Control Barrier Functions for Safe Admittance Control of a Rehabilitation Cycle for DMD

Emily J. Griffis, Wanjiku A. Makumi, Hannah M. Sweatland, Kimberly J. Stubbs, Tanja Taivassalo, Donovan J. Lott, Warren E. Dixon

Abstract: Duchenne muscular dystrophy (DMD) is a progressive type of muscular dystrophy that causes a steady degradation of muscle fibers and leads to a progressive loss of muscle strength and functional abilities in young boys. Recent studies have shown that rehabilitative motor-assisted cycling can potentially delay loss of functional abilities in individuals with DMD. However, previous results of motor-assisted cycling for DMD participants only consider open-loop control schemes. In this paper, a motor-assisted stationary rehabilitation cycle is developed for DMD participants. A dual-objective control scheme is developed for the motor control input of the developed rehabilitative device. Specifically, a control barrier function (CBF) is designed to restrict the cadence of the rider within a user-defined desired cadence range to maximize rehabilitative efforts. A closed-loop adaptive admittance control scheme is developed to provide indirect torque tracking while the cadence of the rider is within the desired region. A Lyapunov-like stability analysis is used to guarantee asymptotic tracking of the admittance errors within the desired cadence range and uniform global asymptotic stability of the safe set.