Multi-query TDSP for Path Planning in Time-varying Flow Fields

Many applications of path planning in time-varying flow fields, particularly in areas such as marine robotics and ship routing, can be modelled as instances of the time-varying shortest path (TDSP) problem. Although there are no known polynomial-time solutions to TDSP in general, our recent work has identified a tractable case where the flow is modelled as piecewise constant. Extending this method to allow for computational reuse in larger multi-query problems, however, requires additional thought. This paper shows that the piecewise-linear form of the cost function employed in previously work can be used to build an analogy of a shortest path tree, thereby enabling optimal concatenation of sub-problem solutions in the absence of an optimal substructure, and without uniform time discretisation. We present a framework for multi-query TDSP that finds an optimal path that passes through a defined sequence of waypoints and is computationally efficient. Performance comparison is provided in simulation that shows large (up to 100x) speedup compared to a naive approach. This result is significant for applications such as ship routing, where route evaluation is a desirable capability.