Symbolic Pattern Temporal Numeric Planning with Intermediate Conditions and Effects

TL;DR

This work extends Symbolic Pattern Planning to Temporal Numeric Planning with ICEs by introducing rolling of durative actions, a pattern formalism that encodes causal and interleaving orders, and an SMT-based encoding that enforces both causal and temporal constraints. The approach leverages an arpg to compute patterns and transforms them into a pattern-encoded planning problem, with correctness and completeness guaranteed under well-orderability assumptions. Empirical results across domains including InSTraDi demonstrate that Patty solves the largest number of instances (168/190) and often outperforms or matches state-of-the-art search- and PAS-based planners, especially in ICE-rich domains. The findings indicate that pattern-guided symbolic planning can effectively tackle complex temporal-numeric problems and suggest future work integrating additional search strategies and exploring incomplete-pattern variants to balance completeness and efficiency.

Abstract

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.

Figures (3)

• Figure 1: The motivating InSTraDi example with two trains, red and blue. The train red is stopping at platform $\texttt{II}$ oriented towards the green signal $\texttt{22}$ which allows entering route 22-02 to exit the station from the exit point 02. Train blue is about to enter the station from the entry point 03 using route 03-23 to reach platform III.
• Figure 2: Initial state of our motivating example. The red train is occupying platform $\texttt{II}$. The blue train is arriving in $5s$ in 03.
• Figure 3: Number of problems solved ($x$-axis) in a given time ($y$-axis), by all the presented systems. In the legend, the planners are listed in reverse order of when their curve intersects the timeout line.

Theorems & Definitions (15)

• Theorem 1
• proof
• Corollary 1
• proof
• Example
• Example
• Theorem 2
• proof
• Example
• Example