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Online Obstacle evasion with Space-Filling Curves

Ashay Wakode, Arpita Sinha

TL;DR

This work addresses online obstacle evasion for region exploration using Space-Filling Curves, presenting a graph-based waypoint planner that follows an SFC while avoiding unknown obstacles. The method builds a dual graph of SFC waypoints, memory of detected obstacles, and uses shortest-path planning to reach the next unblocked waypoint, updating as obstacles are discovered. It demonstrates completeness in reachable areas and adapts via SFC iteration to balance coverage and agility, with demonstrations on Hilbert curves and discussions of non-uniform coverage. The approach is validated through Python simulations, illustrating robustness to both normal and sparse obstacles and offering practical pathways for extensions to 3D, dynamic environments, and multi-agent systems.

Abstract

The paper presents a strategy for robotic exploration problems using Space-Filling curves (SFC). The region of interest is first tessellated, and the tiles/cells are connected using some SFC. A robot follows the SFC to explore the entire area. However, there could be obstacles that block the systematic movement of the robot. We overcome this problem by providing an evading technique that avoids the blocked tiles while ensuring all the free ones are visited at least once. The proposed strategy is online, implying that prior knowledge of the obstacles is not mandatory. It works for all SFCs, but for the sake of demonstration, we use Hilbert curve. We present the completeness of the algorithm and discuss its desirable properties with examples. We also address the non-uniform coverage problem using our strategy.

Online Obstacle evasion with Space-Filling Curves

TL;DR

This work addresses online obstacle evasion for region exploration using Space-Filling Curves, presenting a graph-based waypoint planner that follows an SFC while avoiding unknown obstacles. The method builds a dual graph of SFC waypoints, memory of detected obstacles, and uses shortest-path planning to reach the next unblocked waypoint, updating as obstacles are discovered. It demonstrates completeness in reachable areas and adapts via SFC iteration to balance coverage and agility, with demonstrations on Hilbert curves and discussions of non-uniform coverage. The approach is validated through Python simulations, illustrating robustness to both normal and sparse obstacles and offering practical pathways for extensions to 3D, dynamic environments, and multi-agent systems.

Abstract

The paper presents a strategy for robotic exploration problems using Space-Filling curves (SFC). The region of interest is first tessellated, and the tiles/cells are connected using some SFC. A robot follows the SFC to explore the entire area. However, there could be obstacles that block the systematic movement of the robot. We overcome this problem by providing an evading technique that avoids the blocked tiles while ensuring all the free ones are visited at least once. The proposed strategy is online, implying that prior knowledge of the obstacles is not mandatory. It works for all SFCs, but for the sake of demonstration, we use Hilbert curve. We present the completeness of the algorithm and discuss its desirable properties with examples. We also address the non-uniform coverage problem using our strategy.
Paper Structure (8 sections, 1 theorem, 5 equations, 4 figures, 1 algorithm)

This paper contains 8 sections, 1 theorem, 5 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries on SFCs
  4. Problem Formulation and Proposed Solution
  5. Proposed Solution
  6. Discussion
  7. Results
  8. Conclusion

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 and Sierpinski curve
  • Figure 2: Hilbert curve as mapped from $I$
  • Figure 3: Hilbert curve iterations 1 to 5; Colored circles represent specific translation + rotation rules for creating $n^{th}$ iteration from $n-1^{th}$ iteration
  • Figure 4: Region blocked by tight space reachable through the use of higher iteration (4) of Hilbert curve

Theorems & Definitions (2)

  • Lemma 1
  • proof