Worst-case optimal average consensus estimators for robot swarms

Average consensus estimators enable robots in a communication network to calculate the mean of their local inputs in a distributed manner. Many distributed control methods for robot swarms rely on these estimators. The performance of such estimators depends on their design and the network topology. For mobile sensor networks, this topology may be unknown, making it difficult to design average consensus estimators for optimal performance. We introduce a design method for proportional-integral (PI) average consensus estimators that decouples estimator synthesis from network topology. This method also applies to the more general internal model (IM) estimator, yielding extended PI estimators that improve convergence rates without increasing communication costs. In simulations over many geometric random graphs, the extended PI estimator consistently reduces the estimation error settling time by a factor of five.