during the search process. The expression is shown in formula (5) and formula (6).

[0012] P = {p1 p2 p3 ... p} i ...p n} (4)

[0013] d=|p i+1 -p i | (5)

[0014] F pun =λ*count d (6)

[0015] In formula (5), d represents the difference between the preceding and following angles in the angular sequence planned by the robotic arm, and count d This represents the number of angles that do not conform to the expected planning. After each update of the robot arm's planned angle sequence, if the difference d is less than the element step size threshold Δe, then count. d Add one, where λ represents the penalty coefficient, and calculate F. pun The value of the function is then added to the value function in the algorithm, and the optimal position of the whale is found by comparing the fitness function after the fusion penalty value.

[0016] By adopting the above technical solutions, the present invention has the following advantages:

[0017] This invention addresses the shortcomings of the original whale optimization algorithm by developing an enhanced whale optimization algorithm. By introducing a piecewise decay rate and inertia weight, the algorithm ensures fast convergence, strong global search capability, and effective avoidance of getting trapped in local optima. Furthermore, the introduction of a penalty strategy improves the efficiency of position updates during the search process.

[0018] Applying the enhanced whale optimization algorithm to the trajectory planning of a robotic arm, under the premise of ensuring certain physical constraints, enables the robotic arm to move to the target position in the shortest time through the optimization algorithm, which is of great significance for improving the work efficiency of robots in tasks such as assembly and palletizing. Attached Figure Description

[0019] Figure 1 It is a graph of the piecewise parameter a.

[0020] Figure 2 This is the flowchart of the enhanced whale optimization algorithm.

[0021] Figure 3.1It is the convergence curve of the value function obtained by testing with bealfunction.

[0022] Figure 3.2 It is the convergence curve of the value function obtained by testing with boothfunction.

[0023] Figure 3.3 The convergence curve of the value function is obtained by testing using a cross-in-tray function.

[0024] Figure 3.4 It is the convergence curve of the value function obtained by testing using the levy function.

[0025] Figure 3.5 The convergence curve of the value function is obtained by testing with the six-hump camel function. Detailed Implementation

[0026] The invention will be further described below with reference to the accompanying drawings.

[0027] Figure 1 The curves represent the decay rates of the piecewise parameter 'a', where 'primitive' represents the decay rate of 'a' in the original whale algorithm, and 'segment' represents the decay rate of the piecewise parameter 'a'. Observing the curves, it can be seen that the decay rate of parameter 'a' is fast in the early stages of the search and slows down in the later stages. The introduction of piecewise decay rates improves the search capability and global search range of the whale algorithm in robotic arm trajectory optimization, and enhances the ability to update angle sequences in robotic arm trajectory planning.

[0028] Figure 2 The flowchart of the enhanced whale optimization algorithm is shown below, and the specific implementation process is as follows:

[0029] Step 1: Initialize the population size N, set the relevant parameters of the algorithm, set the penalty gain λ, initialize the population position P, and set the maximum number of iterations t for the robotic arm trajectory planning. max Set the fitness function F fitStep 2: Calculate the fitness of each search individual based on the fitness function and generate a random probability p. Step 3: If p < 0.5 and |A| < 1, perform encirclement predation to update the position; if |A| > 1, perform a random search to update the position. Step 4: If p > 0.5, perform a bubble net attack on the prey in a spiral motion direction to update the position. Step 5: After the position update, recalculate the fitness of all individuals in the population using a penalty function. Compare the calculated fitness with the previous optimal state; if the current update is optimal, replace the previous state. Step 6: Determine if the maximum number of iterations for the robotic arm trajectory planning has been reached. If the maximum number of iterations has been reached, the algorithm ends, and the time-optimal motion angle sequence and fitness of the robotic arm are output; otherwise, return to Step 3.

[0030] To verify the effectiveness of the enhanced whale optimization algorithm proposed in this invention in robotic arm trajectory optimization, five different optimization test functions were used for verification, and its fitness convergence curve is shown below. Figures 3.1-3.5 As shown in Table 1, the error is summarized after comparing the optimal value of the test function with the true value. Here, WOA represents the original whale algorithm, WOA-a represents the algorithm that modifies only parameter a, replacing the original linear decay with sin function decay, and EWOA represents the enhanced whale optimization algorithm proposed in this invention.

[0031] Table 1: Comparison of errors between the optimal and true values ​​of the test function under different algorithms

[0032]

[0033] Multi-point trajectory planning was performed using a 7-DOF robotic arm, and the path point information and motion time are shown in Table 2.

[0034] Table 2: Angle values ​​and planning time for each joint

[0035]

[0036] Using a robotic arm to perform a transfer task between two points, the trajectory was optimized using different algorithms. The time taken after performing multiple tasks is shown in Table 3.

[0037] Table 3: Cumulative Time Taken for Robotic Arm to Perform Transfer Tasks under Different Algorithms

[0038]

[0039] In Table 3, t(s) represents the time taken by the robotic arm to perform the task under the original planning algorithm, and t woa (s) represents the time taken to execute the task under the original whale algorithm optimization, t ewoa(s) represents the time taken to execute the task using the enhanced whale optimization algorithm proposed in this invention. The comparison shows that the time taken after trajectory optimization using the enhanced whale optimization algorithm proposed in this invention is the shortest, reducing the original time by 21.54 seconds, effectively improving the working efficiency of the robotic arm.

Claims

1. A time-optimal robotic arm trajectory planning method, characterized in that, This method improves the convergence speed of the whale algorithm and enhances its global search capability by using a piecewise decay rate and introducing nonlinear weights, thus enabling the finding of the shortest motion trajectory in the planning process. In the whale algorithm, the parameter 'a' determines the search capability and range of the population, i.e., the range of angles that the robotic arm can choose during planning. In the early stages of the search, a large parameter 'a' is needed to enhance the global search capability of the whale algorithm and improve the convergence speed. In the later stages of the search, the parameter a is reduced to increase the influence rate of the current best individual in the population; the parameter a is expressed in a piecewise manner, and the sigmoid function is introduced to ensure that its function convergence region is still [0,2], and its expression is shown in formula (2); ； t represents the current iteration number of the robotic arm's planning process. The maximum number of iterations for planning the robotic arm; the inertia weights Inertia weights are introduced into the whale algorithm for robotic arm trajectory optimization. The value decreases non-linearly with the increase of the number of planning iterations by the robotic arm; inertia weight The expression is shown in formula (3); ； Let P be the position information of the whale, i.e., the angle sequence in the trajectory planning of the robotic arm, and its expression is shown in formula (4). Each angle of the joint is represented by i, which takes values ​​from 1 to n. A penalty strategy is introduced to penalize populations with low position element update efficiency during the search process. The expressions are shown in formulas (5) and (6). ； ； ； In formula (5), d represents the difference between the preceding and following angles in the angular sequence planned by the robotic arm. This represents the number of angles that do not conform to the expected planning; after each update of the robot arm's planned angle sequence, if the difference d is less than the element step size threshold... but Add one, This represents the penalty coefficient, which is calculated as follows. The value of the function is then added to the inertia weight in the inertia algorithm. In this study, the optimal whale position is found by comparing the fitness function after fusion penalty value.

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