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Examples ofquaternion

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Again, = 1 for the reals, = 2 for 2 2 the complexes, and = 4 for thequaternion.

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Defining the problem in the space of planar quaternions results in a definition of the parallel manipulator workspace as the intersection of quadratic equations.

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In this section we will illustrate how the previously presented robust controller can be extended to enable the use of unit quaternions.

From theCambridge English Corpus

The noise is added as absolute value to the unit rotationquaternionand as relative value to the translation vector.

From theCambridge English Corpus

While we expect our readers to be familiar with real and complex matrices, it is reasonable to considerquaternionmatrices as well.

From theCambridge English Corpus

In this paper, we describe a new hand-eye calibration method, which applies the rotation quaternions in the motion constraints of hand-eye geometry.

From theCambridge English Corpus

We then extended our result to unitquaternionbased end-effector orientation to illustrate the flexibility of our controller design.

From theCambridge English Corpus

Sections 45 to 60 then outline the development of quaternions from 1843 onward.

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Quaternionbased orientation tracking errors in experimetal studies.

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Thequaternionalgebra is therefore seen to be a subset of the geometric algebra of 3-space.

From theCambridge English Corpus

As a final remark, the closed-loop system withquaternionfeedback (35) is nonlinear.

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It can be shown12 that the vector part of thisquaternioncoincides with (34), which has indeed motivated the use of the same symbol.

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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.

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The breakthrough of thequaternionfeedback scheme stands in its applicability for any magnitude of the orientation error, since it is inherently based on a singularity-free representation of orientation.

From theCambridge English Corpus

Zhuang8 et al. based on thequaternionalgebra, propose a linear solution that allows the simultaneous computation of these two kinematic transformations.

From theCambridge English Corpus

On the other hand, assigning the equivalent angle and axis directly leads to specifying a desired trajectory in terms of a unitquaternionvia (8), (9).

From theCambridge English Corpus

These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.

单词	quaternion
释义	BETA Examples ofquaternion Dictionary> Examples ofquaternion quaternionisn’t in the Cambridge Dictionary yet. You can help! Add a definition Again, = 1 for the reals, = 2 for 2 2 the complexes, and = 4 for thequaternion. From theCambridge English Corpus Defining the problem in the space of planar quaternions results in a definition of the parallel manipulator workspace as the intersection of quadratic equations. From theCambridge English Corpus In this section we will illustrate how the previously presented robust controller can be extended to enable the use of unit quaternions. From theCambridge English Corpus The noise is added as absolute value to the unit rotationquaternionand as relative value to the translation vector. From theCambridge English Corpus While we expect our readers to be familiar with real and complex matrices, it is reasonable to considerquaternionmatrices as well. From theCambridge English Corpus In this paper, we describe a new hand-eye calibration method, which applies the rotation quaternions in the motion constraints of hand-eye geometry. From theCambridge English Corpus We then extended our result to unitquaternionbased end-effector orientation to illustrate the flexibility of our controller design. From theCambridge English Corpus Sections 45 to 60 then outline the development of quaternions from 1843 onward. From theCambridge English Corpus Quaternionbased orientation tracking errors in experimetal studies. From theCambridge English Corpus Thequaternionalgebra is therefore seen to be a subset of the geometric algebra of 3-space. From theCambridge English Corpus As a final remark, the closed-loop system withquaternionfeedback (35) is nonlinear. From theCambridge English Corpus It can be shown12 that the vector part of thisquaternioncoincides with (34), which has indeed motivated the use of the same symbol. From theCambridge English Corpus 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. From theCambridge English Corpus The breakthrough of thequaternionfeedback scheme stands in its applicability for any magnitude of the orientation error, since it is inherently based on a singularity-free representation of orientation. From theCambridge English Corpus Zhuang8 et al. based on thequaternionalgebra, propose a linear solution that allows the simultaneous computation of these two kinematic transformations. From theCambridge English Corpus On the other hand, assigning the equivalent angle and axis directly leads to specifying a desired trajectory in terms of a unitquaternionvia (8), (9). From theCambridge English Corpus These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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