Satplan

Satplan is an approach to automated planning that leverages satisfiability (SAT) solvers to find solutions to planning problems. The core idea is to encode a planning problem as a propositional formula such that models (satisfying assignments) of the formula correspond to valid plans. If a SAT solver finds a model for the formula, a plan can be extracted from it. If the formula is unsatisfiable, it indicates that no plan of the specified length exists, and the process is typically repeated with a longer plan horizon.

The encoding typically involves representing states, actions, and their preconditions and effects as propositional variables. Constraints are then added to ensure that actions are only executed when their preconditions are met, that actions have the desired effects, and that the initial state is as specified. Frame axioms, which state that variables not affected by an action remain unchanged, are also often included to simplify the encoding.

Satplan approaches commonly use a bounded-length encoding, where the planning problem is encoded for a specific plan length (number of steps). The length is increased iteratively until a solution is found or a maximum length is reached.

Key advantages of Satplan include its ability to leverage the significant advancements in SAT solver technology and its completeness (it can find a plan if one exists within the bounded length). However, the size of the propositional formula can grow rapidly with the size and complexity of the planning problem, potentially leading to scalability issues.

Variations and extensions of the basic Satplan approach include using different SAT encodings (e.g., state-variable encodings, action-based encodings), incorporating techniques for symmetry breaking, and using incremental SAT solving to speed up the search process.