Improving Heuristics for Planning as Search in Belief Space

Search in the space of beliefs has been proposed as a convenient framework for tackling planning under uncertainty. Significant improvements have been recently achieved, especially thanks to the use of symbolic model checking techniques such as Binary Decision Diagrams. However, the problem is extremely complex, and the heuristics available so far are unable to provide enough guidance for an informed search. In this paper we tackle the problem of defining effective heuristics for driving the search in belief space. The basic intuition is that the "degree of knowledge" associated with the belief states reached by partial plans must be explicitly taken into account when deciding the search direction. We propose a way of ranking belief states depending on their degree of knowledge with respect to a given set of boolean functions. This allows us to define a planning algorithm based on the identification and solution of suitable "knowledge subgoals", that are used as intermediate steps during the search. The solution of knowledge subgoals is based on the identification of "knowledge acquisition conditions", i.e. subsets of the state space from where it is possible to perform knowledge acquisition actions. We show the effectiveness of the proposed ideas by observing substantial improvements in the conformant planning algorithms of MBP.