Temporal Planning for Interacting Durative Actions with Continuous Effects

One of the most important properties of temporal planners is their capability of integrating planning into scheduling so that time can be considered as an optimization objective. Forward chaining temporal planners provides tight coupling of planning and scheduling. In these planners, a search node is represented by a world state including the applied action directly attached with a world clock which defines starting time of that action. The search proceeds by applying a new action or advancing the world clock which moves the time forward. To avoid infinite branching factor, forward chaining temporal planners can set a world clock only at certain points in time called decision epochs for which an at-end effect of a previously applied action is scheduled. Since all necessary timestamps in continuous time line are not covered, the resulting plan may be suboptimal for planning problems that include both discrete effects and time-dependent continuous linear effects. Continuous linear effects occur especially when agents share time-dependent critical resources. In these cases, besides discrete and continuous changes, their interactions should also be taken into consideration. Some of the earlier studies have investigated planning domains including actions with continuous linear effects. TM-LPSAT (Shin & Davis 2005) is an extension to SATbased planning framework to handle concurrent actions with continuous change. COLIN (Coles et al. 2009) is another effective planner which plans with mixed discrete continuous numeric changes. Both of these planners support PDDL+ (Fox & Long 2006) language which provides representation of continuous process effects in planning domains. However, the focus of both systems is to handle increase and decrease in the value of singular variables. Neither of the studies considers interactions among continuous effects of different actions in planning domain. This paper presents an extension to forward chaining temporal planning to handle continuous linear effects of actions and interactions among them. The main motivation is providing completeness considering these effects. We propose an action lifting approach in order to ensure completeness in domains with interacting linear continuous