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Partial Derivatives of the Inverse Mass Matrix of Multibody Systems via Its Factorization

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1 Author(s)
Muller, A. ; Inst. of Mechatronics, Chemnitz Univ. of Technol.

A closed expression for repeated partial derivatives of the inverse mass matrix is developed. It rests on the factorization of the inverse mass matrix in terms of a single configuration-dependent block-diagonal matrix. Thereupon, partial derivatives of the inverse mass matrix are given in terms of derivatives of the diagonal blocks. It turns out that the derivatives are nonvanishing only for a single block of this block-diagonal matrix. The result for open kinematic chains is extended to the mass matrix of mechanisms with kinematic loops

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Robotics, IEEE Transactions on  (Volume:23 ,  Issue: 1 )