Hierarchical Task Network Planning as Satisfiability

Abstract

Casting planning problems as propositional satisfiability (SAT) has recently been shown to be an effective way of scaling up plan synthesis. Until now, the benefits of this approach have been utilized only in primitive action-based planning models. Motivated by the conventional wisdom in the planning community about the effectiveness of hierarchical task network (HTN) planning models, in this dissertation, we adapt the “planning as satisfiability” approach to HTN planning models. HTN planning models can be thought of as an augmentation of primitive action based planning models with a grammar of legal solutions, provided in the form of non-primitive tasks and task reduction schemas. Accordingly, we argue that any primitive action-based SAT encoding scheme can be generalized to handle HTN planning. Informally, this generalization involves adding constraints to the encoding to ensure that the solutions produced by solving the encoding will conform to the grammar provided by the HTN planning model. The constraints can be added in either a “topdown” or “bottom-up” fashion, resulting in two HTN encoding schemes for each primitive action-based encoding scheme. We illustrate this process by providing three different HTN encodings. We report the asymptotic sizes of these encodings, as well as conduct an empirical evaluation of the complexity of finding their models. We show that the causal HTN encodings are significantly easier to solve than the action-based causal encodings, when the constraints from the task reduction schemas are propagated to simplify the encodings. We develop a procedure to achieve this simplification. Our strategy of simplifying the encodings before generating them as opposed to simplifying them a posteriori also avoids the memory problem where the unsimplified encodings require an impractical amount of disk space to store. This dissertation is also the first work to report promising empirical results on the hitherto under-represented and claimed to be hard to solve causal encodings.