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

`so2`	SO(2) rotation
`so3`	SO(3) rotation
`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

`se2`	SE(2) homogeneous transformation
`se3`	SE(3) homogeneous transformation
`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
`contopptraj`	Generate trajectory subject to kinematic constraints
`cubicpolytraj`	Generate third-order polynomial trajectories
`minjerkpolytraj`	Generate minimum jerk trajectory through waypoints
`minsnappolytraj`	Generate minimum snap trajectory through waypoints
`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
`waypointTrajectory`	Waypoint trajectory generator
`polynomialTrajectory`	Piecewise-polynomial trajectory generator

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
Minimum Jerk Polynomial Trajectory	Generate minimum jerk polynomial trajectories through multiple waypoints
Minimum Snap Polynomial Trajectory	Generate minimum snap polynomial trajectories through multiple waypoints

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.

Featured Examples

Plan Minimum Jerk Trajectory for Robot Arm

Plan a minimum jerk polynomial trajectory for a robotic manipulator. The example shows how to load an included robot model, plan a path for the robot model in an environment with obstacles, generate a minimum jerk trajectory from the path, and visualize the generated trajectories and the robot motion.

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Design Trajectory with Velocity Limits Using Trapezoidal Velocity Profile

Use the trapezoidal velocity profile to design a trajectory with input bounds rather than parameters.

Open Live Script