Hierarchical planning has attracted renewed interest in the last couple of years, which led to numerous novel formalisms, problem classes, and theoretical investigations. Yet it is important to differentiate between the various formalisms and problem classes, since they show -- sometimes fundamental -- differences with regard to their expressivity and computational complexity: Some of them can be regarded equivalent to non-hierarchical formalisms while others are clearly more expressive. We survey the most important hierarchical problem classes and explain their differences and similarities. We furthermore give pointers to some of the best-known planning systems capable of solving the respective problem classes.

Hierarchical task network (HTN) planning is wellknown for being an efficient planning approach. This is mainly due to the success of the HTN planning system SHOP2. However, its performance depends on hand-designed search control knowledge. At the time being, there are only very few domainindependent heuristics, which are designed for differing hierarchical planning formalisms. Here, we propose an admissible heuristic for standard HTN planning, which allows to find optimal solutions heuristically. It bases upon the so-called task decomposition graph (TDG), a data structure reflecting reachable parts of the task hierarchy. We show (both in theory and empirically) that rebuilding it during planning can improve heuristic accuracy thereby decreasing the explored search space. The evaluation further studies the heuristic both in terms of plan quality and coverage.

The research in hierarchical planning has made considerable progress in the last few years. Many recent systems do not rely on hand-tailored advice anymore to find solutions, but are supposed to be domain-independent systems that come with sophisticated solving techniques. In principle, this development would make the comparison between systems easier (because the domains are not tailored to a single system anymore) and – much more important – also the integration into other systems, because the modeling process is less tedious (due to the lack of advice) and there is no (or less) commitment to a certain planning system the model is created for. However, these advantages are destroyed by the lack of a common input language and feature set supported by the different systems. In this paper, we propose an extension to PDDL, the description language used in non-hierarchical planning, to the needs of hierarchical planning systems.

Both search-based and translation-based planning systems usually operate on grounded representations of the problem. Planning models, however, are commonly defined using lifted description languages. Thus, planning systems usually generate a grounded representation of the lifted model as a preprocessing step. For HTN planning models, only one method to ground lifted models has been published so far. In this paper we present a new approach for grounding HTN planning problems that produces smaller groundings in a shorter timespan than the previously published method.

From a theoretical perspective, judging the expressivity of planning formalisms helps to understand the relationship of different representations and to infer theoretical properties. From a practical point of view, it is important to be able to choose the best formalism for a problem at hand, or to ponder the consequences of introducing new representation features. Most work on the expressivity is based either on compilation approaches, or on the computational complexity of the plan existence problem. Recently, we introduced a new notion of expressivity. It is based on comparing the structural complexity of the set of solutions to a planning problem by interpreting the set as a formal language and classifying it with respect to the Chomsky hierarchy. This is a more direct measure than the plan existence problem and enables also the comparison of formalisms that can not be compiled into each other. While existing work on that last approach focused on different hierarchical problem classes, this paper investigates STRIPS with and without conditional effects; though we also tighten some existing results on hierarchical formalisms. Our second contribution is a discussion on the language-based expressivity measure with respect to the other approaches.