Examples of quaternion

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Again, = 1 for the reals, = 2 for 2 2 the complexes, and = 4 for the quaternion.
Defining the problem in the space of planar quaternions results in a definition of the parallel manipulator workspace as the intersection of quadratic equations.
In this section we will illustrate how the previously presented robust controller can be extended to enable the use of unit quaternions.
The noise is added as absolute value to the unit rotation quaternion and as relative value to the translation vector.
While we expect our readers to be familiar with real and complex matrices, it is reasonable to consider quaternion matrices as well.
In this paper, we describe a new hand-eye calibration method, which applies the rotation quaternions in the motion constraints of hand-eye geometry.
We then extended our result to unit quaternion based end-effector orientation to illustrate the flexibility of our controller design.
Sections 45 to 60 then outline the development of quaternions from 1843 onward.
Quaternion based orientation tracking errors in experimetal studies.
The quaternion algebra is therefore seen to be a subset of the geometric algebra of 3-space.
As a final remark, the closed-loop system with quaternion feedback (35) is nonlinear.
It can be shown12 that the vector part of this quaternion coincides with (34), which has indeed motivated the use of the same symbol.
If the notion of combining them had occurred to him, he might have been led to the quaternions; but those he seems to have altogether failed to perceive.
The breakthrough of the quaternion feedback scheme stands in its applicability for any magnitude of the orientation error, since it is inherently based on a singularity-free representation of orientation.
Zhuang8 et al. based on the quaternion algebra, propose a linear solution that allows the simultaneous computation of these two kinematic transformations.
On the other hand, assigning the equivalent angle and axis directly leads to specifying a desired trajectory in terms of a unit quaternion via (8), (9).

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