Singularity-free Formation Path Following of Underactuated AUVs: Extended Version

This paper proposes a method for formation path following control of a fleet of underactuated autonomous underwater vehicles. The proposed method combines several hierarchic tasks in a null space-based behavioral algorithm to safely guide the vehicles. Compared to the existing literature, the algorithm includes both inter-vehicle and obstacle collision avoidance, and employs a scheme that keeps the vehicles within given operation limits. The algorithm is applied to a six degree-of-freedom model, using rotation matrices to describe the attitude to avoid singularities. Using the results of cascaded systems theory, we prove that the closed-loop system is uniformly semiglobally exponentially stable. We use numerical simulations to validate the results.