Safety-Critical Control for Dynamical Bipedal Walking with Precise Footstep Placement**This work is partially supported through funding from the Google Faculty Award and NSF Grant IIS-1464337.

This paper presents a novel methodology to achieve dynamic walking for underactu-ated and hybrid dynamical bipedal robots subject to safety-critical position-based constraints. The proposed controller is based on the combination of control Barrier functions and control Lyapunov functions implemented as a state-based online quadratic program to achieve stability under input and state constraints, while simultaneously enforcing safety. The main contribution of this paper is the control design to enable stable dynamical bipedal walking subject to strict safety constraints that arise due to walking over a terrain with randomly generated discrete footholds and overhead obstacles. Evaluation of our proposed control design is presented on a model of RABBIT, a fve-link planar underacted bipedal robot with point feet.