Conditional Planning under Partial Observability as Heuristic-Symbolic Search in Belief Space

Planning under partial observability in nondeterministic domains is a very significant and challenging problem, which requires de aling with uncertainty together with and-or search. In this paper, we propose a new algorithm for tack- ling this problem, able to generate conditional plans that a re guaranteed to achieve the goal despite of the uncertainty in the initial condition and the uncertain effects of actions. The proposed algorithm combines heuristic search in the and-or space of beliefs with symbolic BDD-based techniques, and is fully amenable to the use of selection functions. The experimental evaluation shows that heuristic-symbolic search may behave much better than state-of-the-art search algorithms, based on a depth-first search (D FS) style, on several domains. In this paper, we tackle the problem of conditional planning under partial observability, where only part of the information concerning the domain status is available at run time. In its generality, this problem is extremely challenging. C ompared to the limit case of full observability, it requires dealing with uncertainty a bout the state in which the ac- tions will be executed. Compared to the limit case of null observability, also known as conformant planning, it requires the ability to search for, and construct, plans repre- senting conditional courses of actions. Several approache s to this problem have been previously proposed, e.g. (WAS98), based on extensions of GraphPlan, and (BG00), based on Partially Observable Markov Decision Processes (POMDP). Our work builds on the approach proposed in (BCRT01), where planning is seen as and-or search of the (possibly cyclic) graph induced by th e domain, and BDD-based techniques borrowed from symbolic model checking provide efficient search primitives. We propose a new algorithm for planning under partial observability, able to generate conditional acyclic plans that are guaranteed to achieve th e goal despite of the uncer- tainty in the initial condition and in the effects of actions . The main feature of the algorithm is the heuristic style of the search, that is amena ble to the use of selection functions, and is fully compatible with the use of a symbolic, BDD-based representa- tion. We call this approach heuristic-symbolic search. The proposed approach differs from (and improves) the depth-first search proposed in (BCRT01) in several respects. First, depending on the selection function, it can implement different styles of search, including DFS. Furthermore, the use of selection functions allows to over come poten- tially bad initial choices, and can therefore result in more efficient computations and higher quality plans. Finally, it opens up the possibility o f using preprocessing tech- niques for determining domain/problem-dependent heuristics. The heuristic-symbolic algorithm was implemented in the MBP planner (BCP 01), and an extensive experi- mental evaluation was carried out. The results show that, even considering a simple domain-independent heuristic, for several classes of prob lems the heuristic-symbolic algorithm significantly improves the performance and const ructs better plans with re- spect to DFS.