Modelling Mixed Discrete-Continuous Domains for Planning
  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.
