A "piano movers" problem reformulated

David Wilson, J H Davenport, M England, R J Bradford

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

15 Citations (Scopus)
83 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. These simpler formulations allow CAD to 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 of SYNASC 2013: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
PublisherIEEE
Pages53-60
Number of pages8
DOIs
Publication statusPublished - 2013
EventSYNASC 2013: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania
Duration: 23 Sep 201326 Sep 2013

Conference

ConferenceSYNASC 2013: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
CountryRomania
CityTimisoara
Period23/09/1326/09/13

Keywords

  • Cylindrical Algebraic Decomposition
  • Robot Motion Planning

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    Wilson, D., Davenport, J. H., England, M., & Bradford, R. J. (2013). A "piano movers" problem reformulated. In Proceedings of SYNASC 2013: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (pp. 53-60). IEEE. https://doi.org/10.1109/SYNASC.2013.14