Generating contour plots using multiple sensor platforms

We prove a convergent strategy for a group of mobile sensors to generate contour plots, i.e., to automatically detect and track level curves of a scalar field in the plane. The group can consist of as few as four mobile sensors, where each sensor can take only a single measurement at a time. The shape of the formation of mobile sensors is determined to minimize the least mean square error in the estimates of the scalar field and its gradient. The algorithm to generate a contour plot is based on feedback control laws for each sensor platform. The control laws serve two purposes: to guarantee that the center of the formation moves along one level curve at unit speed; and to stabilize the shape of the formation. We prove that both goals can be achieved asymptotically. We show simulation results that illustrate the performance of the control laws in noisy environments.