Safety-Guaranteed Real-Time Trajectory Planning for Underwater Vehicles in Plane-Progressive Waves

Trajectory planning is a central task for operating autonomous underwater vehicles. However, strong disturbances in underwater environments such as currents and waves can cause large deviations between a planned trajectory and the vehicle, resulting in obstacle collision. In this paper, we address this problem by modelling wave disturbances first as a time-varying and position-independent and then as a time-varying and position-dependent function. A Hamilton-Jacobi differential game formulation is then used to compute a value function and level set. Obstacles in an environment are subsequently augmented by this set, and model predictive control is then used for trajectory planning whilst guaranteeing safety. We find that modelling disturbances in this way results in less-conservative safety-guaranteed trajectory planning compared to the case of time-invariant disturbances.