Formation Path Following Control of Underactuated AUVs -- With Proofs

This paper proposes a novel method for formation path following of multiple underactuated autonomous underwater vehicles. The method combines line-of-sight guidance with null-space-based behavioral control, allowing the vehicles to follow curved paths while maintaining the desired formation. We investigate the dynamics of the path-following error using cascaded systems theory, and show that the closed-loop system is uniformly semi-globally exponentially stable. We validate the theoretical results through numerical simulations.