Exploring scalar fields using multiple sensor platforms: Tracking level curves

Autonomous mobile sensor networks are employed to measure large scale environmental scalar fields. Yet an optimal strategy for mission design addressing both the cooperative motion control and the collaborative sensing is still under investigation. We develop one strategy which uses four moving sensor platforms to explore a noisy scalar field defined in the plane; each platform can only take one measurement at a time. We derive a Kalman filter in conjunction with a nonlinear filter to produce estimates for the field value, the gradient and the Hessian along the averaged trajectories of the moving platforms. The shape of the platform formation is designed to minimize error in the estimates, and a cooperative control law is designed to asymptotically achieve the optimal formation. We develop a motion control law to allow the center of the platform formation to move along level curves of the averaged field. Convergence of the control laws are proved, and performance of both the filters and the control laws are demonstrated in simulated ocean fields.