Cooperative Formation Control of Multiple Deep-Sea Mining Vehicles Based on an Improved Virtual Spring Method

To address cooperative control challenges of multiple deep-sea mining vehicles under strong disturbances, kinematic constraints, and obstacle interference, this paper proposes an improved virtual spring-based formation control method. Firstly, a leaderfollower framework is established to ensure stable formation maintenance through relative distance and bearing constraints. Then, an enhanced virtual spring strategy is developed for path planning and obstacle avoidance. By introducing a relative collision region and a directional projection mechanism, the proposed method overcomes target unreachability and improves avoidance efficiency. Finally, simulation results demonstrate that the method shortens avoidance paths, reduces velocity fluctuations, and enhances formation stability and convergence smoothness compared with conventional approaches, verifying its effectiveness and engineering applicability in deep-sea environments.