Coordinate Transformations

Quaternions, rotation matrices, transformations

Robotics System Toolbox™ provides functions for transforming coordinates and units into the format required for your applications. To learn more about the different coordinate systems, see Coordinate Transformations in Robotics.

Objects

`se2`	SE(2) homogeneous transformation (Since R2022b)
`se3`	SE(3) homogeneous transformation (Since R2022b)
`so2`	SO(2) rotation (Since R2022b)
`so3`	SO(3) rotation (Since R2022b)
`quaternion`	Create quaternion array

Functions

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Axis-Angles

`axang2quat`	Convert axis-angle rotation to quaternion
`axang2rotm`	Convert axis-angle rotation to rotation matrix
`axang2tform`	Convert axis-angle rotation to homogeneous transformation

Euler Angles

`eul2quat`	Convert Euler angles to quaternion
`eul2rotm`	Convert Euler angles to rotation matrix
`eul2tform`	Convert Euler angles to homogeneous transformation

Quaternions

`quat2axang`	Convert quaternion to axis-angle rotation
`quat2eul`	Convert quaternion to Euler angles
`quat2rotm`	Convert quaternion to rotation matrix
`quat2tform`	Convert quaternion to homogeneous transformation

Rotation Matrices

`rotm2axang`	Convert rotation matrix to axis-angle rotation
`rotm2eul`	Convert rotation matrix to Euler angles
`rotm2quat`	Convert rotation matrix to quaternion
`rotm2tform`	Convert rotation matrix to homogeneous transformation

Homogeneous Transformations

`tform2axang`	Convert homogeneous transformation to axis-angle rotation
`tform2eul`	Extract Euler angles from homogeneous transformation
`tform2quat`	Extract quaternion from homogeneous transformation
`tform2rotm`	Extract rotation matrix from homogeneous transformation
`tform2trvec`	Extract translation vector from homogeneous transformation

Coordinate Conversions

`angdiff`	Difference between two angles
`cart2hom`	Convert Cartesian coordinates to homogeneous coordinates
`hom2cart`	Convert homogeneous coordinates to Cartesian coordinates
`trvec2tform`	Convert translation vector to homogeneous transformation

Plot Transformations

plotTransforms Plot 3-D transforms from translations and rotations

Blocks

Coordinate Transformation Conversion

Convert to a specified coordinate transformation representation

Topics

Standard Units for Robotics System Toolbox
List of standard units used in the Robotics System Toolbox.
Coordinate Transformations in Robotics
Summary of the different coordinate transformations used in robotics.

Teaching Resources

Robotic Manipulators

Learn the concepts of robot arm motion through coordinate system transformations, DH parameters, and forward/inverse kinematics.