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. 
M. Fox, D. Long
cs.AI