Polar Map: A Digital Representation of Closed Structures for Underwater Robotic Inspection

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. The first case shows a simulated example when mapping 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.