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

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.