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  • 1
    Electronic Resource
    Electronic Resource
    Motor Algebra for 3D Kinematics: The Case of the Hand-Eye Calibration (2000)
    Springer
    Journal of mathematical imaging and vision 13 (2000), S. 79-100 
    Details
    ISSN: 1573-7683
    Keywords: computer vision ; kinematics ; visual robotics ; Clifford algebra ; geometric algebra ; rotors ; motors ; screws ; hand-eye calibration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026567812984
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The Motor Extended Kalman Filter: A Geometric Approach for Rigid Motion Estimation (2000)
    Springer
    Journal of mathematical imaging and vision 13 (2000), S. 205-228 
    Details
    ISSN: 1573-7683
    Keywords: computer vision ; Clifford algebra ; geometric algebra ; kinematics ; dynamics ; rotors ; motors ; screws ; Kalman filter techniques ; extended Kalman filter ; visual robotics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the motor algebra for linearizing the 3D Euclidean motion of lines is used as the oretical basis for the development of a novel extended Kalman filter called the motor extended Kalman filter (MEKF). Due to its nature the MEKF can be used as online approach as opposed to batch SVD methods. The MEKF does not encounter singularities when computing the Kalman gain and it can estimate simultaneously the translation and rotation transformations. Many algorithms in the literature compute the translation and rotation transformations separately. The experimental part demonstrates that the motor extended Kalman filter is an useful approach for estimation of dynamic motion problems. We compare the MEKF with an analytical method using simulated data. We present also an application using real images of a visual guided robot manipulator; the aim of this experiment is to demonstrate how we can use the online MEKF algorithm. After the system has been calibrated, the MEKF estimates accurately the relative position of the end-effector and a 3D reference line. We believe that future vision systems being reliably calibrated will certainly make great use of the MEKF algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011293515286
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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