Stabilization of Collective Motion in a Time-Invariant Flowfield on a Rotating Sphere

We provide Lyapunov-based control laws that stabilize relative equilibria in a model consisting of particles that travel on the surface of a rotating sphere in a time-invariant flowfield. These control laws are of interest because they have applications in planetary-scale mobile sensing networks in air and sea. A rotating sphere is introduced so that the particles are subject to the Coriolis effect that occurs on the Earth. A point vortex generates a time-invariant flowfield in the model and depicts naturally occurring phenomena such as ocean currents, hurricanes, and tornadoes. We show that particles can be steered into circular formations in a time-invariant flow using a theoretically justified algorithm. Simulations show that the same algorithm stabilizes circular formations in a time-varying flow, and this draws particular interest because it suggests that formations of autonomous vehicles could potentially be used in real-world applications.