Planning in a Continuous Domain—An Introduction

Abstract

SUMMARYMuch of the work of Artificial Intelligence concerns the representation and symbolic manipulation of various domains. One problem shared by existing systems is their limitation to discrete states and state changes, brought about by the linking of declarative states with points in time. With this identification, models of continuous processes must forego such declarative states, resulting in a loss of decomposability that limits the amount of complexity that can be handled by a given amount of computation.In this paper we develop a model for robot problem solving over a domain of continuous actions. The proposed world model consists of a vector of piecewise defined functions of time, i.e. functions that can be represented using finite sets of expressions and finite partitions of time intervals. The critical points of these functions are represented symbolically as discrete events. The goal is represented as a point through which the world model vector must thread at some point in model time. World model functions are transformed by adding events at various discrete points in time which transform the trajectories in the direction of the goal. As events are added, formulas relating the event times are added to the description of the world. The result is a partial order of events which represents a plan for “forcing” the world function to achieve the goal.The relationships between this model and the classical problem-solving systems (e.g. STRIPS) are utilized in order to produce a planning procedure. This procedure is applied to a robot problem which can be solved using the model. We conclude by presenting an analysis and prospectus of considerations for an actual implementation of these ideas.