Interpolating Industrial Robot Orientation with Hermite Spline Curve Based on Logarithmic Quaternion

基于对数四元数的工业机器人Hermite样条曲线姿态插值

¹ Laboratory of Contemporary Design and Integrated Technology, Northwestern Polytechnical University, Xi'an 710072, China
² College of Engineering, Honghe University, Mengzi 661100, China

Received: 25 December 2018

Abstract

Smooth orientation planning has an important influence on the working quality and service life as for industrial robot. Based on the logarithmic quaternion, a compact method to map a spline curve from Cartesian space to quaternion space is proposed, and consequently the multi-orientation smooth interpolation of quaternion is realized. Combining with the relevant example case, the detailed method and steps of multi-orientation interpolation are introduced for mapping Hermite spline curve into quaternion space, and the validity of the principle is verified by using the example case. The present multi-orientation smooth interpolation of quaternion has the characteristics of simple construction, easy implementation and intuitive understanding. The method is not only applicable to multi-orientation interpolation of quaternion with Hermite spline curve, but also can extended to the spline curves such as Bezier spline and B-spline.

摘要

平滑的姿态规划对工业机器人工作质量、使用寿命有着重要的影响。以对数四元数为基础，提出一种从笛卡尔空间样条曲线映射到四元数空间的方法，从而实现四元数多姿态平滑插值。结合相关算例，详细介绍了笛卡尔空间Hermite样条曲线映射到时四元数空间的多姿态插值方法与步骤，验证了该方法进行四元数多姿态插值的合理性。提出的四元数多姿态平滑插值具有构造方法简单、易于实现、直观易理解的特点。该方法除了适用于Hermite样条曲线的四元数多姿态插值，还可延伸到贝赛尔曲线、B样条曲线等样条曲线上。