Distributed bearing-based localization under switching graph topologies

Abstract

This paper addresses a distributed localization problem for n (n ≥ 2)-agent systems defined in d (d ≥ 2)-dimensional space under undirected switching graph topologies. It is assumed that each agent in the formation can measure the bearing to the neighboring agents and communicate with them, and at least one agent has access to its global position. Novel distributed position observers are designed under which each agent estimates its global position using its velocity, the relative bearing measurements, and the position estimates of neighboring agents received over a communication network. The main contribution of this work is that i) it relaxes the classical bearing rigidity assumption (typically required) for bearing-based localization problems addressed in the current literature and ii) it covers time-varying bearing measurements and/or time-varying graph topologies. Furthermore, the efficiency of the proposed observers is guaranteed by the rigorous mathematical analysis (i.e., uniform global exponential stability of the estimation error) along with illustrative simulation results.