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Geometry for robot path planning

Published online by Cambridge University Press:  01 November 2007

Lyle Noakes  and
Tomasz Popiel
Lyle Noakes*
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Nedlands, WA 6009 Perth, Australia.
Tomasz Popiel
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Nedlands, WA 6009 Perth, Australia.
*
*Corresponding author. E-mail: [email protected]
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Summary

There have been many interesting recent results in the area of geometrical methods for path planning in robotics. So it seems very timely to attempt a description of mathematical developments surrounding very elementary engineering tasks. Even with such limited scope, there is too much to cover in detail. Inevitably, our knowledge and personal preferences have a lot to do with what is emphasised, included, or left out.

Part I is introductory, elementary in tone, and important for understanding the need for geometrical methods in path planning. Part II describes the results on geometrical constructions that imitate well-known constructions from classical approximation theory. Part III reviews a class of methods where classical criteria are extended to curves in Riemannian manifolds, including several recent mathematical results that have not yet found their way into the literature.

Keywords

Path planningInterpolationLie groupLie quadraticAsymptotic estimateRigid body
Type
Article
Information
Robotica , Volume 25 , Issue 6 , November 2007 , pp. 691 - 701
Copyright
Copyright © Cambridge University Press 2007

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