Optimal Robust Time-Varying Safety-Critical Control With Application to Dynamic Walking on Moving Stepping Stones

Abstract

This paper presents a novel methodology to handle time-varying safety-critical constraints under high level of model uncertainty with application to dynamic bipedal walking with strict foot-placement constraints. This paper builds off recent work on optimal robust control through quadratic programs that can handle stability, input / state dependent constraints, as well as safety-critical constraints, in the presence of high level of model uncertainty. Under the assumption of bounded uncertainty, the proposed controller strictly guarantees time-varying constraints without violating them. We evaluate our proposed control design for achieving dynamic walking of an underactuated bipedal robot subject to (a) torque saturation constraints (input constraints), (b) contact force constraints (state constraints), and (c) precise time-varying footstep placements (time-varying and safety-critical constraints). We present numerical results on RABBIT, a five-link planar bipedal robot, subject to a large unknown load on its torso. Our proposed controller is able to demonstrate walking while strictly enforcing the above constraints with an unknown load of up to 15 Kg (47% of the robot mass).