Overview

This repo contains a model predictive controller based on the single rigid body model and written in Python. It comes in two flavours: gradient-based via acados or sampling-based via jax. The controller is tested on real robots and is compatible with Mujoco.

Features gradient-based mpc:

• less than 5ms computation on an intel i7-13700H cpu
• optional integrators for model mismatch
• optional smoothing for the ground reaction forces
• optional foothold optimization
• optional real-time iteration or advanced-step real-time iteration
• optional zero moment point/center of mass constraints
• optional lyapunov-based criteria

Features sampling-based mpc:

• 10000 parallel rollouts in less than 2ms on an nvidia 4050 mobile gpu!
• optional step frequency adaptation for enhancing robustness
• implements different strategies: random sampling, mppi, or cemppi
• different control parametrizations: zero-order, linear splines or cubic splines (see mujoco-mpc)

Citing this work

If you find the work useful, please consider citing one of our works:

On the Benefits of GPU Sample-Based Stochastic Predictive Controllers for Legged Locomotion (IROS-2024):

@INPROCEEDINGS{turrisi2024sampling,
  author={Turrisi, Giulio and Modugno, Valerio and Amatucci, Lorenzo and Kanoulas, Dimitrios and Semini, Claudio},
  booktitle={2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, 
  title={On the Benefits of GPU Sample-Based Stochastic Predictive Controllers for Legged Locomotion}, 
  year={2024},
  pages={13757-13764},
  doi={10.1109/IROS58592.2024.10801698}}

Adaptive Non-Linear Centroidal MPC With Stability Guarantees for Robust Locomotion of Legged Robots (RAL-2025):

@ARTICLE{elobaid2025adaptivestablempc,
  author={Elobaid, Mohamed and Turrisi, Giulio and Rapetti, Lorenzo and Romualdi, Giulio and Dafarra, Stefano and Kawakami, Tomohiro and Chaki, Tomohiro and Yoshiike, Takahide and Semini, Claudio and Pucci, Daniele},
  journal={IEEE Robotics and Automation Letters}, 
  title={Adaptive Non-Linear Centroidal MPC With Stability Guarantees for Robust Locomotion of Legged Robots}, 
  year={2025},
  volume={10},
  number={3},
  pages={2806-2813},
  doi={10.1109/LRA.2025.3536296}}

Dependencies

Gradient-based MPC: It uses CasADI to define the model and acados to solve the optimal control problem. Sampling-based MPC: jax for both. The simulation environment is based on Mujoco.

Installation

1. install miniforge (x86_64 or arm64 depending on your platform)

2. create an environment using the file in the folder installation choosing between nvidia and integrated gpu, either with or without ros (to run the simulation, you don't need ros!):

   conda env create -f mamba_environment.yml

3. clone the other submodules:

   git submodule update --init --recursive

4. activate the conda environment

   conda activate quadruped_pympc_env

5. go inside the folder acados and compile it pressing:

   mkdir build
   cd build
   cmake -DACADOS_WITH_SYSTEM_BLASFEO:BOOL=ON -DCMAKE_POLICY_VERSION_MINIMUM=3.5 ..
   make install -j4
   pip install -e ./../interfaces/acados_template
   

6. inside the file .bashrc, given your path_to_acados, put:

   export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:"/path_to_acados/lib"
   export ACADOS_SOURCE_DIR="/path_to_acados"
   

   Notice that if you are using Mac, you should modify the file .zshrc adding

   export DYLD_LIBRARY_PATH=$LD_LIBRARY_PATH:"/path_to_acados/lib"
   export ACADOS_SOURCE_DIR="/path_to_acados"
   

The first time you run the simulation with acados, in the terminal you will be asked to install tera_render. You should accept to proceed.

7. go to Quadruped-PyMPC initial folder and install it:

   pip install -e .
   

How to run - Simulation

1. activate the conda environment

   conda activate quadruped_pympc_env
   

2. go in the main Quadruped-PyMPC folder and press

   python3 simulation/simulation.py
   

In the file config.py, you can set up the robot, the mpc type (gradient, sampling..), its proprierties (real time iteration, sampling type, foothold optimization..), and other simulation params (reference, gait type..).

3. you can interact with the simulation with your mouse to add disturbances, or with the keyboard by pressing

arrow up, arrow down -> add positive or negative forward velocity
arrow left, arrow right -> add positive or negative yaw velocity
ctrl -> set zero all velocities

How to run - ROS2

During the installation procedure, use the file mamba_environment_ros2.yml. Then:

1. activate the conda environment

   conda activate quadruped_pympc_ros2_env
   

2. go in the folder ros2/msgs_ws and compile the messages

colcon build
source install/setup.bash

3. you can run now the script

python3 ros2/run_controller.py

4. if you want to test the above node with a simulator, for example to test ros2 delay, you can run

python3 ros2/run_simulator.py

5. joystick

ros2 launch teleop_twist_joy teleop-launch.py joy_config:='xbox'

6. for a real-robot deployment, use a nice state estimator

Maintainer

This repository is maintained by Giulio Turrisi and Daniel Ordonez.