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.
|Title of host publication||Proceedings - 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013|
|Publisher||IEEE Computer Society|
|Number of pages||8|
|Publication status||Published - 2014|
|Event||15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania|
Duration: 23 Sep 2013 → 26 Sep 2013
Conference number: 15
|Conference||15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing|
|Abbreviated title||SYNASC 2013|
|Period||23/09/13 → 26/09/13|
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- Cylindrical algebraic decomposition
- Piano movers problem
- Robot motion planning
- Design automation
- Complexity theory
- Path planning
- Geometric analysis
- Piano movers problem reformulated
- Right angled corridor
ASJC Scopus subject areas
- Modelling and Simulation