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Online Adaptation for Flying Quadrotors in Tight Formations

Pei-An Hsieh, Kong Yao Chee, M. Ani Hsieh

TL;DR

This work tackles the challenge of flying quadrotor teams in tight formations where aerodynamic wake interactions are nonlinear and time-varying. It introduces the ${\cal L}_1$ KNODE-DW MPC framework, which blends mixed-expert downwash modeling (DW or KNODE-DW) with an ${\cal L}_1$ adaptive module to enable online disturbance compensation during formation flights. Extensive experiments with three quadrotors in V-stack and I-stack configurations demonstrate that ${\cal L}_1$ KNODE-DW MPC outperforms baseline MPC variants, achieving substantially lower RMSE and vertical deviation and enabling a compact I-stack formation with vertical separations as small as $0.2$ m. The results highlight the benefit of pairing an accurate disturbance model with adaptive control, advancing robust, high-precision formation flight applicable to manipulation, inspection, and cooperative tasks in cluttered environments.

Abstract

The task of flying in tight formations is challenging for teams of quadrotors because the complex aerodynamic wake interactions can destabilize individual team members as well as the team. Furthermore, these aerodynamic effects are highly nonlinear and fast-paced, making them difficult to model and predict. To overcome these challenges, we present L1 KNODE-DW MPC, an adaptive, mixed expert learning based control framework that allows individual quadrotors to accurately track trajectories while adapting to time-varying aerodynamic interactions during formation flights. We evaluate L1 KNODE-DW MPC in two different three-quadrotor formations and show that it outperforms several MPC baselines. Our results show that the proposed framework is capable of enabling the three-quadrotor team to remain vertically aligned in close proximity throughout the flight. These findings show that the L1 adaptive module compensates for unmodeled disturbances most effectively when paired with an accurate dynamics model. A video showcasing our framework and the physical experiments is available here: https://youtu.be/9QX1Q5Ut9Rs

Online Adaptation for Flying Quadrotors in Tight Formations

TL;DR

This work tackles the challenge of flying quadrotor teams in tight formations where aerodynamic wake interactions are nonlinear and time-varying. It introduces the KNODE-DW MPC framework, which blends mixed-expert downwash modeling (DW or KNODE-DW) with an adaptive module to enable online disturbance compensation during formation flights. Extensive experiments with three quadrotors in V-stack and I-stack configurations demonstrate that KNODE-DW MPC outperforms baseline MPC variants, achieving substantially lower RMSE and vertical deviation and enabling a compact I-stack formation with vertical separations as small as m. The results highlight the benefit of pairing an accurate disturbance model with adaptive control, advancing robust, high-precision formation flight applicable to manipulation, inspection, and cooperative tasks in cluttered environments.

Abstract

The task of flying in tight formations is challenging for teams of quadrotors because the complex aerodynamic wake interactions can destabilize individual team members as well as the team. Furthermore, these aerodynamic effects are highly nonlinear and fast-paced, making them difficult to model and predict. To overcome these challenges, we present L1 KNODE-DW MPC, an adaptive, mixed expert learning based control framework that allows individual quadrotors to accurately track trajectories while adapting to time-varying aerodynamic interactions during formation flights. We evaluate L1 KNODE-DW MPC in two different three-quadrotor formations and show that it outperforms several MPC baselines. Our results show that the proposed framework is capable of enabling the three-quadrotor team to remain vertically aligned in close proximity throughout the flight. These findings show that the L1 adaptive module compensates for unmodeled disturbances most effectively when paired with an accurate dynamics model. A video showcasing our framework and the physical experiments is available here: https://youtu.be/9QX1Q5Ut9Rs

Paper Structure

This paper contains 15 sections, 9 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Contribution
  3. Technical Approach
  4. Modeling Complex Aerodynamic Interactions
  5. Formation Controller Synthesis
  6. Baseline MPC
  7. $\mathcal{L}_1$ Adaptive Module
  8. $\mathcal{L}_1$ KNODE-DW MPC
  9. Results
  10. Performance of the Center Quadrotor
  11. Performance of the Bottom Quadrotor
  12. Achieving Tight I-stack Formations
  13. Discussions
  14. Conclusion and Future Work
  15. Acknowledgements

Figures (4)

  • Figure 1: Schematics of V-stack and I-stack formations:$z_1$ and $z_2$ represent the vertical separations between the top and center quadrotors, and between the center and bottom quadrotors, respectively. r denotes the horizontal separation of the top and the center quadrotors in V-stack.
  • Figure 2: Center quadrotor statistics: Performance of the center quadrotor flying in V-stack and I-stack formations. The top subplot shows RMSEs, and the bottom subplot shows the maximum vertical deviation $z_{\max}$. Markers and error bars represent the mean and standard deviation.
  • Figure 3: Bottom quadrotor statistics: Performance of the bottom quadrotor in V-stack and I-stack formations. The top subplot shows RMSEs, and the bottom subplot shows $z_{\max}$. Markers and error bars represent the mean and standard deviation.
  • Figure 4: Time history and real-world trajectory: The plot on the left shows the $z$ position and thrust histories of the three quadrotors flying a tight I-stack formation. The blue, orange, and green lines represent the top, center, and bottom quadrotors, respectively. The composite photo on the right captures the second half of the same real-world experiment, showing the quadrotors in flight.