Observability-based Optimization of Coordinated Sampling Trajectories for Recursive Estimation of a Strong, Spatially Varying Flowfield

Autonomous vehicles are effective environmental sampling platforms whose sampling performance can be optimized by path-planning algorithms that drive vehicles to specific regions of the operational domain containing the most informative data. In this paper, we apply tools from nonlinear observability, nonlinear control, and Bayesian estimation to derive a multi-vehicle control algorithm that steers vehicles to an optimal sampling formation in an estimated flowfield. Sampling trajectories are optimized using the empirical observability gramian, which quantifies the sensitivity of output measurements to variations of the flowfield parameters. We reconstruct the parameters of the flowfield from noisy flow measurements collected along the sampling trajectories using a recursive Bayesian filter.