Spatial partitioning for distributed agents driven by a line-of-sight navigation law in a spatiotemporal drift field

We consider the problem of characterizing a Voronoi-like partition of a two-dimensional Euclidean space which encodes information about the proximity relations between a team of spatially distributed aerial/marine vehicles and arbitrary points in the plane. In particular, a point in the plane is assigned to a particular vehicle if the latter can reach this point faster than any other vehicle from the same team. It is assumed that each vehicle is constrained to travel along the line-of-sight direction to its destination point in the presence of a spatiotemporal drift field, which is induced by, say, local winds/currents. We present an efficient scheme for the computation of the Voronoi-like partition which exploits the direct correspondence between the level sets of the Euclidean distance and those of the time-to-go by means of a bijective mapping. Next, we identify a number of important topological properties enjoyed by the generators and the cells of the partition. Finally, we present simulation results using data from real drift fields.