Real-Time Linear MPC for Quadrotors on SE(3): An Analytical Koopman-Based Realization
Santosh Mohan Rajkumar, Chengyu Yang, Yuliang Gu, Sheng Cheng, NAIRA HOVAKIMYAN, Debdipta Goswami
AI summary
Problem
Quadrotor control faces a trade-off between the high computational cost of nonlinear MPC and the reduced accuracy of linear MPC, while existing data-driven Koopman methods require extensive training data and lack generalization.
Approach
The authors derive an analytical, data-free Koopman linear parameter-varying representation of quadrotor dynamics on SE(3) using carefully designed observables, enabling a compact lifted-space model that preserves control dimensions and supports convex QP-based MPC.
Key results
- Analytical Koopman-linear representation preserving original control dimensions
- Formal proof of controllability for the derived lifted-space model
- KQ-LMPC framework enforcing explicit state and input constraints via convex QP
- Experimental validation demonstrating real-time feasibility and NMPC-comparable tracking
Why it matters
Provides a computationally efficient, constraint-aware, and data-free control framework enabling safe, agile quadrotor flight on resource-constrained embedded hardware.
Abstract
This letter presents an analytical linear parameter- varying (LPV) representation of quadrotor dynamics utilizing Koopman theory, facilitating computationally efficient linear model predictive control (LMPC) for real-time trajectory track- ing. By leveraging carefully designed Koopman observables, the proposed approach enables a compact lifted-space evolution that mitigates the curse of dimensionality while preserving the non- linear characteristics of the system. Although model predictive control (MPC) is a powerful strategy for quadrotor control, it faces a trade-off between the high computational cost of nonlinear MPC (NMPC) and the reduced accuracy of LMPC. To address this gap, we introduce KQ-LMPC (Koopman Quasilinear LPV MPC), which leverages the Koopman-lifted LPV formulation to enforce constraints, ensure lower computational burden and real- time feasibility, and deliver tracking performance comparable to NMPC. Experimental validation confirms the effectiveness of the framework in reasonably agile flight. To the best of our knowledge, this is the first experimentally validated LMPC for quadrotors that employs analytically derived Koopman observ- ables without requiring training data.