Gp-$\mathcal{L}_{1}$ NMPC for Quadrotors Agile Flight

Quadrotor's agile flight in complex environments has numerous potential applications such as search and rescue. Recently, nonlinear model predictive control (NMPC) has shown more advantageous results in agile quadrotor control. However, it relies on highly accurate models for maximum tracking accuracy and lacks the capability to reject external disturbances. Model uncertainties, including unmodeled complex aerodynamic effects and external disturbances, will degrade the system's performance. In this paper, we propose gaussian process-<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{1}$</tex>-nonlinear model predictive control (GP-<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{1}$</tex>-NMPC), a novel hybrid adaptive NMPC approach that leverages Gaussian process regression to learn complex unmodeled aerodynamic effects and employs <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{1}$</tex> adaptive control to compensate for external disturbances in real time. Specifically, we use the nominal model enhanced with the Gaussian process model as a reference model for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{1}$</tex> adaptive control to reduce tracking error. The proposed method demonstrates immense tracking accuracy and robustness, with more than 90% tracking error reduction over baseline NMPC without any gain tuning at a speed of 10 m/s.