Practical multiagent rendezvous through modified circumcenter algorithms

We present a class of modified circumcenter algorithms that allow a group of agents to achieve “practical rendezvous” when they are only able to take noisy measurements of their neighbors. Assuming a uniform detection probability in a disk of radius σ about each neighbor's true position, we show how initially connected agents converge to a practical stability ball. More precisely, a deterministic analysis allows us to guarantee convergence to such a ball under r-disk graph connectivity in 1D under the condition that r/σ be sufficiently large. A stochastic analysis leads to a similar convergence result in probability, but for any r/σ>1, and under a sequence of switching graphs that contains a connected graph within bounded time intervals. We include several simulations to discuss the performance of the proposed algorithms.