Trajectory planning and tracking control for upper limb traction rehabilitation training_Journal of Biomedical Engineering

Authors：

LUO Shengguo ¹ , LI Xiangyun ² ,  LU Qi ³ , CHEN Peng ⁴ , LI Kang ²

1. College of Electrical Engineering, Sichuan University, Chengdu 610065, P. R. China;
2. West China Biomedical Big Data Center, West China Hospital, Sichuan University, Chengdu 610041, P. R. China;
3. College of Pittsburgh, Sichuan University, Chengdu 610065, P. R. China;
4. College of Mechanical Engineering, Southwest Jiaotong University, Chendu 610031, P. R. China;

Corresponding author：

LU Qi, Email: qi.lu@scu.edu.cn

Keywords：

Upper limb rehabilitation; Interactive space; Singularity avoidance; Backstepping control; Radial basis function neural network

DOI：

10.7507/1001-5515.202501049

Video：

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Abstract Full text Figures/Tables Video References Cited by

To solve the safety problems caused by the restriction of interaction space and the singular configuration of rehabilitation robot in terminal traction upper limb rehabilitation training, a trajectory planning and tracking control scheme for rehabilitation training is proposed. The human-robot safe interaction space was obtained based on kinematics modeling and rehabilitation theory, and the training trajectory was planned based on the occupational therapy in rehabilitation medicine. The singular configuration of the rehabilitation robot in the interaction space was avoided by exponential adaptive damped least square method. Then, a nonlinear controller for the upper limb rehabilitation robot was designed based on the backstepping control method. Radial basis function neural network was used to approximate the robot model information online to achieve model-free control. The stability of the controller was proved by Lyapunov stability theory. Experimental results demonstrate the effectiveness and superiority of the proposed singular avoidance control scheme.

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2.	Bustrén E L, Sunnerhagen K S, Murphy M A. Movement kinematics of the ipsilesional upper extremity in persons with moderate or mild stroke. Neurorehabil Neural Repair, 2017, 31(4): 376-386.
3.	Jones T A, Allred R P, Adkins D L, et al. Remodeling the brain with behavioral experience after stroke. Stroke, 2009, 40(3): 136-138.
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8.	李贺立, 杨冬, 杨德志, 等. 双臂机器人避关节极限与避奇异位形优化研究. 科学技术与工程, 2017, 17(3): 98-104.
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10.	Lu L, Zhang L, Fan C, et al. High-order joint-smooth trajectory planning method considering tool-orientation constraints and singularity avoidance for robot surface machining. J Manuf Process, 2022, 80(12): 789-804.
11.	Li Y, Wang L. Comprehensive research and analysis on obstacle–singularity–joint limit avoidance of redundant robot. Int J Adv Robot Syst, 2024, 21(1): 1-10.
12.	Yang Y M. Research on active–passive training control strategies for upper limb rehabilitation robot. Machines, 2024, 12(11): 784-804.
13.	Ju C Q, Chen Z Q, Qin H, et al. Design and control of a cable-driven upper limb exoskeleton robot for rehabilitation// 2023 29th International Conference on Mechatronics and Machine Vision in Practice (M2VIP). Queenstown: IEEE, 2023: 1-6.
14.	Li S Y, Su C P, Huang L, et al. Personalized passive training control strategy for a lower limb rehabilitation robot with specified step lengths. Intell Serv Robotics, 2025, 18(9): 137-156.
15.	Wang P, Liu L Y, Nan F H, et al. The sliding mode controller with composite reaching law for upper limb rehabilitation robot. Ind Robot, 2025, 52(2): 277-286.
16.	Roderick S, Liszka M, Carignan C. Design of an arm exoskeleton with scapula motion for shoulder rehabilitation// ICAR '05. 12th International Conference on Advanced Robotics. Seattle: IEEE, 2005: 524-531.
17.	Agur A M R, Dalley A F. Grant’s altas of anatomy. 12th Edition. American: Lippincott Williams & Wilkins, 2009: 923-928.
18.	于长隆. 骨科康复学. 北京: 人民卫生出版社, 2010: 359-380.
19.	葛国强, 张卫锋, 李敬涵, 等. 一种10自由度外骨骼康复机器人结构设计与运动学分析. 机械传动, 2022, 46(8): 131-138,145.
20.	Hubbard I J, Parsons M W, Neilson C, et al. Task-specific training: evidence for and translation to clinical practice. Occup Ther Int, 2009, 16(3-4): 175-189.
21.	Buss S R, Kim J S. Selectively damped least squares for inverse kinematics. J Graph GPU Game Tools, 2005, 10(3): 37-49.
22.	杨震, 杨文玉, 张晓平. 机器人逆运动学的奇异鲁棒性算法. 中国机械工程, 2014, 25(8): 995-1000.
23.	Lv Z Y, Ning D H, Liu P F, et al. PD control with gravity compensation for 3-RPS parallel manipulator// 2023 IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS). Xiangtan: IEEE, 2023: 1744-1749.

