-- 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.

This paper proposes a novel approach for modeling and controlling nonlinear systems with varying parameters. The approach introduces the use of a parameter-varying Koopman operator (PVKO) in a lifted space, which provides an efficient way to understand system behavior and design control algorithms that account for underlying dynamics and changing parameters. The PVKO builds on a conventional Koopman model by incorporating local time-invariant linear systems through interpolation within the lifted space. This paper outlines a procedure for identifying the PVKO and designing a model predictive control using the identified PVKO model. Simulation results demonstrate that the proposed approach improves model accuracy and enables predictions based on future parameter information. The feasibility and stability of the proposed control approach are analyzed, and their effectiveness is demonstrated through simulation.