This work proposes new approaches to contingent planning using alternative belief state representations extended from those in conformant planning and a new AND/OR forward search algorithm, called PrAO, for contingent solutions. Each representation was implemented in a new contingent planner. The important role of belief state representation has been confirmed by the fact that our planners all outperform other stateof- the-art planners on most benchmarks and the comparison of their performances varies across all the benchmarks even using the same search algorithm PrAO and same unsophisticated heuristic scheme. The work identifies the properties of each representation method that affect the performance.

This paper compares in depth the effectiveness of two conjunctive belief state representations in contingent planning: prime implicates and minimal CNF, a compact form of CNF formulae, which were initially proposed in conformant planning research (To et al. 2010a; 2010b). Similar to the development of the contingent planner CNFct for minimal CNF (To et al. 2011b), the present paper extends the progression function for the prime implicate representation in (To et al. 2010b) for computing successor belief states in the presence of incomplete information to handle non-deterministic and sensing actions required in contingent planning. The idea was instantiated in a new contingent planner, called PIct, using the same AND/OR search algorithm and heuristic function as those for CNFct. The experiments show that, like CNFct, PIct performs very well in a wide range of benchmarks. The study investigates the advantages and disadvantages of the two planners and identifies the properties of each representation method that affect the performance.

This paper investigates the effectiveness of two state representations, CNF and DNF, in contingent planning. To this end, we developed a new contingent planner, called CNFct, using the AND/OR forward search algorithm PrAO [To et al., 2011] and an extension of the CNF representation of [To et al., 2010] for conformant planning to handle nondeterministic and sensing actions for contingent planning. The study uses CNFct and DNFct [To et al., 2011] and proposes a new heuristic function for both planners. The experiments demonstrate that both CNFct and DNFct offer very competitive performance in a large range of benchmarks but neither of the two representations is a clear winner over the other. The paper identifies properties of the representation schemes that can affect their performance on different problems.

This paper introduces a highly competitive contingent planner, that uses the novel idea of encoding belief states as disjunctive normal form formulae (To et al. 2009), for the search for solutions in the belief state space. In (To et al. 2009), a complete transition function for computing successor belief states in the presence of incomplete information has been defined. This work extends the function to handle non-deterministic and sensing actions in the AND/OR forward search paradigm for contingent planning solutions. The function allows one, under reasonable assumptions, to compute successor belief states efficiently, i.e., in polynomial time. The paper also presents a novel variant of an AND/OR search algorithm, called PrAO (Pruning AND/OR search), which allows the planner to significantly prune the search space; furthermore, by the time a solution is found, the remaining search graph is also the solution tree for the contingent planing problem. The strength of these techniques is confirmed by the empirical results obtained from a large set of benchmarks available in the literature.