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A method for computing the Hessian tensor of loop closing conditions in multibody systems

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Abstract

This paper presents a method for computing the Hessian tensor of loop closing conditions employing the relative coordinate systems for the multibody system dynamics. Based on the efficient Jacobian computation method proposed by Orin et al., the derivatives of Jacobian matrix are evaluated for all combinations of revolute and prismatic joints. It is shown that all cases can be summarized in one simple formula and the Hessian tensor can be computed easily from the elements of the Jacobian matrix.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka, 814-0180, Japan

    Makoto Iwamura

  2. Product Development Division-3, SMC Corporation, Tsukubamirai, Ibaraki, 300-2492, Japan

    Masafumi Nagao

Authors
  1. Makoto Iwamura
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  2. Masafumi Nagao
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Correspondence to Makoto Iwamura.

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Iwamura, M., Nagao, M. A method for computing the Hessian tensor of loop closing conditions in multibody systems. Multibody Syst Dyn 30, 173–184 (2013). https://doi.org/10.1007/s11044-012-9334-7

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  • DOI: https://doi.org/10.1007/s11044-012-9334-7

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