Sensor-Based Exploration: The Hierarchical Generalized Voronoi Graph

Author:

Choset Howie1,Burdick Joel2

Affiliation:

1. Carnegie Mellon University, Scaife Hall, Pittsburgh, Pennsylvania 15213 USA

2. California Institute of Technology, Mail Code 104-44, Pasadena, California 91125 USA

Abstract

The hierarchical generalized Voronoi graph (HGVG) is a new roadmap developed for sensor-based exploration in unknown environments. This paper defines the HGVG structure: a robot can plan a path between two locations in its work space or configuration space by simply planning a path onto the HGVG, then along the HGVG, and finally from the HGVG to the goal. Since the bulk of the path planning occurs on the one-dimensional HGVG, motion planning in arbitrary dimensioned spaces is virtually reduced to a one-dimensional search problem. A bulk of this paper is dedicated to ensuring the HGVG is sufficient for motion planning by demonstrating the HGVG (with its links) is an arc-wise connected structure. All of the proofs in this paper that lead toward the connectivity result focus on a large subset of spaces in R3, but wherever possible, results are derived in Rm. In fact, under a strict set of conditions, the HGVG (the GVG by itself) is indeed connected, and hence sufficient for motion planning. The chief advantage of the HGVG is that it possesses an incremental construction procedure, described in a companion paper, that constructs the HGVG using only line-of-sight sensor data. Once the robot constructs the HGVG, it has effectively explored the environment, because it can then use the HGVG to plan a path between two arbitrary configurations.

Publisher

SAGE Publications

Subject

Applied Mathematics,Artificial Intelligence,Electrical and Electronic Engineering,Mechanical Engineering,Modeling and Simulation,Software

Reference11 articles.

1. Voronoi diagrams—a survey of a fundamental geometric data structure

2. Avis, D., and Bhattacharya, B. K. 1983. Algorithms for computing D-dimensional Voronoi diagrams and their duals . Advances in Computing Research 1: 159–180 .

3. Brooks, R. A. 1986. A robust layered control system for a mobile robot . IEEE Journal on Robotics and Automation RA-2(March).

4. An opportunistic global path planner

5. Choset, H. 1998. Nonsmooth analysis, convex analysis, and their applications to motion planning . Special issue of Int. J. Comp. Geom. and Apps. To appear.

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