Multi-objective Trajectory Planning of Manipulators Based on Improved SSA

doi:10.3969/j.issn.1004-132X.2025.09.017

Abstract

Abstract:

To optimize the three objectives of efficiency， energy consumption and impacts at the same time， a multi-objective trajectory planning model was proposed based on an improved SSA. Firstly， the artificial potential field method （APF） was used for path planning to obtain the shortest and collision-free path of the manipulator grasping the materials， and the key motion sequence was extracted to establish a multi-objective function. Then， aiming at the problems of multi-objective salp swarm algorithm （MSSA）， such as poor diversity of initial population， easy to fall into local optimum and slow convergence in solution set space， an improved algorithm namely logistic-sine multi-objective salp swarm algorithm（LMSSA）was proposed. The algorithm combined logistic-sine chaotic mapping， pinhole imaging learning strategy and golden sine development strategy to optimize the control nodes of the seventh-order B-spline curve and complete the multi-objective motion trajectory planning of the robotic arms. Finally， the trajectory planning model was applied to the actual grasping tasks of the manipulator UR16e by building MATLAB-CoppeliaSim-UR16e experimental platform. Experimental results show that based on LMSSA， the manipulator motion planning method realizes the accurate， efficient and energy-saving motion trajectory planning of the manipulator， and is successfully applied to the actual operation scenes.

Key words: trajectory planning, multi-objective optimization, manipulator, salp swarm algorithm（SSA）

摘要：

提出了一种基于改进樽海鞘群算法（SSA）的机械臂多目标轨迹规划模型，以同时优化效率、能耗和冲击三个目标。利用人工势场法（APF）进行路径规划，得到机械臂抓取物料的最短、无碰撞路径，并提取关键运动序列，建立多目标函数。针对多目标樽海鞘群算法（MSSA）的初始种群多样性差、容易陷入局部最优以及在解集空间中收敛缓慢等问题，提出了一种改进的多目标樽海鞘群算法（LMSSA）。该算法结合logistic-sine混沌映射、小孔成像学习策略和黄金正弦开发策略来优化七阶B样条曲线的控制节点从而完成机械臂的多目标运动轨迹规划。搭建MATLAB-CoppeliaSim-UR16e实验平台，将轨迹规划模型应用于机械臂UR16e的实际抓取任务。实验结果表明，基于LMSSA算法的机械臂运动规划方法实现了机械臂准确、高效且节能的运动轨迹规划，并成功应用于实际操作场景中。

关键词: 轨迹规划, 多目标优化, 机械臂, 樽海鞘群算法

CLC Number:

TP241.2

Jianlin LIU, Haisong HUANG, Qingsong FAN, Chi MA, Langlang ZHANG. Multi-objective Trajectory Planning of Manipulators Based on Improved SSA[J]. China Mechanical Engineering, 2025, 36(9): 2047-2056.

刘建林, 黄海松, 范青松, 马驰, 张浪浪. 基于改进樽海鞘群算法的机械臂多目标轨迹规划研究[J]. 中国机械工程, 2025, 36(9): 2047-2056.

Figures/Tables 19

Fig.1 Path planning of 6-DOF robotic arm

Tab.1 Joint position sequence of 6-DOF robotic arm （°）

关节	1	2	3	4	5	6
位置0	$-$ 20.17	$-$ 8.05	89.70	8.39	$-$ 90.05	$-$ 69.88
位置1	$-$ 34.62	$-$ 4.67	104.30	$-$ 9.58	$-$ 90.05	$-$ 55.43
位置2	$-$ 37.27	0.75	100.92	$-$ 11.62	$-$ 90.05	$-$ 52.77
位置3	$-$ 49.45	8.65	97.50	$-$ 16.10	$-$ 90.05	$-$ 40.60
位置4	$-$ 76.38	8.06	97.15	$-$ 15.17	$-$ 90.05	$-$ 13.67
位置5	$-$ 80.19	13.02	89.92	$-$ 12.89	$-$ 90.05	$-$ 9.86
位置6	$-$ 93.38	14.49	81.42	$-$ 5.87	$-$ 90.05	3.33
位置7	$-$ 109.56	5.76	77.03	7.26	$-$ 90.05	19.51

Tab.1 Joint position sequence of 6-DOF robotic arm （°）

关节	1	2	3	4	5	6
位置0	$-$ 20.17	$-$ 8.05	89.70	8.39	$-$ 90.05	$-$ 69.88
位置1	$-$ 34.62	$-$ 4.67	104.30	$-$ 9.58	$-$ 90.05	$-$ 55.43
位置2	$-$ 37.27	0.75	100.92	$-$ 11.62	$-$ 90.05	$-$ 52.77
位置3	$-$ 49.45	8.65	97.50	$-$ 16.10	$-$ 90.05	$-$ 40.60
位置4	$-$ 76.38	8.06	97.15	$-$ 15.17	$-$ 90.05	$-$ 13.67
位置5	$-$ 80.19	13.02	89.92	$-$ 12.89	$-$ 90.05	$-$ 9.86
位置6	$-$ 93.38	14.49	81.42	$-$ 5.87	$-$ 90.05	3.33
位置7	$-$ 109.56	5.76	77.03	7.26	$-$ 90.05	19.51

