Spatial Detection of Areas of Abrupt Change by Robotic Networks

This paper studies robotic sensor networks performing spatial detection of areas of rapid change in physical phenomena. We encode the task by means of an objective function, called wombliness, which measures the change of the spatial field along the open polygonal curve defined by the positions of the robotic sensors. This curve can become self-intersecting when evolving along the gradient flow of the wombliness. Borrowing tools from discontinuous dynamics and hybrid systems, we design an algorithm that allows for network re-positioning, splitting, and merging, while guaranteeing the monotonic evolution of the wombliness. We analyze its convergence properties and illustrate our approach in simulations.