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MPC-Based Trajectory Tracking for a Quadrotor UAV with Uniform Semi-Global Asymptotic Stability Guarantees

Qian Yang, Miaomiao Wang, Abdelhamid Tayebi

Abstract

This paper proposes a model predictive trajectory tracking approach for quadrotors subject to input constraints. Our proposed approach relies on a hierarchical control strategy with an outer-loop feedback generating the required thrust and desired attitude and an inner-loop feedback regulating the actual attitude to the desired one. For the outer-loop translational dynamics, the generation of the virtual control input is formulated as a constrained model predictive control problem with time-varying input constraints and a control strategy, endowed with uniform global asymptotic stability guarantees, is proposed. For the inner-loop rotational dynamics, a hybrid geometric controller is adopted, achieving semi-global exponential tracking of the desired attitude. Finally, we prove that the overall cascaded system is semi-globally asymptotically stable. Simulation results illustrate the effectiveness of the proposed approach.

MPC-Based Trajectory Tracking for a Quadrotor UAV with Uniform Semi-Global Asymptotic Stability Guarantees

Abstract

This paper proposes a model predictive trajectory tracking approach for quadrotors subject to input constraints. Our proposed approach relies on a hierarchical control strategy with an outer-loop feedback generating the required thrust and desired attitude and an inner-loop feedback regulating the actual attitude to the desired one. For the outer-loop translational dynamics, the generation of the virtual control input is formulated as a constrained model predictive control problem with time-varying input constraints and a control strategy, endowed with uniform global asymptotic stability guarantees, is proposed. For the inner-loop rotational dynamics, a hybrid geometric controller is adopted, achieving semi-global exponential tracking of the desired attitude. Finally, we prove that the overall cascaded system is semi-globally asymptotically stable. Simulation results illustrate the effectiveness of the proposed approach.

Paper Structure

This paper contains 18 sections, 10 theorems, 101 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation and Definitions
  4. Problem Formulation
  5. Control System Design
  6. Thrust, Desired Attitude and Input Constraints
  7. Model Predictive Control
  8. Stability for Continuous-Time System
  9. Inner-Loop Tracking
  10. Stability of Cascaded System
  11. Simulation Results
  12. Conclusions And Future Work
  13. Proof of Lemma 1
  14. The expressions of $\omega_d$ and $\dot{\omega}_d$
  15. Proof of Lemma 3
  16. ...and 3 more sections

Key Result

Lemma 1

For all $a>0, b\in[0,1]$, and $x\in\mathbb{R}$, the following inequality holds:

Figures (3)

  • Figure 2: 3D plot of the reference and actual trajectories, where the black dot indicates the starting point of the actual trajectory.
  • Figure 3: Tracking errors.
  • Figure 4: Desired accelerations $\mu_d$ and MPC input $u_{\mathrm{MPC}}$.

Theorems & Definitions (24)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Remark 1
  • Theorem 1
  • ...and 14 more