We study the complexity-theoretic boundaries of tractability for three classical problems in the context of Hierarchical Task Network Planning: the validation of a provided plan, whether an executable plan exists, and whether a given state can be reached by some plan. We show that all three problems can be solved in polynomial time on primitive task networks of constant partial order width (and a generalization thereof), whereas for the latter two problems this holds only under a provably necessary restriction to the state space. Next, we obtain an algorithmic meta-theorem along with corresponding lower bounds to identify tight conditions under which general polynomial-time solvability results can be lifted from primitive to general task networks. Finally, we enrich our investigation by analyzing the parameterized complexity of the three considered problems, and show that (1) fixed-parameter tractability for all three problems can be achieved by replacing the partial order width with the vertex cover number of the network as the parameter, and (2) other classical graph-theoretic parameters of the network (including treewidth, treedepth, and the aforementioned partial order width) do not yield fixed-parameter tractability for any of the three problems.

The Hierarchical Task Network (HTN) formalism is used to express a wide variety of planning problems as task decompositions, and many techniques have been proposed to solve them. However, few works have been done on temporal HTN. This is partly due to the lack of a formal and consensual definition of what a temporal hierarchical planning problem is as well as the difficulty to develop heuristics in this context. In response to these inconveniences, we propose in this paper a new general POCL (Partial Order Causal Link) approach to represent and solve a temporal HTN problem by using existing heuristics developed to solve non temporal problems. We show experimentally that this approach is performant and can outperform the existing ones.

Real world applications as in industry and robotics need modelling rich and diverse automated planning problems. Their resolution usually requires coordinated and concurrent action execution. In several cases, these problems are naturally decomposed in a hierarchical way and expressed by a Hierarchical Task Network (HTN) formalism. HDDL, a hierarchical extension of the Planning Domain Definition Language (PDDL), unlike PDDL 2.1 does not allow to represent planning problems with numerical and temporal constraints, which are essential for real world applications. We propose to fill the gap between HDDL and these operational needs and to extend HDDL by taking inspiration from PDDL 2.1 in order to express numerical and temporal expressions. This paper opens discussions on the semantics and the syntax needed for a future HDDL 2.1 extension.

Do It Yourself, but Not Alone: Companion-Technology for Home Improvement – Bringing a Planning-Based Interactive DIY Assistant to Life.

Do It Yourself, but Not Alone: Com- panion-Technology for Home Improvement – Bringing a Planning-Based Interactive DIY Assistant to Life.

The majority of search-based HTN planning systems can be divided into those searching a space of partial plans (a plan space) and those performing progression search, i.e., that build the solution in a forward manner. So far, all HTN planners that guide the search by using heuristic functions are based on plan space search. Those systems represent the set of search nodes more effectively by maintaining a partial ordering between tasks, but they have only limited information about the current state during search. In this article, we propose the use of progression search as basis for heuristic HTN planning systems. Such systems can calculate their heuristics incorporating the current state, because it is tracked during search. Our contribution is the following: We introduce two novel progression algorithms that avoid unnecessary branching when the problem at hand is partially ordered and show that both are sound and complete. We show that defining systematicity is problematic for search in HTN planning, propose a definition, and show that it is fulfilled by one of our algorithms. Then, we introduce a method to apply arbitrary classical planning heuristics to guide the search in HTN planning. It relaxes the HTN planning model to a classical model that is only used for calculating heuristics. It is updated during search and used to create heuristic values that are used to guide the HTN search. We show that it can be used to create HTN heuristics with interesting theoretical properties like safety, goal-awareness, and admissibility. Our empirical evaluation shows that the resulting system outperforms the state of the art in search-based HTN planning.

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. We restrict our language to a basic feature set shared by many recent systems, give an extension of PDDL's EBNF syntax definition, and discuss our extensions with respect to several planner-specific input languages from related work.

In this paper, we propose a novel SAT-based planning approach for hierarchical planning by introducing the SAT-based planner totSAT for the class of totally-ordered HTN planning problems. We use the same general approach as SAT planning for classical planning does: bound the problem, translate the problem into a formula, and if the formula is not satisfiable, increase the bound. In HTN planning, a suitable bound is the maximum depth of decomposition. We show how totally-ordered HTN planning problems can be translated into a SAT formula, given this bound. Furthermore, we have conducted an extensive empirical evaluation to compare our new planner against state-of-the-art HTN planners. It shows that our technique outperforms any of these systems.

Plan-Verification is the task of determining whether a plan is a solution to a given planning problem. Any plan verifier has, apart from showing that verifying plans is possible in practice, a wide range of possible applications. These include mixed-initiative planning, where a user is integrated into the planning process, and local search, e.g., for post-optimising plans or for plan repair. In addition to its practical interest, plan verification is also a problem worth investigating for theoretical reasons. Recent work showed plan verification for hierarchical planning problems to be NP-complete, as opposed to classical planning where it is in P. As such, plan verification for hierarchical planning problem was — until now — not possible. We describe the first plan verifier for hierarchical planning. It uses a translation of the problem into a SAT formula. Further we conduct an empirical evaluation, showing that the correct output is produced within acceptable time.

Hierarchical Task Network (HTN) planning with task insertion (TIHTN planning) is a variant of HTN planning. In HTN planning, the only means to alter task networks is to decompose compound tasks. In TIHTN planning, tasks may also be inserted directly. In this paper we provide tight complexity bounds for TIHTN planning along two axis: whether variables are allowed and whether methods must be totally ordered.