Switched Concurrent Learning Adaptive Control for Treadmill Walking Using a Lower Limb Hybrid Exoskeleton

Lower limb hybrid exoskeletons integrate powered mechanisms and functional electrical stimulation (FES) to provide assistive forces and activate muscles for walking. Technical challenges exist to customize the control of these hybrid devices due to the nonlinear and uncertain walking and muscle dynamics of the combined human-exoskeleton system. Different from gait optimization techniques, this article exploits a learning-based strategy to interface a hybrid exoskeleton for treadmill walking. An adaptive control approach provides torque assistance about the hip and knee joints using a four-degrees-of-freedom (DoFs) cable-driven exoskeleton and activates the quadriceps and hamstrings muscle groups via FES. The human-exoskeleton system is modeled with phase-dependent switched pendular dynamics to capture gait phase transitions (i.e., right leg in stance while left leg swings and vice versa). A concurrent learning adaptive controller is designed to achieve kinematic joint tracking and estimate the uncertain parameters in the lower limb dynamics. The stability of the overall switched system is ensured using a multiple Lyapunov function approach and dwell time analysis to guarantee exponential tracking and parameter estimation convergence across gait phase transitions. The developed learning controller was implemented during walking experiments at a constant speed in two nondisabled individuals. To illustrate the tracking benefit of the learning method, the performance of the concurrent learning controller and a classical gradient-based adaptive controller are compared during 8-min treadmill walking trials. The results highlight the better performance of concurrent learning compared with the classical adaptive controller. On average, concurrent learning significantly reduces 22.6% in the mean root-mean-squared (rms) kinematic tracking error ( $e$ ) for the knee and hip joints. Notably, the concurrent learning system demonstrates average parameter convergence in less than 145 s, whereas the classical adaptive control approach fails to exhibit convergence within the 8-min trial duration.