Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

This research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.