A 'piano movers' problem reformulated

David Wilson; James H. Davenport; Matthew England; Russell Bradford

doi:10.1109/SYNASC.2013.14

A 'piano movers' problem reformulated

David Wilson, James H. Davenport, Matthew England, Russell Bradford

University of Bath

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

18 Citations (Scopus)

54 Downloads (Pure)

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.

Original language	English
Title of host publication	Proceedings - 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013
Publisher	IEEE Computer Society
Pages	53-60
Number of pages	8
ISBN (Electronic)	978-1-4799-3036-4
ISBN (Print)	978-1-4799-3035-7
DOIs	https://doi.org/10.1109/SYNASC.2013.14
Publication status	Published - 2014
Externally published	Yes
Event	15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania Duration: 23 Sept 2013 → 26 Sept 2013 Conference number: 15

Conference

Conference	15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Abbreviated title	SYNASC 2013
Country/Territory	Romania
City	Timisoara
Period	23/09/13 → 26/09/13

Bibliographical note

© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

Cylindrical algebraic decomposition
Piano movers problem
Robot motion planning
Design automation
Polynomials
Planning
Robots
Cognition
Complexity theory
Algebra
Path planning
Geometric analysis
Piano movers problem reformulated
CAD
Right angled corridor

ASJC Scopus subject areas

Software
Modelling and Simulation

Access to Document

10.1109/SYNASC.2013.14

Post-PrintAccepted author manuscript, 693 KBLicence: CC BY-NC

Cite this

Wilson, D, Davenport, JH, England, M & Bradford, R 2014, A 'piano movers' problem reformulated. in Proceedings - 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013., 6821131, IEEE Computer Society, pp. 53-60, 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 23/09/13. https://doi.org/10.1109/SYNASC.2013.14

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note = "{\textcopyright} 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Copyright {\textcopyright} and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders. ; 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013 ; Conference date: 23-09-2013 Through 26-09-2013",

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A 'piano movers' problem reformulated

Abstract

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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