Topological heterogeneity and optimality analysis for multiagent formation

In this paper, we extend the results of the previous paper in the 2011 American Control Conference into a more general case. In the previous literature, the topologies for the velocity and position are assumed to be the same. However, in some cases, both topologies are different, even one of them is disconnected, due to a different detection technique. Therefore in this paper, we investigate the topological heterogeneity for the formation control and synchronization protocols. The requirement of connectivity for both topologies is relaxed. Since the choice of the topology in this case is much more available than that of the connected topology, now the question is which one is the best combination of the position and velocity topologies? Here we propose an optimization problem for choosing the topology by considering the tradeoff between the communication cost and convergence rate. To solve this optimization problem numerically, an adjusted binary particle swarm optimization algorithm is developed. Finally, some simulation results are provided to verify our formation and synchronization protocols.