Fused-like angles: replacement for roll-pitch-yaw angles for a six-degree-of-freedom grating interferometer

Abstract

Representation of orientation is important in a six-degree-of-freedom grating interferometer but only a few studies have focused on this topic. Roll-pitch-yaw angles, widely used in aviation, navigation, and robotics, are now being brought to the field of multi-degree-of-freedom interferometric measurement. However, the roll-pitch-yaw angles are not the exact definitions the metrologists expected in interferometry, because they require a certain sequential order of rotations and may cause errors in describing complicated rotations. The errors increase as the tip and tilt angles of the grating increase. Therefore, a replacement based on fused angles in robotics is proposed and named “fused-like angles.” The fused-like angles are error-free, so they are more in line with the definitions in grating interferometry and more suitable for six-degree-of-freedom measurements. Fused-like angles have already been used in research on the kinematic model and decoupling algorithm of the six-degree-of-freedom grating interferometer.

摘要

光栅姿态角表达方法是六自由度光栅干涉测量的重要课题, 但仅有少量相关研究. 目前, 广泛用于航空航天、 导航和机器人领域的导航角 (roll-pitch-yaw) 被引入六自由度光栅干涉测量领域. 然而, 因导航角存在固有旋转顺序, 在描述绕多个测量轴的复杂旋转时会引起溯源偏差, 且该偏差随光栅偏摆角度增加而增大, 并不符合干涉系统中的精确定义. 基于机器人领域的融合角 (fused angles) 表达法, 本文提出 “无偏溯源角 (fused-like angles)” 表达法, 因无偏溯源角不会引起溯源偏差, 更加符合光栅干涉仪中的定义, 从而更适合六自由度测量. 提出的无偏溯源角已应用于六自由度光栅干涉的运动模型和解耦算法研究.