TY - GEN

T1 - 3D relative pose estimation from six distances

AU - Trawny, Nikolas

AU - Zhou, Xun S.

AU - Roumeliotis, Stergios

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In this paper, we present three fast, hybrid numericalgebraic methods to solve polynomial systems in floating point representation, based on the eigendecomposition of a so-called multiplication matrix. In particular, these methods run using standard double precision, use only linear algebra packages, and are easy to implement. We provide the proof that these methods do indeed produce valid multiplication matrices, and show their relationship. As a specific application, we use our algorithms to compute the 3D relative translation and orientation between two robots, based on known egomotion and six robotto- robot distance measurements. Equivalently, the same system of equations arises when solving the forward kinematics of the general Stewart-Gough mechanism. Our methods can find all 40 solutions, trading off speed (0.08s to 1.5s, depending on the choice of method) for accuracy.

AB - In this paper, we present three fast, hybrid numericalgebraic methods to solve polynomial systems in floating point representation, based on the eigendecomposition of a so-called multiplication matrix. In particular, these methods run using standard double precision, use only linear algebra packages, and are easy to implement. We provide the proof that these methods do indeed produce valid multiplication matrices, and show their relationship. As a specific application, we use our algorithms to compute the 3D relative translation and orientation between two robots, based on known egomotion and six robotto- robot distance measurements. Equivalently, the same system of equations arises when solving the forward kinematics of the general Stewart-Gough mechanism. Our methods can find all 40 solutions, trading off speed (0.08s to 1.5s, depending on the choice of method) for accuracy.

UR - http://www.scopus.com/inward/record.url?scp=84959504091&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959504091&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84959504091

SN - 9780262514637

T3 - Robotics: Science and Systems

SP - 233

EP - 240

BT - Robotics

A2 - Castellanos, Jose A.

A2 - Matsuoka, Yoky

A2 - Trinkle, Jeff

PB - MIT Press Journals

T2 - International Conference on Robotics Science and Systems, RSS 2009

Y2 - 28 June 2009 through 1 July 2009

ER -