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Coordinate Transformation Conversion

Convert to a specified coordinate transformation representation

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  • Coordinate Transformation Conversion block

Libraries:
Robotics System Toolbox / Utilities
Navigation Toolbox / Utilities
ROS Toolbox / Utilities
UAV Toolbox / Utilities

Description

The Coordinate Transformation Conversion block converts a coordinate transformation from the input representation to a specified output representation. The input and output representations use the following forms:

  • Axis-Angle (AxAng) – [x y z theta]

  • Euler Angles (Eul) – [z y x], [z y z], or [x y z]

  • Homogeneous Transformation (TForm) – 4-by-4 matrix

  • Quaternion (Quat) – [w x y z]

  • Rotation Matrix (RotM) – 3-by-3 matrix

  • Translation Vector (TrVec) – [x y z]

All vectors must be column vectors.

To accommodate representations that only contain position or orientation information (TrVec or Eul, for example), you can specify two inputs or outputs to handle all transformation information. When you select the Homogeneous Transformation as an input or output, an optional Show TrVec input/output port parameter can be selected on the block mask to toggle the multiple ports.

Examples

Convert Coordinate System Transformations

Convert Coordinate System Transformations

How to convert some basic coordinate system transformations into other coordinate systems using Coordinate Transformation Conversion block. Input vectors are expected to be vertical vectors.

Open Live Script

Ports

Input

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Input transformation, specified as a coordinate transformation. The following representations are supported:

  • Axis-Angle (AxAng) – [x y z theta]

  • Euler Angles (Eul) – [z y x], [z y z], or [x y z]

  • Homogeneous Transformation (TForm) – 4-by-4 matrix

  • Quaternion (Quat) – [w x y z]

  • Rotation Matrix (RotM) – 3-by-3 matrix

  • Translation Vector (TrVec) – [x y z]

All vectors must be column vectors.

To accommodate representations that only contain position or orientation information (TrVec or Eul, for example), you can specify two inputs or outputs to handle all transformation information. When you select the Homogeneous Transformation as an input or output, an optional Show TrVec input/output port parameter can be selected on the block mask to toggle the multiple ports.

Translation vector, specified as a 3-element column vector, [x y z], which corresponds to a translation in the x, y, and z axes respectively. This port can be used to input or output the translation information separately from the rotation vector.

Dependencies

You must select Homogeneous Transformation (TForm) for the opposite transformation port to get the option to show the additional TrVec port. Enable the port by clicking Show TrVec input/output port.

Output Arguments

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Output transformation, returned as a coordinate transformation with the specified representation. The following representations are supported:

  • Axis-Angle (AxAng) – [x y z theta]

  • Euler Angles (Eul) – [z y x], [z y z], or [x y z]

  • Homogeneous Transformation (TForm) – 4-by-4 matrix

  • Quaternion (Quat) – [w x y z]

  • Rotation Matrix (RotM) – 3-by-3 matrix

  • Translation Vector (TrVec) – [x y z]

To accommodate representations that only contain position or orientation information (TrVec or Eul, for example), you can specify two inputs or outputs to handle all transformation information. When you select the Homogeneous Transformation as an input or output, an optional Show TrVec input/output port parameter can be selected on the block mask to toggle the multiple ports.

Translation vector, returned as a three-element column vector, [x y z], which corresponds to a translation in the x, y, and z axes respectively. This port can be used to input or output the translation information separately from the rotation vector.

Dependencies

You must select Homogeneous Transformation (TForm) for the opposite transformation port to get the option to show the additional TrVec port. Enable the port by clicking Show TrVec input/output port.

Parameters

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Select the representation for both the input and output port for the block. If you are using a transformation with only orientation information, you can also select the Show TrVec input/output port when converting to or from a homogeneous transformation.

Order of the Euler angle axis rotations, specified as ZYX, ZYZ, or XYZ. The order of the angles in the input or output port Eul must match this rotation sequence. The default order ZYX specifies an orientation by:

  • Rotating about the initial z-axis

  • Rotating about the intermediate y-axis

  • Rotating about the second intermediate x-axis

Dependencies

You must select Euler Angles for the Representation input or output parameter. The axis rotation sequence only applies to Euler angle rotations.

Toggle the TrVec input or output port when you want to specify or receive a separate translation vector for position information along with an orientation representation.

Dependencies

You must select Homogeneous Transformation (TForm) for the opposite transformation port to get the option to show the additional TrVec port.

  • Interpreted execution — Simulate model using the MATLAB® interpreter. This option shortens startup time but has a slower simulation speed than Code generation. In this mode, you can debug the source code of the block.

  • Code generation — Simulate model using generated C code. The first time you run a simulation, Simulink® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time, but the speed of the subsequent simulations is comparable to Interpreted execution.

Tunable: No

Extended Capabilities

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

Version History

Introduced in R2017b

See Also

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