Three-Dimensional Motion Coordination in a Spatiotemporal Flowfield

Decentralized algorithms to stabilize 3-D formations of unmanned vehicles in a flowfield that varies in space and time have applications in environmental monitoring in the atmosphere and ocean. In this note, we provide a Lyapunov-based control design to steer a system of self-propelled particles traveling in three dimensions at a constant speed relative to a spatiotemporal flowfield. We assume that the flow is known locally to each particle and that it does not exceed the particle speed. Multiple particles can be steered to form 3-D parallel or helical formations in a flowfield. Also presented are motion coordination results for a special case of the 3-D model in which the particles travel in a circular formation on the surface of a rotating sphere.