COLIN: Planning with Continuous Linear Numeric Change
  In this paper we describe COLIN, a forward-chaining heuristic search planner,
capable of reasoning with COntinuous LINear numeric change, in addition to the
full temporal semantics of PDDL. Through this work we make two advances to the
state-of-the-art in terms of expressive reasoning capabilities of planners: the
handling of continuous linear change, and the handling of duration-dependent
effects in combination with duration inequalities, both of which require
tightly coupled temporal and numeric reasoning during planning. COLIN combines
FF-style forward chaining search, with the use of a Linear Program (LP) to
check the consistency of the interacting temporal and numeric constraints at
each state. The LP is used to compute bounds on the values of variables in each
state, reducing the range of actions that need to be considered for
application. In addition, we develop an extension of the Temporal Relaxed
Planning Graph heuristic of CRIKEY3, to support reasoning directly with
continuous change. We extend the range of task variables considered to be
suitable candidates for specifying the gradient of the continuous numeric
change effected by an action. Finally, we explore the potential for employing
mixed integer programming as a tool for optimising the timestamps of the
actions in the plan, once a solution has been found. To support this, we
further contribute a selection of extended benchmark domains that include
continuous numeric effects. We present results for COLIN that demonstrate its
scalability on a range of benchmarks, and compare to existing state-of-the-art
planners.
