In these two examples plans must interact with the background continuous behaviours that are triggered by the world. In the refinery domain concurrent episodes of continuous change (such as the filling and emptying of a tank) affect the same variable (such as the sulphur content of the crude oil in the tank), and the flow into and out of the tank must be carefully controlled to achieve a mixture with the right chemical composition. In the Beagle 2 domain the power generation and consumption processes act concurrently on the power supply in a way that must be controlled to avoid the supply dropping below the critical minimal threshold. In both domains the continuous processes are subject to discontinuous first derivative effects, resulting from events being triggered, actions being executed or processes interacting. When events trigger the discontinuities might not coincide with the end-points of actions. A planner needs an explicit model of how such events might be triggered in order to be able to reason about their effects.
We argue that discretisation represents an inappropriate simplification of these domains, and that adequate modelling of the continuous dynamics is necessary to capture their critical features for planning.Derek Long 2006-10-09