Three-dimensional motion coordination in a time-invariant flowfield

Three-dimensional motion coordination in a flowfield has applications in environmental monitoring with autonomous vehicles. Motion-coordination algorithms designed using a flow-free motion model often fail to converge in even moderate flow speeds. We apply Lyapunov-based methods to design decentralized feedback laws for use in a three-dimensional, time-invariant flowfield that does not exceed the speed of each platform relative to the flow. The control laws stabilize moving formations in a dynamic model of identical particles that travel at constant speed relative to the flow. Specifically, we provide theoretically justified algorithms to stabilize parallel, helical, and circular formations in a three dimensional flowfield. In ongoing work, we seek to extend the three-dimensional motion-coordination framework to address strong and time-varying flowfields that represent more realistic environmental dynamics in the atmosphere and ocean.