Efficient Optimal Planning in non-FIFO Time-Dependent Flow Fields

TL;DR

This paper introduces a polynomial-time algorithm for solving the continuous-time non-FIFO shortest path problem in flow fields with piecewise-constant travel times, relevant for autonomous ocean vehicles affected by currents.

Contribution

It presents the first polynomial-time solution for non-FIFO flow fields with piecewise-constant edge functions, extending shortest path algorithms to this complex setting.

Findings

Algorithm efficiently solves non-FIFO shortest path in polynomial time.

Embeds the algorithm within an asymptotically optimal sampling framework.

Demonstrates effectiveness on ocean vortex models and graph examples.

Abstract

We propose an algorithm for solving the time-dependent shortest path problem in flow fields where the FIFO (first-in-first-out) assumption is violated. This problem variant is important for autonomous vehicles in the ocean, for example, that cannot arbitrarily hover in a fixed position and that are strongly influenced by time-varying ocean currents. Although polynomial-time solutions are available for discrete-time problems, the continuous-time non-FIFO case is NP-hard with no known relevant special cases. Our main result is to show that this problem can be solved in polynomial time if the edge travel time functions are piecewise-constant, agreeing with existing worst-case bounds for FIFO problems with restricted slopes. We present a minimum-time algorithm for graphs that allows for paths with finite-length cycles, and then embed this algorithm within an asymptotically optimal sampling-based framework to find time-optimal paths in flows. The algorithm relies on an efficient data structure to represent and manipulate piecewise-constant functions and is straightforward to implement. We illustrate the behaviour of the algorithm in an example based on a common ocean vortex model in addition to simpler graph-based examples.