Ansys Preoperative Planning Fea

Arxiv:2306.07353V1 [Cs.Ai] 12 Jun 2023

HDDL 2.1: Towards Defining a Formalism and a Semantics

For Temporal Htn Planning

Damien Pellier,1 Alexandre Albore,2 Humbert Fiorino,1 Rafael Bailon-Ruiz 2

Abstract

Real world applications as in industry and robotics need mod- elling rich and diverse automated planning problems. Their resolution usually requires coordinated and concurrent ac- tion execution. In several cases, these problems are naturally decomposed in a hierarchical way and expressed by a Hi- erarchical Task Network (HTN) formalism. HDDL, a hier- archical extension of the Planning Domain Definition Lan- guage (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.

Introduction

Real world applications of Automated Planning, like in in- dustry and robotics, require modelling rich and diverse sce- narios. Such planning problems are often naturally decom- posed in a hierarchical way, with compound tasks that refine in different ways their execution model. These real world ap- plications of planning use both numerical and temporal con- straints to define the agents synchronisation on collabora- tive tasks, and sub-task decomposition. In fact, concurrency between actions, their duration, and agents coordination in HTN problems are needed to find solutions for nontrivial tasks in complex scenarios and require to make explicit the representation of time (Ghallab, Nau, and Traverso 2016).

The Hierarchical Task Network (HTN) formalism (Erol, Hendler, and Nau 1994) is used to express a wide variety of planning problems in real-world applications, e.g., in task allocation for robot fleets (Milot et al. 2021), video games (Menif, Jacopin, and Cazenave 2014) or industrial contexts such as software deployment (Georgievski et al. 2017). Over the last years, much progress has been made in the field of hierarchical planning (Bercher, Alford, and H¨oller 2019).

Novel systems based on the traditional, search-based tech- niques have been introduced (Bit-Monnot, Smith, and Do 2016; Ramoul et al. 2017; Shivashankar, Alford, and Aha 2017; Bercher et al. 2017; H¨oller et al. 2019, 2020; H¨oller and Bercher 2021), but also new techniques like the transla- tion to STRIPS/ADL (Alford, Kuter, and Nau 2009; Alford et al. 2016; Behnke et al. 2022), or revisited approaches like the translation to propositional logic (Behnke, H¨oller, and Biundo 2018, 2019; Schreiber et al. 2019; Schreiber 2021; Behnke 2021). Despite these advances, not all planning sys- tems use the same formalism to represent hierarchical task decomposition, making it difficult to compare approaches and promote HTN planning techniques.

An Extension Of Pddl (Planning Domain Description

Language) (Mcdermott et al. 1998), called HDDL (Hier- archical Planning Domain Description Language) (H¨oller et al. 2020), has been proposed to address this issue. HDDL is based on PDDL 2.1 (Fox and Long 2003) and is the result of several discussions within the planning commu- nity (Behnke et al. 2019) to fill the need of a standard lan- guage for the first Hierarchical Planning track of Interna- tional Planning Competitions (IPC) in 2020. However, it was decided that the first version of HDDL would not include any of the temporal or numerical features of PDDL due to efforts to develop the language and related tools. In this pa- per, we illustrate the challenge of defining the semantics for a temporal extension of HDDL to meet the needs of the plan- ning community and planning applications.

Our motivation is grounded on the compelling need to devise applications involving autonomous systems. We pro- pose to extend HDDL, by including elements of PDDL 2.1 and ANML (Action Notation Modeling Language) (Smith, Frank, and Cushing 2008), to express temporal and numeri- cal constraints. This is intended to initiate discussions within the HTN community on establishing a standard – HDDL 2.1 – aimed at filling the gaps between existing hierarchical- temporal planning approaches. To that end, we make this preliminary extension of HDDL an open source project with a public repository, where we propose a full syntax as well as a set of benchmarks based on this extension1 and a parser for it, as part of the PDDL4J2 library (Pellier and Fiorino 2018).

The rest of the paper is organised as follows. In Section 2 we define the basic concepts of the proposed extension. In Sections 3 and 4 we set down the semantics for Temporal

2Https://Github.Com/Pellierd/Pddl4J

HTN planning. We conclude on the central aspects of this planning paradigm, and on future work.

Lifted Temporal Htn Planning

Throughoutthis section, we will use common notations from first-order logic, which we assume to be known. In the lifted formalism of HDDL 2.1, we assume for the sake of sim- plicity that all logical formulas are over a function-free first- order logic language L = (V, C, P). L consists of suffi- ciently many constant c ∈C representing the objects in the real world, variables x ∈V and predicates p ∈P. Predi- cates have parameters that are either variables or constants.

