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Direction Cosine Matrix to Rodrigues

Convert direction cosine matrix to Euler-Rodrigues vector

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  • Direction Cosine Matrix to Rodrigues block

Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The Direction Cosine Matrix to Rodrigues block determines the 3-by-3 direction cosine matrix from a three-element Euler-Rodrigues vector. The input direction cosine matrix and resulting Euler-Rodrigues vector represent a right-hand passive transformation from frame A to frame B. For more information on the direction cosine matrix, see Algorithms.

Ports

Input

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Direction cosine matrix, specified as a 3-by-3 matrix, from which to determine the Euler-Rodrigues vector.

Data Types: double

Output

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Euler-Rodrigues vector, returned as a three-element vector.

Data Types: double

Parameters

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Block behavior when direction cosine matrix is invalid (not orthogonal).

  • Warning — Displays warning and indicates that the direction cosine matrix is invalid.

  • Error — Displays error and indicates that the direction cosine matrix is invalid.

  • None — Does not display warning or error (default).

Programmatic Use

Block Parameter: action
Type: character vector
Values: 'None' | 'Warning' | 'Error'
Default: 'None'

Data Types: char | string

Tolerance of direction cosine matrix validity, specified as a scalar. The block considers the direction cosine matrix valid if these conditions are true:

  • The transpose of the direction cosine matrix times itself equals 1 within the specified tolerance (transpose(n)*n == 1±tolerance)

  • The determinant of the direction cosine matrix equals 1 within the specified tolerance (det(n) == 1±tolerance).

Programmatic Use

Block Parameter: tolerance
Type: character vector
Values: 'eps(2)' | scalar
Default: 'eps(2)'

Data Types: double

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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