Necessary and sufficient conditions for localization of multiple robot platforms

Fan Zhang, University of Pennsylvania
R. Vijay Kumar, University of Pennsylvania
Guilherme A. S. Pereira, Universidade Federal de Minas Gerais

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Postprint version. Published in Proceedings of the 2004 ASME Design Engineering Technical Conference (DETC 2004), 28th Biennial Mechanisms and Robotics Conference, Volume 2A, pages 13-22.

Abstract

In this paper, we consider the problem of cooperatively localizing a formation of networked robots/vehicles in SE(2). First, we propose necessary and sufficient conditions to establish when a team of robots with heterogeneous sensors can be localized. We then show how these conditions are analogous to well-known results in the literature on kinematics of planar mechanisms. We show how localization is equivalent to solving a system of nonlinear closure equations. Depending on what sensors are available for each robot, the multirobot formation can be modeled as a sensing graph consisting of vertices representing robots and edges corresponding to sensory information. We establish conditions that must be satisfied by this graph and show how this graph influences estimates of positions and orientations of the robots in a team through experiments and simulations.