Sensor Based Planning for Rod Shaped Robots in Three Dimensions: Piece-wise Retracts of R^3 x S^2
Abstract
We describe a new roadmap, termed the rod-HGVG, for motion planning of a rod-shaped robot operating in a three-dimensional volume. This roadmap is defined in terms of work space distance enabling us to prescribe an incremental construction procedure. This allows the rod to explore its configuration space, R/sup 3//spl times/S/sup 2/, without ever explicitly constructing the configuration space. In fact, the rod robot need not know the work space ahead of time. We term the rod-HGVG a piecewise retract because it comprises many retracts. Homotopy theory asserts that there cannot be in general a one dimensional retract of noncontractable five-dimensional space. Instead, we define an exact cellular decomposition on R/sup 3//spl times/S/sup 2/ and a retract in each cell. Next, we "connect" the retracts of each cell forming a piecewise retract of the rod's configuration space.
BibTeX
@conference{Lee-2001-8236,author = {Ji Yeong Lee and Howie Choset and Alfred Rizzi},
title = {Sensor Based Planning for Rod Shaped Robots in Three Dimensions: Piece-wise Retracts of R^3 x S^2},
booktitle = {Proceedings of (ICRA) International Conference on Robotics and Automation},
year = {2001},
month = {May},
volume = {1},
pages = {991 - 999},
}