mpc_python

A (hopefully) easy-to-follow Iterative MPC tracking controller built with CVXPY and paired with MuJoCo. Designed to help anyone looking to transition from basic control to real-time convex optimization.

This mainly uses CVXPY to maintain a strict quadratic programming framework rather than relying on a non-linear solver like CasADi (which I love btw!). But, implementing an iMPC, we can still bridge the gap between convex optimization and real-world vehicle physics, allowing you to handle non-linear kinematics through iterative linearization.

Note: I've also preserved my original notebooks on Model Predictive Control for path-following problems here for historical context, a bit outdated.

This repo builds upon code and ideas from other open-source projects; please check them out in the Special Thanks section!

A Nix flake is provided for a reproducible development shell.

Just run the 2 examples below:

nix run --impure .#mujoco-demo
nix run .#nosim-demo

Otherwise, enter the development shell: this is heavier but also includes jupyter lab to experiment with the notebooks.

nix develop --impure

GUI demos require nixGL (auto-detects Intel/AMD/NVIDIA GPU):

nixGL python mpc_python/mpc_demo_mujoco.py

Headless demos run without it:

python mpc_python/mpc_demo_nosim.py

conda env create -f env.yml
conda activate simulation

Then run the scripts:

python3 mpc_demo_mujoco.py
python3 mpc_demo_nosim.py

1. Model derivation — analytical and numerical derivation (1.0, parametrized curves, differential, motion model)

2. MPC — implementation and testing of various tweaks (2.0, 2.1, 2.2, 2.3)

3. Obstacle Avoidance — halfplane constraints to avoid track collisions (3.0, 3.1) — Still work in progress!

• Prof. Borrelli - mpc papers and material
• AtsushiSakai - pythonrobotics
• alexliniger - mpcc and his paper
• arex18 - rocket-lander
• prl-mushr - mushr for the vehicle used