Balancing cyclic pursuit by means of set-theoretic techniques

We propose a decentralized and non cooperative algorithm for estimation and control in a multi-agent system of oscillators to achieve a balanced circular formation. Each agent gathers an uncertain measurement of its phase distance from other agents only when they are in its proximity. Based on this uncertain and intermittent data and on the a priori knowledge of the nominal (e.g. uncontrolled) agent's velocities, we employ an estimation algorithm to reconstruct the relative angular positions. The algorithm combines the information coming from the collected measures with the information on the agents' dynamics, and its convergence is proved by means of Interval Analysis. Interesting connection are highlighted with contractions and fractals. Then, we develop a bang-bang controller to achieve a balanced circular formation. The ovelty of the approach is that the balanced formation is achieved by using proximity sensors rather than distance transducers. Moreover, the bang-bang control strategy is designed so that the control goal is achieved even when the range of the sensors is lower than the desired spacing distance. The e?ectiveness of the approach is illustrated through extensive numerical simulations.