Koopman-Based Linear MPC with INDI for Quadrotor Trajectory Tracking Control

This paper proposes an analytical Koopman-based linear model predictive control (MPC) method for real-time quadrotor trajectory tracking. While linear MPC offers computational efficiency, it sacrifices modeling fidelity; nonlinear MPC solved via sequential quadratic programming achieves high accuracy but requires multiple iterations at each control step. We develop a systematic procedure to derive Koopman observables that lift the dynamics into a quasi-linear model with state-dependent control matrix. An assumed state trajectory converts this to a linear time-varying system at each control period, enabling quadratic program formulation with guaranteed real-time solvability. An incremental nonlinear dynamic inversion (INDI)-based robust control allocation scheme is proposed, which requires no precise control effectiveness model. Simulation results demonstrate tracking performance comparable to nonlinear MPC with deterministic computation times. The proposed method requires no training data collection, making it straightforward to implement.