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toppra: Time-Optimal Path Parameterization



toppra is a library for computing the time-optimal path parametrization for robots subject to kinematic and dynamic constraints. In general, given the inputs:

  1. a geometric path p(s), s in [0, s_end];
  2. a list of constraints on joint velocity, joint accelerations, tool Cartesian velocity, et cetera.

toppra returns the time-optimal path parameterization: s_dot (s), from which the fastest trajectory q(t) that satisfies the given constraints can be found.

Documentation and tutorials are available here.

You can install the package with pip:

pip install toppra

To install from source for development:

pip install -r requirement3.txt
pip install -e .


Bug tracking

Please report any issues, questions or feature request via Github issues tracker.

Have a quick question? Try asking in our slack channel.


Pull Requests are welcome! Create a Pull Request and we will review your proposal!


toppra was originally developed by Hung Pham (Eureka Robotics, former CRI Group) and Phạm Quang Cường (Eureka Robotics, CRI Group) with major contributions from talented contributors:

If you have taken part in developing and supporting the library, feel free to add your name to the list.

The development is also generously supported by Eureka Robotics.

Citing toppra

If you use this library for your research, we encourage you to

  1. reference the accompanying paper A new approach to Time-Optimal Path Parameterization based on Reachability Analysis, IEEE Transactions on Robotics, vol. 34(3), pp. 645-659, 2018.
  2. put a star on this repository.