![](bg4.png)
with partial initial condition. On the other hand, ND-
FCP(Kuter and Nau, 2004) is an extended one for
solving nondeterministic planning problems. Both
algorithms do just one search trial and expand only
one candidate of solution subgraph during the search
trial. They do not try to update heuristic values with
new information. Therefore, they do not guarantee to
find a solution and cannot be used for solving
contingent planning problems with both partial
observations and nondeterministic actions.
5 EXPERIMENTS
Figure 7: The number of search trials.
Figure 8: The number of value updates.
Figure 9: The number of generated states.
We implemented the HSCP algorithm, and
compared it with LAO
*
and RTDP on two partially-
observable, nondeterministic planning domains that
are well-known from previous experimental studies:
Robot Navigation and Blocks World. Three random
problems were generated from each domain for
experiments. We compared three different search
algorithms in terms of the number of search trials,
the number of value updates, and the number of
generated states. Figure 7 ~ Figure 9 show the
experimental results. While RTDP has performed
lots of search trials to get the optimal values of states,
our HSCP and LAO
*
have done just one or two trials
for each problem. Out of three search algorithms,
RTDP has tried value updates the most, but HSCP
has done the least. Considering the number of
generated states, we find out HSCP has explored
much smaller search space than the other two
algorithms.
6 CONCLUSIONS
We have presented a new heuristic search algorithm
for solving contingent planning problems with the
partial initial condition and nondeterministic actions.
Through several experiments, we have evaluated the
efficiency of this algorithm.
ACKNOWLEDGEMENTS
Industrial Strategic Technology Development
Program (10032108), funded by the Ministry of
Knowledge Economy(MKE, Korea).
REFERENCES
Bonet, B., Geffner, H., 2003. Labeled RTDP: Improving
the convergence of real-time dynamic programming.
In ICAPS’03, 13
th
International Conference on
Automated Planning and Scheduling. AAAI Press.
Ghallab, M., Nau, D., Traverso, P., 2004. Automated
planning: theory and practice, Morgan Kaufmann.
Hansen, E., Zilberstein, S., 2001. LAO*: A heuristic
search algorithm that finds solutions with loops.
Artificial Intelligence, vol. 129, No. 1-2, pp. 35-62.
Hoffmann, J., Brafman, R., 2005. Contingent planning via
heuristic forward search with implicit belief states. In
ICAPS’05, 15
th
International Conference on
Automated Planning and Scheduling. AAAI Press.
Kuter, U., Nau, D., Reisner, E., Goldman, R., 2007.
Conditionalization: Adapting forward-chaining
planners to partially observable environments. In
ICAPS’07, 17
th
International Conference on
Automated Planning and Scheduling. AAAI Press.
Kuter, U., Nau, D., 2004. Forward-chaining planning in
nondeterministic domains. In AAAI’04, 19
th
National
Conference on Artificial Intelligence. AAAI Press.
CONTINGENT PLANNING AS BELIEF SPACE SEARCH
697