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A Perception-feedback position-tracking control for quadrotors

Eduardo Espindola, Yu Tang

TL;DR

<3-5 sentence high-level summary>The paper tackles robust quadrotor position tracking using perception feedback without state estimation, leveraging onboard vector measurements and gyro-rate data. It integrates a translational controller with a vector-measurement–based attitude controller and a gyro-bias observer, all analyzed under Lyapunov theory to prove practical stability and almost global semiglobal exponential stability in the disturbance-free case. Key contributions include bypassing attitude estimation, bias compensation for low-cost gyros, and a modular design supporting stability guarantees and robustness to noise and parameter uncertainty. The work demonstrates significant practical impact by enabling precise tracking with low-cost sensors in realistic scenarios and lays groundwork for integrating learning-based elements in future extensions.

Abstract

In this paper a position-tracking controller for quadrotors based on perception feedback is developed, which directly uses measurements from onboard sensors such as low cost IMUs and GPS to generate the control commands without state estimation. Bias in gyros sensors are corrected to enhance the tracking performance. Practical stability of the origin of the tracking error system in the presence of external disturbances is proved using the Lyapunov analysis, which turns out to exponential stability in the absence of external disturbances. Numerical simulations are included to illustrate the proposed control scheme and to verify the robustness of the proposed controller under noisy measurements and parameter uncertainties.

A Perception-feedback position-tracking control for quadrotors

TL;DR

<3-5 sentence high-level summary>The paper tackles robust quadrotor position tracking using perception feedback without state estimation, leveraging onboard vector measurements and gyro-rate data. It integrates a translational controller with a vector-measurement–based attitude controller and a gyro-bias observer, all analyzed under Lyapunov theory to prove practical stability and almost global semiglobal exponential stability in the disturbance-free case. Key contributions include bypassing attitude estimation, bias compensation for low-cost gyros, and a modular design supporting stability guarantees and robustness to noise and parameter uncertainty. The work demonstrates significant practical impact by enabling precise tracking with low-cost sensors in realistic scenarios and lays groundwork for integrating learning-based elements in future extensions.

Abstract

In this paper a position-tracking controller for quadrotors based on perception feedback is developed, which directly uses measurements from onboard sensors such as low cost IMUs and GPS to generate the control commands without state estimation. Bias in gyros sensors are corrected to enhance the tracking performance. Practical stability of the origin of the tracking error system in the presence of external disturbances is proved using the Lyapunov analysis, which turns out to exponential stability in the absence of external disturbances. Numerical simulations are included to illustrate the proposed control scheme and to verify the robustness of the proposed controller under noisy measurements and parameter uncertainties.

Paper Structure

This paper contains 18 sections, 5 theorems, 52 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Quadrotor model
  5. Measurements
  6. Control problem statement
  7. Tracking controller design
  8. Positioning controller design
  9. Attitude controller design
  10. Main result
  11. Simulations
  12. Scenario 1. Ideal situation.
  13. Scenario 2. Noisy measurements
  14. Scenario 3. Parametric uncertainty.
  15. Scenario 4. Apparent acceleration.
  16. ...and 3 more sections

Key Result

Proposition 1

Consider the dynamics of translational errors eq:xTldP-eq:vTldP in closed loop with the control law eq:CtrlPs-eq:eta. Under Assumption A3, let the control gains be such that $0<k_x<g-\mu_d$, $k>k_x$, and $\lambda_{\min}(K_f)>\frac{k_x}{4m^2}$. Then the origin $(\tilde{x},\tilde{v})=0_{6\times 1}$ is

Figures (6)

  • Figure 1: Reference frames of the quadrotor.
  • Figure 2: Scenario 1 (ideal situation). Performance of the proposed controller under noise-free measurements and known inertia matrix.
  • Figure 3: Scenario 1 (ideal situation). The actual path of the quadrotor (blue) tracks the desired path (red). (a) A 3D view in the inertial frame $\{e_{x},e_{y},e_{z}\}$ [m]. (b) Plane $\{e_{x}-e_{y}\}$ view. (c) Plane $\{e_{x}-e_{z}\}$ view.
  • Figure 4: Scenario 2 (noisy-measurement situation). Performance of the proposed controller under noisy measurements.
  • Figure 5: Scenario 3 (uncertain inertia matrix). Performance of the proposed controller under uncertainty in the inertia matrix.
  • ...and 1 more figures

Theorems & Definitions (15)

  • Remark 1
  • Proposition 1: Practical stability of position subsystem
  • proof
  • Lemma 1: Alignment error variables $\varepsilon (t)$ and $z(t)$
  • proof
  • Proposition 2: Stability of the rotational error dynamics
  • proof
  • Remark 2
  • Theorem 1: Tracking control
  • proof
  • ...and 5 more