Mechanical Arm Trajectory Planning Based on B-Spline and Whale Optimization Algorithm

doi:10.12068/j.issn.1005-3026.2024.05.010

Abstract

Abstract:

In order to improve the efficiency of mechanical arms， the time optimal trajectory planning method based on the B?spline and whale optimization algorithm（WOA） is proposed. The Monte?Carlo method is used to describe the workspace of the mechanical arms， and then the B?spline is used to interpolate the given path points. According to the performance of each joint of the manipulator， the angular velocity and angular acceleration constraints are introduced， and the boundary conditions are added. After constructing the target function with optimal time， the WOA with inertia weight is used to optimize the running time of the mechanical arm. Finally， using Matlab for simulation， the results show that the algorithm presented is better than the traditional quintic polynomial method in terms of time optimization， and the angular velocity and angular acceleration curve are continuously smoothed， which verifies the validity and feasibility of the algorithm.

Key words: mechanical arm, time optimal trajectory planning, Monte?Carlo method, B?spline, whale optimization algorithm （WOA）

CLC Number:

TP 242

Zhi-guo LU, Xiao WANG. Mechanical Arm Trajectory Planning Based on B-Spline and Whale Optimization Algorithm[J]. Journal of Northeastern University(Natural Science), 2024, 45(5): 683-689.

Figures/Tables 10

Fig.1 Chaotic mapping of population distribution

Fig.2 WOA flow diagram

Fig.3 Mechanical arm

Table 1 DH parameters

关节编号	$θ i$ /(°)	d_i /m	$α i$ /(°)	a_i /m
1	$θ 1$	0.130 5	90	0
2	$θ 2$	0	0	0.350 0
3	$θ 3$	0	0	0.225 3
4	$θ 4$	0	90	0.072 0
5	$θ 5$	0	90	0
6	$θ 6$	0.098 2	0	0

Table 1 DH parameters

关节编号	$θ i$ /(°)	d_i /m	$α i$ /(°)	a_i /m
1	$θ 1$	0.130 5	90	0
2	$θ 2$	0	0	0.350 0
3	$θ 3$	0	0	0.225 3
4	$θ 4$	0	90	0.072 0
5	$θ 5$	0	90	0
6	$θ 6$	0.098 2	0	0

Fig.4 Model of the mechanical arm

Table 2 Angular velocity and angular acceleration

变量	关节编号
变量	1	2	3	4	5	6
角速度/（rad·s^-1）	120	120	100	180	145	180
角加速度/（rad·s^-2）	100	100	100	100	100	100

Fig.5 Adaptive convergence curve

Fig.6 Joint angle curves

Fig.7 Joint angular velocity curves

Fig.8 Joint angular acceleration curve

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