Loughborough University
Structurally_aware_3D_gas_distribution_mapping_with_a_mobile_sensor_using_Gaussian_belief_propagation (accepted version).pdf (13.88 MB)

Structurally aware 3D gas distribution mapping using belief propagation: A real-time algorithm for robotic deployment

Download (13.88 MB)
journal contribution
posted on 2023-03-06, 16:33 authored by Callum Rhodes, Cunjia LiuCunjia Liu, Wen-Hua ChenWen-Hua Chen

This paper proposes a new 3D gas distribution mapping technique based on Gaussian belief propagation, which is capable of resolving in real time, the concentration estimates in 3D space whilst accounting for the obstacle information within the scenario, the first of its kind in the literature. The gas mapping problem is formulated as a 3D factor graph of Gaussian potentials, the connections of which are conditioned on local occupancy values. The Gaussian belief propagation framework is introduced as the solver and a new hybrid message scheduler is introduced to increase the rate of convergence. The factor graph problem is then redesigned as a dynamically expanding inference task, coupling the information of consecutive gas measurements with local spatial structure obtained by the robot. The proposed algorithm is compared to the state of the art methods in 2D and 3D simulations and is found to resolve distribution maps orders of magnitude quicker than typical direct solvers. The proposed framework is then deployed onboard a ground robot in a 3D mapping and exploration task. The system is shown to be able to resolve multiple sensor inputs and output high resolution 3D gas distribution maps in a GPS denied cluttered scenario in real time. This online inference of complicated gas dispersion provides a new layer of contextual information over its 2D counterparts and enables autonomous systems to take advantage of real time estimates to inform potential next best sampling locations. Note to Practitioners —The motivation of this work arises from the need to develop the robotic gas distribution mapping capability that can provide real-time situational awareness of the scenarios. The output distribution maps can be used to inform human first responders as to what areas of the environment contain a hazard, but looking towards autonomous robots, they can also be used by the robot itself to inform where should be measured next to gather more information about the environment. When performing these mapping tasks in unknown indoor environments, it is very important that the sensing robot can build up the knowledge of its physical surroundings together with how the obstacles in the environment affect the 3D gas distribution. The Gaussian belief propagation algorithm allows us to achieve all of this in real-time onboard the sensing robot, something that is yet to be achieved in the literature. 


Informative path planning for exploration and mapping of unknown environments using multiple robots

Engineering and Physical Sciences Research Council

Find out more...

Goal-Oriented Control Systems (GOCS): Disturbance, Uncertainty and Constraints

Engineering and Physical Sciences Research Council

Find out more...



  • Aeronautical, Automotive, Chemical and Materials Engineering


  • Aeronautical and Automotive Engineering

Published in

IEEE Transactions on Automation Science and Engineering






1623 - 1637


Institute of Electrical and Electronics Engineers (IEEE)


  • AM (Accepted Manuscript)

Rights holder


Publisher statement

© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Acceptance date


Publication date


Copyright date







  • en


Dr Cunjia Liu. Deposit date: 3 March 2023

Usage metrics

    Loughborough Publications


    Ref. manager