Temporal-numeric planning with control parameters

Over the last decade, significant progress has been made in task planning to explore temporal and numerical features of the real world. Interaction between time and metric fluents and temporal coordination problems have been well-addressed by innovative approaches in planning and scheduling. A standardised language, PDDL, has enabled modelling the conceptual models and benchmarking the work of numerous researchers since it was released. Although PDDL is an expressive modelling language, a significant limitation is imposed on the structure of actions: the parameters of actions are restricted to values from finite (in fact, explicitly enumerated) domains. There is one exception to this, introduced in PDDL2.1, which is that durative actions may have durations that are chosen (possibly subject to explicit constraints in the action models) by the planner. A motivation for this limitation is that it ensures that the set of grounded actions is finite and, ignoring duration, the branching factor of action choices at a state is therefore finite. Although the duration parameter can make this choice infinite, very few planners support this possibility, but restrict themselves to durative actions with fixed durations. In this thesis we motivate a proposed extension to PDDL to allow actions with infinite domain parameters, which we call control parameters. We illustrate reasons for using this modelling feature and then describe a planning approach that can handle domain models that exploit it, implemented in a new planner, called POPCORN. We propose an extension to a delete-relaxation heuristic, called the Temporal Relaxed Planning Graph, to tackle problems with control parameters; especially in problems with producer-consumer relationship of actions. We show that this approach scales to solve interesting problems. We apply this work in a task and motion planning scenario to show that our work has a great potential of re-inventing the way task planners are used in robot navigation.