The submetric formalism for task representation

Abstract We argue that the planning of tasks for autonomous, goal-directed systems is appropriately represnted by continuous rather than discrete models, and that there is no true distinction between the planning of tasks and the planning of continuous actions. We choose a trivial and very general operation on continuous metric spaces (cost-wave propagation and gradient-following) to define the semantics ofplanning for a general autonomous system. We then present a means of task representation in continuous task-configuration spaces. The approach encompasses the planning of complete behavioral sequences, taking as input the statement of the goal, the initial conditions, the constraints on behavior, and the definition of optimal performance. It produces representation of global plans as continuous paths through the configuration space of the task. The fundamental approach is a model of a problem state-space in which physical objects, laws of physics, rules of ‘common sense’, and arbitrary constraints or rules defining the problem, all share a common representation.