提出高阶递推动力学算法，用于浮基机器人在SE(3)上的高效计算。
Lie Group Formulation of Recursive Dynamics Algorithms of Higher Order for Floating-Base Robots
- 基于李群框架构建高阶导数递推算法，适用于浮基机械臂系统。
- 实现12自由度飞行机械臂的几何正逆动力学及其一阶导数的解析表达。
- 相比自动微分，计算开销仅随阶数平方增长，适合高阶动力学应用。
本文描述了用于浮基树状结构机器人的高阶时间导数计算方法，其中基座构型在SE(3)上演化，连杆机构为配置位于(n1+n2)维流形T^{n1}×R^{n2}的开链结构，采用空间速度表示。给出算法后，将递推结果整合为闭式运动方程，识别出满足无源性条件的柯里奥利矩阵，并证明关节惯性张量在所有时间导数下保持不变。随后应用于12-DoF空中机械臂，推导其几何正逆动力学及一阶导数的解析表达式；数值模拟成功验证了五阶动力学求解。最后通过基准测试表明，在所考虑测试中，该方法的计算成本随导数阶数呈二次增长，而自动微分基线则呈指数增长。
原文摘要 · Abstract (English)
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.
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