Rigidity theory in SE(2) for unscaled relative position estimation using only bearing measurements

Daniel Zelazo, Antonio Franchi, Paolo Robuffo Giordano

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

30 Citations (Scopus)

Abstract

This work considers the problem of estimating the unscaled relative positions of a multi-robot team in a common reference frame from bearing-only measurements. Each robot has access to a relative bearing measurement taken from the local body frame of the robot, and the robots have no knowledge of a common reference frame. An extension of rigidity theory is made for frameworks embedded in the special Euclidean group SE(2) = R2 × S1. We introduce definitions describing rigidity for SE(2) frameworks and provide necessary and sufficient conditions for when such a framework is infinitesimally rigid in SE(2). We then introduce the directed bearing rigidity matrix and show that an SE(2) framework is infinitesimally rigid if and only if the rank of this matrix is equal to 2|V| - 4, where |V| is the number of agents in the ensemble. The directed bearing rigidity matrix and its properties are then used in the implementation and convergence proof of a distributed estimator to determine the unscaled relative positions in a common frame. Simulation results are given to support the analysis.

Original languageEnglish
Title of host publication2014 European Control Conference, ECC 2014
Place of PublicationPiscataway, NJ
PublisherIEEE
Pages2703-2708
Number of pages6
ISBN (Electronic)978-3-9524269-1-3
DOIs
Publication statusPublished - 22 Jul 2014
Externally publishedYes
Event13th European Control Conference, ECC 2014 - Strasbourg, France
Duration: 24 Jun 201427 Jun 2014

Conference

Conference13th European Control Conference, ECC 2014
CountryFrance
CityStrasbourg
Period24/06/1427/06/14

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