Towards real-time parameter optimization for feasible nonlinear control with applications to robot locomotion

Abstract

This paper considers the application of classical control methods, designed for unconstrained nonlinear systems, to systems with nontrivial input constraints. As shown throughout the literature, unconstrained classical methods can be used to stabilize constrained systems, however, (without modification) these unconstrained methods are not guaranteed to work for a general control problem. In this paper, we propose conditions for which classical unconstrained methods can be guaranteed to exponentially stabilize constrained systems - which we term “feasibility” conditions - and we provide examples of how to construct explicitly feasible controllers. The control design methods leverage control Lyapunov functions (CLF) describing the “desired behavior” of the system; and we claim that in the event that a system's input constraints prevent the production of an exponentially stabilizing input for a particular CLF, a new, locally feasible CLF must be produced. To this end, we propose a novel hybrid feasibility controller consisting of a continuous-time controller which implements a CLF and a discrete parameter update law which finds feasible controller parameters as needed. Simulation results suggest that the proposed method can be used to overcome certain catastrophic infeasibility events encountered in robot locomotion.