Symbolic Pattern Temporal Numeric Planning with Intermediate Conditions and Effects

Recently, a Symbolic Pattern Planning (SPP) approach was proposed for numeric planning where a pattern (i.e., a finite sequence of actions) suggests a causal order between actions. The pattern is then encoded in a SMT formula whose models correspond to valid plans. If the suggestion by the pattern is inaccurate and no valid plan can be found, the pattern is extended until it contains the causal order of actions in a valid plan, making the approach complete. In this paper, we extend the SPP approach to the temporal planning with Intermediate Conditions and Effects (ICEs) fragment, where $(i)$ actions are durative (and thus can overlap over time) and have conditions/effects which can be checked/applied at any time during an action’s execution, and $(ii)$ one can specify plan’s conditions/effects that must be checked/applied at specific times during the plan execution. Experimental results show that our SPP planner Patty $(i)$ outperforms all other planners in the literature in the majority of temporal domains without ICEs, $(ii)$ obtains comparable results with the SoTA search planner for ICS in literature domains with ICEs, and $(iii)$ outperforms the same planner in a novel domain based on a real-world application.

💡 Research Summary

The paper presents a significant extension of Symbolic Pattern Planning (SPP), originally devised for numeric planning, to the more expressive domain of temporal numeric planning with Intermediate Conditions and Effects (ICEs). In classic planning, actions are instantaneous and constraints are purely propositional, leading to PSPACE‑complete decision problems. Introducing numeric variables already pushes many problems into undecidability, and adding durative actions with overlapping execution further complicates the landscape. ICEs allow both actions and the overall plan to specify conditions and effects at arbitrary moments during execution, a feature essential for real‑world domains such as railway dispatching, robotic coordination, and manufacturing where safety windows, maintenance periods, and priority rules must be respected.

The authors formalize a Temporal Numeric Planning task with ICEs as a tuple Π = ⟨X, A, I, G, C, E⟩. X contains propositional and rational‑valued numeric variables. Each durative action b = ⟨icond(b), ieff(b),