CAREER: Matroids, polytopes, and their valuations in algebra and geometry
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The configuration space of a robotic arm in a tunnel of width 2
Federico Ardila (1) (2), Hanner Bastidas (3), Cesar Ceballos (4) (5) (6), John Guo (2)
(1) Universidad de los Andes [Bogota]
(2) Department of Mathematics [San Francisco]
(3) Universidad del Valle [Cali]
(4) Faculty of Mathematics [Vienna]
(5) Faculty of Mathematics [Univ. Vienna]
(6) Faculty of Mathematics = Fakultät für Mathematik [Vienne, Autriche]
Abstract
We study the motion of a robotic arm inside a rectangular tunnel of width 2. We prove that the configuration space S of all possible positions of the robot is a CAT(0) cubical complex. Before this work, very few families of robots were known to have CAT(0) configuration spaces. This property allows us to move the arm optimally from one position to another.
