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
This example provides an overview of the types of trajectories available in Robotics System Toolbox™.
Generate Time-Optimal Trajectories with Constraints Using TOPP-RA Solver
This example shows how to generate trajectories that satisfy velocity and acceleration limits.
Manipulator Shape Tracing in MATLAB and Simulink
This example shows how to trace a predefined 3-D shape in space.

Featured Examples

Perform Safe Trajectory Tracking Control Using Robotics Manipulator Blocks

Use Simulink® with manipulator algorithm blocks to achieve safe trajectory tracking control of a simulated robot.

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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.

Open Live Script

Design Trajectory with Velocity Limits Using Trapezoidal Velocity Profile

Use the trapezoidal velocity profile to design a trajectory with input bounds rather than 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 from an initial to a desired end-effector pose. The timing of the trajectories is based on an approximate desired end of arm tool (EOAT) speed.

Open Live Script

Model and Control a Manipulator Arm with Robotics and Simscape

Execute a pick-and-place workflow using an ABB YuMi robot, which demonstrates how to design robot algorithms in Simulink®, and then simulate the action in a test environment using Simscape™. The example also shows how to model a system with different levels of fidelity to better focus on the associated algorithm design.

Open Live Script