High-Order Control Barrier Function for Constraining Position in Motorized Rehabilitative Cycling

Hannah M. Sweatland, Axton Isaly, Warren E. Dixon

Abstract: Control barrier functions (CBFs) have commonly been used to encode the safety requirements of a dynamical system and to constrain the control input to guarantee forward invariance of a safe set. High­order control barrier functions (HOCBFs) are a method of ensuring the safety of a system of high relative degree. The method developed in this paper can be applied to a variety of nonlinear systems with more general dynamics than previous works, and is demonstrated on a motorized rehabilitative cycle of relative degree two. A motor controller is designed to constrain the crank position to a time­varying user­defined safe range. Because of the uncertain and nonlinear dynamics of the system, robust control methods are borrowed from Lyapunov theory to develop worst-case controllers that render the intersection of a series of sets forward invariant. The controller is designed so that it provides minimal assistance within the safe range, maximizing the efforts of the rider and facilitating more effective therapy.