Hierarchical Planning in Time-Dependent Flow Fields for Marine Robots

We present an efficient approach for finding shortest paths in flow fields that vary as a sequence of flow predictions over time. This approach is applicable to motion planning for slow marine robots that are subject to dynamic ocean currents. Although the problem is NP-hard in general form, we incorporate recent results from the theory of finding shortest paths in time-dependent graphs to construct a polynomial-time algorithm that finds continuous trajectories in time-dependent flow fields. The algorithm has a hierarchical structure where a graph is constructed with time-varying edge costs that are derived from sets of continuous trajectories in the underlying flow field. We show that the continuous algorithm retains the time complexity and path quality properties of the discrete graph solution, and demonstrate its application to surface and underwater vehicles including a traversal along the East Australian Current with an autonomous marine vehicle. Results show that the algorithm performs efficiently in practice and can find paths that adapt to changing ocean currents. These results are significant to marine robotics because they allow for efficient use of time-varying ocean predictions for motion planning.