Learning environmental fields with micro underwater vehicles: a path integral—Gaussian Markov random field approach

Autonomous underwater vehicles (AUVs) are advancing the state of the art in numerous scientific and commercial applications. The current surge in micro electronics enables the development of small micro AUVs (\(\mu \)AUVs) which are expected to gain increasing popularity in industrial applications such as monitoring of liquid-based processes. This paper presents an information theoretic approach for exploration and monitoring of liquid containing tanks with \(\mu \)AUVs. The controller is based on ideas from path integral control and inference with Gaussian Markov random fields (GMRFs). Both parts are combined in a receding horizon scheme to the PI-GMRF controller. The control problem is formulated within the stochastic optimal control domain and a solution is stated as a path integral. In order to close the control theoretic loop each \(\mu \)AUV maintains a belief representation of the environment expressed with GMRFs which allows reasoning by computing posterior distributions conditioned on measurements. Each \(\mu \)AUV has its own controller instance and the system is decentral. Only the exchange of measurements and intended control inputs of each \(\mu \)AUV is required through the communication link. The approach is validated in simulations for an advection–diffusion scenario and benchmarked against random walk, which it outperforms.