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. ((c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the observability properties of a particular type of nonlinear system that often arises in multi-robot localization problems. By constructing an extended relative position measurement graph (ERPMG), the authors integrate various influencing factors of observability, such as the motion inputs and relative position measurements of robots. The authors analyze the observability of such systems by establishing a connection between the nonlinear observability matrix and the spectral matrix of the ERPMG. They derive a necessary and sufficient observability condition for the multi-robot system represented by the spectral graph properties of the ERPMG for the first time. The authors also develop an algorithm to efficiently check observability and validate their theoretical results through simulation experiments.