Managing Temporal cycles in Planning Problems Requiring Concurrency

In order to correctly model certain real-world planning problems, it is essential to take into account time. This is the case for problems requiring the concurrent execution of actions (known as temporally-expressive problems). In this paper we define and study the notion of temporally-cyclic problems, that is problems involving sets of cyclically-dependent actions. We characterize those temporal planning languages which can express temporally-cyclic problems. We also present a polynomial-time algorithm which transforms a temporallycyclic problem into an equivalent acyclic problem. Applying our transformation allows any temporal planner to solve temporally-cyclic problems without explicitly managing cyclicity. We first present our results for temporal PDDL 2.1 and then extend them to a language which allows conditions over arbitrary intervals and effects at arbitrary instants.