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Fixed-time Disturbance Observer-Based MPC Robust Trajectory Tracking Control of Quadrotor

Liwen Xu, Bailing Tian, Cong Wang, Junjie Lu, Dandan Wang, Zhiyu Li, Qun Zong

Abstract

In this paper, a fixed-time disturbance observerbased model predictive control algorithm is proposed for trajectory tracking of quadrotor in the presence of disturbances. First, a novel multivariable fixed-time disturbance observer is proposed to estimate the lumped disturbances. The bi-limit homogeneity and Lyapunov techniques are employed to ensure the convergence of estimation error within a fixed convergence time, independent of the initial estimation error. Then, an observerbased model predictive control strategy is formulated to achieve robust trajectory tracking of quadrotor, attenuating the lumped disturbances and model uncertainties. Finally, simulations and real-world experiments are provided to illustrate the effectiveness of the proposed method.

Fixed-time Disturbance Observer-Based MPC Robust Trajectory Tracking Control of Quadrotor

Abstract

In this paper, a fixed-time disturbance observerbased model predictive control algorithm is proposed for trajectory tracking of quadrotor in the presence of disturbances. First, a novel multivariable fixed-time disturbance observer is proposed to estimate the lumped disturbances. The bi-limit homogeneity and Lyapunov techniques are employed to ensure the convergence of estimation error within a fixed convergence time, independent of the initial estimation error. Then, an observerbased model predictive control strategy is formulated to achieve robust trajectory tracking of quadrotor, attenuating the lumped disturbances and model uncertainties. Finally, simulations and real-world experiments are provided to illustrate the effectiveness of the proposed method.
Paper Structure (16 sections, 3 theorems, 35 equations, 17 figures, 3 tables)

This paper contains 16 sections, 3 theorems, 35 equations, 17 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Model and Control Objective Statement
  3. Design of FxTDO-MPC Algorithm and INDI Angular Velocity Controller
  4. Related Lemmas
  5. Fixed-Time Disturbance Observer Design
  6. Trajectory Tracking Controller Design
  7. FxTDO-based MPC controller
  8. INDI Angular Velocity Controller
  9. Simulation and Experiment
  10. Simulation Setups
  11. Simulation Results
  12. Real-world Experiment Setups
  13. Real-world Experiment Results
  14. Hover performance with persistent wind disturbance (Scenario 1)
  15. Trajectory tracking with complex disturbances (Scenario 2)
  16. ...and 1 more sections

Key Result

Lemma 1

cruz2021high Let $\eta: {\mathbb{R}}^n \to {\mathbb{R}}$ and $\gamma : {\mathbb{R}}^n \to {\mathbb{R}}_+$ be two upper semicontinuous, single-valued bl-homogeneous functions, with the same weights, degrees and approximating functions. Suppose that $\forall x \in {\mathbb{R}}^n$, $\left\lbrace x \in

Figures (17)

  • Figure 1: Trajectory visualization utilizing the proposed FxTDO-MPC algorithm in real-world experiments. More details can be found in the attached video at https://youtu.be/O4BDXRdd0Do or https://www.bilibili.com/video/BV11h4y1i7oF/.
  • Figure 2: Quadrotor model with World frame $W$ and Body frame $B$. $T_i$ and $\Omega_i$ are respectively single thrust and speed of the individual rotors.
  • Figure 3: System overview of the proposed algorithm applied to quadrotor system. The frequencies of MPC and FxTDO are decided based on the computational time of FxTDO-MPC running on the onboard computer. Besides, the frequency of INDI angular velocity controller is selected based on the PX4 Autopilot User Guide. Additionally, the generating frequency of the desired trajectory is chosen to cooperate with the controller.
  • Figure 4: The quadrotor used for real-world experiments.
  • Figure 5: Disturbances in real-world experiments. (a) Disturbances in hovering tests (Scenario 1). (b) Disturbances in trajectory tracking tests (Scenario 2).
  • ...and 12 more figures

Theorems & Definitions (4)

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