Simple Agents Learn to Find Their Way: An Introduction on Mapping Polygons

TL;DR

This paper introduces the problem of autonomous agents mapping simple polygons by reconstructing their visibility graphs using minimal sensors and movement, highlighting algorithmic challenges and techniques in combinatorial geometry.

Contribution

It provides an overview of methods for agents with simple sensors to reconstruct polygon layouts and discusses related combinatorial and graph exploration problems.

Findings

Agents can reconstruct visibility graphs with angle sensors.

Techniques include local observations to infer global polygon structure.

Challenges arise from limited sensor data and movement constraints.

Abstract

This paper gives an introduction to the problem of mapping simple polygons with autonomous agents. We focus on minimalistic agents that move from vertex to vertex along straight lines inside a polygon, using their sensors to gather local observations at each vertex. Our attention revolves around the question whether a given configuration of sensors and movement capabilities of the agents allows them to capture enough data in order to draw conclusions regarding the global layout of the polygon. In particular, we study the problem of reconstructing the visibility graph of a simple polygon by an agent moving either inside or on the boundary of the polygon. Our aim is to provide insight about the algorithmic challenges faced by an agent trying to map a polygon. We present an overview of techniques for solving this problem with agents that are equipped with simple sensorial capabilities. We illustrate these techniques on examples with sensors that mea- sure angles between lines of sight or identify the previous location. We give an overview over related problems in combinatorial geometry as well as graph exploration.