Safety-Critical Planning and Control for Dynamic Obstacle Avoidance Using Control Barrier Functions

Dynamic obstacle avoidance is a challenging topic for optimal control and optimization-based trajectory planning problems. Many existing works use Control Barrier Functions (CBFs). CBFs are typically formulated based on the distance to obstacles, or integrated with path planning algorithms as a safety enhancement tool. However, these approaches usually require knowledge of the obstacle boundary equations or have very slow computational efficiency. In this paper, we propose a framework based on model predictive control (MPC) with discrete-time high-order CBFs (DHOCBFs) to generate a collision-free trajectory. The DHOCBFs are first obtained from convex polytopes generated through grid mapping, without the need to know the boundary equations of obstacles. Additionally, a path planning algorithm is incorporated into this framework to ensure the global optimality of the generated trajectory. We demonstrate through numerical examples that our framework allows a unicycle robot to safely and efficiently navigate tight, dynamically changing environments with both convex and nonconvex obstacles. By comparing our method to established CBF-based benchmarks, we demonstrate superior computing efficiency, length optimality, and feasibility in trajectory generation and obstacle avoidance.