The configuration space of a robotic arm in a tunnel of width 2

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.

Keywords

• [math.math-co]mathematics [math]/combinatorics [math.co]