Autonomous underwater gliders use buoyancy control to achieve forward propulsion via a sawtooth-like, rise-and-fall trajectory. Because gliders are slow-moving relative to ocean currents, glider control must consider the effect of oceanic flows. In previous work, we proposed a method to control underwater vehicles in the (horizontal) plane by describing such oceanic flows in terms of streamlines, which are the level sets of stream functions. However, the general analytical form of streamlines in 3D is unknown. In this paper, we show how streamline control can be used in 3D environments by assuming a 2.5D model of ocean currents. We provide an efficient algorithm that acts as a steering function for a single rise or dive component of the gliders sawtooth trajectory, integrate this algorithm within a sampling-based motion planning framework to support long-distance path planning, and provide several examples in simulation in comparison with a baseline method. The key to our methods computational efficiency is an elegant dimensionality reduction to a 1D control region. Streamline-based control can be integrated within various sampling-based frameworks and allows for online planning for gliders in complicated oceanic flows.
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