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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.

Isokinetic muscle strength training is a type of rehabilitation therapy that can effectively improve the motor dysfunction of limbs and enhance joint muscle strength. In active isokinetic training, how to plan the speed reasonably and improve the performance of speed control to fit individualized needs is the core problem of isokinetic muscle strength training equipment control. In this study, a control strategy for isokinetic muscle strength training equipment is proposed, which identifies the user’s motion intention and performs speed planning according to the user’s motion participation so that the equipment produces a dynamic damping effect. This ensures active interaction between the user and the equipment and meets the force-speed requirements of elbow joint muscle training. To handle the uncertain disturbance in the training process, a linear extended state observer is used to estimate the disturbance term, and a tracking differentiator and nonlinear error feedback control are used to improve the speed tracking performance. The experimental results show that the proposed control scheme realizes effective speed control in isokinetic muscle strength training. Note to Practitioners—The bottleneck of isokinetic muscle strength training equipment control system lies in how to plan the speed according to the patient’s movement intention reasonably, and how to improve the performance of speed control in the process of rehabilitation training. This paper designs a speed auto disturbance rejection control strategy for isokinetic muscle strength training system with external interference and model uncertainty in practical application. The experimental results show that the performance of the controller is better than the traditional PI controller, and it can realize isokinetic muscle training. This study provides a method for practitioners interested in developing control systems for isokinetic rehabilitation training equipment.