3D relative pose estimation from six distances

Nikolas Trawny, Xun S. Zhou, Stergios Roumeliotis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationRobotics
Subtitle of host publicationScience and Systems V
EditorsJose A. Castellanos, Yoky Matsuoka, Jeff Trinkle
PublisherMIT Press Journals
Number of pages8
ISBN (Print)9780262514637
StatePublished - Jan 1 2010
EventInternational Conference on Robotics Science and Systems, RSS 2009 - Seattle, United States
Duration: Jun 28 2009Jul 1 2009

Publication series

NameRobotics: Science and Systems
ISSN (Print)2330-7668
ISSN (Electronic)2330-765X


OtherInternational Conference on Robotics Science and Systems, RSS 2009
Country/TerritoryUnited States


Dive into the research topics of '3D relative pose estimation from six distances'. Together they form a unique fingerprint.

Cite this