Coordinate Transformations and Trajectories

Quaternions, rotation matrices, transformations, trajectory generation

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. You can also generate trajectories using polynomial equations, B-splines, rotation matrices, homogeneous transformations, or trapezoidal velocity profiles.

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
`quaternion`	Create a quaternion array

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

Trajectory Generation

`bsplinepolytraj`	Generate polynomial trajectories using B-splines
`cubicpolytraj`	Generate third-order polynomial trajectories
`quinticpolytraj`	Generate fifth-order trajectories
`rottraj`	Generate trajectories between orientation rotation matrices
`transformtraj`	Generate trajectories between two transformations
`trapveltraj`	Generate trajectories with trapezoidal velocity profiles

Plot Transformations

plotTransforms Plot 3-D transforms from translations and rotations

Blocks

Coordinate Transformation Conversion	Convert to a specified coordinate transformation representation
Polynomial Trajectory	Generate polynomial trajectories through waypoints
Rotation Trajectory	Generate trajectory between two orientations
Transform Trajectory	Generate trajectory between two homogeneous transforms
Trapezoidal Velocity Profile Trajectory	Generate trajectories though multiple waypoints using trapezoidal velocity profiles

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

Documentation