Modelling Mixed Discrete-Continuous Domains for Planning

TL;DR

This paper introduces pddl+, a language for modeling complex mixed discrete-continuous planning problems, with formal semantics linking it to hybrid automata to leverage their theoretical properties.

Contribution

The paper presents pddl+, a novel planning language with formal semantics based on hybrid automata, enabling better modeling of time-dependent effects in planning domains.

Findings

pddl+ offers a flexible modeling style for complex time-dependent effects

Formal semantics map pddl+ to hybrid automata and transition systems

Decidability results for certain classes of hybrid automata

Abstract

In this paper we present pddl+, a planning domain description language for modelling mixed discrete-continuous planning domains. We describe the syntax and modelling style of pddl+, showing that the language makes convenient the modelling of complex time-dependent effects. We provide a formal semantics for pddl+ by mapping planning instances into constructs of hybrid automata. Using the syntax of HAs as our semantic model we construct a semantic mapping to labelled transition systems to complete the formal interpretation of pddl+ planning instances. An advantage of building a mapping from pddl+ to HA theory is that it forms a bridge between the Planning and Real Time Systems research communities. One consequence is that we can expect to make use of some of the theoretical properties of HAs. For example, for a restricted class of HAs the Reachability problem (which is equivalent to Plan Existence) is decidable. pddl+ provides an alternative to the continuous durative action model of pddl2.1, adding a more flexible and robust model of time-dependent behaviour.