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Cooperative Visual Convex Area Coverage using a Tessellation-free Strategy

Sotiris Papatheodorou, Anthony Tzes

TL;DR

A scheme focusing on the assignment to each MAA of certain parts of the mosaic of the current covered area is proposed, and a gradient ascent algorithm is then employed to increase in a monotonic manner the covered area by the MAA-fleet.

Abstract

The objective in this article is to develop a control strategy for coverage purposes of a convex region by a fleet of Mobile Aerial Agents (MAAs). Each MAA is equipped with a downward facing camera that senses a convex portion of the area while its altitude flight is constrained. Rather than relying on typical Voronoi-like tessellations of the area to be covered, a scheme focusing on the assignment to each MAA of certain parts of the mosaic of the current covered area is proposed. A gradient ascent algorithm is then employed to increase in a monotonic manner the covered area by the MAA-fleet. Simulation studies are offered to illustrate the effectiveness of the proposed scheme.

Cooperative Visual Convex Area Coverage using a Tessellation-free Strategy

TL;DR

A scheme focusing on the assignment to each MAA of certain parts of the mosaic of the current covered area is proposed, and a gradient ascent algorithm is then employed to increase in a monotonic manner the covered area by the MAA-fleet.

Abstract

The objective in this article is to develop a control strategy for coverage purposes of a convex region by a fleet of Mobile Aerial Agents (MAAs). Each MAA is equipped with a downward facing camera that senses a convex portion of the area while its altitude flight is constrained. Rather than relying on typical Voronoi-like tessellations of the area to be covered, a scheme focusing on the assignment to each MAA of certain parts of the mosaic of the current covered area is proposed. A gradient ascent algorithm is then employed to increase in a monotonic manner the covered area by the MAA-fleet. Simulation studies are offered to illustrate the effectiveness of the proposed scheme.

Paper Structure

This paper contains 10 sections, 1 theorem, 26 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Coverage Quality Function
  4. Sensed Space Partitioning
  5. Spatially Distributed Coordination Algorithm
  6. Simulation Studies
  7. Case Study I
  8. Case Study II
  9. Case Study III
  10. Conclusions

Key Result

Theorem 1

In an MAA visual network consisting of nodes governed by the kinematics in (eq:kinematics), sensing performance as in (eq:sensing) and using the space partitioning (eq:partitioning), the control law where $\alpha_{i,q}, ~\alpha_{i,z}, ~\alpha_{i,\theta}$ are positive constants, $\upsilon_i^i$, $\nu_i^i$ and $\tau_i^i$ are the Jacobian matrices of the points $q \in \partial W_i$ with respect to $q

Figures (9)

  • Figure 1: MAA-visual area coverage concept
  • Figure 2: Uniform coverage quality function [Left] and its derivative [Right].
  • Figure 3: Sensed space partitioning examples.
  • Figure 4: Decomposition of $\partial W_i$ into disjoint sets.
  • Figure 5: Case Study I: Initial [Left] and final coverage quality.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Definition 1
  • Remark 1
  • Theorem 1
  • proof