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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.


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axang2quatConvert axis-angle rotation to quaternion
axang2rotmConvert axis-angle rotation to rotation matrix
axang2tformConvert axis-angle rotation to homogeneous transformation
eul2quatConvert Euler angles to quaternion
eul2rotmConvert Euler angles to rotation matrix
eul2tformConvert Euler angles to homogeneous transformation
quat2axangConvert quaternion to axis-angle rotation
quat2eulConvert quaternion to Euler angles
quat2rotmConvert quaternion to rotation matrix
quat2tformConvert quaternion to homogeneous transformation
quaternionCreate a quaternion array
so2SO(2) rotational transformation
so3SO(3) rotational transformation
rotm2axangConvert rotation matrix to axis-angle rotation
rotm2eulConvert rotation matrix to Euler angles
rotm2quatConvert rotation matrix to quaternion
rotm2tformConvert rotation matrix to homogeneous transformation
se2SE(2) homogeneous transformation
se3SE(3) homogeneous transformation
tform2axangConvert homogeneous transformation to axis-angle rotation
tform2eulExtract Euler angles from homogeneous transformation
tform2quatExtract quaternion from homogeneous transformation
tform2rotmExtract rotation matrix from homogeneous transformation
tform2trvecExtract translation vector from homogeneous transformation
angdiffDifference between two angles
cart2homConvert Cartesian coordinates to homogeneous coordinates
hom2cartConvert homogeneous coordinates to Cartesian coordinates
trvec2tformConvert translation vector to homogeneous transformation
bsplinepolytrajGenerate polynomial trajectories using B-splines
contopptrajGenerate trajectory subject to kinematic constraints
cubicpolytrajGenerate third-order polynomial trajectories
minjerkpolytrajGenerate minimum jerk trajectory through waypoints
minsnappolytrajGenerate minimum snap trajectory through waypoints
quinticpolytrajGenerate fifth-order trajectories
rottrajGenerate trajectories between orientation rotation matrices
transformtrajGenerate trajectories between two transformations
trapveltrajGenerate trajectories with trapezoidal velocity profiles
waypointTrajectoryWaypoint trajectory generator
plotTransformsPlot 3-D transforms from translations and rotations


Coordinate Transformation ConversionConvert to a specified coordinate transformation representation
Polynomial TrajectoryGenerate polynomial trajectories through waypoints
Rotation TrajectoryGenerate trajectory between two orientations
Transform TrajectoryGenerate trajectory between two homogeneous transforms
Trapezoidal Velocity Profile TrajectoryGenerate trajectories though multiple waypoints using trapezoidal velocity profiles
Minimum Jerk Polynomial TrajectoryGenerate minimum jerk polynomial trajectories through multiple waypoints
Minimum Snap Polynomial TrajectoryGenerate minimum snap polynomial trajectories through multiple waypoints