Online Non-linear Centroidal MPC with Stability Guarantees for Robust Legged Robots Locomotion

Paper

The paper appeared in the March issue of IEEE RA-L 2025. The preprint is available in the following link https://arxiv.org/pdf/2409.01144

https://github.com/user-attachments/assets/95e4774c-9b37-42a9-8d3a-af2524bffbc6

Code organization

The MPC problem formulation for both the humanoid case and the quadruped case are housed in submodules. The code is organized as follows - examples houses example code and scripts allowing to install and run the MPC and produce plots/simulations for a bipedal and a quadruped. - humanoid-mpc points to the implementation of the Centroidal MPC (Casadi + IPOPT) with the possibility of setting a flag enabling or disabling the stability constraints - quadruped-mpc points to the implementation of the Centroidal MPC through ACADOS with the possibility of using different quadruped robots and terrains.

Examples and usage

To use the examples in the example directory you can simply run the corresponding run_and_plot.sh script as in the following

humanoid example

The humanoid example simulates using the Centroidal MPC with the flag enable_stability_cstr off and then on. It then generates gifs/animation of the data of the footsteps and CoM trajectory in both cases. The simulation, to test for edge cases, runs the MPC with dt = 200ms with a horizon length of 5 steps. In this way we emphasize the role played by the stability constraints in ensuring success as opposed to the nominal case. To run the example you simply do

bash cd examples/humanoid chmod +x run_and_plot.sh ./run_and_plot.sh The above script builds the MPC suite housed in the submodule humanoid-mpc . Make a build directory for the example in main.cpp , build and install it, and then run the matlab plotting scripts for the generated data. If successful, you should be able to see animations of this kind in your build/bin directory

Simulations without (left) and With (right) Stability for a biped

⚠️ The `run_and_plot.sh` script assumes you have the dependencies of the `bipedallocomotionframework` housed in the submodule `humanoid-mpc`. Please check https://github.com/ami-iit/bipedal-locomotion-framework/?tab=readme-ov-file#page_facing_up-mandatory-dependencies for the details

⚠️ Do not build `bipedallocomotioninterface` from master. The script will handle building and installing the correct version with the relevant commit. Only ensure you have the dependencies installed in your system

Quadruped example

The quadruped example simulates using the MPC with and without the stability constraints with a quadruped (Aliengo). It produces the simulations using mojoco. To run the example you simply do

bash cd examples/quadruped chmod +x run_and_plot.sh ./run_and_plot.sh

You should be able to see something similar to (with obvious difference in performance between nominal and stable centroidal MPC)

https://github.com/user-attachments/assets/bc05ba45-fcff-4a21-9281-8ed78c6ea37a

Citing this work

Feel free to open issues on this repo for specific questions. If you find this work useful, consider citing it

``` @article{elobaid2024online, title={Online Non-linear Centroidal MPC with Stability Guarantees for Robust Locomotion of Legged Robots}, 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={arXiv preprint arXiv:2409.01144}, year={2024} }

```

Maintainers

👨‍💻 @Mohamed Elobaid