Robust Optimal Agile Flight of Quadrotors: An Internal Model-Based Nonlinear Model Predictive Optimization Approach

Achieving robust agile quadrotor flight under unknown external disturbances and parametric uncertainty remains a significant challenge. Inspired by robust output regulation theory, this paper proposes IM-NMPO, an Internal Model-based Nonlinear Model Predictive Optimization framework for robust optimal planning and control during agile flight. The core insight is the systematic decoupling of uncertain dynamics from the optimization loop via the internal model principle (IMP), enabling real-time disturbance learning and rejection while reducing reliance on high-fidelity physical models. This allows both time-optimal planning and nonlinear model predictive control (NMPC) to operate on the same disturbance-decoupled nominal dynamics. The proposed framework comprises three main components: translational and rotational nonlinear internal model compensators for real-time disturbance rejection, an NMPC optimization stabilizer for constrained agile trajectory tracking, and a receding-horizon polynomial waypoint allocation module for efficient online time-optimal reference generation. Robust constraint satisfaction, recursive feasibility and asymptotic stability are guaranteed through rigorous theoretical analysis. The effectiveness and generalizability are validated through extensive flight experiments under various disturbances, including unknown payloads, persistent fan-induced winds, and time-varying gusts, across quadrotors with different wheelbases. The framework was successfully deployed in the 2024 DJI Robomaster Intelligent MAV Championship for Planning and Control of Quadrotors, where it completed challenging racing courses at speeds up to 23.3 m/s, ranking first and finishing in less than one-third of the time taken by the second-place.