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.

Functions

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Time-Optimal Trajectory

contopptraj Generate trajectory subject to kinematic constraints (Since R2022b)

Minimum Jerk and Snap Trajectories

`minjerkpolytraj`	Generate minimum jerk trajectory through waypoints (Since R2021b)
`minsnappolytraj`	Generate minimum snap trajectory through waypoints (Since R2021b)

Trapezoidal Velocity Profile Trajectory

trapveltraj Generate trajectories with trapezoidal velocity profiles

Cubic and Quintic Polynomial Trajectories

`cubicpolytraj`	Generate third-order polynomial trajectories
`quinticpolytraj`	Generate fifth-order trajectories

B-Spline and Piecewise Polynomial Trajectories

`bsplinepolytraj`	Generate polynomial trajectories using B-splines
`polynomialTrajectory`	Piecewise-polynomial trajectory generator (Since R2023a)

Rotation and Transformation Trajectories

`rottraj`	Generate trajectories between orientation rotation matrices
`transformtraj`	Generate trajectories between two transformations

Waypoint Trajectory

waypointTrajectory Waypoint trajectory generator (Since R2022a)

Blocks

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 through multiple waypoints using trapezoidal velocity profiles
Minimum Jerk Polynomial Trajectory	Generate minimum jerk polynomial trajectories through multiple waypoints (Since R2022a)
Minimum Snap Polynomial Trajectory	Generate minimum snap polynomial trajectories through multiple waypoints (Since R2022a)

Topics

Choose Trajectories for Manipulator Paths
Explore and compare different manipulator trajectory types by generating paths for these trajectory profiles.
Generate Time-Optimal Trajectories with Constraints Using TOPP-RA Solver
Generate trajectories within velocity and acceleration limits using TOPP-RA solver for time-optimal path planning.
Manipulator Shape Tracing in MATLAB and Simulink
Generate a smooth 3-D path for Sawyer robot end-effector by tracing predefined 3-D shapes.

Featured Examples

Perform Safe Trajectory Tracking Control Using Robotics Manipulator Blocks

Achieve safe trajectory tracking control of a simulated robot using manipulator algorithm blocks in Simulink^®.

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Plan Minimum Jerk Trajectory for Robot Arm

Plan and visualize a minimum jerk trajectory for a robotic arm navigating through obstacles.

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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 in place of parameters.

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Plan and Execute Task- and Joint-Space Trajectories Using Kinova Gen3 Manipulator

Generate and simulate interpolated joint trajectories to move to a desired end-effector pose using Kinova^® Gen3 manipulator.

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Model and Control a Manipulator Arm with Robotics and Simscape

Design YuMi robot algorithms in Simulink and simulate in Simscape™, emphasizing algorithm precision and system modeling.

Open Live Script

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