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.

翻译：本文提出了一种方法，用于确定二维平面中线扫传感器在执行区域覆盖任务时的探测面积。准确掌握探测面积对于机器人领域的诸多应用至关重要，例如地图构建、监控和覆盖优化。所提出的方法利用环境覆盖度量的概念及其与平面拓扑度之间的关系，来估计探测区域的范围。此外，我们通过区间分析将该方法扩展至不确定性覆盖度量值。这一贡献使得探测面积的特征描述具有保障性，考虑到区域覆盖任务通常具有关键性。最后，本文还提出了一种新颖的二维平面拓扑度计算算法，可计算感兴趣区域内所有点的拓扑度，这与现有仅计算单点拓扑度的解决方案不同。通过实际实验验证了该方法的适用性。