  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 algorithm's
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 method's
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.
