Distributed Estimation and State Assignment for Stochastically Interacting Robots*

We consider a distributed tracking problem where agents interact locally with limited information. Each agent maintains both a discrete value and an estimate of the mean of that value taken over all agents. In earlier work, we designed an estimator that converged to the desired value with a finite variance and here, we derive a different estimator with zero variance. We design the controller and estimator separately, prove their simultaneous convergence and stability, finally demonstrate the results in simulation. While we present this work in the context of of stochastic self-assembly, the algorithm can be applied other settings.