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
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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 -