Homological sensing for mobile robot localization

In this paper, we consider a multi-phased, minimalistic approach to mobile robot localization that constrains the robot´s ability to sense its environment to a binary detection of uniquely identifiable landmarks having unknown position (e.g., a WiFi transceiver detecting network SSIDs). Central to the proposed solution are dual landmark and observation complexes (instances of simplicial nerve complexes), which can be iteratively built through local observations without any metric or time-sequenced information. We have shown that these complexes approximate the topology of the underlying physical environment. Specifically, the notion of a “hole” (i.e., a topological invariant) within these complexes naturally represents a physical structure (e.g., a building) that limits landmark visibility/communication with respect to the robot´s location. Taking advantage of this property, we formulate a homological sensing model that operates on these constructs enabling the robot to “count” the number of structures in its vicinity using local homology computations as a pseudo-metric surrogate sensor. Our homological sensor is highlighted in the context of a Monte-Carlo localization algorithm that resolves robot location by correlating the measured number of topological invariants with an unlabeled, metric map location.