Research on Constrained Programming of Manipulator Using RRT* Algorithm and Ellipse Prior

doi:10.16182/j.issn1004731x.joss.24-0545

Abstract

Abstract:

There are problems in the traditional RRT* algorithm using a uniform sampling strategy applied in constrained programming problems, such as inaccurate turning guidance of sampling points and unnecessary node cost comparisons, which lead to an increase in additional time costs. To address these issues, an improved RRT* algorithm was proposed. This algorithm leveraged a heuristic function cost of the projected sampling points to make an ellipse prior judgment on the sampling points. Based on the ellipse prior, the sampling points were judged to determine whether they could optimize the path and shorten the programming time. The geodesics were used to further estimate the current cost of the projected sampling points. Simulation results show that the planned path by the improved RRT* algorithm has an average time cost reduction of 73.27% compared to that by the traditional RRT* algorithm and an average path cost reduction of 4.49% compared to the RRT* algorithm that directly incorporates the ellipse prior.

Key words: manipulator, sampling point, constraint programming, RRT*, ellipse prior, geodesic, time cost, path cost

CLC Number:

TP391.9

Yang Zhen, Su Li, Cheng Zhiyu. Research on Constrained Programming of Manipulator Using RRT* Algorithm and Ellipse Prior[J]. Journal of System Simulation, 2025, 37(10): 2643-2651.

Figures/Tables 11

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 1

DH parameters of UR5 manipulator

自由度	$a i$	$α i$	$d i$	$θ i$
1	0	90	89.2	$θ 1$
2	-425	0	0	$θ 2$
3	-392.2	0	0	$θ 3$
4	0	90	109.3	$θ 4$
5	0	-90	94.65	$θ 5$
6	0	0	82.3	$θ 6$

