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Multirotor Nonlinear Model Predictive Control based on Visual Servoing of Evolving Features

Sotirios N. Aspragkathos, Panagiotis Rousseas, George C. Karras, Kostas J. Kyriakopoulos

TL;DR

This article presents a Visual Servoing Nonlinear Model Predictive Control scheme for autonomously tracking a moving target using multirotor Unmanned Aerial Vehicles (UAVs) for surveillance and tracking of contour-based areas with evolving features.

Abstract

This article presents a Visual Servoing Nonlinear Model Predictive Control (NMPC) scheme for autonomously tracking a moving target using multirotor Unmanned Aerial Vehicles (UAVs). The scheme is developed for surveillance and tracking of contour-based areas with evolving features. NMPC is used to manage input and state constraints, while additional barrier functions are incorporated in order to ensure system safety and optimal performance. The proposed control scheme is designed based on the extraction and implementation of the full dynamic model of the features describing the target and the state variables. Real-time simulations and experiments using a quadrotor UAV equipped with a camera demonstrate the effectiveness of the proposed strategy.

Multirotor Nonlinear Model Predictive Control based on Visual Servoing of Evolving Features

TL;DR

This article presents a Visual Servoing Nonlinear Model Predictive Control scheme for autonomously tracking a moving target using multirotor Unmanned Aerial Vehicles (UAVs) for surveillance and tracking of contour-based areas with evolving features.

Abstract

This article presents a Visual Servoing Nonlinear Model Predictive Control (NMPC) scheme for autonomously tracking a moving target using multirotor Unmanned Aerial Vehicles (UAVs). The scheme is developed for surveillance and tracking of contour-based areas with evolving features. NMPC is used to manage input and state constraints, while additional barrier functions are incorporated in order to ensure system safety and optimal performance. The proposed control scheme is designed based on the extraction and implementation of the full dynamic model of the features describing the target and the state variables. Real-time simulations and experiments using a quadrotor UAV equipped with a camera demonstrate the effectiveness of the proposed strategy.
Paper Structure (19 sections, 5 theorems, 50 equations, 16 figures)

This paper contains 19 sections, 5 theorems, 50 equations, 16 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Methodology
  4. Extraction of features dynamics
  5. Control Development
  6. Constraint embedding via barrier functions
  7. Vision-based NMPC Framework for Deformable Target Tracking
  8. Stability Analysis
  9. Feasibility Analysis
  10. Convergence Analysis
  11. Implementation Details
  12. Level frame mapping
  13. Multirotor Low-Level Control
  14. Multirotor Under-actuation
  15. Results
  16. ...and 4 more sections

Key Result

Lemma 1

Given an input sequence, the error between the predicted and actual state of the system at time step $k+i$ is bounded by: where $\sum_{j=0}^{i-1} (L_f)^{j} = \frac{L_{f}^{i}-1}{L_f-1}$ and $L_f$ is the Lipschitz constant of the nominal system.

Figures (16)

  • Figure 1: Geometric representation of a downward-looking camera mounted on a UAV, during autonomous contour surveillance flight.
  • Figure 2: Image plane description of the polygonal target of complex shape and evolving features.
  • Figure 3: Camera of a UAV tracking a deformable target inside a Matlab Machine Vision Toolbox and ROS simulation environment.
  • Figure 4: (a) Proposed control strategy visualization. (b)Deformable target 1 described with a polygon that includes it, with $n$ vertices (Index of each vertex $n$ is unknown in each iteration). (c) Deformable target 2 described with a polygon that includes it, with $n$ vertices (Index of each vertex $n$ is unknown in each iteration).
  • Figure 5: Deformable Target 1: Centroid error along x-axis (upper left), y-axis (upper right, in pixels, normalized polygon area error (middle left) and the polygon angle error in degrees (middle right) concerning $y$-axis of the image plane during the first simulation scenario conducting evolving features deformable target tracking. The value of the constraint function according to the centroid position in the image plane (lower left) and the $\bar{\sigma}$ value (lower right) (area of the polygon including the detected target) converge to the desired value 1 as depicted from \ref{['eq:1st_bar_function_constraint']} and \ref{['eq:2nd_bar_function_constraint']}.
  • ...and 11 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Definition 1
  • Lemma 5