Sampling-Based Methods for Discrete Planning

Methods for automated planning have been of continued interest for several decades, with roots extending as far back as (Newell & Simon 1963). Since that time, extensions and refinements have been made to the problem definition – concurrent actions and partial ordering, resource constraints, uncertainty etc– but the core problem has remained essentially the same since (Fikes & Nilsson 1971): In the context of a set of states and actions, we are given an initial state and a goal region. The task is to find a sequence of actions that move the state of the system into the goal region. The distinguishing feature of planning problems considered historically by the AI community has been a discrete search space. Only recently have continuous quantities been tackled seriously. In contrast, research in other communities has been devoted to methods for planning in continuous search spaces. The field of motion planning deals with selecting actions for physical systems to complete tasks in a world in which geometry is relevant. Perhaps the earliest attempt is that of (Nilsson 1969), which introduced the idea of a multiresolution grid. Contemporary motion planning generally uses multi-resolution search and randomization to search complex, high-dimensional spaces (Hwang & Ahuja 1992, Latombe 1991). These methods are mature and of general usefulness for planning in continuous spaces with complex obstacles and constraints. Our work is based on the observation that these two long lines of research share conceptually similar problem sets. Moreover, it is our contention that these problems are similar enough to merit consideration as a unified whole. In this abstract, we begin to develop a case for such a unified view of planning and present preliminary results on one particular approach – that of borrowing the samplingbased planning ideas that have proven quite effective in continuous domains. Specifically, we describe a generalization of the Rapidly-exploring Random Tree (RRT) algorithm (LaValle & Kuffner 2000) to solve discrete planning problems. Our long-term goal is to discover a set of essential features for classifying planning problems and to develop a methodology for selecting solution methods based on these