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$\mathcal{L}_1$Quad: $\mathcal{L}_1$ Adaptive Augmentation of Geometric Control for Agile Quadrotors with Performance Guarantees

Zhuohuan Wu, Sheng Cheng, Pan Zhao, Aditya Gahlawat, Kasey A. Ackerman, Arun Lakshmanan, Chengyu Yang, Jiahao Yu, Naira Hovakimyan

TL;DR

This work tackles robust quadrotor control under complex, nonlinear, time- and state-dependent uncertainties on the $SE(3)$ manifold. It introduces $L_1$Quad, which augments a geometric controller with an $L_1$ adaptive layer that decouples estimation from control using a state predictor, a piecewise-constant adaptation law, and a low-pass filter, yielding a total input $u = u_b + u_{ad}$ with tunable, provable performance. Theoretical results provide a tube-based bound $x(t) \in \mathcal{O}(x_d(t),\rho)$ and a uniform ultimate bound $\mu(\omega,T_s,t_1)$ that improves with higher bandwidth $\omega$ and smaller $T_s$, balancing performance and robustness. Extensive flight experiments on a custom $0.63$ kg quadrotor validate the approach across eleven uncertain scenarios with a single parameter set, demonstrating consistently smaller tracking errors than competitive controllers and highlighting practical robustness gains for agile, disturbance-prone operations.

Abstract

Quadrotors that can operate predictably in the presence of imperfect model knowledge and external disturbances are crucial in safety-critical applications. We present L1Quad, a control architecture that ensures uniformly bounded transient response of the quadrotor's uncertain dynamics on the special Euclidean group SE(3). By leveraging the geometric controller and the L1 adaptive controller, the L1Quad architecture provides a theoretically justified framework for the design and analysis of quadrotor's tracking controller in the presence of nonlinear (time- and state-dependent) uncertainties on both the translational and rotational dynamics. In addition, we validate the performance of the L1Quad architecture through extensive experiments for eleven types of uncertainties across various trajectories. The results demonstrate that the L1Quad can achieve consistently small tracking errors despite the uncertainties and disturbances and significantly outperforms existing state-of-the-art controllers.

$\mathcal{L}_1$Quad: $\mathcal{L}_1$ Adaptive Augmentation of Geometric Control for Agile Quadrotors with Performance Guarantees

TL;DR

This work tackles robust quadrotor control under complex, nonlinear, time- and state-dependent uncertainties on the manifold. It introduces Quad, which augments a geometric controller with an adaptive layer that decouples estimation from control using a state predictor, a piecewise-constant adaptation law, and a low-pass filter, yielding a total input with tunable, provable performance. Theoretical results provide a tube-based bound and a uniform ultimate bound that improves with higher bandwidth and smaller , balancing performance and robustness. Extensive flight experiments on a custom kg quadrotor validate the approach across eleven uncertain scenarios with a single parameter set, demonstrating consistently smaller tracking errors than competitive controllers and highlighting practical robustness gains for agile, disturbance-prone operations.

Abstract

Quadrotors that can operate predictably in the presence of imperfect model knowledge and external disturbances are crucial in safety-critical applications. We present L1Quad, a control architecture that ensures uniformly bounded transient response of the quadrotor's uncertain dynamics on the special Euclidean group SE(3). By leveraging the geometric controller and the L1 adaptive controller, the L1Quad architecture provides a theoretically justified framework for the design and analysis of quadrotor's tracking controller in the presence of nonlinear (time- and state-dependent) uncertainties on both the translational and rotational dynamics. In addition, we validate the performance of the L1Quad architecture through extensive experiments for eleven types of uncertainties across various trajectories. The results demonstrate that the L1Quad can achieve consistently small tracking errors despite the uncertainties and disturbances and significantly outperforms existing state-of-the-art controllers.
Paper Structure (23 sections, 6 theorems, 106 equations, 17 figures, 6 tables, 1 algorithm)

This paper contains 23 sections, 6 theorems, 106 equations, 17 figures, 6 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Quadrotor Dynamics and Geometric controller
  3. Uncertainty Characterization
  4. $\mathcal{L}_1$ Adaptive Augmentation
  5. Performance Analysis
  6. Experimental results
  7. Uncertainty estimation and compensation
  8. Slosh payload
  9. Tunnel
  10. Chipped propeller
  11. Mixed propellers
  12. Voltage drop
  13. Ground effect
  14. Downwash
  15. Hanging off-center weights
  16. ...and 8 more sections

Key Result

Proposition 1

Consider the thrust magnitude $f_b$ and moment vector $M_b$ defined by equations eq:thrust control and eq:torque control, respectively. Suppose the initial condition $x(0) = \left(p(0),v(0),R(0),\Omega(0)\right)$ satisfies for $\Psi(R,R_d)\triangleq \text{tr}(I-R_d^\top R)/2$ being the rotation error function. Define $W_1$, $W_{12}$, $W_2 \in \mathbb{R}^{2 \times 2}$ as follows: and define $M_{1

Figures (17)

  • Figure 1: The quadrotor and reference frames.
  • Figure 2: The framework of geometric control with $\mathcal{L}_1$ adaptive augmentation for quadrotors. The $\mathcal{L}_1$ adaptive controller is highlighted in blue.
  • Figure 3: Results for the experiments with injected uncertainties on the thrust channel. Details about Adaptive 1, 2, and 3 are provided in Section \ref{['subsec: injected unc']}.
  • Figure 4: Slosh payload experiment.
  • Figure 5: Results for the tunnel experiment.
  • ...and 12 more figures

Theorems & Definitions (21)

  • Proposition 1
  • Remark 1
  • Remark 2
  • Proposition 2
  • proof
  • Proposition 3
  • Remark 3
  • Proposition 4
  • Remark 4
  • Theorem 1
  • ...and 11 more