Dynamic Collision Avoidance Using Velocity Obstacle-Based Control Barrier Functions

Abstract: Designing safety-critical controllers for acceleration-controlled unicycle robots is challenging, as control inputs may not appear in the constraints of control Lyapunov functions(CLFs) and control barrier functions (CBFs), leading to invalid controllers. Existing methods often rely on state-feedback-based CLFs and high-order CBFs (HOCBFs), which are computationally expensive to construct and fail to maintain effectiveness in dynamic environments with fast-moving, nearby obstacles. To address these challenges, we propose constructing velocity obstacle-based CBFs (VOCBFs) in the velocity space to enhance dynamic collision avoidance capabilities, instead of relying on distance-based CBFs that require the introduction of HOCBFs. Additionally, by extending VOCBFs using variants of VO, we enable reactive collision avoidance between robots. We formulate a safety-critical controller for acceleration-controlled unicycle robots as a mixed-integer quadratic programming (MIQP), integrating state-feedback-based CLFs for navigation and VOCBFs for collision avoidance. To enhance the efficiency of solving the MIQP, we split the MIQP into multiple sub-optimization problems and employ a decision network to reduce computational costs. Numerical simulations demonstrate that our approach effectively guides the robot to its target while avoiding collisions. Compared to HOCBFs, VOCBFs exhibit significantly improved dynamic obstacle avoidance performance, especially when obstacles are fast-moving and close to the robot. Furthermore, we extend our method to distributed multi-robot systems.