An extension of SATPLAN for planning with constraints

Abstract

In this paper we present C-SATPLAN, a planner which realizes an extension to the satisfiability based planning system SATPLAN for solving constrained planning problems, whose architecture is independent from the SAT solver algorithm being used.

C-SATPLAN is able to manage general planning constraints expressed in PCDL, a language which has been introduced in a previous work of the authors [2].

PCDL constraints are defined in terms of a quantified predicate over plan steps and facts, and can express several kinds of planning constraints as achievement goals, activity goals, presence or absence of operators, precedence and codesignation constraints.

Former results about PCDL [2] showed that constraints belonging to a significant sublanguage (PCL-1) of PCDL can be compiled within the planning domain, i.e. there exists an effective procedure which produces a new planning domain whose solutions solve the original constrained planning problem. Therefore PCL-1 planning problems can be solved with an ordinary planner after a translation phase.

In this paper we show that solving general constrained planning problems requires the extension of SATPLAN, a planning approach for unconstrained domains based on the equivalence between satisfiability and classical unconstrained planning [7].

The C-SATPLAN extension exploits the feature that planning constraints can be encoded as additional clauses in the clausal representation of the planning problem.

This method is independent from the SAT solver engine used, therefore any SAT solver can be used to solve a constrained planning problem. Following this approach the architecture of the constrained planning system C-SATPLAN, composed by three interacting modules, has been designed and implemented. The first module takes as input a planning problem, produces a planning graph and finally translates it as a SAT instance. The second module generates the additional component of the SAT instance by translating the PCDL constraint in clausal form. The final module incorporates two different SAT solver engines which are able to produce the solutions, if any, of the original constrained planning problem by proving the satisfiability of the clausal instance.