Title :
Rigidity theory in SE(2) for unscaled relative position estimation using only bearing measurements
Author :
Zelazo, Daniel ; Franchi, Antonio ; Giordano, Paolo Robuffo
Author_Institution :
Fac. of Aerosp. Eng., Technion - Israel Inst. of Technol., Haifa, Israel
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.
Keywords :
mobile robots; multi-robot systems; position control; bearing-only measurements; directed bearing rigidity matrix; distributed estimator; infinitesimally rigid framework; multirobot team; rigidity theory; special Euclidean group; unscaled relative position estimation; unscaled relative positions; Estimation; Jacobian matrices; Position measurement; Robot sensing systems; Vectors;
Conference_Titel :
Control Conference (ECC), 2014 European
Conference_Location :
Strasbourg
Print_ISBN :
978-3-9524269-1-3
DOI :
10.1109/ECC.2014.6862558