Abstract This article presents a novel 2.5D map representation, termed polar map, that has a memory consumption of O(ML), where M and L depend on the map's angular and depth resolution, respectively. The map has a computational effort of O(1) in the update and evaluation process, where updates are performed through the use of Kalman filters. The representation can only be applied to structures in an environment that can be represented uniquely in a cylindrical coordinate system, such as fish cages, and square and cylindrical tanks. The work presents two case studies that compare the proposed polar map with the octomap approach to mapping. The first case shows the simulated example of a fish cage. The second, an experiment in a square tank, where an unmanned underwater vehicle performs simultaneous localization and mapping (SLAM) using both the polar map and octomap representation. The results show that the polar map performs better, both in terms of memory consumption and computation effort, in both mapping and SLAM in the selected case studies.

中文翻译：

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极坐标图：用于水下机器人检测的封闭结构的数字表示

摘要 本文提出了一种新颖的 2.5D 地图表示，称为极坐标图，其内存消耗为 O(ML)，其中 M 和 L 分别取决于地图的角度分辨率和深度分辨率。该地图在更新和评估过程中的计算工作量是 O(1)，其中更新是通过使用卡尔曼滤波器执行的。该表示只能应用于可以在圆柱坐标系中唯一表示的环境中的结构，例如鱼笼、方形和圆柱形水箱。这项工作提出了两个案例研究，将提议的极地地图与八角地图方法进行比较。第一个案例显示了鱼笼的模拟示例。第二个，在方形水箱中的实验，其中无人水下航行器使用极坐标图和八角图表示执行同步定位和映射 (SLAM)。结果表明，极坐标图在所选案例研究中的映射和 SLAM 中的内存消耗和计算工作量方面都表现更好。