Assist-As-Needed Backstepping Control of Lower-Limb Exoskeletons with Human Effort Estimation and Comparative Evaluation Against Sliding Mode and PID Controllers

Abstract

In this paper, we propose an assist-as-needed (AAN) backstepping control scheme for a lower-limb exoskeleton with nonlinear dynamics and uncertain human–robot interactions. The main objective is to achieve a good trajectory tracking capability while adaptively controlling the assistance of the robot according to the user’s effort. The adopted dynamic model is nonlinear, which includes joint dynamics and external human interaction torque. This allows for the derivation of the tracking error formulation. The backstepping control law, formulated based on the filtered tracking error, ensures stable closed-loop performance with bounded tracking errors. We incorporate an AAN scaling framework based on estimated human effort to regulate the overall control torque as a convex combination of the nominal backstepping torque and the impedance-based assistance torque. The proposed controller was tested by numerical simulations and was compared with the sliding mode control (SMC) and the proportional–integral–derivative (PID) control. The overall root-mean-square tracking error for the proposed controller was 0.0962 rad, while for the SMC controller and PID controller, it was 0.0819 rad and 0.1246 rad, respectively. Moreover, the proposed controller reduced the peak human–robot interaction torque to 14.68 N·m compared to 15.36 N·m for SMC and 15.81 N·m for PID, adaptively controlling assistance based on the applied effort of the user. The assistance ratio went down from an average of 0.7988 in the low-effort condition to 0.6960 in the higher-effort condition, indicating effective adaptation while maintaining stable tracking performance. Although the PID controller achieved the lowest torque-variation index, the proposed controller achieved a more favorable trade-off among tracking accuracy, adaptive assistance, and acceptable torque smoothness. Finally, the proposed AAN backstepping controller achieved a practical trade-off between tracking accuracy, adaptive assistance, torque smoothness, and interaction safety, suggesting its potential in rehabilitation and assistive exoskeleton applications.