Consensus Collision‐Free Trajectory Planning for Multi‐AUV Formation Gathering

Formation gathering of multiple autonomous underwater vehicles (AUVs) is a fundamental prerequisite for cooperative underwater missions. It enables AUVs initially located at dispersed positions to form a prescribed geometric configuration before formation‐based exploration, observation, or survey tasks. Each AUV must reach its assigned terminal position and heading while ensuring coordinated motion and inter‐vehicle safety. Trajectory planning must simultaneously account for inter‐AUV collision avoidance, vehicle kinematic constraints, motion feasibility, and limited underwater acoustic communication. This paper proposes a consensus‐based distributed trajectory planning method for multi‐AUV formation gathering by integrating finite‐control‐set model predictive control (FCS‐MPC) with optimal reciprocal collision avoidance (ORCA) constraints. Before trajectory execution, common initial mission information is obtained through polling‐based acoustic broadcasting. Based on this shared information, each AUV independently generates a consistent gathering trajectory set without requiring continuous inter‐vehicle communication. The terminal pose of each AUV is determined from the target pose of the leader AUV and the prescribed formation geometry. A staged guidance strategy is introduced to improve convergence through position approach and terminal heading regulation. Meanwhile, ORCA‐based velocity‐space constraints are incorporated into the FCS‐MPC framework to generate collision‐free and feasible motion subject to constraints on surge speed, yaw rate, and minimum turning radius. The proposed method was evaluated through randomized simulations and lake trials. In 50 randomized simulation runs involving six AUVs, formation gathering was successfully completed in all runs without inter‐AUV collisions. The minimum inter‐AUV distance was 26.82 m. The maximum terminal position and heading errors were 0.954 m and , respectively, and the average planning time was 2.662 s. In lake trials involving three Wukong 1000 AUVs, UHF radio was used to emulate polling‐based acoustic broadcasting for initial mission‐information synchronization. The AUVs then executed the independently planned trajectories. The average tracking error of each AUV was below 1 m, while the terminal position and heading errors remained within the prescribed tolerances of 10 m and , respectively. These results demonstrate the safety, feasibility, and implementation potential of the proposed method for multi‐AUV formation gathering without continuous inter‐AUV communication.