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A light-weight and extensible C++ library for trajectory optimization for legged robots.

Build Status Documentation ROS hosting CodeFactor License BSD-3-Clause

A base-set of variables, costs and constraints that can be combined and extended to formulate trajectory optimization problems for legged systems. These implementations have been used to generate a variety of motions such as monoped hopping, biped walking, or a complete quadruped trotting cycle, while optimizing over the gait and step durations in less than 100ms (paper).

✔️ Intuitive and efficient formulation of variables, cost and constraints using Eigen.
✔️ ifopt enables using the high-performance solvers Ipopt and Snopt.
✔️ Elegant rviz visualization of motion plans using xpp.
✔️ ROS/catkin integration (optional).
✔️ Light-weight (~6k lines of code) makes it easy to use and extend.



The easiest way to install is through the ROS binaries:

sudo apt-get install ros-<ros-distro>-towr-ros

In case these don't yet exist for your distro, there are two ways to build this code from source:

  • Option 1: core library and hopper-example with pure CMake.
  • Option 2 (recommended): core library & GUI & ROS-rviz-visualization built with catkin and ROS.

Building with CMake

  • Install dependencies CMake, Eigen, Ipopt:

    sudo apt-get install cmake libeigen3-dev coinor-libipopt-dev

    Install ifopt, by cloning the repo and then: cmake .. && make install on your system.

  • Build towr:

    git clone && cd towr/towr
    mkdir build && cd build
    cmake .. -DCMAKE_BUILD_TYPE=Release
    sudo make install # copies files in this folder to /usr/local/*
    # sudo xargs rm < install_manifest.txt # in case you want to uninstall the above
  • Test ( Generates a motion for a one-legged hopper using Ipopt

    ./towr-example # or ./towr-test if gtest was found
  • Use: You can easily customize and add your own constraints and variables to the optimization problem. Herefore, add the following to your CMakeLists.txt:

    find_package(towr 1.2 REQUIRED)
    add_executable(main main.cpp) # Your custom variables, costs and constraints added to TOWR
    target_link_libraries(main PUBLIC towr::towr) # adds include directories and libraries

Building with catkin

We provide a ROS-wrapper for the pure cmake towr library, which adds a keyboard interface to modify goal state and motion types as well as visualizes the produces motions plans in rviz using xpp.

  • Install dependencies CMake, catkin, Eigen, Ipopt, ROS, xpp, ncurses, xterm:

    sudo apt-get install cmake libeigen3-dev coinor-libipopt-dev libncurses5-dev xterm
    sudo apt-get install ros-<ros-distro>-desktop-full ros-<ros-distro>-xpp
  • Build workspace:

    cd catkin_workspace/src
    git clone
    git clone
    cd ..
    catkin_make_isolated -DCMAKE_BUILD_TYPE=Release # or `catkin build`
    source ./devel_isolated/setup.bash
  • Use: Include in your catkin project by adding to your CMakeLists.txt

    find_package(catkin COMPONENTS towr) 
    target_link_libraries(foo ${catkin_LIBRARIES})

    Add the following to your package.xml:



Launch the program using

roslaunch towr_ros towr_ros.launch  # debug:=true  (to debug with gdb)

Click in the xterm terminal and hit 'o'.

Information about how to tune the paramters can be found here.


Library overview

  • The relevant classes and parameters to build on are collected modules.
  • A nice graphical overview as UML can be seen here.
  • The doxygen documentation provides helpful information for developers.

Problem formulation

  • This code formulates the variables, costs and constraints using ifopt, so it makes sense to briefly familiarize with the syntax using this example.
  • A minimal towr example without ROS, formulating a problem for a one-legged hopper, can be seen here and is great starting point.
  • We recommend using the ROS infrastructure provided to dynamically visualize, plot and change the problem formulation. To define your own problem using this infrastructure, use this example as a guide.

Add your own variables, costs and constraints

  • This library provides a set of variables, costs and constraints to formulate the trajectory optimization problem. An example formulation of how to combine these is given, however, this formulation can probably be improved. To add your own e.g. constraint-set, define a class with it's values and derivatives, and then add it to the formulation nlp.AddConstraintSet(your_custom_constraints); as shown here.

Add your own robot

  • Want to add your own robot to towr? Start here.
  • To visualize that robot in rviz, see xpp.


We love pull request, whether its new constraint formulations, additional robot models, bug fixes, unit tests or updating the documentation. Please have a look at for more information.
See here the list of contributors who participated in this project.

Projects using towr


All publications underlying this code can be found here. The core paper is:

  author    = {Winkler, Alexander W and Bellicoso, Dario C and 
               Hutter, Marco and Buchli, Jonas},
  title     = {Gait and Trajectory Optimization for Legged Systems 
               through Phase-based End-Effector Parameterization},
  journal   = {IEEE Robotics and Automation Letters (RA-L)},
  year      = {2018},
  month     = {July},
  pages     = {1560-1567},
  volume    = {3},
  doi       = {10.1109/LRA.2018.2798285},

A broader overview of the topic of Trajectory optimization and derivation of the Single-Rigid-Body Dynamics model used in this work: DOI 10.3929/ethz-b-000272432


Alexander W. Winkler - Initial Work/Maintainer

The work was carried out at the following institutions: