Hierarchical Task Network Methods

• Hierarchical Task Network methods are formal schemas that decompose compound tasks into primitive actions using expert procedural knowledge.
• They integrate domain-specific preconditions and constraints to guide recursive task refinement and efficient plan search.
• HTN methods enable practical AI applications in robotics, service composition, and resource planning through structured operational integration.

Hierarchical Task Network (HTN) methods are formal schemas that specify when and how compound (i.e., non-primitive) tasks are to be decomposed into finer-grained subtasks until a network of primitive tasks (i.e., executable actions) is produced. HTN methods are central to the expressiveness, search properties, and practical effectiveness of HTN planning, which underpins many real-world AI planning systems. HTN methods formalize expert procedural domain knowledge and offer a representational bridge between domain engineering and automated task decomposition. The precise definition, operational integration, learning, and optimization of HTN methods are vibrant areas of research, with recent advances in method learning, dynamic modification, and planning under uncertainty.

1. Formal Definition and Semantics of HTN Methods

In the standard formalism, an HTN planning problem is a tuple $P = (S_0, T_0, M, O)$, where $S_0$ is an initial world state, $T_0$ is the root task network (possibly a list or partial order of tasks), $M$ is a set of methods, and $O$ a set of operators (primitive actions) (Au et al., 2011, Georgievski et al., 2014).

An HTN method is defined as a tuple

$m = (\text{head}(m), \text{pre}(m), \text{sub}(m))$

• head(m): a compound task symbol (possibly with parameters), i.e., the task pattern the method can refine.
• pre(m): a set of (lifted) preconditions—first-order formulas or conjunctions thereof specifying when the method may apply.
• sub(m): a task network—a (partially or totally ordered) set of subtasks, each of which may itself be primitive or compound.

Mathematically, for a ground compound task $t = \tau(\vec{c})$, method $m$ applies with substitution $\theta$ if $\tau(\vec{x})\theta = \tau(\vec{c})$ and the preconditions are true in the current state. The effect of decomposition is to replace the occurrence of $t$ in the active task network by the appropriately grounded subtasks, preserving and extending ordering constraints (Georgievski et al., 2014, Au et al., 2011).

Methods support partial orders on subtasks and constraints such as causal links or variable bindings, and can express complex procedural knowledge, including condition-dependent flows and resource or temporal constraints (Au et al., 2011, Pellier et al., 2022).

2. Operational Integration and Search Algorithms

HTN planning algorithms are typically classified as plan-based (plan-space) or state-based (state-space) (Georgievski et al., 2014). In both, methods drive the recursive decomposition:

• State-based (e.g., SHOP2/JSHOP2): Selects the next task (observing ordering constraints), applies a method if the task is compound (refining it in the current state), or applies an operator if primitive (updating the state and removing the task), repeating until only primitive tasks remain (Au et al., 2011, Georgievski et al., 2011, Lallement et al., 2014).
• Plan-based: Maintains a partially ordered task network, selects decomposable compound tasks, and incrementally refines the plan by applying methods, with least commitment to variable binding and ordering (Georgievski et al., 2014).

Soundness and completeness results: Given restrictions on method usage (e.g., acyclicity, bounded variables), and assuming all necessary operators and methods are present, the sequence of applied methods and operators is shown to generate correct plans (Au et al., 2011). In the general case, plan existence for unrestricted HTN models is undecidable, but for commonly used restrictions (e.g., totally ordered decompositions) it is EXPSPACE- or PSPACE-complete (Georgievski et al., 2014).

3. Learning, Refining, and Optimizing HTN Methods

The specification of methods is a knowledge engineering bottleneck; as a result, several machine learning approaches target acquisition and repair of HTN methods:

• Landmark-driven and curriculum-based learning: Methods such as CURRICULAMA automatically induce hierarchical methods from traces by using extracted landmarks and a curriculum learning strategy that orders the induction of simpler before complex methods (Li et al., 9 Apr 2024). This eliminates the need for manual annotation and produces empirically sound and complete method sets comparable to prior semi-automatic approaches.
• Task-insertion-based refinement: When given partial or incomplete expert knowledge, task-insertion planning (TIHTN) and refinement frameworks identify missing tasks in traces and assign their insertion locations under prioritized stratification of methods, yielding minimal repairs that preserve original knowledge as much as possible (Xiao et al., 2019).
• Grammar induction from partial and noisy data: HierAMLSI casts HTN method induction as grammar learning, inducing context-free productions (methods) from observed traces under partial observability and noise, and refining them through dependency-aware covering and precondition/effect inference (Grand et al., 2022).
• LLM-based and hybrid learning: Hybrid planners such as ChatHTN and its method-augmenting successors use LLMs to propose decompositions when no method applies; these decompositions are then generalized via goal regression and lifted to create reusable methods, integrating them into the method database for future planning (Munoz-Avila et al., 17 May 2025, Xu et al., 17 Nov 2025).

