Coordinate Transformation Conversion

Convert to a specified coordinate transformation representation

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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, the optional Show TrVec input port or Show TrVec output port parameters can be selected on the block mask to toggle the multiple ports.

Examples

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

Input transformation — Coordinate transformation

column vector | 3-by-3 matrix | 4-by-4 matrix

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, the optional Show TrVec input port or Show TrVec output port parameters can be selected on the block mask to toggle the multiple ports.

TrVec — Translation vector

3-element column vector

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 for the output Representation parameter to get the option to show the additional TrVec input port. Enable the port by clicking Show TrVec input port.

Output Arguments

Output transformation — Coordinate transformation

column vector | 3-by-3 matrix | 4-by-4 matrix

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, the optional Show TrVec input port or Show TrVec output port parameters can be selected on the block mask to toggle the multiple ports.

TrVec — Translation vector

three-element column vector

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 for the input Representation parameter to get the option to show the additional TrVec output port. Enable the port by clicking Show TrVec output port.

Parameters

Input

Representation — Input representation

Axis-Angle | Euler Angles | Homogeneous Transformation | Quaternion | Rotation Matrix | Translation Vector

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

Axis rotation sequence — Order of Euler angle axis rotations

ZYX (default) | ZYZ | XYZ

Order of the Euler angle axis rotations, specified as ZYX, ZYZ, or XYZ. The order of the angles in the input 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 input Representation parameter. The axis rotation sequence only applies to Euler angle rotations.

Show TrVec input port — Toggle TrVec port

off (default) | on

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

Dependencies

You must select Homogeneous Transformation for the output Representation parameter to get the option to show the additional TrVec input port. Enable the port by clicking Show TrVec input port.

Output

Representation — Output representation

Axis-Angle | Euler Angles | Homogeneous Transformation | Quaternion | Rotation Matrix | Translation Vector

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

Axis rotation sequence — Order of Euler angle axis rotations

ZYX (default) | ZYZ | XYZ

Order of the Euler angle axis rotations, specified as ZYX, ZYZ, or XYZ. The order of the angles in the 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 output Representation parameter. The axis rotation sequence only applies to Euler angle rotations.

Show TrVec output port — Toggle TrVec port

off (default) | on

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

Dependencies

You must select Homogeneous Transformation for the input Representation parameter to get the option to show the additional TrVec output port. Enable the port by clicking Show TrVec output port.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

• 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