Hierarchical Task Network (HTN) planning is the problem of decomposing an initial task into a sequence of executable steps. Often viewed as just a way to encode human knowledge to solve classical planning problems faster, HTN planning is more expressive than classical planning, even to the point of being undecidable in the general case. However, HTN planning is not just a way to solve planning problems faster, but is itself a search problem that can benefit from its own distinct search algorithms and heuristics.

The dissertation examines the complexities of various HTN planning problem classes in order to motivate the development of heuristic search algorithms for HTN planning which are guaranteed to terminate on a large class of syntactically identifiable problems, as well as domain independent heuristics for those algorithms to use. This will allow HTN planning to be used in a number of areas where the solvability of a problem is in question, including during the initial development of a domain and for use in policy generation in non-deterministic planning environments.

In particular, this dissertation analyzes two commonly used algorithms for HTN planning and describes the subsets of HTN problems that these algorithms terminate on. This allows us to discuss the run-times of these algorithms and com- pare the expressivity of the classes of problems they decide. We provide two new HTN algorithms which terminate on a strictly broader and more expressive set of HTN problems.

We also analyze the complexity of delete-free HTN planning, an analogue to delete-free classical planning which is the base of many classical planning heuristics. We show that delete-free HTN planning is NP-complete, putting the existence of strict-semantics delete-relaxation-based HTN heuristics out of reach for practical purposes.

Finally, we provide a translation of a large subset of HTN planning to classical planning, which allows us to use a classical planner as a surrogate for a heuristic HTN planner. Our experiments show that even small amounts and incomplete amounts of HTN knowledge, when translated into PDDL using our algorithm, can greatly improve a classical planner's performance.