Variable Structure Cooperative Avoidance Control for Multiple Vehicles in a Three-Dimensional Space

This paper presents a variable structure control approach for collision avoidance and trajectory tracking of multiple vehicles in 3D obstacle environments. Instead of relying only on barrier or avoidance functions, this method utilizes a sliding surface derived from the time derivative of a collision risk assessment function to trigger the avoidance control. Under this control framework, vehicles encountering avoidance conflicts smoothly converge toward the predefined sliding surface, achieving a collision avoidance strategy that balances conservatism and aggressiveness without compromising system safety. Auxiliary trajectories with avoidance information feedback are introduced to guide the vehicles, which autonomously facilitate the coordination between tracking and avoidance, eliminating the need for prioritization. This paper provides theoretical guarantees for the convergence and safety of the system through Lyapunov analysis. Two simulations, one involving multiple vehicles with obstacles and the other with dense obstacles, are conducted to showcase the effectiveness and reliability of the approach.