Tiny aerial robots hold great promise for applications such as environmental monitoring and search-and-rescue, yet face significant control challenges due to limited onboard computing power and nonlinear dynamics. Model Predictive Control (MPC) enables agile trajectory tracking and constraint handling but depends on an accurate dynamics model. While existing Learning-Based (LB) MPC methods, such as Gaussian Process (GP) MPC, enhance performance by learning residual dynamics, their high computational cost restricts onboard deployment on tiny robots. This paper introduces Tiny LB MPC, a co-designed MPC framework and optimization solver for resource-constrained micro multirotor platforms. The proposed approach achieves 100 Hz control on a Crazyflie 2.1 equipped with a Teensy 4.0 microcontroller, demonstrating a 43% average improvement in tracking performance over existing embedded MPC methods under model uncertainty, and achieving the first onboard implementation of LB MPC on a 53 g multirotor.

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