  We present a novel method of optimal robust control through quadratic
programs that offers tracking stability while subject to input and state-based
constraints as well as safety-critical constraints for nonlinear dynamical
robotic systems in the presence of model uncertainty. The proposed method
formulates robust control Lyapunov and barrier functions to provide guarantees
of stability and safety in the presence of model uncertainty. We evaluate our
proposed control design on dynamic walking of a five-link planar bipedal robot
subject to contact force constraints as well as safety-critical precise foot
placements on stepping stones, all while subject to model uncertainty. We
conduct preliminary experimental validation of the proposed controller on a
rectilinear spring-cart system under different types of model uncertainty and
perturbations.
