2 research outputs found
Omnidirectional Bats, Point-to-Plane Distances, and the Price of Uniqueness
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.Comment: 5 pages, 8 figures, submitted to ICASSP 201
Shapes from Echoes: Uniqueness from Point-to-Plane Distance Matrices
We study the problem of localizing a configuration of points and planes from
the collection of point-to-plane distances. This problem models simultaneous
localization and mapping from acoustic echoes as well as the notable "structure
from sound" approach to microphone localization with unknown sources. In our
earlier work we proposed computational methods for localization from
point-to-plane distances and noted that such localization suffers from various
ambiguities beyond the usual rigid body motions; in this paper we provide a
complete characterization of uniqueness. We enumerate equivalence classes of
configurations which lead to the same distance measurements as a function of
the number of planes and points, and algebraically characterize the related
transformations in both 2D and 3D. Here we only discuss uniqueness;
computational tools and heuristics for practical localization from
point-to-plane distances using sound will be addressed in a companion paper.Comment: 13 pages, 13 figure