Markov Decision Processes with Unknown State Feature Values for Safe Exploration using Gaussian Processes

When exploring an unknown environment, a mobile robot must decide where to observe next. It must do this whilst minimising the risk of failure, by only exploring areas that it expects to be safe. In this context, safety refers to the robot remaining in regions where critical environment features (e.g. terrain steepness, radiation levels) are within ranges the robot is able to tolerate. More specifically, we consider a setting where a robot explores an environment modelled with a Markov decision process, subject to bounds on the values of one or more environment features which can only be sensed at runtime. We use a Gaussian process to predict the value of the environment feature in unvisited regions, and propose an estimated Markov decision process, a model that integrates the Gaussian process predictions with the environment model transition probabilities. Building on this model, we propose an exploration algorithm that, contrary to previous approaches, considers probabilistic transitions and explicitly reasons about the uncertainty over the Gaussian process predictions. Furthermore, our approach increases the speed of exploration by selecting locations to visit further away from the currently explored area. We evaluate our approach on a real-world gamma radiation dataset, tackling the challenge of a nuclear material inspection robot exploring an a priori unknown area.