Adaptive and Distributed Coordination Algorithms for Mobile Sensing Networks

Consider n sites evolving within a convex polygon according to one of the following interaction laws: (i) each site moves away from the closest other site or polygon boundary, (ii) each site moves toward the furthest vertex of its own Voronoi polygon, or (iii) each site moves toward a geometric center (centroid, circumcenter, incenter, etc) of its own Voronoi polygon. These interaction laws give rise to strikingly simple dynamical systems whose behavior remains largely unknown. Which are their critical points? What is their asymptotic behavior? Are they optimizing any aggregate function? In what way do these local interactions give rise to distributed systems? Are they of any engineering use in robotic coordination problems and in the design of mobile sensor networks? This paper addresses these questions.