Synergistic control barrier functions with application to obstacle avoidance for nonholonomic vehicles

Control barrier functions (CBFs) have recently emerged as a means to ensure safety of controlled dynamical systems. CBFs are suitable for obstacle avoidance, where the CBF is often constructed from the distance and relative velocity between the vehicle and the obstacle. For vehicles required to maintain non-zero forward speed, ordinary (non-hybrid) CBFs cannot ensure safety due to vanishing control authority when the vehicle is oriented directly towards the obstacle. In this paper, synergistic CBFs are proposed, which is an intuitive extension of CBFs using ideas from synergistic Lyapunov functions. A synergistic CBF for obstacle avoidance for nonholonomic vehicles is constructed by shifting the orientations with vanishing control authority. This induces a penalty for traversing the obstacle in the counterclockwise or clockwise direction, where a logic variable is used to determine the preferred direction. The performance of the CBF is illustrated by a case study.