Trajectory Optimization Method for Portable Robots in Confined Spaces Based on Multi-objective Constraints

doi:10.3969/j.issn.1004-132X.2026.06.023

Abstract

Abstract:

Aiming at the challenges in ship narrow-space welding， such as the restricted workspace， multiple constraints on torch posture， high risk of trajectory interference， and poor welding accessibility， a time-optimization scheme was proposed for welding trajectory optimization based on an improved IGA-PSO， to achieve welding with the robotic arm in the shortest time. Three-dimensional models of the portable robots， workpiece， and working scene were constructed， the motion logic of the robots was clarified， and the welding trajectory model and processes were established. A multi-objective constrained fitness function was designed by comprehensively considering both welding time and accessibility， and the objective functions for time optimization and accessibility rate were formulated. By integrating the genetic and particle swarm algorithms， improvements were introduced： a linearly decreasing and exponentially decreasing mechanism for the inertia weight was adopted； the learning factors were designed for exploration， exploitation， and convergence stages； and the mutation operation was adjusted nonlinearly， thereby enhancing the algorithm's performance. Algorithm testing， simulation verification， and on-site validation were carried out through a case study to verify the proposed method. The results show that the optimized robotic arms exhibit smooth displacement， velocity， and acceleration curves without abrupt changes， and the welding accessibility reaches 90%， which verifies the effectiveness of the IGA-PSO.

Key words: multi-objective optimization, narrow-space welding, path optimization, improved genetic algorithm-particle swarm optimization（IGA-PSO）, adaptive mechanism

摘要：

针对船舶狭小空间焊接时作业空间受限、焊枪姿态约束多、轨迹干涉风险高、焊接可达性差等挑战，以机械臂最短时间完成焊接为目标，提出基于改进遗传粒子群算法（IGA-PSO）的时间优化方案以优化焊接轨迹。构建便携式机器人、工件和场景的三维模型，明确机器人运动逻辑，建立焊接轨迹模型并确定焊接工艺；综合考虑焊接时间和可达性，设计多目标约束适应度函数，并建立时间优化与可达率目标函数；结合遗传和粒子群算法，对惯性权重引入线性递减和指数递减机制，对学习因子设计探索、开发和收敛阶段，对变异进行非线性调整，以提高算法的性能。通过算法测试、仿真验证和现场验证对该方法进行了案例验证，结果表明，优化后的机械臂位移、速度、加速度曲线平滑、无突变，且焊接可达率达到90%，验证了IGA-PSO算法的有效性。

关键词: 多目标优化, 狭小空间焊接, 路径优化, 改进遗传粒子群算法, 自适应机制

CLC Number:

TP18

LIU Jinfeng, GU Shimin, ZHANG Zhanhu, LI Su, CHEN Yu, WANG Xuemin, QIAN Tianlong. Trajectory Optimization Method for Portable Robots in Confined Spaces Based on Multi-objective Constraints[J]. China Mechanical Engineering, 2026, 37(6): 1508-1517.

刘金锋, 顾世民, 张占虎, 李苏, 陈宇, 王学敏, 钱天龙. 基于多目标约束的狭小空间便携式机器人轨迹优化方法[J]. 中国机械工程, 2026, 37(6): 1508-1517.

Figures/Tables 20

Fig.1 Robot model

Fig.2 Bottom and side compartment model of bulk carrier

Fig.3 Welding simulation environment

Fig.4 The D-H coordinate system

Tab.1 D-H parameters

关节i	连杆长度 $l i - 1$ /mm	连杆扭角 $α i - 1$ /（°）	连杆偏距 $d i$ /mm	关节角 $θ i$ /（°）	关节角范围/（°）
0-1	0	90	192.5	$θ 1$	$-$ 360~360
1-2	266	180	0	$θ 2$	$-$ 135~135
2-3	0	$-$ 90	0	$θ 3$	$-$ 153~153
3-4	0	90	324	$θ 4$	$-$ 360~360
4-5	0	$-$ 90	0	$θ 5$	$-$ 180~180
5-6	0	0	155	$θ 6$	$-$ 360~360

