On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
An efficient and simple motion planning algorithm for a ladder amidst polygonal barriers
Journal of Algorithms
Moving a ladder in three dimensions: upper and lower bounds
SCG '87 Proceedings of the third annual symposium on Computational geometry
Separating two simple polygons by a sequence of translations
Discrete & Computational Geometry
On the general motion planning problem with two degrees of freedom
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Triangles in space or building (and analyzing) castles in the Air
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Planning algorithm for a convex polygonal object in two-dimensional polygonal space
Discrete & Computational Geometry
ACM SIGACT News
On the general motion planning problem with two degrees of freedom
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Triangles in space or building (and analyzing) castles in the Air
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Multiple object semilinear motion planning
Journal of Symbolic Computation
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We present an &Ogr;(n2) algorithm for planning a coordinated collision-free motion of two independent robot systems of certain kinds, each having two degrees of freedom, which move in the plane amidst polygonal obstacles having a total of n corners. We exemplify our technique in the case of two “planar Stanford arms”, but also discuss the case of two discs or convex translating objects. The algorithm improves previous algorithms for this kind of problems, and can be extended to a fairly simple general technique for obtaining efficient coordinated motion planning algorithms.