Direction Cosine Matrix to Rotation Angles

Convert direction cosine matrix to rotation angles

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  • Direction Cosine Matrix to Rotation Angles block

Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The Direction Cosine Matrix to Rotation Angles block converts a 3-by-3 direction cosine matrix (DCM) into the rotation angles R1, R2, and R3, respectively. The block Rotation Order parameter specifies both the rotation sequence as well as the order of the rotation angles in the output. For example, if Rotation Order has a value of ZYX, the block outputs are in the rotation order z-y-x (yaw, pitch, and roll). The direction cosine matrix represents a 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.

Ports

Input

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Direction cosine matrix from which to determine the rotation angles, specified as a 3-by-3 matrix.

Data Types: double

Output

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Rotation angles, returned as a 3-by-1 vector, in radians.

Data Types: double

Parameters

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Rotation order for three rotation angles.

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

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

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

Extended Capabilities

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

Version History

Introduced in R2007b

See Also

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