Stepwise Cooperative Trajectory Planning for Multiple BUVs Based on Temporal–Spatial Bezier Curves

Biomimetic underwater vehicles (BUVs) are important instrumentation in applications such as water quality monitoring and underwater detection. In this article, we study the cooperative trajectory planning problem for multiple BUVs and propose a stepwise trajectory planning algorithm based on the temporal–spatial Bezier curves to enable cooperative formations. We introduce the time variable into the 3-D Bezier curve, designing a 4-D temporal–spatial Bezier curve. Considering the various physical constraints of the BUV, we obtain a smooth and feasible trajectory using particle swarm optimization (PSO) when taking the shortest trajectory distance as the optimization goal. On this basis, we propose a method to perform cooperative trajectory planning and efficient obstacle avoidance replanning for multiple BUVs by integrating the real-time collision avoidance, real-time detection, and underwater complex terrain constraints. We verify the effectiveness of the proposed cooperative planning method through simulation and comparison.