提出一种高效算法，可快速计算机械臂的运动与受力需求。
An $O(n$)-Algorithm for the Higher-Order Kinematics and Inverse Dynamics of Serial Manipulators using Spatial Representation of Twists
- 采用空间旋量表示，实现递归式O(n)计算
- 同时求解四阶正逆运动学与二阶逆动力学
- 适合需要实时控制的高自由度机械臂应用
一般最优控制，特别是基于平坦性的控制，需要计算实现期望运动所需关节力矩/力的一阶和二阶时间导数。为满足计算效率要求，已提出递归的O(n)算法。为获得紧凑且高效的表达形式，最近提出了基于李群的公式，利用体固连和混合表示的旋量与力矩。本文引入了基于空间表示的公式，配套提出四阶正逆运动学与二阶逆动力学算法。所有李群形式的优势在于其可由直接可用的矢量参数化。该方法在7自由度Franka Emika Panda机器人上进行了验证。
原文摘要 · Abstract (English)
Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required computational efficiency, recursive $O(n)$-algorithms were proposed to this end. Aiming at compact yet efficient formulations, a Lie group formulation was recently proposed, making use of body-fixed and hybrid representation of twists and wrenches. In this paper a formulation is introduced using the spatial representation. The second-order inverse dynamics algorithm is accompanied by a fourth-order forward and inverse kinematics algorithm. An advantage of all Lie group formulations is that they can be parameterized in terms of vectorial quantities that are readily available. The method is demonstrated for the 7 DOF Franka Emika Panda robot.
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