1. Guo Z N, Zeng S N, Ling K Y, et al. Experiences and needs of older patients with stroke in China involved in rehabilitation decision-making: a qualitative study. BMC Med Inform Decis Mak, 2024, 24(1): 9-18.
2. Bustrén E L, Sunnerhagen K S, Murphy M A. Movement kinematics of the ipsilesional upper extremity in persons with moderate or mild stroke. Neurorehabil Neural Repair, 2017, 31(4): 376-386.
3. Jones T A, Allred R P, Adkins D L, et al. Remodeling the brain with behavioral experience after stroke. Stroke, 2009, 40(3): 136-138.
4. 彭亮, 侯增广, 王晨, 等. 康复辅助机器人及其物理人机交互方法. 自动化学报, 2018, 44(11): 2000-2010.
5. 姚玉峰, 裴硕, 郭军龙, 等. 上肢康复机器人研究综述. 机械工程学报, 2024, 60(11): 115-134.
6. 李辽远, 韩建海, 李向攀, 等. 上肢康复机器人关键技术研究进展. 机械设计与研究, 2021, 37(6): 28-34.
7. Lee S H, Park G, Cho D Y, et al. Comparisons between end-effector and exoskeleton rehabilitation robots regarding upper extremity function among chronic stroke patients with moderate-to-severe upper limb impairment. Sci Rep, 2020, 10(1): 1806-1814.
8. 李贺立, 杨冬, 杨德志, 等. 双臂机器人避关节极限与避奇异位形优化研究. 科学技术与工程, 2017, 17(3): 98-104.
9. Petrović L, Marić F, Marković I, et al. Trajectory optimization with geometry-aware singularity avoidance for robot motion planning// 2021 21st International Conference on Control, Automation and Systems (ICCAS). Jeju: IEEE, 2021: 1760-1765.
10. Lu L, Zhang L, Fan C, et al. High-order joint-smooth trajectory planning method considering tool-orientation constraints and singularity avoidance for robot surface machining. J Manuf Process, 2022, 80(12): 789-804.
11. Li Y, Wang L. Comprehensive research and analysis on obstacle–singularity–joint limit avoidance of redundant robot. Int J Adv Robot Syst, 2024, 21(1): 1-10.
12. Yang Y M. Research on active–passive training control strategies for upper limb rehabilitation robot. Machines, 2024, 12(11): 784-804.
13. Ju C Q, Chen Z Q, Qin H, et al. Design and control of a cable-driven upper limb exoskeleton robot for rehabilitation// 2023 29th International Conference on Mechatronics and Machine Vision in Practice (M2VIP). Queenstown: IEEE, 2023: 1-6.
14. Li S Y, Su C P, Huang L, et al. Personalized passive training control strategy for a lower limb rehabilitation robot with specified step lengths. Intell Serv Robotics, 2025, 18(9): 137-156.
15. Wang P, Liu L Y, Nan F H, et al. The sliding mode controller with composite reaching law for upper limb rehabilitation robot. Ind Robot, 2025, 52(2): 277-286.
16. Roderick S, Liszka M, Carignan C. Design of an arm exoskeleton with scapula motion for shoulder rehabilitation// ICAR '05. 12th International Conference on Advanced Robotics. Seattle: IEEE, 2005: 524-531.
17. Agur A M R, Dalley A F. Grant’s altas of anatomy. 12th Edition. American: Lippincott Williams & Wilkins, 2009: 923-928.
18. 于长隆. 骨科康复学. 北京: 人民卫生出版社, 2010: 359-380.
19. 葛国强, 张卫锋, 李敬涵, 等. 一种10自由度外骨骼康复机器人结构设计与运动学分析. 机械传动, 2022, 46(8): 131-138,145.
20. Hubbard I J, Parsons M W, Neilson C, et al. Task-specific training: evidence for and translation to clinical practice. Occup Ther Int, 2009, 16(3-4): 175-189.
21. Buss S R, Kim J S. Selectively damped least squares for inverse kinematics. J Graph GPU Game Tools, 2005, 10(3): 37-49.
22. 杨震, 杨文玉, 张晓平. 机器人逆运动学的奇异鲁棒性算法. 中国机械工程, 2014, 25(8): 995-1000.
23. Lv Z Y, Ning D H, Liu P F, et al. PD control with gravity compensation for 3-RPS parallel manipulator// 2023 IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS). Xiangtan: IEEE, 2023: 1744-1749.

Journal of Biomedical Engineering

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