Cooperative detection of areas of rapid change in spatial fields

This paper proposes a distributed coordination algorithm for robotic sensor networks to detect boundaries that separate areas of rapid change of planar spatial phenomena. We consider an aggregate objective function, termed wombliness, to measure the change of the spatial field along the closed polygonal curve defined by the location of the sensors. We encode the network task as the optimization of the wombliness and characterize the smoothness properties of the objective function. In general, the complexity of the spatial phenomena may make the gradient flow cause self-intersections in the polygonal curve described by the network. We design the hybrid wombling algorithm that allows for network splitting and merging and guarantees local convergence to the critical configurations of the wombliness, while monotonically optimizing it. The technical approach combines ideas from statistical estimation, dynamical systems, and hybrid modeling and design.