Approach	Key Features	Reference
CURRICULAMA	No manual annotation; landmarks	(Li et al., 9 Apr 2024)
Task-insertion refinement	Minimal necessary insertion	(Xiao et al., 2019)
HierAMLSI	Inductive grammar; noisy/partial	(Grand et al., 2022)
ChatHTN+Method Learning	Online LLM-based generalization	(Munoz-Avila et al., 17 May 2025, Xu et al., 17 Nov 2025)

4. Extensions: Expressiveness, Temporal and Numeric Methods

HTN methods are increasingly extended to capture richer task properties:

• Temporal and numeric methods: HDDL 2.1 generalizes HTN methods to allow "durative methods", associating not only subtasks but also duration constraints, state/trajectory temporal constraints, and numeric (resource) constraints at the method level. This bridges traditional PDDL 2.1 ANML-style constructs with hierarchical decomposition, enabling real-world, concurrent, and constrained planning (Pellier et al., 2022).
• Task modifiers and dynamic task lists: Extensions such as "task modifiers" ($\mathit{TM}$) define schema-independent functions that can rewrite the agent’s current task list based on the observed state, dynamically inserting, removing, or reordering tasks in response to exogenous events. This allows HTN planning to function robustly in dynamic, partially observable, or stochastic environments (Yuan et al., 2022).
• Risk-aware methods: Methods can additionally be annotated with cost distributions and linked to utility functions representing risk attitude (e.g., risk-seeking, risk-averse), enabling computation of plans maximizing expected utility, a significant departure from risk-neutral models (Alnazer et al., 2022).

5. Practical Applications and Heuristic Optimization

HTN methods are applied across diverse domains and are critical for efficient solution of complex, real-world planning tasks:

• Robotics and Multi-Agent Systems: Robotic frameworks such as HATP use extended HTN methods to represent complex, agent-centric actions with object- and agent-oriented abstractions, supporting social, temporal, and geometric constraints for human-robot interaction, multi-agent collaboration, and real-time execution (Lallement et al., 2014, Mu et al., 2023).
• Economic Mobilization and Resource Planning: HTN methods define the decomposition of mobilization objectives into actionable production and transport tasks, with explicit handling of resource constraints and shortages; heuristics on method and task selection optimize throughput and minimize overall cost (Zhao, 2023).
• Web Services and Automated Composition: In service-oriented architectures, methods capture process control structure, enabling composition, substitution, and optimization of processes with minimal user input (Georgievski et al., 2014).

Optimization and compilation:

Recent planners implement full instantiation and simplification of methods at compile time, allowing efficient heuristic computation (e.g., relaxed planning graphs, landmarks), SAT/CSP encodings, and pruning of unreachable or redundant decompositions (Ramoul et al., 2018, Magnaguagno et al., 2022). Preprocessing passes such as "pull-up" (lifting preconditions through the hierarchy), predicate specialization, and cycle detection in method graphs yield substantial runtime, search depth, and memory improvements.

6. Limitations, Challenges, and Future Directions

While HTN methods are powerful, several challenges remain:

• Knowledge acquisition cost: High manual engineering effort for method definition persists, notwithstanding advances in learning.
• Method completeness and robustness: Incomplete or poorly ordered methods can lead to plan failure or inefficiency; this motivates integration with learning, LLMs, and dynamic task modification.
• Expressivity and scalability: While methods can encode unboundedly rich procedural knowledge (HTN planning is Turing-complete (Au et al., 2011)), tractable subsets and benchmarks are essential for practical deployment.
• Integration with other paradigms: Ongoing work focuses on combining HTN with temporal/continuous, stochastic, or multi-agent reasoning, as well as with reinforcement learning, to achieve more adaptive and interpretable planners (Mu et al., 2023, Pellier et al., 2022).
• Standardization: Progress depends on more unified languages (e.g., HDDL), cross-planner benchmarks, and transparent evaluation metrics.

HTN methods remain a foundational and rapidly evolving construct in hierarchical planning, with ongoing research advancing their learnability, dynamic adaptation, formal properties, and practical applicability across domains (Georgievski et al., 2014, Xiao et al., 2019, Yuan et al., 2022, Li et al., 9 Apr 2024, Munoz-Avila et al., 17 May 2025).