Nonlinear observability analysis of multi-robot cooperative localization

In this paper, the observability property of relative position-based cooperative localization is investigated by using spectral graph theory. First, a directed graph, called Extended Relative Measurement Graph (ERMG), is constructed in which all influencing factors of observability are integrated. Then, the rank equivalence is established between the nonlinear observability matrix and the configuration matrix associated with a reduced ERMG. Then, a necessary and sufficient observability condition is proved. Moreover, an analytic relation is derived by which the configuration matrix can be directly attained according to fundamental cycles of a reduced ERMG. Then, it is shown that the observability is uniquely determined by the number and placement of fundamental cycles in a reduced ERMG. The minimum number of fundamental cycles required to guarantee an n-robot system observable is given. Additionally, a sufficient condition is provided by which reduced ERMGs can be designed to enable an n-robot system observable. Finally, a graph-based observability checking algorithm is developed which greatly improves the computation efficiency. Some illustrative examples are presented to validate the theoretical results.