Uncertainty-aware model predictive control with learning-based residual dynamics compensation for agile quadrotor trajectory tracking

Achieving high-precision trajectory tracking for quadrotors during high-speed and agile maneuvers remains a significant challenge, primarily due to uncertainty induced by model inaccuracies and external disturbances. To address this issue, we propose an Uncertainty-aware Learning-based Model Predictive Control (UL-MPC) method. Specifically, we learn residual dynamics using a probabilistic neural network that outputs both the residual mean and covariance. The learned mean compensates the nominal model, while the predicted uncertainty is incorporated into chance-constrained MPC via covariance propagation and adaptive constraint tightening, leading to improved tracking accuracy while enhancing robust constraint satisfaction. Furthermore, we provide a Lyapunov-based analysis to establish local mean-square boundedness of the linearized closed-loop error dynamics. High-fidelity Gazebo simulations with stochastic wind and aggressive trajectories demonstrate consistent improvements over nominal MPC and state-of-the-art learning-based MPC baselines, achieving approximately a 32% reduction in tracking errors and a 44% reduction in safety-boundary violation rate relative to the strongest baseline.