Omnidirectional Bats, Point-to-Plane Distances, and the Price of Uniqueness
This addresses the design of collocated range-only SLAM systems, with incremental extensions from 2D to 3D revealing fundamental differences in uniqueness.
The paper tackles the 3D simultaneous localization and mapping problem using a device that measures distances from walls via reflections, showing that unlike the 2D case, uniqueness is absent in rooms with fewer than nine walls, and proposes a robust solution for inexact measurements.
We study simultaneous localization and mapping with a device that uses reflections to measure its distance from walls. Such a device can be realized acoustically with a synchronized collocated source and receiver; it behaves like a bat with no capacity for directional hearing or vocalizing. In this paper we generalize our previous work in 2D, and show that the 3D case is not just a simple extension, but rather a fundamentally different inverse problem. While generically the 2D problem has a unique solution, in 3D uniqueness is always absent in rooms with fewer than nine walls. In addition to the complete characterization of ambiguities which arise due to this non-uniqueness, we propose a robust solution for inexact measurements similar to analogous results for Euclidean Distance Matrices. Our theoretical results have important consequences for the design of collocated range-only SLAM systems, and we support them with an array of computer experiments.