Fast terminal sliding mode control with rapid reaching law for a pediatric gait exoskeleton system

Abstract

The parametric variations and external perturbations in the coupled subject-exoskeleton system delay and hinder effective gait tracking in clinical rehabilitation. This problem becomes more challenging in the case of the pediatric exoskeleton system. In this work, to address this benchmark challenge, a fast terminal sliding mode with a rapid reaching law (FTSM-RRL) control scheme is introduced for an uncertain lower-extremity exoskeleton aimed at assisting pediatric gait under different walking speeds. At first, the computer-aided design of the gait exoskeleton system is demonstrated with details of the desired gait trajectories of a male boy aged 12 years (weight: 40 kg, height: 132 cm). A fast terminal sliding mode controller is proposed with a varied exponential approaching rule to guarantee the rapid convergence of system states on the sliding manifold and then towards the origin in a finite period. After that, an upper limit criterion is involved within the reaching control law to compensate for the adverse effects of uncertainties and disturbances as a lumped parameter. Lyapunov’s theory is presented to ensure the expeditious convergence of the tracking error in the reaching and sliding phases. The proposed FTSM-RRL strategy is incorporated to obtain the desired trajectory tracking at slow, self-selected, and fast walking speeds. From numerical experiments, the proposed FTSM-RRL controller is found to be consistently effective ( \(> 71\%\) in X-direction and \(> 62\%\) in Y-direction) over the PID controller and ( \(> 7\%\) in X-direction and \(> 10\%\) in Y-direction) over the FTSM-ERL controller. In joint space, the proposed FTSM-RRL control consistently surpasses both PID and FTSM-ERL controls in tracking hip movement. While the proposed controller outperforms PID and FTSM-ERL for knee joint tracking, the extent of improvement diminishes at higher speeds. For ankle joint tracking, the proposed control exhibits substantial enhancement at slow speeds but comparatively poorer performance at self-selected and fast speeds when compared to PID control. However, FTSM-RRL consistently outperforms FTSM-ERL across all speeds for ankle joint tracking. Compared to FTSM-ERL control, the proposed FTSM-RRL control accelerates the hip and knee joint sliding surface convergence by 0.52s and 0.24s (slow walking), 0.55s and 0.33s (self-selected walking), and 0.61s and 0.09s (fast walking). The results obtained in this study ensure fast and efficient passive-assist gait training for the pediatric groups using exoskeleton technology.