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Accuracy and stability are common requirements for Quadrotor trajectorytracking systems. Designing an accurate and stable tracking controller remainschallenging, particularly in unknown and dynamic environments with complexaerodynamic disturbances. We propose a Quantile-approximation-basedDistributional-reinforced Uncertainty Estimator (QuaDUE) to accurately identifythe effects of aerodynamic disturbances, i.e., the uncertainties between thetrue and estimated Control Contraction Metrics (CCMs). Taking inspiration fromcontraction theory and integrating the QuaDUE for uncertainties, our novelCCM-based trajectory tracking framework tracks any feasible referencetrajectory precisely whilst guaranteeing exponential convergence. Moreimportantly, the convergence and training acceleration of the distributional RLare guaranteed and analyzed, respectively, from theoretical perspectives. Wealso demonstrate our system under unknown and diverse aerodynamic forces. Underlarge aerodynamic forces (>2m/s^2), compared with the classic data-drivenapproach, our QuaDUE-CCM achieves at least a 56.6% improvement in trackingerror. Compared with QuaDRED-MPC, a distributional RL-based approach,QuaDUE-CCM achieves at least a 3 times improvement in contraction rate.

QuaDUE-CCM: Interpretable Distributional Reinforcement Learning using Uncertain Contraction Metrics for Precise Quadrotor Trajectory Tracking