A method for robust robotic bipedal walking on rough terrain: L1-optimal event-based feedback controller

Abstract

Feedback controller for robotic bipedal walking models can be multi-layered, consisting of low-level continuous-time controller and high-level event-based controller. Stimulated by the success in our preceding study that demonstrates the validity of the l∞-induced norm as an adequate performance measure, we suggest a systematic methodology to design optimal event-based feedback controller for bipedal models walking on rough terrains. More precisely, we first assume that the system is already equipped with a low-level continuous-time feedback controller, capable of stable flat-ground-walking, and then formulate the design problem of the high-level event-based feedback control as the l1-optimal control problem for discrete-time linear systems defined on the linearized Poincarè map. In order to validate the proposed methodology, nonlinear dynamic simulations are conducted with a simple biped model walking on rough terrain. The terrain slope randomly varies at each footstep while the magnitude of slope variation is bounded by some maximum value. Simulation results indicate that the optimal system equipped with the proposed controller can successfully overcome a rough terrain on which the original system could not walk and fall.