Stabilization of Collective Motion in a Time-Invariant Flowfield

Abstract

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 maritime domains can be pushed off course by strong and variable environmental dynamics. However, most existing cooperative-control algorithms are based on simple motion models that do not include a flowfield. Existing models that include the flowfield often include speed control to compensate for the flow. In this paper, we describe a constant-speed self-propelled particle model that explicitly incorporates a time-invariant flowfield. Each vehicle is represented by a Newtonian particle subject to a gyroscopic steering control. We describe the Lyapunov-based design of decentralized control algorithms that stabilize collective motion in a known flowfield. In the case of a spatially variable flow, we provide an algorithm to stabilize synchronized motion, in which all of the particles move in the same direction, and circular motion, in which all of the particles orbit an inertially fixed point at a constant radius. For a spatially invariant flow, we provide an algorithm to stabilize balanced motion, in which the particle position centroid is inertially fixed, and symmetric circular formations, in which the particle spacing around a circle is temporally regulated. Via the latter algorithm, we provide a method of stabilizing a circular formation in which the particles are evenly spaced in time and the formation is centered on a moving target. The theoretical results are illustrated with two numerical examples based on applications in environmental monitoring and target surveillance.