Fig.2 Distribution of chaotic mapping

Fig.3 PIL strategy

Fig.4 Golden sine development strategy

Fig.5 Trajectory planning model

Fig.6 Model of 6-DOF robotic arm

Tab.2 Joint constraints of 6-DOF robotic arm

关节	a/ （m·s^-2）	d/m	α/ rad	最大速度/ （（°）·s^-1）	最大加速度/ （（°）·s^-2）	最大关节急动度/（（°）·s^-3）	最大扭矩/（N∙m）
1	0	0.1807	π/2	120	45	90	327
2	$-$ 0.4784	0	0	120	40	80	167
3	$-$ 0.36	0	0	180	75	70	167
4	0	0.174 15	π/2	180	70	55	20
5	0	0.119 85	$-$ π/2	180	90	60	10
6	0	0.11655	0	180	80	60	10

Tab.2 Joint constraints of 6-DOF robotic arm

关节	a/ （m·s^-2）	d/m	α/ rad	最大速度/ （（°）·s^-1）	最大加速度/ （（°）·s^-2）	最大关节急动度/（（°）·s^-3）	最大扭矩/（N∙m）
1	0	0.1807	π/2	120	45	90	327
2	$-$ 0.4784	0	0	120	40	80	167
3	$-$ 0.36	0	0	180	75	70	167
4	0	0.174 15	π/2	180	70	55	20
5	0	0.119 85	$-$ π/2	180	90	60	10
6	0	0.11655	0	180	80	60	10

Tab.3 Comparison experiment parameter settings

对比算法	参数设置
MSSA	无
MODA	无
MOGOA	c_max=1，c_min=0.000 04
MOMVO	W_EPmax=1，W_EPmin=0.2
LMSSA	无

Fig.7 Motion path of the robot arm

Fig.8 Pareto solution set for multi-objective trajectory planning

Tab.4 Optimization results of Pareto frontier points

多目标算法	前沿点	f₁/s	f₂/（（°）·s^-2）	f₃/（（°）·s^-3）
MSSA	A	22.1084	5.0871	6.5298
MODA	B	17.3987	46.6482	64.3333
MOGOA	C	19.3285	63.9597	83.4501
MOMVO	D	25.5248	84.4578	93.3547
LMSSA	E	14.7123	29.7611	71.8474

Tab.5 Comparison of Pareto solution set results

		MSSA	MODA	MOGOA	MOMVO	LMSSA
Pareto解集个数		21	26	40	36	62
时间/s	最小值	20.5116	17.3987	19.3285	17.3014	14.7123
时间/s	最大值	34.0801	38.1684	37.2126	38.5459	49.2208
能耗/ （（°）·s^-2）	最小值	4.0654	4.8909	1.7769	3.0430	2.6992
能耗/ （（°）·s^-2）	最大值	95.4776	75.2556	87.0272	85.5218	29.7611
冲击/ （（°）·s^-3）	最小值	3.7635	5.0333	1.6662	2.4648	1.9407
冲击/ （（°）·s^-3）	最大值	89.2185	83.6998	94.0682	93.354 69	71.8474
间距（SP）		9.9845	10.2340	5.2948	5.8237	1.0383
运行时间（s）		3421	3786	4082	3562	3289

Tab.6 Node variables after Pareto frontier point optimization

	关节轨迹时间节点	B样条曲线控制节点向量
MSSA	(1.12,1.20,1.00,0.66,1.20,1.36,0.54)	(0,0,0,0,0,0,0,0,0.16,0.33,0.47,0.56,0.73,0.92,1,1,1,1,1,1,1,1)
MODA	(0.30,6.91,5.01,4.66,4.66,2.35,0.84)	(0,0,0,0,0,0,0,0,0.01,0.29,0.49,0.68,0.87,0.97,1,1,1,1,1,1,1,1)
MOGOA	(6.91,3.17,4.55, 1.16,2.24,2.33,4.12)	(0,0,0,0,0,0,0,0,0.28,0.41,0.60,0.65,0.74,0.83,1,1,1,1,1,1,1,1)
MOMVO	(1.73,1.40,1.41, 0.63,0.57,1.24,0.12）	(0,0,0,0,0,0,0,0,0.24,0.44,0.64,0.73,0.81,0.98,1,1,1,1,1,1,1,1）
LMSSA	(4.36,0.91,1.43, 2.53,0.69,1.66,2.13）	(0,0,0,0,0,0,0,0,0.32,0.38,0.49,0.67,0.72,0.84,1,1,1,1,1,1,1,1）

Fig.9 Experimental results of multi-object trajectory planning

Fig.10 Comparison between the optimized path and the original path

Fig.11 MATLAB-CoppeliaSim-UR16e experimental platform

Fig.12 UR16e grasping experiment

Tab.7 Multi-objective indicators of trajectory planning

	时间/s	能耗/（（°）·s^-2）	冲击/（（°）·s^-3）
原始方法	3.74	243.65	342.13
本文方法	2.67	191.81	278.91
优化效果	28.61%	21.28%	18.48%

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