Efficient Optimal Planning in nonFIFO TimeDependent Flow Fields
Abstract
We propose an algorithm for solving the timedependent shortest path problem in flow fields where the FIFO (firstinfirstout) 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 timevarying ocean currents. Although polynomialtime solutions are available for discretetime problems, the continuoustime nonFIFO case is NPhard 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 piecewiseconstant, agreeing with existing worstcase bounds for FIFO problems with restricted slopes. We present a minimumtime algorithm for graphs that allows for paths with finitelength cycles, and then embed this algorithm within an asymptotically optimal samplingbased framework to find timeoptimal paths in flows. The algorithm relies on an efficient data structure to represent and manipulate piecewiseconstant 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 graphbased examples.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.02198
 Bibcode:
 2019arXiv190902198L
 Keywords:

 Computer Science  Robotics;
 Computer Science  Data Structures and Algorithms
 EPrint:
 10 pages, 20 figures