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TIDE: A Trace-Informed Depth-First Exploration for Planning with Temporally Extended Goals

Yuliia Suprun, Khen Elimelech, Lydia E. Kavraki, Moshe Y. Vardi

TL;DR

This work tackles planning with temporally extended goals expressed as $LTL_f$ formulas over finite traces, where traditional product-graph approaches scale poorly. It introduces TIDE, a trace-informed depth-first exploration that incrementally selects a promising DFA trace and realizes it as a sequence of classical reach-avoid subproblems solved by off-the-shelf planners, guided by a cost-based trace ranking and adaptive backtracking. The method guarantees completeness and demonstrates strong empirical performance across TB15, Blocksworld scaling benchmarks, and Openstacks backtracking problems, often outperforming Exp, Poly, FOND4LTL$_f$, and Plan4Past. By decomposing temporal goals into planner-friendly subproblems and caching realized transitions, TIDE improves scalability and practicality for temporally constrained tasks in fully observable deterministic domains. The approach is also supported by open-source implementations, showing potential for integration into real-world robotic planning pipelines that require reliable temporal coordination.

Abstract

Task planning with temporally extended goals (TEGs) is a critical challenge in AI and robotics, enabling agents to achieve complex sequences of objectives over time rather than addressing isolated, immediate tasks. Linear Temporal Logic on finite traces (LTLf ) provides a robust formalism for encoding these temporal goals. Traditional LTLf task planning approaches often transform the temporal planning problem into a classical planning problem with reachability goals, which are then solved using off-the-shelf planners. However, these methods often lack informed heuristics to provide a guided search for temporal goals. We introduce TIDE (Trace-Informed Depth-first Exploration), a novel approach that addresses this limitation by decomposing a temporal problem into a sequence of smaller, manageable reach-avoid sub-problems, each solvable using an off-the-shelf planner. TIDE identifies and prioritizes promising automaton traces within the domain graph, using cost-driven heuristics to guide exploration. Its adaptive backtracking mechanism systematically recovers from failed plans by recalculating costs and penalizing infeasible transitions, ensuring completeness and efficiency. Experimental results demonstrate that TIDE achieves promising performance and is a valuable addition to the portfolio of planning methods for temporally extended goals.

TIDE: A Trace-Informed Depth-First Exploration for Planning with Temporally Extended Goals

TL;DR

This work tackles planning with temporally extended goals expressed as formulas over finite traces, where traditional product-graph approaches scale poorly. It introduces TIDE, a trace-informed depth-first exploration that incrementally selects a promising DFA trace and realizes it as a sequence of classical reach-avoid subproblems solved by off-the-shelf planners, guided by a cost-based trace ranking and adaptive backtracking. The method guarantees completeness and demonstrates strong empirical performance across TB15, Blocksworld scaling benchmarks, and Openstacks backtracking problems, often outperforming Exp, Poly, FOND4LTL, and Plan4Past. By decomposing temporal goals into planner-friendly subproblems and caching realized transitions, TIDE improves scalability and practicality for temporally constrained tasks in fully observable deterministic domains. The approach is also supported by open-source implementations, showing potential for integration into real-world robotic planning pipelines that require reliable temporal coordination.

Abstract

Task planning with temporally extended goals (TEGs) is a critical challenge in AI and robotics, enabling agents to achieve complex sequences of objectives over time rather than addressing isolated, immediate tasks. Linear Temporal Logic on finite traces (LTLf ) provides a robust formalism for encoding these temporal goals. Traditional LTLf task planning approaches often transform the temporal planning problem into a classical planning problem with reachability goals, which are then solved using off-the-shelf planners. However, these methods often lack informed heuristics to provide a guided search for temporal goals. We introduce TIDE (Trace-Informed Depth-first Exploration), a novel approach that addresses this limitation by decomposing a temporal problem into a sequence of smaller, manageable reach-avoid sub-problems, each solvable using an off-the-shelf planner. TIDE identifies and prioritizes promising automaton traces within the domain graph, using cost-driven heuristics to guide exploration. Its adaptive backtracking mechanism systematically recovers from failed plans by recalculating costs and penalizing infeasible transitions, ensuring completeness and efficiency. Experimental results demonstrate that TIDE achieves promising performance and is a valuable addition to the portfolio of planning methods for temporally extended goals.
Paper Structure (117 sections, 2 theorems, 31 equations, 16 figures, 15 tables, 4 algorithms)

This paper contains 117 sections, 2 theorems, 31 equations, 16 figures, 15 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Motivation
  4. The Challenge of Scalability
  5. Proposed Solution: TIDE
  6. Overview
  7. Related Work
  8. Goal Progression-Based Approaches
  9. Compilation-Based Approaches
  10. Dynamic Generation of Successive Reachability Goals
  11. Problem Definition
  12. Classical Planning with Final-State Goals
  13. Illustrative Example: Classical Planning in Blocksworld
  14. Task Planning Domain
  15. Classical Planning with Reachability Goals
  16. ...and 102 more sections

Key Result

Lemma 4.1

Let $f$ be a Boolean function over variables $x_1, x_2, \ldots, x_n$. For a variable $x_i$:

Figures (16)

  • Figure 1: Example of a classical planning problem with final-state goals in the Blocksworld domain.
  • Figure 2: Problem with a Temporally Extended Goal: reverse the order of the blocks and then place them all on the table.
  • Figure 3: BDD representation of the function $f(x_1, x_2, x_3) = (x_1 \land x_2 \land \neg x_3) \lor (\neg x_1 \land x_3)$. Dashed lines represent transitions to the low child (false), and solid lines represent transitions to the high child (true).
  • Figure 4: DFA for Cost Calculation Example. Each edge is labeled with its guard, and edge costs are determined by the difference in required predicates ($\Delta$) between the guard of the edge leading to the new state (in red) and the guard of the current state's self-edge (in blue).
  • Figure 5: DFA for Problem 1: $F (on\_b2\_b1 \land X(F(on\_b3\_b2)))$.
  • ...and 11 more figures

Theorems & Definitions (21)

  • Definition 3.1: Task Planning Domain
  • Definition 3.2: Classical Planning Problem with Reachability Goals
  • Definition 3.3: Planning Problem with Reach-Avoid Goals
  • Definition 3.4: Interpreted Task Planning Domain
  • Definition 3.5: Planning Problem with Propositional Reach-Avoid Goals
  • Definition 3.6: Syntax of LTL$_f$
  • Definition 3.7: Semantics of LTL$_f$
  • Definition 3.8: Planning Problem with LTL$_f$ Goals
  • Definition 4.1: Deterministic Finite Automaton
  • Definition 4.2: Non-deterministic Finite Automaton
  • ...and 11 more