A 'piano movers' problem reformulated

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

Research output: Chapter in Book/Report/Conference proceedingConference proceedingpeer-review

18 Citations (Scopus)
35 Downloads (Pure)


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
Number of pages8
ISBN (Electronic)978-1-4799-3036-4
ISBN (Print)978-1-4799-3035-7
Publication statusPublished - 2014
Externally publishedYes
Event15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania
Duration: 23 Sept 201326 Sept 2013
Conference number: 15


Conference15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Abbreviated titleSYNASC 2013

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  • 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


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