Hierarchical Planning: Relating Task and Goal Decomposition with Task Sharing

Considerable work has focused on enhancing the semantics of Hierarchical Task Networks (HTNs) in order to advance the state-of-the-art in hierarchical planning. For instance, the Hierarchical Goal Network (HGN) formalism operates over a hierarchy of goals to facilitate tighter integration of decompositional planning with classical planning. Another example is the Action Notation Markup Language (ANML) which adds aspects of generative planning and task-sharing to the standard HTN semantics. The aim of this work is to formally analyze the effects of these modifications to HTN semantics on the computational complexity and expressivity of HTN planning. To facilitate analysis, we unify goal and task planning into Goal-Task Network (GTN) planning. GTN models use HTN and HGN constructs, but have a solution-preserving mapping back to HTN planning. We then show theoretical results that provide new insights into both the expressivity as well as computational complexity of GTN planning under a number of different semantics. Our work lays a firm footing to clarify exact semantics for recent planners based on ANML, HGNs, and similar hierarchical languages.