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dcm2angle

Create rotation angles from direction cosine matrix

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Syntax

[rotationAng1 rotationAng2 rotationAng3] = dcm2angle(dcm)
[rotationAng1 rotationAng2 rotationAng3] = dcm2angle(dcm,rotationSequence)
[rotationAng1 rotationAng2 rotationAng3] = dcm2angle(dcm,rotationSequence,lim)
[rotationAng1 rotationAng2 rotationAng3] = dcm2angle(dcm,rotationSequence,lim,action)
[rotationAng1 rotationAng2 rotationAng3] = dcm2angle(dcm,rotationSequence,lim,action,tolerance)

Description

Basic Syntax

example

[rotationAng1rotationAng2rotationAng3] = dcm2angle(dcm)calculates the rotation angles,rotationAng1,rotationAng2,rotationAng3, for a direction cosine matrix,dcm. The rotation used in this function is a passive transformation between two coordinate systems.

[rotationAng1rotationAng2rotationAng3] = dcm2angle(dcm,rotationSequence)calculates the rotation angles for a specified rotation sequence,rotationSequence.

Constraint, Action, and Tolerance Syntax

example

[rotationAng1rotationAng2rotationAng3] = dcm2angle(dcm,rotationSequence,lim)计算指定的旋转角度和le constraint,lim. Specifylimafter all other input arguments.

[rotationAng1rotationAng2rotationAng3] = dcm2angle(dcm,rotationSequence,lim,action)calculates the rotation angles and performs an action if the direction cosine matrix is not orthogonal. Specifyactionafter all other input arguments.

[rotationAng1rotationAng2rotationAng3] = dcm2angle(dcm,rotationSequence,lim,action,tolerance)calculates the rotation angles and uses atolerancelevel to evaluate if the direction cosine matrix is orthogonal. Specifytoleranceafter all other input arguments.

Examples

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迪特rmine the rotation angles from the direction cosine matrix.

dcm = [1 0 0; 0 1 0; 0 0 1]; [yaw, pitch, roll] = dcm2angle(dcm)
yaw = 0 pitch = 0 roll = 0

迪特rmine the rotation angles from multiple direction cosine matrices.

dcm = [ 1 0 0; 0 1 0; 0 0 1]; dcm(:,:,2) = [ 0.85253103550038 0.47703040785184 -0.21361840626067;...-0.43212157513194 0.87319830445628 0.22537893734811;...0.29404383655186 -0.09983341664683 0.95056378592206]; [pitch, roll, yaw] = dcm2angle(dcm,'YXZ','Default','None',0.1)
pitch = 0 0.3000 roll = 0 0.1000 yaw = 0 0.5000

Calculate the rotation angles from direction cosine matrix and specify the rotation order and angle constraint.

dcm = [1 0 0; 0 1 0; 0 0 1]; [yaw, pitch, roll] = dcm2angle( dcm,'zyx','robust')
yaw = 0 pitch = 0 roll = 0

Calculate the rotation angles from direction cosine matrix, specifying the rotation order, angle constraint, and action.

dcm = [1 0 0; 0 1 0; 0 0 1]; [yaw, pitch, roll] = dcm2angle( dcm,'zyx','robust','warning')
yaw = 0 pitch = 0 roll = 0

Calculate the rotation angles from direction cosine matrix, specifying the rotation order, angle constraint, action, and tolerance.

dcm = [1 0 0; 0 1 0; 0 0 1]; [yaw, pitch, roll] = dcm2angle( dcm,'zyx','robust','warning', 0.01)
yaw = 0 pitch = 0 roll = 0

Input Arguments

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Direction cosine matrices, specified as a 3-by-3-by-mmatrix, wheremis the number of direction cosine matrices. The direction cosine matrices must be orthogonal with determinant +1.

Rotation sequence, specified as:

  • 'ZYX'

  • 'ZYZ'

  • 'ZXY'

  • 'ZXZ'

  • 'YXZ'

  • 'YXY'

  • 'YZX'

  • 'YZY'

  • 'XYZ'

  • 'XZY'

  • 'XYX'

  • 'XZX'

whererotationAng1is thez-axis rotation,rotationAng2is they-axis rotation, androtationAng3is thex-axis rotation.

Data Types:char|string

Angle constraint, specified as:

  • 'Default'— Returns the default case of R1, R2, and R3. In the event of a gimbal lock, use'ZeroR3'or'Robust'.

  • 'ZeroR3'— In the event of gimbal lock, sets R3 to0and solves for R1 and R2.

  • 'Robust'— Returns R1, R2, and R3 from either the'Default'or'ZeroR3'case that produces a rotation matrix that most closely matches the input matrix.

For more information on angle constraints, seeLimitations.

Action for invalid direction cosine matrix, specified as:

  • '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.

Valid direction cosine matrices are orthogonal and proper when:

  • The transpose of the direction cosine matrix times itself equals1within the specified tolerancetolerance(transpose(dcm)*dcm == 1±tolerance)

  • The determinant of the direction cosine matrix equals1within the specified tolerance (det(dcm) == 1±tolerance).

Data Types:char|string

Relative tolerance level to evaluate if the direction cosine matrix,dcm, is orthogonal, specified as a scalar.

Data Types:char|string

Output Arguments

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First rotation angles, returned as anm-by-1 array, in rads.

Second rotation angles, returned as anm-by-1 array, in rads.

Third rotation angles, returned as anm-by-1 array, in rads.

Limitations

  • The'Default'limitations for the'ZYX','ZXY','YXZ','YZX','XYZ', and'XZY'implementations generate anrotationAng2angle that lies between ±90 degrees, androtationAng1androtationAng3angles that lie between ±180 degrees.

  • The'Default'limitations for the'ZYZ','ZXZ','YXY','YZY','XYX', and'XZX'implementations generate arotationAng2angle that lies between 0–180 degrees, androtationAng1androtationAng3angles that lie between ±180 degrees.

  • The'ZeroR3'limitations for the'ZYX','ZXY','YXZ','YZX','XYZ', and'XZY'implementations generate arotationAng2angle that lies between ±90 degrees, androtationAng1androtationAng3angles that lie between ±180 degrees. However, whenrotationAng2is ±90 degrees,rotationAng3is set to 0 degrees.

  • The'ZeroR3'limitations for the'ZYZ','ZXZ','YXY','YZY','XYX', and'XZX'implementations generate arotationAng2angle that lies between 0–180 degrees, androtationAng1androtationAng3angles that lie between ±180 degrees. However, whenrotationAng2is 0 or ±180 degrees,rotationAng3is set to 0 degrees.

Version History

Introduced in R2006b

See Also

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