Spatial Repetitive Impedance Learning Control for Robot-Assisted Rehabilitation

In robot-assisted rehabilitation and leg exoskeletons, humans and robots are required to collaboratively complete repetitive tasks with fixed periodic paths. In such applications, impedance learning control can provide variable impedance regulation for improving the performance of physical interactions; however, designing such control is highly challenging owing to the difficulty in modeling human time-varying dynamics. By exploiting the spatial periodicity characteristics of the desired trajectory and human impedance, we propose a novel spatial repetitive impedance learning control strategy to enhance interaction performance. First, a defined spatial operator serves as the mathematics foundation for constructing the robot dynamics in the spatial domain. Then, a spatial impedance learning controller is designed. In this article, time-varying impedance profiles are estimated using spatial full-saturation iterative learning laws, while robotic parameter uncertainties are estimated using the differential adaptation law with projection modification. We validate the uniform convergence of the tracking error through a Lyapunov-like analysis and demonstrate the control effectiveness using an illustrative example. Compared with related results on temporal repetitive learning control, the proposed control approach can enable human–robot system to complete a repetitive task with unspecified speeds according to the users' strengths and motion capacity.