Coordinate-free formulation of a 3-2-1 wire-based tracking device using Cayley-Menger determinants

descriptionPublicationkeyboard_double_arrow_right Article , Conference object 02 Mar 2004 Italy, Spain Publisher:IEEEJournal:2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422), volume 1, pages 355-361

Authors: THOMAS F.; OTTAVIANO, Erika; ROS L.; CECCARELLI M.;

doi: 10.1109/robot.2003.1241621

handle: 10261/30266 , 11580/6157

Coordinate-free formulation of a 3-2-1 wire-based tracking device using Cayley-Menger determinants

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Abstract

This paper deals with the problem of estimating the pose of a rigid moving object by measuring the length of six wires attached to it. Among all possible locations for the attachments on the moving object, the "3-2-1" configuration exhibits the highest number of favorable properties. A closed-form coordinate-free solution to the forward kinematics of this particular configuration is given in terms of Cayley-Menger determinants. The proposed formulation is mathematically more tractable compared to previous ones because all terms are determinants with geometric meaning. This accommodates a more thorough investigation of the properties of the device and leads to formulas whose numerical conditioning is independent from the chosen reference frames.

This work was supported by the project 'Resolución de sistemas de ecuaciones cinemáticas para la simulación de mecanismos, posicionado interactivo de objetos y conformación de moléculas' (070-722).

IEEE International Conference on Robotics and Automation (ICRA), 2003, Taipei (Taiwán)

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Countries

Italy, Spain

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Keywords

Automation: Robots, Robotics, Robots, Robots [Automation]

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