Estimating the Coverage Measure and the Area Explored by a Line-Sweep Sensor on the Plane

TL;DR

This paper introduces a novel method to accurately estimate and characterize the explored area by a line-sweep sensor in 2D environments, incorporating topological degree and interval analysis for uncertainty management.

Contribution

It presents a new approach combining coverage measure, topological degree, and interval analysis to estimate and guarantee the explored area in 2D coverage missions.

Findings

Effective area estimation demonstrated in real-world experiments.

Extension to uncertain coverage measures with guaranteed characterization.

A novel algorithm for computing topological degree for entire areas.

Abstract

This paper presents a method for determining the area explored by a line-sweep sensor during an area-covering mission in a two-dimensional plane. Accurate knowledge of the explored area is crucial for various applications in robotics, such as mapping, surveillance, and coverage optimization. The proposed method leverages the concept of coverage measure of the environment and its relation to the topological degree in the plane, to estimate the extent of the explored region. In addition, we extend the approach to uncertain coverage measure values using interval analysis. This last contribution allows for a guaranteed characterization of the explored area, essential considering the often critical character of area-covering missions. Finally, this paper also proposes a novel algorithm for computing the topological degree in the 2-dimensional plane, for all the points inside an area of interest, which differs from existing solutions that compute the topological degree for single points. The applicability of the method is evaluated through a real-world experiment.