Stochastic Path Planning for Autonomous Underwater Gliders with Safety Constraints

Autonomous underwater gliders frequently execute extensive missions with high levels of uncertainty due to limitations of sensing, control and oceanic forecasting. Glider path planning seeks an optimal path with respect to conflicting objectives, such as travel cost and safety, that must be explicitly balanced subject to these uncertainties. In this paper, we derive a set of recursive equations for state probability and expected travel cost conditional on safety, and use them to implement a new stochastic variant of FMT* in the context of two types of objective functions that allow a glider to reach a destination region with minimum cost or maximum probability of arrival given a safety threshold. We demonstrate the framework using three simulated examples that illustrate how user-prescribed safety constraints affect the results.