Moving a robotic arm in a tunnel

We study the motion of a robotic arm inside a rectangular tunnel. We prove that the configuration space of all possible positions of the robot is a CAT(0) cubical complex. To do this we use a bijection between rooted CAT(0) cubical complexes and a family of combinatorial objects that we call “posets with inconsistent pairs”. This bijection allows us to use techniques from geometric group theory and poset theory to find the optimal way of moving the arm from one position to another. We also compute the diameter of the configuration space, that is, the longest distance between two positions of the robot. This talk will include joint work with Tia Baker, Hanner Bastidas, Cesar Ceballos, John Guo, Megan Owen, Seth Sullivant, and Rika Yatchak, and will assume no previous knowledge of the subject.

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