The predicate arity is the number of predicate parameters. For instance, p(x, c) is a 2-arity predicate. We can now de- fine formulas in a function-free first-order logic: (i) a pred- icate is a formula ; (ii) if φ and ψ are formulas, then ¬φ, φ ∨ψ and φ ∧ψ are formulas ; (iii) if φ is a formula and x is a variable, then ∀xφ is a formula. We define ∃xφ as ¬∀x¬φ, and φ →ψ as ¬φ ∨ψ. ∀and ∃are respectively the uni- versal and the existential quantifier. Conceptually, ground- ing a formula consists in generating a set of variable-free i.e. ground formulas (Helmert 2009) as follows: a variable x in a quantifier-free formula φ is eliminated by replacing φ with |C| copies, one for each c ∈C, where x is substituted with c in the respective copy. This substitution is denoted by φ[x/c]. Regarding quantified formulas, ∀xφ is replaced by

C∈C Φ[X/C]. We Refer The Reader

to the work of by Behnke et al. (2020); Ramoul et al. (2017) for further details on grounding implementation. Note that it is always possible to transform a formula in function-free first-order logic into a finite set of ground formulas in propo- sitional logic.

A state s is a set of ground predicates. For the sake of con- ciseness, we will also consider s as a Herbrand interpretation that assigns true to all ground predicates in s, and false to all ground predicates not in s. From this, a truth value can be computed for every ground formula from L by using the usual rules for logical composition. Without loss of general- ity, a formula (not necessarily ground) φ is true in s if and only if grounding φ generates at least one ground formula true in s. We will use the notation s |= φ to mean that the formula φ is true in s.

A key concept in HTN planning and a fortiori in temporal HTN planning is the concept of task. Each task is given by a name and a list of parameters. We distinguish two kinds of tasks: the primitive tasks (also called actions), and the abstract tasks (or compound tasks). Primitive tasks are car- ried out by durative actions in the sense of classical temporal planning (Fox and Long 2003), while abstract tasks can be refined by applying methods that define the decomposition of the task into subtasks. The purpose of abstract tasks is not to induce a state transition. Instead, they refer to a predefined mapping to one or more tasks that can refine the abstract task. For instance, in the task of serving a dinner, deliver- dinner(?food-style, ?place) is the compound task consist- ing in performing first the task of serving the starters, then the main course, etc. In that sense, deliver-dinner(?food- style, ?place) can be refined in: ⟨serve-starters(?food-style, ?place), serve-main-course(?food-style, ?place), etc.⟩This

Inv(A)

Figure 1: Timeline of a durative action a application. mapping between tasks is achieved by a set of decomposi- tion methods, namely the methods (Def. 5) and the Temporal Task Networks (Def. 6).

We first define the planning domain and problem for Tem- poral HTN Planning.

Definition

1.

Tuple

(L, T , J , α, A, M), where L is the first-order logic language, T is the set of tasks, J is the set of task identi- fiers3, α : J →T is the function that maps task identifiers to tasks, A is a set of actions constituted by snap actions (Def. 3) and durative actions (Def. 4), M is the set of methods (Def. 5).

The domain implicitly defines the set of all states S de- fined over all subsets of all ground predicates in L.

Definition

2.

Tuple

(D, s0, w0, g), where D is a planning domain, s0 ∈S is the initial state, w0 is the initial temporal task network (not necessary ground), and g is a formula (not necessary ground) describing the goal.

Let us start by defining the concepts of snap and durative actions, which are the primitive tasks, based on the defini- tions from Abdulaziz and Koller (2022). A snap action is an action whose execution is instantaneous in the sense of clas- sical planning, meaning that it has a null duration between checking the preconditions and applying the effects.

Definition 3 (Snap Action). A snap action a is a tu-

, Where Name(A) Is The

name of a, the precondition precond(a) is a first-order for- mula, and the effects effect(a) = effect+(a) ∪effect−(a) (effect+(a) ∩effect−(a) = ∅), effect+(a) and effect−(a) are conjunctions of predicates.

Definition 4 (Durative Action). A durative action a is a tuple

: Name(A) Is The Name

of a; start(a) and end(a) are snap actions; inv(a) is a first- order formula that must hold in all the states after the exe- cution of start(a) and until the execution of end(a), and δ is the duration of a.

Actions do change the state of the world. Durative actions also change the time of the model, shifting it by a quantity δ, as shown in Figure 1. State transitions will be formally defined in Section 3.

Unlike a primitive task, a compound task does not directly change the world state. A compound task is identified by a name and defines the way other –possibly ordered– tasks (ei- ther primitive or compound) must be achieved with respect 3Task identifiers are arbitrary symbols, which serve as place holders for the actual tasks they represent. Identifiers are needed because tasks can occur multiple times within the same task net- work, as we will see below.

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