An Executable Semantics of Flexible Plans in Terms of Timed Game Automata

Robust plan execution in uncertain and dynamic environments is a critical issue for plan-based autonomous systems, especially when uncertain events coexist with temporal flexibility. In this regard, many Planning and Scheduling systems model temporal uncertainty by means of flexible timelines, each of which describes the behavior of one of the system components, and consists of a sequence of events whose begin and end times range within given intervals. This work enriches a previously proposed formal characterization of flexible timelines and plans, considering the difference between controllable and uncontrollable activities. Two main sources of uncertainty are considered: i) some components of the system may depend on an external environment and cannot be planned by the executive, ii) there may be tasks whose duration cannot be exactly foreseen in advance. Such notions are formally defined and the consequent controllability issues are addressed, focusing, in particular, on dynamic controllability. Partially controllable flexible plans are given a semantics in terms of networks of timed game automata (TGA), showing how they can be encoded into such networks. The translation allows for exploiting existing verification tools for TGA, such as UPPAAL-TIGA, in order to check the dynamic controllability property for flexible plans and, possibly, generate a dynamic execution strategy that can be used for robust plan execution. Some preliminary experiments aimed at evaluating the feasibility of the approach are also presented.