Graph-based observability analysis for mutual localization in multi-robot systems

In this paper, we investigate the observability properties of a type of nonlinear system, which often arises from multi-robot mutual localization problems. An extended relative position measurement graph (ERPMG) is constructed to integrate all influencing factors of observability, including the motion inputs and relative position measurements of robots. We analyze the observability of such systems by bridging the connection between the nonlinear observability matrix and the spectral matrix of the ERPMG. A necessary and sufficient observability condition for MRS represented by spectral graph properties of the ERPMG is derived for the first time. We then develop an algorithm to efficiently check the observability and further validate the proposed theoretical results by simulation experiments.