Direction Cosine Matrix to Rodrigues

Convert direction cosine matrix to Euler-Rodrigues vector

  • Library:
  • Aerospace Blockset / Utilities / Axes Transformations

Description

The Direction Cosine Matrix to Rodrigues block determines the 3-by-3 direction cosine matrix from a 3-element Euler-Rodrigues vector.

Ports

Input

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Direction cosine matrix from which to determine the Euler-Rodrigues vector.

Data Types: double

Output

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Euler-Rodrigues vector determined from the direction cosine matrix.

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).

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).

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™.

Introduced in R2017a