Dynamic Altitude Control for Motion Coordination in an Estimated Shear Flow

Abstract

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. Nomenclature NNumber of particles in the system k Particle index; 1, . . . , N