Estimation of Rotation and Translation Simultaneously Using Dual Quaternion
Date Issued
2007
Date
2007
Author(s)
Huang, Po-Yen
DOI
zh-TW
Abstract
In this thesis, we use dual-quaternion to replace rotation matrix and translation vector which expressed object’s transformation in usual. The best benefit of dual-quaternion is that it is able to handle rotation and translation simultaneously and apply continuous product of dual-quaternion operating with a kind of special vector－dual vector to express a serious of rotation and translation.. The process of finding the dual-quaternion is to take out corresponding dual-vectors of object before transformation and past. Then we compare those corresponding dual-vectors to find the dual-quaternion expressing rotation and translation of object. We also called this process as closed-form solution of dual-quaternion. The standard method to find closed-form solution presently is to use the matrix relationship of dual-quaternion and dual-vector, and then apply SVD method to solve the equation. We improve this standard method and make the operation simpler.
In the machine vision and robot control, connecting the information of image plane in 2-D observing and object transformation in 3-D world is very important and which is also called hand-eye problem in robot control. We find that dual-quaternion has special relationship in 3-D transformation and 2-D image plane, and use this relationship to estimate object’s transformation from 2-D observing image. Because of the benefit of dual-quaternion－easily to handle and express a serious of transformation, we make above estimation more practically and reality using dual-quaternion. At last, we design a simulation to prove our method has better practicality and is more convenient to estimate 3-D transformation.
Subjects
雙四元數
轉移
估測
dual quaternion
transformation
estimation
Type
thesis
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