Planning under uncertainty is a difficult problem that is of critical importance in the field of robotic exploration. Agents must decide on actions to take that minimize resources expended while maximizing the gain of valuable information. A central task in these decision making problems is to compute the expected value of a cost (or reward) function given that some action is taken or decision made. Using these computations, we can optimize plans that collect that information and make decisions.

Figure 1: Image of a random clustered rock field.

A stated goal of scientific planetary exploration is the collection of certains rocks of interest. In the FIRE project, we are considering spatial statistical models of rock formations of interest in scientific exploration. Although the type of model applied is well known in computational geology (Figure 1), it is computationally quite difficult to extract probability distributions of rocks at each location. We are applying techniques developed in the statistical physics and quantum-field theory communities, namely renormalization group transformations and mean-field inference, to make tractable approximations to the expected gains in information. From this we hope to scale to be able to evaluate plans and improve plans to uncover rocks of interests while minimizing the use of resources. In Figure(2) a graphical depiction of the inference procedures shows areas of high confidence of rock in brighter colors, with red indicating the discovery of an interesting rock at the grid location.

Figure 2: Image of Inference Procedure

Our work also focuses on the decision making aspects. In particular, we have worked on algorithms that plan using partial probabilistic models, either learning the model on-the-fly or ensuring behavior remains robust even to fairly large deviations from a nominal model. We expect this kind of model learning and robustness will be particularly useful in the context of scientific exploration with muliple agents where it will be very difficult to have good apriori models of the environment.

• Drew Bagnell
• Jeff Schneider

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