On Temporal Planning as CSP

(Appears as a regular paper in the proceedings of IEEE International Conference on Tools with Artificial Intelligence (ICTAI), IEEE Computer Society, Washington D.C. Nov. 2002, pp. 75-82.) Recent advances in constraint satisfaction and heuristic search have made it possible to solve classical planning problems significantly faster. There is an increasing amount of work on extending these advances to solving more expressive planning problems which contain metric time, quantifiers and resource quantities. One can broadly classify classical planners into two categories: (i) planners doing refinement search and (ii) planners iteratively processing a representation of finite size like a SAT encoding or planning graph or a constraint satisfaction problem (CSP). One key challenge in the development of planners casting planning as SAT or CSP is the identification of constraints which are satisfied if and only if there is a plan of steps. This task is even more complex for planners handling metric time and/or resource quantities and/or quantifiers. In this paper we show how such a SAT encoding can be synthesized for temporal planning. This encoding contains twenty kinds of constraints. We show how this encoding can be simplified. The set of constraints we identify makes it easier to develop temporal planners casting planning as a constraint satisfaction problem other than SAT, like integer linear programming (ILP). The SAT encoding can be easily adapted to more complex cases of temporal planning like the one in which different preconditions and effects of an action may be true at different times during its execution. We also discuss two additional SAT encodings of temporal planning. The encoding schemes make it easier to exploit progress in SAT and CSP solving to solve temporal planning problems.