NDLI: A "Piano Movers" Problem Reformulated

Content Provider	IEEE Xplore Digital Library
Author	Wilson, D. Davenport, J.H. England, M. Bradford, R.
Copyright Year	2013
Description	Author affiliation: Dept. of Comput. Sci., Univ. of Bath, Bath, UK (Wilson, D.; Davenport, J.H.; England, M.; Bradford, R.)
Abstract	It has long been known that cylindrical algebraic decompositions (CADs) can in theory be used for robot motion planning. However, in practice even the simplest examples can be too complicated to tackle. We consider in detail a ``Piano Mover's Problem'' which considers moving an infinitesimally thin piano (or ladder) through a right-angled corridor. Producing a CAD for the original formulation of this problem is still infeasible after 25 years of improvements in both CAD theory and computer hardware. We review some alternative formulations in the literature which use differing levels of geometric analysis before input to a CAD algorithm. Simpler formulations allow CAD to easily address the question of the existence of a path. We provide a new formulation for which both a CAD can be constructed and from which an actual path could be determined if one exists, and analyse the CADs produced using this approach for variations of the problem. This emphasises the importance of the precise formulation of such problems for CAD. We analyse the formulations and their CADs considering a variety of heuristics and general criteria, leading to conclusions about tackling other problems of this form.
Starting Page	53
Ending Page	60
File Size	395403
Page Count	8
File Format	PDF
ISBN	9781479930357
e-ISBN	9781479930364
DOI	10.1109/SYNASC.2013.14
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-09-23
Publisher Place	Romania
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Design automation piano movers problem Polynomials Cognition cylindrical algebraic decomposition Planning Complexity theory robot motion planning Robots
Content Type	Text
Resource Type	Article

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