Cooperative control of an autonomous sampling network in an external flow field

Cooperative steering controls enable mobile sampling platforms to conduct synoptic, adaptive surveys of dynamic spatiotemporal processes by appropriately regulating the space-time separation of their sampling trajectories. Sensing platforms in the air and sea are often pushed off course by strong and variable flow fields such as atmospheric winds and ocean currents. However, many existing cooperative control algorithms are based on simple motion models that do not include a drift vector field. In this paper, we describe a planar motion model that explicitly incorporates a uniform and constant flow field. We also provide decentralized control algorithms that stabilize circular motion, in which all of the particles travel around a circle with a fixed center, and times-play circular motion, in which the vehicle velocities are synchronized modulo a constant time delay. The proposed time-splay circular formation algorithm - a composition of the circular formation algorithm and a delay differential equation on the N-torus - generates a set of vehicle trajectories that collectively sample each point on the circle at a regular interval.