Multi-Agent Formations and Sensor Networks

We investigate three intertwined problems concerned with distributed cooperative control of groups of autonomous mobile agents. These problems are the consensus problem in mobile networks, the localization problem in sensor networks and the formation maintenance problem in autonomous robotic teams. In Vicsek's model of the network consensus problem, a group of agents are moving in the plane with the same speed but with different headings. Each agent always knows the headings of its "neighbors'' and its heading is updated using a local rule based on the average of the headings of its neighbors. One feature of the Vicsek problem which sharply distinguishes it from other consensus problems is that each agent's neighbors change with time, because all agents are in motion. We present a graphical approach which generalizes the existing explanation for why Vicsek's agents are able to reach a common heading. By taking this graphical approach, we are able to further establish results on estimating worst case convergence rates and dealing with modified Vicsek's models with measurement delays and asynchronous events. We have proved that for the modified Vicsek's model the conditions under which consensus is achieved are essentially the same as the conditions under which consensus is achieved in the synchronous and delay-free case. We briefly discuss a sequential algorithm called Sweeps which can effectively localize with high probability most of the uniquely localizable nodes in a network even when node density is low and most of the existing localization techniques fail. We also use tools in Distance Geometry to tackle sensor network localization problem with distance measurement errors. Using concepts from switched adaptive control theory, we provide a provably correct solution to the problem of maintaining the position of a point modelled mobile autonomous agent in a moving formation in the plane using only range measurements to three of its neighbors. The performance of the resulting system degrades gracefully in the face of measurement and miss-alignment errors, provided the measurement errors are not too large.