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O(n) mass matrix inversion for serial manipulators and polypeptide chains using Lie derivatives

Published online by Cambridge University Press:  01 November 2007

Kiju Lee ,
Yunfeng Wang  and
Gregory S. Chirikjian
Kiju Lee
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
Yunfeng Wang
Affiliation:
Department of Mechanical Engineering, The College of New Jersey, Ewing, NJ 08628, USA.
Gregory S. Chirikjian*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
*
*Corresponding author. E-mail: gregc@jhu.edu
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Summary

Over the past several decades, a number of O(n) methods for forward and inverse dynamics computations have been developed in the multibody dynamics and robotics literature. A method was developed by Fixman in 1974 for O(n) computation of the mass-matrix determinant for a serial polymer chain consisting of point masses. In other of our recent papers, we extended this method in order to compute the inverse of the mass matrix for serial chains consisting of point masses. In the present paper, we extend these ideas further and address the case of serial chains composed of rigid-bodies. This requires the use of relatively deep mathematics associated with the rotation group, SO(3), and the special Euclidean group, SE(3), and specifically, it requires that one differentiates real-valued functions of Lie-group-valued argument.

Keywords

Serial manipulatorsMass-matrix inversionForward dynamicsPolymer chainsPolypeptides
Type
Article
Information
Robotica , Volume 25 , Issue 6 , November 2007 , pp. 739 - 750
Copyright
Copyright © Cambridge University Press 2007

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