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arXiv · 1909.02198

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

James Ju Heon Lee·Chanyeol Yoo·Stuart Anstee·Robert Fitch
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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.

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James Ju Heon Lee, Chanyeol Yoo, Stuart Anstee, Robert Fitch. 2019-09-05. Efficient Optimal Planning in non-FIFO Time-Dependent Flow Fields. https://arxiv.org/abs/1909.02198

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