  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 glider's 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 method's
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.
