Spatiotemporal Cooperative Guidance Law with Singularity-Free Obstacle Avoidance for Multiple Flight Vehicles

This paper develops a distributed cooperative guidance law for the spatiotemporal cooperative arrival of underactuated flight vehicles with uncontrollable axial acceleration under obstacle avoidance constraints. First, a singularity-free obstacle avoidance guidance law is proposed based on a linear projection function to avoid singularity-induced surges in acceleration commands. The proposed law has a simple structure and bounded magnitude, and it ensures that the flight vehicles safely avoid obstacle regions. Then, error dynamics theory is adopted to design a cooperative guidance law for arrival angle control and arrival time synchronization, which guarantees that the coordination errors of the flight vehicles converge to zero before reaching the target. Moreover, a buffer zone is constructed around each obstacle, which provides a distance-dependent transition region. Accordingly, a continuous and smooth weighting function is designed to shift the guidance priority from cooperative guidance to obstacle avoidance, thereby avoiding abrupt jumps in acceleration commands during task switching. Finally, the effectiveness of the proposed guidance law is verified through numerical simulations in typical scenarios and Monte Carlo experiments.