Rigidity Theory in SE(2) for Unscaled Relative Position Estimation using only Bearing

TitleRigidity Theory in SE(2) for Unscaled Relative Position Estimation using only Bearing
Publication TypeConference Paper
Year of Publication2014
AuthorsZelazo, D, Franchi, A, Robuffo Giordano, P
Conference Name2014 European Control Conference
Date Published06/2014
Conference LocationStrasbourg, France
KeywordsLocalization of ground robots, Motion control of multiple robots, Rigidity mainenance

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) = R^2 × 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

Citation Key2014f-ZelFraRob
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