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Adaptive Attitude Control for Foldable Quadrotors

Karishma Patnaik, Wenlong Zhang

Abstract

Recent quadrotors have transcended conventional designs, emphasizing more on foldable and reconfigurable bodies. The state of the art still focuses on the mechanical feasibility of such designs with limited discussions on the tracking performance of the vehicle during configuration switching. In this article, we first present a common framework to analyse the attitude errors of a folding quadrotor via the theory of switched systems. We then employ this framework to investigate the attitude tracking performance for two case scenarios - one with a conventional geometric controller for precisely known system dynamics; and second, with our proposed morphology-aware adaptive controller that accounts for any modeling uncertainties and disturbances. Finally, we cater to the desired switching requirements from our stability analysis by exploiting the trajectory planner to obtain superior tracking performance while switching. Simulation results are presented that validate the proposed control and planning framework for a foldable quadrotor's flight through a passageway.

Adaptive Attitude Control for Foldable Quadrotors

Abstract

Recent quadrotors have transcended conventional designs, emphasizing more on foldable and reconfigurable bodies. The state of the art still focuses on the mechanical feasibility of such designs with limited discussions on the tracking performance of the vehicle during configuration switching. In this article, we first present a common framework to analyse the attitude errors of a folding quadrotor via the theory of switched systems. We then employ this framework to investigate the attitude tracking performance for two case scenarios - one with a conventional geometric controller for precisely known system dynamics; and second, with our proposed morphology-aware adaptive controller that accounts for any modeling uncertainties and disturbances. Finally, we cater to the desired switching requirements from our stability analysis by exploiting the trajectory planner to obtain superior tracking performance while switching. Simulation results are presented that validate the proposed control and planning framework for a foldable quadrotor's flight through a passageway.
Paper Structure (27 sections, 72 equations, 7 figures)

This paper contains 27 sections, 72 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Error Definitions
  4. Controller Design and Stability Analysis
  5. Case with the precise model, $\Delta = [0~0~0]^T$
  6. Attitude tracking of individual subsystems
  7. Stability of the overall switched system
  8. Case with model uncertainties in $\textit{H}_\textit{p}$ , $\Delta = [0 ~0 ~0]^T$
  9. Attitude tracking for individual subsystems
  10. Stability of the switched system
  11. Case with model uncertainties in $\textit{H}_\textit{p}$ and external disturbances, $\Delta \neq [0 ~0 ~0]^T$
  12. Control-Aware Minimum Jerk Trajectory
  13. Results and Discussion
  14. Conclusion
  15. Notations and Definitions
  16. ...and 12 more sections

Figures (7)

  • Figure 1: (a) Example of the foldable quadrotors Y+19 considered as switching systems in this work. (b) Illustrates a foldable quadrotor switched system consisting of four individual subsystems.
  • Figure 2: Lyapunov function of the attitude tracking error during configuration switching. $\tau_s$ and $\tau_d$ represent the attitude settling-time and desired dwell-time respectively.
  • Figure 3: Performance of the proposed attitude controller when the vehicle switches between the two configurations shown in Fig. \ref{['fig:lyapunov']}(a) at $t = 30s$ from 1 to 2 (black dash-dotted vertical line) and at $t= 60s$ from 2 to 1 (pink dashed vertical line) by following (\ref{['eqn:switch_condition']}). With the proposed adaptive controller, the attitude errors converge to the reference (horizontal dotted lines).
  • Figure 4: The tracking results for minimum-jerk trajectory and waypoint based methods. The MJT based trajectory leads to low deviations from the trajectory, while the waypoint based one leads to safety constraint violations.
  • Figure 5: Performance comparison between the proposed adaptive controller and a conventional robust controller L+18, without the presence of disturbances, when the configuration switches from 1 to 2 at $t = 30$s and from 2 to 1 at $t = 60$s. The uncertainty bounds assumed for the robust controller are constant across the two subsystems and are too high for the subsystem 2. This leads to high control efforts and chattering. It also demonstrates higher control efforts initially from t = 0 to 1s. The adaptive controller has similar performance, however, with low control efforts through-out the entire flight. Please note that, we define control effort as the magnitude of the control torques computed by the controller.
  • ...and 2 more figures