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Two Constraint Compilation Methods for Lifted Planning

Periklis Mantenoglou, Luigi Bonassi, Enrico Scala, Pedro Zuidberg Dos Martires

TL;DR

This work addresses planning with qualitative state-trajectory constraints in a PDDL fragment by introducing two lifted constraint compilers, LiftedTCORE and LCC, to avoid full grounding. LiftedTCORE extends regression to the lifted domain using $R^{L}$ and $\\Gamma^L$, enabling action-specific preconditions and effects, while LCC uses uniform preconditions/ effects with a final $fin$ action to verify constraints, trading immediate constraint propagation for simpler per-action compilation. The authors prove the correctness of both approaches, derive their worst-case complexities, and benchmark them against grounded baselines on IPC-derived domains, finding that the lifted methods yield significantly more succinct compiled problems and competitive planning performance, with LCC often delivering higher coverage and LiftedTCORE performing well in grounded-like scenarios. Overall, the results demonstrate that lifting constraint compilation can scale planning under temporal constraints and enable more efficient use of state-of-the-art planners in large or high-arity domains, motivating further work on lifted techniques for numeric and time-based constraints.

Abstract

We study planning in a fragment of PDDL with qualitative state-trajectory constraints, capturing safety requirements, task ordering conditions, and intermediate sub-goals commonly found in real-world problems. A prominent approach to tackle such problems is to compile their constraints away, leading to a problem that is supported by state-of-the-art planners. Unfortunately, existing compilers do not scale on problems with a large number of objects and high-arity actions, as they necessitate grounding the problem before compilation. To address this issue, we propose two methods for compiling away constraints without grounding, making them suitable for large-scale planning problems. We prove the correctness of our compilers and outline their worst-case time complexity. Moreover, we present a reproducible empirical evaluation on the domains used in the latest International Planning Competition. Our results demonstrate that our methods are efficient and produce planning specifications that are orders of magnitude more succinct than the ones produced by compilers that ground the domain, while remaining competitive when used for planning with a state-of-the-art planner.

Two Constraint Compilation Methods for Lifted Planning

TL;DR

This work addresses planning with qualitative state-trajectory constraints in a PDDL fragment by introducing two lifted constraint compilers, LiftedTCORE and LCC, to avoid full grounding. LiftedTCORE extends regression to the lifted domain using and , enabling action-specific preconditions and effects, while LCC uses uniform preconditions/ effects with a final action to verify constraints, trading immediate constraint propagation for simpler per-action compilation. The authors prove the correctness of both approaches, derive their worst-case complexities, and benchmark them against grounded baselines on IPC-derived domains, finding that the lifted methods yield significantly more succinct compiled problems and competitive planning performance, with LCC often delivering higher coverage and LiftedTCORE performing well in grounded-like scenarios. Overall, the results demonstrate that lifting constraint compilation can scale planning under temporal constraints and enable more efficient use of state-of-the-art planners in large or high-arity domains, motivating further work on lifted techniques for numeric and time-based constraints.

Abstract

We study planning in a fragment of PDDL with qualitative state-trajectory constraints, capturing safety requirements, task ordering conditions, and intermediate sub-goals commonly found in real-world problems. A prominent approach to tackle such problems is to compile their constraints away, leading to a problem that is supported by state-of-the-art planners. Unfortunately, existing compilers do not scale on problems with a large number of objects and high-arity actions, as they necessitate grounding the problem before compilation. To address this issue, we propose two methods for compiling away constraints without grounding, making them suitable for large-scale planning problems. We prove the correctness of our compilers and outline their worst-case time complexity. Moreover, we present a reproducible empirical evaluation on the domains used in the latest International Planning Competition. Our results demonstrate that our methods are efficient and produce planning specifications that are orders of magnitude more succinct than the ones produced by compilers that ground the domain, while remaining competitive when used for planning with a state-of-the-art planner.

Paper Structure

This paper contains 27 sections, 10 theorems, 16 equations, 3 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Planning with Constraints in PDDL
  4. Regression
  5. LiftedTCORE
  6. Lifted Regression
  7. The LiftedTCORE Compiler
  8. Theoretical Properties.
  9. The Lifted Constraint Compiler
  10. Comparing LiftedTCORE and LCC
  11. Experimental Evaluation
  12. Experimental Results
  13. Summary and Further Work
  14. Proofs for Section \ref{['sec:lccr']}
  15. Proof of Lemma \ref{['prop:lifted_regr_correctness']}
  16. ...and 12 more sections

Key Result

Lemma 1

Consider a state $s$, an action $a$, a closed first-order formula $\phi$, and a ground incarnation $a^{\mathbin{\begin{tikzpicture}[circuit ee IEC,yscale=0.4,xscale=0.3] \draw (0,2ex) to (0,0) node[ground,rotate=-90,xshift=.65ex] {}; \end{tikzpicture}} {}}$ of $a$ such that $a^{\mathbin{\begin{tikzp

Figures (3)

  • Figure 1: Runtime comparison between LiftedTCORE vs. TCORE and between LiftedTCORE vs. LCC.
  • Figure 2: Constrained planning problem generator.
  • Figure 3: Initial state of a problem from the 'Ricochet Robots' domain. 'R1', 'R2', 'R3' and 'R4' denote robots, 'G3' is a goal location, and 'X' symbols denote walls.

Theorems & Definitions (29)

  • Example 1: Blocksworld2
  • Definition 1: Regression Operator
  • Definition 2: Weakest Condition $w^{c}_l(c \triangleright e\xspace)$
  • Example 2: Weakest Condition $w^{c}_l(c \triangleright e\xspace)$
  • Definition 3: $z$-substitution
  • Definition 4: Weakest Condition $w_l(\forall \vec{z}{:} c\triangleright e\xspace)$
  • Example 3: Weakest Condition $w_l(\forall \vec{z}{:} c\triangleright e\xspace)$
  • Definition 5: Lifted Gamma Operator $\Gamma^L_l(a)$
  • Example 4: Lifted Gamma Operator $\Gamma^L_l(a)$
  • Definition 6: Lifted Regression Operator $R^{L}(\phi, a)$
  • ...and 19 more