Motion Control and Singular Perturbation Algorithms for Lower Limb Rehabilitation Robots

Yanchun Xie¹Anna Wang²Xue Zhao³Yang Jiang⁴Yao Wu⁴Hailong Yu^1*

• ¹Department of Orthopaedics, General Hospital of Northern Theater Command, Shenyang, China
• ²Department of Burns and plastic Surgery General Hospital of Northern Theater Command, Shenyang, China
• ³Benedictine University, Daniel L. Goodwin College of Busines, Chicago, United States
• ⁴Faculty of Robot Science and Engineering, Northeastern University, Shenyang, Liaoning Province, China

To better assist patients with lower limb injuries in their rehabilitation training, this paper focuses on motion control and singular perturbation algorithms and their practical applications. First, the paper conducts an in-depth analysis of the mechanical structure of such robots and establishes detailed kinematics and dynamics models. An optimal S-type planning algorithm is proposed, transforming the S-type planning into an iterative solution problem for efficient and accelerated trajectory planning using dynamic equations. This algorithm comprehensively considers joint range of motion, speed constraints, and dynamic conditions, ensuring the smoothness and continuity of motion trajectories.Second, a zero-force control method is introduced, incorporating friction terms into the traditional dynamic equations and utilizing the LuGre friction model for friction analysis to achieve zero-force control. Furthermore, to address the multi-scale dynamic system characteristics present in rehabilitation training, a control method based on singular perturbation theory is proposed. This method enhances the system's robustness and adaptability by simplifying the system model and optimizing controller design, enabling it to better accommodate complex motion requirements during rehabilitation. Finally, experiments verify the correctness of the kinematics and optimal S-type trajectory planning. In lower limb rehabilitation robots, zero-force control can better assist patients in rehabilitation training for lower limb injuries, while the singular perturbation method improves the accuracy, response speed, and robustness of the control system, allowing it to adapt to individual rehabilitation needs and complex motion patterns. The novelty of this paper lies in the integration of the singular perturbation method with the LuGre friction model, significantly enhancing the precision of joint dynamic control, and improving controller design through the introduction of a torque deviation feedback mechanism, thereby increasing system stability and response speed. Experimental results demonstrate significant improvements in tracking error and system response compared to traditional methods, providing patients with a more comfortable and safer rehabilitation experience.