Turning Circle-based Control Barrier Function for Efficient Collision Avoidance of Nonholonomic Vehicles

-- This paper presents a new control barrier function (CBF) designed to improve the efficiency of collision avoidance for nonholonomic vehicles. Traditional CBFs typically rely on the shortest Euclidean distance to obstacles, overlooking the limited heading change ability of nonholonomic vehicles. This often leads to abrupt maneuvers and excessive speed reductions, which is not desirable and reduces the efficiency of collision avoidance. Our approach addresses these limitations by incorporating the distance to the turning circle, considering the vehicle's limited maneuverability imposed by its nonholo-nomic constraints. The proposed CBF is integrated with model predictive control (MPC) to generate more efficient trajectories compared to existing methods that rely solely on Euclidean distance-based CBFs. The effectiveness of the proposed method is validated through numerical simulations on unicycle vehicles and experiments with underactuated surface vehicles. Generating collision-free trajectories is essential for mobile robots and autonomous vehicles, and control barrier functions (CBFs) have gained significant research attention as a crucial tool in achieving this goal. CBFs ensure safety by guaranteeing the forward invariance of a defined safe set [1], [2]. When combined with model predictive control (MPC), which is based on optimal control theory, constraints on state variables can be applied [3], allowing for the determination of integrated planning and control inputs that ensure safe and reliable collision avoidance.