Epidemic Synchronization in Robotic Swarms

Clock synchronization in swarms of networked mobile robots is studied in a probabilistic, epidemic framework. In this setting communication and synchonization is considered to be a randomized process, taking place at unplanned instants of geographical rendezvous between robots. In combination with a Markovian mobility model the synchronization process yields overall evolutionary dynamics for first and second conditional moments of synchronization error given geographical position. The established dynamics assume the shape of partial integro-differential equations and the swarm is subsequently studied as an infinite-dimensional optimal control problem. Illustrative numerical examples are given and commented.