Stable cooperative vehicle distributions for surveillance

A mathematical model for the study of the behavior of a spatially distributed group of heterogeneous vehicles is introduced. We present a way to untangle the coupling between the assignment of any vehicle's position and the assignment of all other vehicle positions by defining general sensing and moving conditions that guarantee that even when the vehicles' motion and sensing are highly constrained, they ultimately achieve a stable emergent distribution. The achieved distribution is optimal in the sense that the proportion of vehicles allocated over each area matches the relative importance of being assigned to that area. Based on these conditions, we design a cooperative control scheme for a multivehicle surveillance problem and show how the vehicles' maneuvering and sensing abilities, and the spatial characteristics of the region under surveillance, affect the desired distribution and the rate at which it is achieved.