Scalable probabilistic gas distribution mapping using Gaussian belief propagation

Abstract

This paper advocates the Gaussian belief propagation solver for factor graphs in the case of gas distribution mapping to support an olfactory sensing robot. The local message passing of belief propagation moves away from the standard Cholesky decomposition technique, which avoids solving the entire factor graph at once and allows for only areas of interest to be updated more effectively. Implementing a local solver means that iterative updates to the distribution map can be achieved orders of magnitude quicker than conventional direct solvers which scale computationally to the size of the map. After defining the belief propagation algorithm for gas mapping, several state of the art message scheduling algorithms are tested in simulation against the standard Cholesky solver for their ability to converge to the exact solution. Testing shows that under the wildfire scheduling method for a large urban scenario, that distribution maps can be iterated at least 10 times faster whilst still maintaining exact solutions. This move to an efficient local framework allows future works to consider 3D mapping, predictive utility and multi-robot distributed mapping.

Structurally Aware 3D Gas Distribution Mapping Using Belief Propagation: A Real-Time Algorithm for Robotic Deployment

“…To overcome this issue, Rhodes et. al [16] advocate the use of the Gaussian belief propagation (GaBP) solver on the GDM factor graph problem. Belief propagation is a message passing technique that can be applied to loopy graph structures [17] (such as those factor graphs in GDM) and has seen increasing prominence in mobile robotics in recent years, especially in the SLAM domain [18]- [20].…”

“…We then propose two major improvements to the GaBP solver proposed in [16] to increase its efficiency when applied to mapping with multiple point sampling sensors. The first improvement concerns the schedule for sending messages in the belief propagation algorithm.…”

“…In our previous work [16], we make use of the typical 2D graph construction of Monroy et al [7]. We now extend the factor graph formulation to account for 3D gas distribution maps.…”

“…In the introductory work on G-GaBP [16], several message scheduling algorithms are tested in a GDM scenario. These are random, round-robin, residual [25] and wildfire [18] schedulers.…”

“…Other information theoretic metrics can also be used and as discussed in [16], but performance of the solver is more affected by the schedule rather than the specific metric (for the case of GDM). Formally, the hybrid message scheduler is outlined in Alg.…”