Minutes of Data, Milliseconds of Control: Shared Physical Structure for Quadrotor World Modeling and Convex MPC

Quadrotor world models must learn from limited noisy observations while supporting optimization at high control rates. We introduce ABS-PWM, a probabilistic world model based on an analytically constructed bilinear lifting of quadrotor dynamics. Its analytical lifting and reconstruction maps maintain physically meaningful predictions, while a structured stochastic transition captures aerodynamic effects, unmodeled dynamics, and observation uncertainty. We train ABS-PWM directly from noisy trajectories using generalized expectation conditional maximization, combining latent-state smoothing with closed-form covariance updates. The same bilinear structure enables BUC-MPC, a convex uncertainty-aware model predictive control (MPC) scheme. Experiments in high-fidelity simulation show that ABS-PWM achieves competitive short-horizon prediction accuracy from limited flight data while providing faster rollouts than the evaluated state-of-the-art baselines. In closed loop, BUC-MPC achieves accurate tracking, high completion rates under shifts in vehicle and environmental dynamics, and computation compatible with high-frequency control. Additional experiments with a separately trained model on a second quadrotor platform demonstrate the framework's applicability across vehicle configurations.