Optimizing Unmanned Underwater Vehicle Surfacing Using a Poisson Process

We present a novel approach for planning locations to surface an unmanned underwater vehicle (UUV) to reset inertial navigation errors by obtaining a GPS fix. Vehicles typically surface at fixed-distance intervals determined by their inertial navigation system performance to maintain acceptable error bounds on navigation. This method, which can result in surfacing in regions with an elevated risk of collision with surface vessels, restricts the means for autonomy to balance the trade-off between surfacing immediately or deferring. The problem of scheduling surfacing locations is further complicated due to the uncertainty between a planned and actual surfacing location, which increases with time submerged. Our approach assumes a spatial point process model for historical maritime traffic that we use to quantify surfacing risk throughout the operational area. Our main contribution is that we model and penalize accumulated navigation uncertainty for each candidate surfacing point of a feasible path. This allows autonomy to balance the trade-off between surfacing risk, navigation performance, and pathlength. The effectiveness of our planner is shown in a numerical illustration. The results show that our planner minimizes path length and number of surfacings while satisfying a constraint on maximum allowable risk.