浮遊ベースロボットの高次再帰的動力学アルゴリズムのリー群定式化
Lie Group Formulation of Recursive Dynamics Algorithms of Higher Order for Floating-Base Robots
浮遊ベースのロボットツリー構造に対して、ニュートン・オイラー法や多体慣性法などの動力学アルゴリズムの高次時間微分をリー群上で計算する手順を提案し、12自由度の空中マニピュレータで検証した。
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著者: Ahmed Ali, Chiara Gabellieri, Antonio Franchi
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
In this paper, we describe procedures for computing higher-order time derivatives of the Lie-group Newton-Euler, Articulated-Body Inertia, and hybrid dynamics algorithms for floating-base trees, where the base configuration evolves on SE(3) and the attached mechanism is an open kinematic tree with configuration on the (n1+n2)-dimensional manifold T^{n1} \times R^{n2}, using spatial representation of twists. After presenting the algorithms, we collect the resulting recursions into closed-form equations of motion, identifying an admissible Coriolis matrix satisfying the passivity property, and showing that the articulated inertia tensor remains unchanged across all time derivatives. We then apply the developed methods to a 12-DoF aerial manipulator to derive analytical expressions for its geometric forward and inverse dynamics along with their first time derivatives whereas the numerical simulations successfully evaluate these dynamics up to fifth order. Finally, to demonstrate their practical utility, we benchmark the proposed extensions and show that, in the considered tests, their computational cost scales quadratically with the derivative order, whereas the automatic-differentiation baseline exhibits exponential scaling.
