Flying Quadrotors in Tight Formations using Learning-based Model Predictive Control

TL;DR

This work proposes a framework that combines the benefits of first-principles modeling and data-driven approaches to construct an accurate and sample efficient representation of the complex aerodynamic effects resulting from quadrotors flying in formation, and achieves exceptional sample efficiency.

Abstract

Flying quadrotors in tight formations is a challenging problem. It is known that in the near-field airflow of a quadrotor, the aerodynamic effects induced by the propellers are complex and difficult to characterize. Although machine learning tools can potentially be used to derive models that capture these effects, these data-driven approaches can be sample inefficient and the resulting models often do not generalize as well as their first-principles counterparts. In this work, we propose a framework that combines the benefits of first-principles modeling and data-driven approaches to construct an accurate and sample efficient representation of the complex aerodynamic effects resulting from quadrotors flying in formation. The data-driven component within our model is lightweight, making it amenable for optimization-based control design. Through simulations and physical experiments, we show that incorporating the model into a novel learning-based nonlinear model predictive control (MPC) framework results in substantial performance improvements in terms of trajectory tracking and disturbance rejection. In particular, our framework significantly outperforms nominal MPC in physical experiments, achieving a 40.1% improvement in the average trajectory tracking errors and a 57.5% reduction in the maximum vertical separation errors. Our framework also achieves exceptional sample efficiency, using only a total of 46 seconds of flight data for training across both simulations and physical experiments. Furthermore, with our proposed framework, the quadrotors achieve an exceptionally tight formation, flying with an average separation of less than 1.5 body lengths throughout the flight. A video illustrating our framework and physical experiments is given here: https://youtu.be/Hv-0JiVoJGo

Figures (5)

• Figure 1: KNODE-DW MPC:Top: A composite photo depicting two Crazyflie (CF) quadrotors flying in lemniscate trajectories, under a stacked formation with a commanded separation of 2 body lengths. This is achieved with our proposed framework. The frames used to create this photo are extracted from a video taken during a physical experiment. Bottom: Schematic of our framework. CF image in schematic: Bitcraze.
• Figure 2: Force $(\tau_d)$ and torque $(\alpha_d)$ predictions: Heatmaps of the prediction root mean squared errors (RMSEs) given by the KNODE, DW and KNODE-DW models, normalized against those given by the nominal model, under different speeds and vertical separations.
• Figure 3: Closed-loop performance: Heatmaps of the tracking RMSEs and maximum vertical separation $\left(z_{{max}}\right)$ of the baseline and proposed MPC frameworks, normalized against those obtained from nominal MPC, under different speeds and vertical separations.
• Figure 4: Experiment statistics: Statistics of the runs for the baselines and the proposed framework. The top subplot depicts the RMSEs, and the maximum vertical separation $(z_{max})$ is shown in the bottom subplot. The markers and the error bars indicate the mean and standard deviation of the runs. The values behind the test cases in the legend, e.g., 0.2m for stacked 0.2m, denote the commanded vertical separation between the two quadrotors.
• Figure 5: Experiment results: Time histories of the vertical $(z)$ and radial $(r)$ separations, and the commanded thrust $(T_{cmd})$ of the bottom quadrotor, under the baselines and KNODE-DW MPC. This is during a more challenging test case, where the vertical separation between the two quadrotors is set at 0.8 body lengths throughout the flight.