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Rotation Angles to Rodrigues

Convert rotation angles to Euler-Rodrigues vector

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  • Rotation Angles to Rodrigues block

Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The Rotation Angles to Rodrigues block converts the rotation described by the three rotation angles R1,R2,R3 into the three-element Euler-Rodrigues vector. The rotation used in this block is a passive transformation between two coordinate systems. The rotation angles represent a series of right-hand intrinsic passive rotations from frame A to frame B. The resulting Euler-Rodrigues vector represents a right-hand passive rotation from frame A to frame B. For more information on Euler-Rodrigues vectors, see Algorithms.

Ports

Input

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Rotation angles, in radians, from which to determine the Euler-Rodrigues vector. Values must be double.

Output

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Euler-Rodrigues vector determined from rotation angles.

Data Types: double

Parameters

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Rotation order for three wind rotation angles.

The default limitations for the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' sequences generate an R2 angle that lies between ±pi/2 radians (± 90 degrees), and R1 and R3 angles that lie between ±pi radians (±180 degrees).

The default limitations for the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' sequences generate an R2 angle that lies between 0 and pi radians (180 degrees), and R1 and R3 angles that lie between ±pi (±180 degrees).

Rodrigues transformation is not defined for rotation angles equal to ±pi radians (±180 deg).

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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