Tab.1 D-H parameters

关节i	连杆长度 $l i - 1$ /mm	连杆扭角 $α i - 1$ /（°）	连杆偏距 $d i$ /mm	关节角 $θ i$ /（°）	关节角范围/（°）
0-1	0	90	192.5	$θ 1$	$-$ 360~360
1-2	266	180	0	$θ 2$	$-$ 135~135
2-3	0	$-$ 90	0	$θ 3$	$-$ 153~153
3-4	0	90	324	$θ 4$	$-$ 360~360
4-5	0	$-$ 90	0	$θ 5$	$-$ 180~180
5-6	0	0	155	$θ 6$	$-$ 360~360

Fig.5 Schematic diagram of the interpolation trajectory

Tab.2 Algorithm parameter settings

算法	参数
GA	p_s=200；g_m=1000；p_c=0.8；p_m=0.5
POS	p_s=100；g_m=1000；w=0.9；c₁=2；c₂=2
GA-POS	p_s=200；g_m=1000； w=0.5； c₁=2；c₂=2；p_c=1；p_m=0.2
IGA-POS	p_s=200；g_m=1000

Fig.6 Tests of four algorithms

Tab.3 Parameters of four path points

路径点	位置/mm	姿态/（°）
1	626.874、222.441、250.428	17.493、 $-$ 29.644、13.771
2	570.753、112.298、222.240	15.658、 $-$ 14.536、18.608
3	627.149、12.745、110.951	18.469、 $-$ 17.230、 $-$ 12.507
4	602.183、 $-$ 63.160、21.949	5.229、1.399、 $-$ 1.433

Tab.3 Parameters of four path points

路径点	位置/mm	姿态/（°）
1	626.874、222.441、250.428	17.493、 $-$ 29.644、13.771
2	570.753、112.298、222.240	15.658、 $-$ 14.536、18.608
3	627.149、12.745、110.951	18.469、 $-$ 17.230、 $-$ 12.507
4	602.183、 $-$ 63.160、21.949	5.229、1.399、 $-$ 1.433

Tab.4 Joint positions

关节	路径点1	路径点2	路径点3	路径点4
1	26.760°	5.462°	13.161°	4.288°
2	$-$ 19.723°	$-$ 13.275°	$-$ 15.686°	3.281°
3	$-$ 4.836°	6.322°	$-$ 22.374°	$-$ 19.235°
4	$-$ 9.235°	$-$ 27.313°	12.382°	$-$ 2.648°
5	$-$ 23.570°	$-$ 57.104°	$-$ 17.640°	$-$ 41.815°
6	$-$ 6.781°	17.640°	$-$ 37.993°	$-$ 5.665°

Tab.4 Joint positions

关节	路径点1	路径点2	路径点3	路径点4
1	26.760°	5.462°	13.161°	4.288°
2	$-$ 19.723°	$-$ 13.275°	$-$ 15.686°	3.281°
3	$-$ 4.836°	6.322°	$-$ 22.374°	$-$ 19.235°
4	$-$ 9.235°	$-$ 27.313°	12.382°	$-$ 2.648°
5	$-$ 23.570°	$-$ 57.104°	$-$ 17.640°	$-$ 41.815°
6	$-$ 6.781°	17.640°	$-$ 37.993°	$-$ 5.665°

Fig.7 Displacement curves of six joint angles （before optimization）

Fig.8 Angular velocity curves of six joints （before optimization）

Fig.9 Angular acceleration curves of six joints （before optimization）

Tab.5 Running time of trajectory planning for six joints

时间	关节序号
时间	1	2	3	4	5	6
t₁	1.16	1.27	1.32	1.22	1.12	1.13
t₂	2.24	2.15	2.05	2.28	2.30	2.28
t₃	1.11	1.18	1.20	1.05	1.11	1.12
总时间t	4.51	4.60	4.58	4.55	4.52	4.53

Fig.10 Spatial curve of piecewise polynomial trajectory planning

Fig.11 Angular displacement curves of six joints （after optimization）

Fig.12 Angular velocity curves of six joints （after optimization）

Fig.13 Angular acceleration curves of six joints （after optimization）

Tab.6 Comparison of experimental results

	机器人			人工
	机器人焊接时间/min	可达率/ %	人工搬运与焊接时间/min	焊接时间/min	工人休息时间/min
工位1	8.23	100	1.30	9.18	1.30
工位2	8.47	96	2.30	9.45	1.50
工位3	6.03	100	1.30	6.36	1.00
工位4	7.02	89	4.38	11.12	1.00
工位5	10.03	92	3.32	11.58	2.30
总时间	54.58 min			56.39 min

Fig. 14 Comparison of welding results

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