A "piano movers" problem reformulated


Wilson, D., Davenport, J. H., England, M. and Bradford, R. J., 2013. A "piano movers" problem reformulated. In: SYNASC 2013: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2013-09-23 - 2013-09-26. IEEE, pp. 53-60.

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    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.


    Item Type Conference or Workshop Items (UNSPECIFIED)
    CreatorsWilson, D., Davenport, J. H., England, M. and Bradford, R. J.
    Related URLs
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    Uncontrolled Keywordscylindrical algebraic decomposition,robot motion planning
    DepartmentsFaculty of Science > Computer Science
    Publisher StatementSYNASCpaper.pdf: © 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.
    ID Code36795


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