SUMMARYOver 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.

中文翻译：

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使用李导数对串行操纵器和多肽链进行 O(n) 质量矩阵求逆

摘要在过去的几十年中，许多○(n) 正向和逆向动力学计算方法已在多体动力学和机器人学文献中得到发展。Fixman 在 1974 年开发了一种方法○(n) 计算由点质量组成的系列聚合物链的质量矩阵行列式。在我们最近的其他论文中，我们扩展了这种方法，以便计算由点质量组成的串行链的质量矩阵的逆。在本文中，我们进一步扩展了这些想法，并解决了由刚体组成的串行链的情况。这需要使用与旋转组相关的相对较深的数学，所以(3) 和特殊的欧几里得群，东南(3)，具体来说，它要求对李群值参数的实值函数进行微分。