Motion planning for vehicles under the influence of flow fields can benefit from the idea of streamline-based planning, which exploits ideas from fluid dynamics to achieve computational efficiency. Important to such planners is an efficient means of computing the travel distance and direction between two points in free space, but this is difficult to achieve in strong incompressible flows such as ocean currents. We propose two useful distance functions in analytical form that combine Euclidean distance with values of the stream function associated with a flow field, and with an estimation of the strength of the opposing flow between two points. Further, we propose steering heuristics that are useful for steering towards a sampled point. We evaluate these ideas by integrating them with RRT* and comparing the algorithms performance with state-of-the-art methods in an artificial flow field and in actual ocean prediction data in the region of the dominant East Australian Current between Sydney and Brisbane. Results demonstrate the methods computational efficiency and ability to find high-quality paths outperforming state-of-the-art methods, and show promise for practical use with autonomous marine robots.
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