Dynamic Altitude Control for Motion Coordination in an Estimated Shear Flow

Windfields present a challenge to multi-vehicle coordination in applications such as environmental sampling. The presence of a windfield can disrupt inter-vehicle spacing such that the group covers less area, expends energy at a faster rate, strays from a desired formation, or provides irregular measurement data. However, an autonomous or remotely piloted vehicle can also take advantage of the vertical variation of a windfield to maintain a desired inertial speed and to coordinate its motion with other vehicles. This paper presents results for motion coordination in an estimated flowfield with wind shear using a three-dimensional self-propelled particle model with a dynamic altitude control. The paper derives conditions specifying the feasibility of speed-regulated trajectories and Lyapunov-based decentralized control algorithms to stabilize parallel formations in a known, uniform shear flow and symmetric circular formations in a known vortex flow. These algorithms are extended to unknown flowfields by presenting a distributed, recursive Bayesian filter that provides local estimates of the flow from noisy flowspeed measurements, allowing particles to utilize flowfield estimates in the control. Theoretical results are illustrated using numerical simulations.