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Petri Net Relaxation for Infeasibility Explanation and Sequential Task Planning

Nguyen Cong Nhat Le, John G. Rogers, Claire N. Bonial, Neil T. Dantam

TL;DR

A Petri net reachability relaxation is proposed to enable robust invariant synthesis, efficient goal-unreachability detection, and helpful infeasibility explanations and further leverage incremental constraint solvers to support goal and constraint updates.

Abstract

Plans often change due to changes in the situation or our understanding of the situation. Sometimes, a feasible plan may not even exist, and identifying such infeasibilities is useful to determine when requirements need adjustment. Common planning approaches focus on efficient one-shot planning in feasible cases rather than updating domains or detecting infeasibility. We propose a Petri net reachability relaxation to enable robust invariant synthesis, efficient goal-unreachability detection, and helpful infeasibility explanations. We further leverage incremental constraint solvers to support goal and constraint updates. Empirically, compared to baselines, our system produces a comparable number of invariants, detects up to 2 times more infeasibilities, performs competitively in one-shot planning, and outperforms in sequential plan updates in the tested domains.

Petri Net Relaxation for Infeasibility Explanation and Sequential Task Planning

TL;DR

A Petri net reachability relaxation is proposed to enable robust invariant synthesis, efficient goal-unreachability detection, and helpful infeasibility explanations and further leverage incremental constraint solvers to support goal and constraint updates.

Abstract

Plans often change due to changes in the situation or our understanding of the situation. Sometimes, a feasible plan may not even exist, and identifying such infeasibilities is useful to determine when requirements need adjustment. Common planning approaches focus on efficient one-shot planning in feasible cases rather than updating domains or detecting infeasibility. We propose a Petri net reachability relaxation to enable robust invariant synthesis, efficient goal-unreachability detection, and helpful infeasibility explanations. We further leverage incremental constraint solvers to support goal and constraint updates. Empirically, compared to baselines, our system produces a comparable number of invariants, detects up to 2 times more infeasibilities, performs competitively in one-shot planning, and outperforms in sequential plan updates in the tested domains.
Paper Structure (27 sections, 2 theorems, 25 equations, 5 figures)

This paper contains 27 sections, 2 theorems, 25 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Definition
  4. Background
  5. Planning Domain Definition Language
  6. Constraint Solvers
  7. Constraint-based Planning
  8. Petri Nets
  9. Method
  10. Petri Nets for Planning Domains
  11. Petri Net Constraints
  12. Relaxed Petri Net Reachability
  13. Invariants from Linear Relaxations
  14. Infeasibility Explanations from Linear Relaxations
  15. Forward and Backward Reachable Sets
  16. ...and 12 more sections

Key Result

proposition thmcounterproposition

A marking ${\mathbf{p}}^{\left\langle{h}\right\rangle}$ resulting in infeasible constraints for the relaxed system dynamics eq:pn:relaxed:dynamics implies that ${\mathbf{p}}^{\left\langle{h}\right\rangle}$ is unreachable at any step under the original system dynamics eq:pn:dynamics and eq:pn:boolflo

Figures (5)

  • Figure 1: Petri net structure for PDDL preconditions and effects. (a) variable in precondition (not in effect). (b) variable in effect (not in precondition). (c) variable in precondition and effect.
  • Figure 2: Two-literal invariants from our PN relaxation and baselines. All methods produce similar numbers of invariants.
  • Figure 3: Average infeasibility detection times over $10$ iterations and counts. Absent data points exceeded a $10$-minute timeout or 8 memory limit. Dashes in the table indicates unsupported numeric domains for Mp and FD.
  • Figure 4: Average one-shot planning times over $10$ iterations. The figures show the numbers of instances solved over time in numeric domains. Excluded data points exceeded the $10$-minute timeout or 8 memory limit.
  • Figure 5: Average cumulative planning times over $10$ iterations for sequential planning. TMKit Gurobi outperforms the baselines in most sequences. Excluded data points exceeded the $30$-minute timeout or 8 memory limit.

Theorems & Definitions (4)

  • proposition thmcounterproposition
  • proof
  • proposition thmcounterproposition
  • proof