Robot motion planning and the single cell problem in arrangements

Dan Halperin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Robot motion planning has become a central topic in robotics and has been studied using a variety of techniques. One approach, followed mainly in computational geometry, aims to develop combinatorial, nonheuristic solutions to motion-planning problems. This direction is strongly related to the study of arrangements of algebraic curves and surfaces in low-dimensional Euclidean space. More specifically, the motion-planning problem can be reduced to the problem of efficiently constructing a single cell in an arrangement of curves or surfaces. We present the basic terminology and the underlying ideas of the approach. We describe past work and then survey a series of recent results in exact motion planning with three degrees of freedom and the related issues of the complexity and construction of a single cell in certain arrangements of surface patches in three-dimensional space.

Original languageEnglish
Pages (from-to)45-65
Number of pages21
JournalJournal of Intelligent and Robotic Systems: Theory and Applications
Issue number1-2
StatePublished - Mar 1994


  • Computational geometry
  • arrangements
  • motion planning
  • robotics


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