Quaternion Approach for Pose Planning of Two-Axis Mechanism
Date Issued
2014
Date
2014
Author(s)
Hu, Zhao-Qing
Abstract
To describe the displacement of a rigid body in 3-dimensional space , the “point” associated to the center of the mass of the rigid body is considered. The displacement of this point will represent the displacement of the rigid body. There are many matured algorithms have been developed to obtain a smoothed translation trajectory. To describe the pose of a rigid body , on the other hand , is much more complicated compared to that of the displacement. Since the rotation of the coordinate frame is involved , the concept of “point” only is not enough , to deal with the rotational operations. We use the unit quaternion to describe the pose of a rigid body. By using the mapping of the log function , the unit quaternion can be transformed to a 3-dimensional vector. The map of pose , which is based on the transformed 3-dimensional vector , is proposed in this thesis. The matured algorithm of smoothed displacement trajectory planning then can be applied to the pose map. Finally , the smoothed pose trajectory is obtained via the mapping of exponential function. The pose trajectory planning of the popular two-axis mechanism in our daily life is investigated. The smoothed trajectory , the obstacle avoiding , and the short route are demonstrated in our work.
Subjects
Rigid body
Pose
Unit Quaternion
smooth trajectory
obstacle avoiding
Two-axis mechanism
Type
thesis
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