Robust and efficient forward, differential, and inverse kinematics using dual quaternions
Robust and efficient forward, differential, and inverse kinematics using dual quaternions
复制标题
DOI：
10.1177/0278364920931948
复制
发表时间：
2020-07
期刊：
影响因子：
--
通讯作者：
Neil T. Dantam
中科院分区：
文献类型：
--
作者：
Neil T. Dantam
机器人运动学的现代方法采用指数公式的乘积，用齐次变换矩阵表示。对偶数上的四元数是一种已建立的替代表示;然而，它们的使用带来了某些挑战：对偶四元数指数和对数包含零角奇点，并且使用对偶四元数的许多常见运算的效率低于矩阵。我们提出了一个新的推导对偶四元数的指数和对数，消除了奇异性，我们表明对偶四元数的隐式表示提供了分析和经验效率的优势相比，矩阵和显式对偶四元数，我们推导出有效的对偶四元数形式的微分和逆位置运动学。从分析上讲，隐式对偶四元数更紧凑，并且对于常见操作（包括链接和指数）需要更少的算术指令。根据经验，我们证明了30-40%的正向运动学和300-500%的逆位置运动学的加速比。这项工作涉及对偶四元数与现代指数坐标，并表明对偶四元数是一个强大的和有效的机器人运动学的表示。
Modern approaches for robot kinematics employ the product of exponentials formulation, represented using homogeneous transformation matrices. Quaternions over dual numbers are an established alternative representation; however, their use presents certain challenges: the dual quaternion exponential and logarithm contain a zero-angle singularity, and many common operations are less efficient using dual quaternions than with matrices. We present a new derivation of the dual quaternion exponential and logarithm that removes the singularity, we show an implicit representation of dual quaternions offers analytical and empirical efficiency advantages compared with both matrices and explicit dual quaternions, and we derive efficient dual quaternion forms of differential and inverse position kinematics. Analytically, implicit dual quaternions are more compact and require fewer arithmetic instructions for common operations, including chaining and exponentials. Empirically, we demonstrate a 30–40% speedup on forward kinematics and a 300–500% speedup on inverse position kinematics. This work relates dual quaternions with modern exponential coordinates and demonstrates that dual quaternions are a robust and efficient representation for robot kinematics.