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Space Filling Curves for Coverage Path Planning with Online Obstacle Avoidance

Ashay Wakode, Arpita Sinha

TL;DR

The paper presents a strategy for robotic exploration problem using Space-Filling curves (SFC) that is online, exhaustive and works in situations demanding non-uniform coverage.

Abstract

The paper presents a strategy for robotic exploration problem using Space-Filling curves (SFC). The strategy plans a path that avoids unknown obstacles while ensuring complete coverage of the free space in region of interest. The region of interest is first tessellated, and the tiles/cells are connected using a SFC pattern. A robot follows the SFC to explore the entire area. However, obstacles can block the systematic movement of the robot. We overcome this problem by determining an alternate path online that avoids the blocked cells while ensuring all the accessible cells are visited at least once. The proposed strategy chooses next waypoint based on the graph connectivity of the cells and the obstacle encountered so far. It is online, exhaustive and works in situations demanding non-uniform coverage. The completeness of the strategy is proved and its desirable properties are discussed with examples.

Space Filling Curves for Coverage Path Planning with Online Obstacle Avoidance

TL;DR

The paper presents a strategy for robotic exploration problem using Space-Filling curves (SFC) that is online, exhaustive and works in situations demanding non-uniform coverage.

Abstract

The paper presents a strategy for robotic exploration problem using Space-Filling curves (SFC). The strategy plans a path that avoids unknown obstacles while ensuring complete coverage of the free space in region of interest. The region of interest is first tessellated, and the tiles/cells are connected using a SFC pattern. A robot follows the SFC to explore the entire area. However, obstacles can block the systematic movement of the robot. We overcome this problem by determining an alternate path online that avoids the blocked cells while ensuring all the accessible cells are visited at least once. The proposed strategy chooses next waypoint based on the graph connectivity of the cells and the obstacle encountered so far. It is online, exhaustive and works in situations demanding non-uniform coverage. The completeness of the strategy is proved and its desirable properties are discussed with examples.
Paper Structure (6 sections, 1 theorem, 6 equations, 4 figures, 1 algorithm)

This paper contains 6 sections, 1 theorem, 6 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation & Proposed Solution
  4. Discussion & Results
  5. Results
  6. Conclusion & Future Work

Key Result

Lemma 1

An agent starting at waypoint $H$ and following the proposed strategy will visit all the waypoints connected to $H$.

Figures (4)

  • Figure 1: Hilbert curve as mapped from $I$ to a tessellated square
  • Figure 2: Hilbert curve iterations 1 to 4; Colored circles represent specific translation + rotation rules for creating $n^{th}$ iteration from $n-1^{th}$ iteration
  • Figure 3: Grey dots: Visited vertices of the graph, Yellow lines: Edges connecting the vertices, Red dots: Vertices adjacent to already visited vertices
  • Figure 4: Region blocked by tight space reachable through the use of higher iteration (4)

Theorems & Definitions (2)

  • Lemma 1
  • proof