Main Content

rod2quat

Convert Euler-Rodrigues vector to quaternion

collapse all in page

Syntax

quat=rod2quat(R)

Description

quat=rod2quat(R) function calculates the quaternion, quat, for a given Euler-Rodrigues (also known as Rodrigues) vector, R. The Euler-Rodrigues vector input and resulting quaternion represent a right-hand passive transformation from frame A to frame B.

Aerospace Toolbox uses quaternions that are defined using the scalar-first convention.

example

Examples

collapse all

Open Live Script

This example shows how to determine the quaternion from Rodrigues vector.r = [.1 .2 -.1];

r = [.1 .2 -.1];
q = rod2quat(r);

Input Arguments

collapse all

M-by-1 array of Rodrigues vectors.

Data Types: double

Output Arguments

collapse all

M-by-4 matrix of M quaternions. quat has its scalar number as the first column.

Algorithms

An Euler-Rodrigues vector b⇀ represents a rotation by integrating a direction cosine of a rotation axis with the tangent of half the rotation angle as follows:

b→=[bxbybz]

where:

bx=tan(12θ)sx,by=tan(12θ)sy,bz=tan(12θ)sz

are the Rodrigues parameters. Vector s⇀ represents a unit vector around which the rotation is performed. Due to the tangent, the rotation vector is indeterminate when the rotation angle equals ±pi radians or ±180 deg. Values can be negative or positive.

References

[1] Dai, J.S. "Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections." Mechanism and Machine Theory, 92, 144-152. Elsevier, 2015.

Version History

Introduced in R2017a

See Also

| | | |