In this paper we have presented a planning domain description language, PDDL+, that supports the modelling of continuous dynamics. We have provided a formal semantics by specifying a mapping from PDDL+ constructs to those of deterministic hybrid automata. We have also related fragments of PDDL+ to automata with different levels of expressive power. Our goal has been to develop a PDDL extension that properly models the passage of time, and the continuous change of quantities over time, to support the modelling of mixed discrete-continuous planning domains.

Our primary goal has been to establish a baseline for mixed discrete-continuous modelling, and to provide a formal semantics for the resulting language. Additionally we wanted to make a strong connection between planning and automata theory in order to facilitate the cross-fertilisation of ideas between the planning and real-time systems and model-checking communities. We have explored the relationship between fragments of PDDL+ and automata-theoretic models on the boundary of decidability in order to better understand what is gained or lost in expressive power by the addition or removal of modelling constructs.

We have not focussed on how to make PDDL+ convenient for modelling because modelling convenience is not related to expressive power. We agree that it might be desirable to build abstract modelling constructs on top of the baseline language in order to enhance modelling convenience. Nevertheless, so that PDDL+ can be used for experimental purposes, in the development of technology for mixed discrete-continuous planning, we have presented it as a usable language that builds directly upon the current standard modelling language for temporal domains. We have presented two examples of domain models that exploit processes, events and durative actions in the succinct representation of continuous change. Future work will consider what more powerful modelling constructs might be built to support the convenient modelling of larger scale mixed discrete-continuous domains. We would like to extend special thanks to David Smith for his detailed critical analysis of earlier drafts of this paper and his many insightful comments and suggestions. We would also like to thank Subbarao Kambhampati and the anonymous referees for helping us to organise and clarify the presentation of this work, and Jeremy Frank, Stefan Edelkamp, Nicola Muscettola, Drew McDermott, Brian Williams and Mark Boddy, all of whom helped us to refine and sharpen our ideas and formulations.

Derek Long 2006-10-09