  This paper presents a safety-critical locomotion control framework for
quadrupedal robots. Our goal is to enable quadrupedal robots to safely navigate
in cluttered environments. To tackle this, we introduce exponential Discrete
Control Barrier Functions (exponential DCBFs) with duality-based obstacle
avoidance constraints into a Nonlinear Model Predictive Control (NMPC) with
Whole-Body Control (WBC) framework for quadrupedal locomotion control. This
enables us to use polytopes to describe the shapes of the robot and obstacles
for collision avoidance while doing locomotion control of quadrupedal robots.
Compared to most prior work, especially using CBFs, that utilize spherical and
conservative approximation for obstacle avoidance, this work demonstrates a
quadrupedal robot autonomously and safely navigating through very tight spaces
in the real world. (Our open-source code is available at
github.com/HybridRobotics/quadruped_nmpc_dcbf_duality, and the video is
available at youtu.be/p1gSQjwXm1Q.)
