Null-Space-Based Prescribed-Time Formation Control With Collision and Obstacle Avoidance

This paper studies the distributed prescribed-time formation tracking control for nonlinear second-order multi-agent systems with collision risk in a null-space-based behavioral control architecture. First, a simplified distributed observer is designed to accurately estimate the position information of a virtual leader within a prescribed time. Additionally, we introduce a switching mechanism and potential-like terms to design the desired states that can simultaneously achieve obstacle avoidance and formation. Subsequently, a sliding mode formation control scheme is proposed to track the desired trajectory generated by the null-space projection between behaviors. Utilizing Lyapunov stability theory, theoretical results for task design and trajectory tracking are obtained. Finally, numerical simulation verifies the effectiveness and superiority of the proposed method.