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Trajectory Generation

Generate polynomial, B-spline, and trapezoidal trajectories

These functions use different mathematical equations for generating trajectories for manipulator robots. Polynomials, B-splines, and trapezoidal velocity profiles enable you to generate trajectories for multi-degree-of-freedom (DOF) systems. You can also interpolate between rotation matrices and homogeneous transformations.

The examples show different applications of trajectory execution including planning, control, and simulation for shape tracing and pick-and-place workflows.


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contopptrajGenerate trajectory subject to kinematic constraints (Since R2022b)
minjerkpolytrajGenerate minimum jerk trajectory through waypoints (Since R2021b)
minsnappolytrajGenerate minimum snap trajectory through waypoints (Since R2021b)
trapveltrajGenerate trajectories with trapezoidal velocity profiles
cubicpolytrajGenerate third-order polynomial trajectories
quinticpolytrajGenerate fifth-order trajectories
bsplinepolytrajGenerate polynomial trajectories using B-splines
polynomialTrajectoryPiecewise-polynomial trajectory generator (Since R2023a)
rottrajGenerate trajectories between orientation rotation matrices
transformtrajGenerate trajectories between two transformations
waypointTrajectoryWaypoint trajectory generator (Since R2022a)


Polynomial TrajectoryGenerate polynomial trajectories through waypoints
Rotation TrajectoryGenerate trajectory between two orientations
Transform TrajectoryGenerate trajectory between two homogeneous transforms
Trapezoidal Velocity Profile TrajectoryGenerate trajectories through multiple waypoints using trapezoidal velocity profiles
Minimum Jerk Polynomial TrajectoryGenerate minimum jerk polynomial trajectories through multiple waypoints (Since R2022a)
Minimum Snap Polynomial TrajectoryGenerate minimum snap polynomial trajectories through multiple waypoints (Since R2022a)