Distributed estimation and control for stochastically interacting robots

We introduce a distributed estimation algorithm for use by a collection of stochastically interacting agents. Each agent has both a discrete value and an estimate of the mean of that value taken over all agents. The estimates are updated according to a local rule when pairs of agents interact. In this paper we prove that the ensemble average of the estimates converges to the correct global average. We then use the estimate information to control the agents to a desired average value. Furthermore, we demonstrate the algorithm experimentally using the Programmable Parts Testbed.