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Adaptive Backstepping and Non-singular Sliding Mode Control for Quadrotor UAVs with Unknown Time-varying Uncertainties

Arezo Shevidi, Hashim A. Hashim

TL;DR

This work tackles robust position and orientation control for underactuated quadrotor UAVs subject to unknown time-varying uncertainties. It introduces a cascaded quaternion-based framework with an outer-loop adaptive backstepping control (QABC) for translation and an inner-loop non-singular adaptive sliding mode control (QASMC) for attitude, with Lyapunov-based proofs of asymptotic stability and adaptive laws to mitigate model variations and chattering. The approach yields singularity-free, robust tracking of both position and orientation, and computes thrust and attitude commands directly from the translational controller. Simulation comparisons against Euler-angle methods demonstrate superior stability, robustness, and avoidance of singularities, highlighting practical benefits for real-world quadrotor flights under large initial errors.

Abstract

This paper presents a novel quaternion-based nonsingular control system for underactuated vertical-take-off and landing (VTOL) Unmanned Aerial Vehicles (UAVs). Position and attitude tracking is challenging regarding singularity and accuracy. Quaternion-based Adaptive Backstepping Control (QABC) is developed to tackle the underactuated issues of UAV control systems in a cascaded way. Leveraging the virtual control (auxiliary control) developed in the QABC, desired attitude components and required thrust are produced. Afterwards, we propose Quaternion-based Sliding Mode Control (QASMC) to enhance the stability and mitigate chattering issues. The sliding surface is modified to avoid singularity compared to conventional SMC. To improve the robustness of controllers, the control parameters are updated using adaptation laws. Furthermore, the asymptotic stability of translational and rotational dynamics is guaranteed by utilizing Lyapunov stability and Barbalet Lemma. Finally, the comprehensive comparison results are provided to verify the effectiveness of the proposed controllers in the presence of unknown time-varying parameter uncertainties and significant initial errors. Keywords: Non-singular Sliding Mode Control, Adaptive Backstepping Control, Unit-quaternion, Drones, Unmanned Aerial Vehicles, Asymptotic Stability, Position and Orientation Control

Adaptive Backstepping and Non-singular Sliding Mode Control for Quadrotor UAVs with Unknown Time-varying Uncertainties

TL;DR

This work tackles robust position and orientation control for underactuated quadrotor UAVs subject to unknown time-varying uncertainties. It introduces a cascaded quaternion-based framework with an outer-loop adaptive backstepping control (QABC) for translation and an inner-loop non-singular adaptive sliding mode control (QASMC) for attitude, with Lyapunov-based proofs of asymptotic stability and adaptive laws to mitigate model variations and chattering. The approach yields singularity-free, robust tracking of both position and orientation, and computes thrust and attitude commands directly from the translational controller. Simulation comparisons against Euler-angle methods demonstrate superior stability, robustness, and avoidance of singularities, highlighting practical benefits for real-world quadrotor flights under large initial errors.

Abstract

This paper presents a novel quaternion-based nonsingular control system for underactuated vertical-take-off and landing (VTOL) Unmanned Aerial Vehicles (UAVs). Position and attitude tracking is challenging regarding singularity and accuracy. Quaternion-based Adaptive Backstepping Control (QABC) is developed to tackle the underactuated issues of UAV control systems in a cascaded way. Leveraging the virtual control (auxiliary control) developed in the QABC, desired attitude components and required thrust are produced. Afterwards, we propose Quaternion-based Sliding Mode Control (QASMC) to enhance the stability and mitigate chattering issues. The sliding surface is modified to avoid singularity compared to conventional SMC. To improve the robustness of controllers, the control parameters are updated using adaptation laws. Furthermore, the asymptotic stability of translational and rotational dynamics is guaranteed by utilizing Lyapunov stability and Barbalet Lemma. Finally, the comprehensive comparison results are provided to verify the effectiveness of the proposed controllers in the presence of unknown time-varying parameter uncertainties and significant initial errors. Keywords: Non-singular Sliding Mode Control, Adaptive Backstepping Control, Unit-quaternion, Drones, Unmanned Aerial Vehicles, Asymptotic Stability, Position and Orientation Control
Paper Structure (12 sections, 3 theorems, 44 equations, 2 figures, 1 table)

This paper contains 12 sections, 3 theorems, 44 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Quaternion-based model representation of VTOL-UAV
  4. UAV Quaternion-based Translational Dynamic
  5. Rotational Dynamic
  6. Quaternion-based control design
  7. Adaptive Back Stepping control for translational motion
  8. Robust quaternion-based sliding mode attitude control
  9. Results and discussion
  10. Discussion
  11. Comparision
  12. conclusion

Key Result

Theorem 1

Consider the translation dynamics described by eq:eqTranslation. If the pose control is implemented as eq:eq19 with adaptation law in eq:ad1p, then the closed-loop translational system is asymptotically stable, meanwhile position and velocity errors are $\tilde{P}\rightarrow 0_{3\times 1}$ and $\til

Figures (2)

  • Figure 1: UAV flight trajectories, errors, and control signals
  • Figure 2: Position and attitude errors in literaturelabbadi2019robust vs proposed work: Euler angles (literaturelabbadi2019robust plotted in red solid line, while proposed approach plotted in blue dash-line.)

Theorems & Definitions (6)

  • Theorem 1
  • Lemma 1
  • proof
  • Remark 1
  • Theorem 2
  • proof