Report Number: CS-TR-90-1345
Institution: Stanford University, Department of Computer Science
Title: Nonholonomic motion planning versus controllability via the
multibody car system example
Author: Laumond, Jean-Paul
Date: December 1990
Abstract: A multibody car system is a non-nilpotent, non-regular,
triangularizable and well-controllable system. One goal of
the current paper is to prove this obscure assertion. But its
main goal is to explain and enlighten what it means.
Motion planning is an already old and classical problem in
Robotics. A few years ago a new instance of this problem has
appeared in the literature: motion planning for nonholonomic
systems. While useful tools in motion planning come from
Computer Science and Mathematics (Computational Geometry,
Real Algebraic Geometry), nonholonomic motion planning needs
some Control Theory and more Mathematics (Differential
Geometry).
First of all, this paper tries to give a computational
reading of the tools from Differential Geometric Control
Theory required by planning. Then it shows that the presence
of obstacles in the real world of a real robot challenges
Mathematics with some difficult questions which are
topological in nature, and have been solved only recently,
within the framework of Sub-Riemannian Geometry.
This presentation is based upon a reading of works recently
developed by (1) Murray and Sastry, (2) Lafferiere and
Sussmann, and (3) Bellaiche, Jacobs and Laumond.
http://i.stanford.edu/pub/cstr/reports/cs/tr/90/1345/CS-TR-90-1345.pdf