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Direction Cosine Matrix to Quaternions

Convert direction cosine matrix to quaternion vector

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  • Direction Cosine Matrix to Quaternions block

Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The Direction Cosine Matrix to Quaternions block transforms a 3-by-3 direction cosine matrix (DCM) into a four-element unit quaternion vector (q0, q1, q2, q3). Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. The direction cosine matrix represents a passive transformation from frame A to frame B. The resulting quaternions represent a series of intrinsic right-hand passive transformations from frame A to frame B. For more information on the direction cosine matrix, see Algorithms.

Examples

Developing the Apollo Lunar Module Digital Autopilot

Developing the Apollo Lunar Module Digital Autopilot

Develop Apollo Lunar Module digital autopilot using Simulink® and Aerospace Blockset.

Ports

Input

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Direction cosine matrix to transform the direction cosine matrix to quaternions, specified as a 3-by-3.

Data Types: double

Output

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Quaternion returned by transformation as a 4-by-1 vector.

Data Types: double

Parameters

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

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

  • Error — Displays error indicating 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 the 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

The DCM is defined as a function of a unit quaternion vector by the following:

DCM=[(q02+q12−q22−q32)2(q1q2+q0q3)2(q1q3−q0q2)2(q1q2−q0q3)(q02−q12+q22−q32)2(q2q3+q0q1)2(q1q3+q0q2)2(q2q3−q0q1)(q02−q12−q22+q32)]

Using this representation of the DCM, a number of calculations arrive at the correct quaternion. The first of these is to calculate the trace of the DCM to determine which algorithms are used. If the trace is greater than zero, the quaternion can be automatically calculated. When the trace is less than or equal to zero, the major diagonal element of the DCM with the greatest value must be identified to determine the final algorithm used to calculate the quaternion. Once the major diagonal element is identified, the quaternion is calculated.

Extended Capabilities

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

Version History

Introduced before R2006a

See Also

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