Table 1

Fig. 5

Table 2

Improved RRT* algorithm parameters

参数	三维数学空间
最大步长 $α$	1.0
目标偏置概率 $β$	0.1
约束投影阈值 $ϵ$	0.01
采样点数目m	2 000
目标阈值e	0.1

Table 2

Table 3

Fig. 6

Fig. 7

Fig. 8

References 20

[1]	糜凯. 面向多种约束的工业机械臂避障运动规划方法研究[D]. 北京: 中国科学院大学, 2020.
[2]	陈伟, 白克强, 李孚洋, 等. 渐进式约束扩展的机械臂运动规划算法[J]. 计算机应用研究, 2020, 37(9): 2754-2757, 2761.
	Chen Wei, Bai Keqiang, Li Fuyang, et al. Progressive Constrained Extended Manipulator Motion Planning Algorithm[J]. Application Research of Computers, 2020, 37(9): 2754-2757, 2761.
[3]	Kingston Z, Moll M, Kavraki L E. Sampling-based Methods for Motion Planning with Constraints[J]. Annual Review of Control, Robotics, and Autonomous Systems, 2018, 1: 159-185.
[4]	胡世军, 刘海亮, 王兵雷, 等. 基于定向探索树算法的四旋翼无人机路径规划[J]. 系统仿真学报, 2025, 37(2): 311-324.
	Hu Shijun, Liu Hailiang, Wang Binglei, et al. Quadrotor UAV Path Planning Based on Rapidly-exploration Directional Tree Algorithm[J]. Journal of System Simulation, 2025, 37(2): 311-324.
[5]	刘文倩, 单梁, 王志强, 等. 机械臂的位姿分离求逆和改进RRT-connect算法研究[J]. 控制工程, 2023, 30(11): 2100-2107.
	Liu Wenqian, Shan Liang, Wang Zhiqiang, et al. Research on Inversion Algorithm of Position and Attitude Separation and Improved RRT-connect Algorithm of Manipulator[J]. Control Engineering of China, 2023, 30(11): 2100-2107.
[6]	Karaman S, Walter M R, Perez Alejandro, et al. Anytime Motion Planning Using the RRT*[C]//Shanghai:2011 IEEE International Conference on Robotics and Automation. Piscataway: IEEE, 2011: 1478-1483.
[7]	Yavari M, Gupta K, Mehrandezh M. Lazy Steering RRT*: An Optimal Constrained Kinodynamic Neural Network Based Planner with No In-exploration Steering[C]//2019 19th International Conference on Advanced Robotics (ICAR). Piscataway: IEEE, 2019: 400-407.
[8]	霍韩淋, 邹湘军, 陈燕, 等. 基于视觉机器人障碍点云映射避障规划及仿真[J]. 系统仿真学报, 2024, 36(9): 2149-2158.
	Huo Hanlin, Zou Xiangjun, Chen Yan, et al. Visual Robot Obstacle Avoidance Planning and Simulation Using Mapped Point Clouds[J]. Journal of System Simulation, 2024, 36(9): 2149-2158.
[9]	Ahmed Hussain Qureshi, Ayaz Yasar. Potential Functions Based Sampling Heuristic for Optimal Path Planning[J]. Autonomous Robots, 2016, 40(6): 1079-1093.
[10]	Bohlin R, Kavraki L E. Path Planning Using Lazy PRM[C]//Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings. Piscataway: IEEE, 2000: 521-528.
[11]	刘潇龙. 基于PRM算法和响应面法的线束路径规划方法[J]. 机械设计与制造工程, 2023, 52(5): 112-116.
	Liu Xiaolong. Harness Path Planning Method Based on PRM Algorithm and Response Surface Method[J]. Machine Design and Manufacturing Engineering, 2023, 52(5): 112-116.
[12]	邹宇星, 李立君, 高自成. 基于改进PRM的采摘机器人机械臂避障路径规划[J]. 传感器与微系统, 2019, 38(1): 52-56.
	Zou Yuxing, Li Lijun, Gao Zicheng. Obstacle Avoidance Path Planning for Harvesting Robot Arm Based on Improved PRM[J]. Transducer and Microsystem Technologies, 2019, 38(1): 52-56.
[13]	Osa Takayuki. Motion Planning by Learning the Solution Manifold in Trajectory Optimization[J]. The International Journal of Robotics Research, 2022, 41(3): 281-311.
[14]	Berenson D, Srinivasa S, Kuffner J. Task Space Regions: A Framework for Pose-constrained Manipulation Planning[J]. International Journal of Robotics Research, 2011, 30(12): 1435-1460.
[15]	Jaillet Léonard, Porta Josep M. Path Planning Under Kinematic Constraints by Rapidly Exploring Manifolds[J]. IEEE Transactions on Robotics, 2013, 29(1): 105-117.
[16]	李娟, 张韵, 陈涛. 改进RRT算法在未知三维环境下AUV目标搜索中的应用[J]. 智能系统学报, 2022, 17(2): 368-375.
	Li Juan, Zhang Yun, Chen Tao. Application of the Improved RRT Algorithm to AUV Target Search in an Unknown 3D Environment[J]. CAAI Transactions on Intelligent Systems, 2022, 17(2): 368-375.
[17]	Kim Beobkyoon, Terry Taewoong Um, Suh Chansu, et al. Tangent Bundle RRT: A Randomized Algorithm for Constrained Motion Planning[J]. Robotica, 2016, 34(1): 202-225.
[18]	Panerati J, Zheng Hehui, Zhou Siqi, et al. Learning to Fly-a Gym Environment with PyBullet Physics for Reinforcement Learning of Multi-agent Quadcopter Control[C]//2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Piscataway: IEEE, 2021: 7512-7519.
[19]	Yang Xintong, Ji Ze, Wu Jing, et al. An Open-source Multi-goal Reinforcement Learning Environment for Robotic Manipulation with Pybullet[C]//Towards Autonomous Robotic Systems. Cham: Springer International Publishing, 2021: 14-24.
[20]	Kebria P M, Al-wais S, Abdi H, et al. Kinematic and Dynamic Modelling of UR5 Manipulator[C]//2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC). Piscataway: IEEE, 2016: 4229-4234.

算法	成功比例	路径代价	规划时间/s
约束RRT*	10/10	11.17±0.16	10.55±3.21
先验约束RRT*	10/10	11.81±0.51	2.23±0.35
改进约束RRT*	10/10	11.28±0.13	2.82±0.43