🚁 🛸 KQ-LMPC: Koopman Quasi-Linear MPC for Quadrotors

kq_lmpc_quadrotor: A complete, hardware-ready Python package for Koopman-based Linear Model Predictive Control (LMPC), delivering real-time trajectory tracking for quadrotors using analytical Koopman lifting (no training data required).

✅ First hardware-deployed real-time Linear MPC for quadrotors derived using Koopman operator theory, no data required.

🌟 Key Features

✅ Analytical Koopman lifting with generalizable observables
    → No neural networks, no training, no data fitting required

✅ Data-free Koopman-lifted LTI + LPV models
    → Derived directly from SE(3) quadrotor dynamics using Lie algebra structure

✅ Real-time Linear MPC (LMPC)
    → Solved as a single convex QP termed KQ-LMPC
    → < 10 ms solve time on Jetson NX / embedded hardware

✅ Trajectory tracking on SE(3)
    → Provable controllability in lifted Koopman space

✅ Closed-loop robustness guarantees
    → Input-to-state practical stability (I-ISpS)

✅ Hardware-ready integration
    → Works with PX4 Offboard Mode, ROS2, MAVSDK, MAVROS

✅ Drop-in MPC module
    → for both KQ-LMPC, NMPC with acados on Python.

🧠 Paper

This work is based on:

"Real-Time Linear MPC for Quadrotors on SE(3): An Analytical Koopman-based Realization"
IEEE Robotics and Automation Letters (RA-L), 2025 (To appear)
Santosh Rajkumar, Chengyu Yang, Yuliang Gu, Sheng Cheng, Naira Hovakimyan, Debdipta Goswami
[Paper PDF] • [ArXiv] • [Video Demos]

If you use this repository, please cite us 🙏

@article{rajkumar2025kqlmpc,
  title={Real-Time Linear MPC for Quadrotors on SE(3): An Analytical Koopman-based Realization},
  author={Rajkumar, Santosh and Yang, Chengyu and Gu, Yuliang and Cheng, Sheng and Hovakimyan, Naira and Goswami, Debdipta},
  journal={IEEE Robotics and Automation Letters},
  year={2025}
}

🔧 Installation

*Virtual environment recommended

Install from PyPI (recommended):

pip install kq_lmpc_quadrotor

Install from source

git clone https://github.com/santoshrajkumar/kq-lmpc-quadrotor.git
cd kq-lmpc-quadrotor
pip install -e .

⚡ Quick Demo

from kq_lmpc_quadrotor import lqr_demo
lqr_demo()

kqlmpc_demo

⚠️ Important Dependency Notice This package relies on acados for fast Model Predictive Control (MPC).
You must configure acados + Python interface before running MPC examples.

Quick Setup Checklist

• Install acados ✅
• Enable Python interface ✅
• Export ACADOS_SOURCE_DIR ✅
• Set library paths:
  • Linux: LD_LIBRARY_PATH
  • macOS: DYLD_LIBRARY_PATH

📚 Install acados: https://docs.acados.org/installation/index.html
🐍 acados Python Interface: https://docs.acados.org/python_interface/index.html
💻 OS Support: Linux/macOS (Not tested on Windows)

📊 Benchmarking: KQ-LMPC vs NMPC (Numerical Simulation)

Experimental Setup:
Python 3.10 • Ubuntu 22.04 • AMD Ryzen 3 PRO CPU
Metrics: Mean solve time (μₜ), Worst-case solve time (tᵥ), and Tracking RMSE (𝓔ₛ).
Prediction horizon Tₕ ∈ {0.8, 1.4, 2.0, 2.8} s across 4 tasks.

🔍 Highlights

• ✅ 2–4× faster mean computation time than NMPC
• ✅ Lower worst-case latency → more reliable for real-time flight
• ✅ Competitive tracking accuracy
• ✅ Scales efficiently with larger prediction horizons

🚀 v2.0 (Coming Soon)
🔧 Complete PX4 Offboard control pipeline for hardware
🔧 Full Gazebo SITL + PX4 integration demos
🔧 Flight-ready example configs

If you find this project useful, please ⭐ star the repo and follow — your support drives development!