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Motor Algebra for 3D Kinematics: The Case of the Hand-Eye Calibration

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Abstract

In this paper we apply the Clifford geometric algebra for solving problems of visually guided robotics. In particular, using the algebra of motors we model the 3D rigid motion transformation of points, lines and planes useful for computer vision and robotics. The effectiveness of the Clifford algebra representation is illustrated by the example of the hand-eye calibration. It is shown that the problem of the hand-eye calibration is equivalent to the estimation of motion of lines. The authors developed a new linear algorithm which estimates simultaneously translation and rotation as components of rigid motion.

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Authors and Affiliations

  1. Centro de Investigacion en Matemáticas, Apartado Postal 402, 36000-, Guanajuato, Gto., Mexico

    Eduardo Bayro-Corrochano

  2. GRASP Laboratory, Pennsylvania University, USA

    Kostas Daniilidis

  3. Computer Science Institute, Christian Albrechts University, Preusserstrasse 1-9, 24105, Kiel, Germany

    Gerald Sommer

Authors
  1. Eduardo Bayro-Corrochano
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  2. Kostas Daniilidis
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  3. Gerald Sommer
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Bayro-Corrochano, E., Daniilidis, K. & Sommer, G. Motor Algebra for 3D Kinematics: The Case of the Hand-Eye Calibration. Journal of Mathematical Imaging and Vision 13, 79–100 (2000). https://doi.org/10.1023/A:1026567812984

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