Design and implementation of a tube nonlinear model predictive controller for quadcopter trajectory tracking

Trajectory tracking of quadrotors is conventionally addressed by a range of control strategies, including cascade Proportional-Integral-Derivative (PID) loops, linear Model Predictive Control (MPC) designed around a hover-linearized model, feedback linearization, sliding-mode control, and nominal nonlinear MPC (NLMPC). Each of these approaches, however, suffers from inherent limitations: linear schemes lose accuracy under aggressive maneuvers, large attitude excursions, and strong nonlinear couplings; feedback linearization relies on exact cancellation of the nonlinear dynamics and degrades rapidly when the dynamic model is not precisely known; sliding-mode controllers are prone to chattering and require conservative disturbance bounds; and nominal NLMPC offers no guarantee of constraint satisfaction in the presence of disturbances and model uncertainty. To overcome these limitations, this article develops a robust Tube-based NLMPC for the full nonlinear 12-state quadrotor model, explicitly accounting for inertia uncertainties along the x , y , and z axes as well as bounded additive disturbances acting on the states. The tube-based formulation optimizes a nominal disturbance-free trajectory online while an ancillary feedback law confines the true state within a robust invariant tube around it, thereby guaranteeing robust constraint satisfaction. Recursive feasibility, asymptotic stability of the nominal closed loop, and input-to-state stability of the perturbed system are formally established. The proposed controller is benchmarked against a conventional cascade PID scheme in constant-reference and helical-path tracking scenarios under injected disturbances. Simulation results show that the Tube NLMPC achieves lower tracking error, faster settling, reduced oscillations, and markedly superior disturbance rejection, while its average per-step computation time of 3.86 ms-well within the 100 ms sampling interval-confirms its real-time feasibility and practical suitability for deployment in unpredictable operating environments.