A 'piano movers' problem reformulated

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

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

11 Citations (Scopus)
16 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 languageEnglish
Title of host publicationProceedings - 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013
PublisherIEEE Computer Society
Pages53-60
Number of pages8
ISBN (Electronic)978-1-4799-3036-4
ISBN (Print)978-1-4799-3035-7
DOIs
Publication statusPublished - 2014
Externally publishedYes
Event15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania
Duration: 23 Sep 201326 Sep 2013
Conference number: 15

Conference

Conference15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Abbreviated titleSYNASC 2013
CountryRomania
CityTimisoara
Period23/09/1326/09/13

Fingerprint

Decomposition
Decompose
Formulation
Geometric Analysis
Path
Motion Planning
Decomposition Algorithm
Ladders
Motion planning
Computer hardware
Robot
Hardware
Heuristics
Robots
Alternatives

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

Cite this

Wilson, D., Davenport, J. H., 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 (pp. 53-60). [6821131] IEEE Computer Society. https://doi.org/10.1109/SYNASC.2013.14

A 'piano movers' problem reformulated. / Wilson, David; Davenport, James H.; England, Matthew; Bradford, Russell.

Proceedings - 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013. IEEE Computer Society, 2014. p. 53-60 6821131.

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

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
Wilson D, Davenport JH, England M, Bradford R. A 'piano movers' problem reformulated. In Proceedings - 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013. IEEE Computer Society. 2014. p. 53-60. 6821131 https://doi.org/10.1109/SYNASC.2013.14
Wilson, David ; Davenport, James H. ; England, Matthew ; Bradford, Russell. / A 'piano movers' problem reformulated. Proceedings - 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013. IEEE Computer Society, 2014. pp. 53-60
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