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Rodrigues to Rotation Angles

Convert Euler-Rodrigues vector to rotation angles

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  • Rodrigues to Rotation Angles block

Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The Rodrigues to Rotation Angles block converts the three-element Euler-Rodrigues vector into rotation angles. The Euler-Rodrigues angles represent a right-hand passive transformation from frame A to frame B. The resulting rotation angles represent a series of right-hand intrinsic passive rotations from frame A to frame B. For more information on Euler-Rodrigues vectors, see Algorithms.

Ports

Input

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Euler-Rodrigues vector determined from rotation angles.

Data Types: double

Output

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Rotation angles, in radians, from which to determine the Euler-Rodrigues vector. Quaternion scalar is the first element.

Data Types: double

Parameters

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Rotation order for three wind rotation angles.

For the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' rotations, the block generates an R2 angle that lies between ±pi/2 radians (±90 degrees), and R1 and R3 angles that lie between ±pi radians (±180 degrees).

For the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' rotations, the block generates an R2 angle that lies between 0 and pi radians (180 degrees), and R1 and R3 angles that lie between ±pi (±180 degrees). However, in the latter case, when R2 is 0, R3 is set to 0 radians.

Programmatic Use

Block Parameter: rotationOrder
Type: character vector
Values: 'ZYX' | 'ZYZ' |'ZXY' | 'ZXZ' | 'YXZ' | 'YXY' | 'YZX' | 'YZY' | 'XYZ' | 'XYX' | 'XZY' | 'XZX'
Default: 'ZYX'

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017a

See Also

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