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Necessary and Sufficient Conditions for Localization of Multiple Robot Platforms

[+] Author Affiliations
Fan Zhang, Vijay Kumar

University of Pennsylvania, Philadelphia, PA

Guilherme A. S. Pereira

Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil

Paper No. DETC2004-57010, pp. 13-21; 9 pages
  • ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B
  • Salt Lake City, Utah, USA, September 28–October 2, 2004
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4695-4 | eISBN: 0-7918-3742-4
  • Copyright © 2004 by ASME


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.

Copyright © 2004 by ASME
Topics: Robots



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