Robots and math: from fast cars to origami

Devin Balkcom

Dartmouth College.

What do Pontryagin's Maximum Principle, the Bellows theorem, and Morse theory have to do with robots? I'll present two robotics problems from my own work that I hope will appeal to mathematicians: geodesics for robotic vehicles and paper-folding.

We'll see that the fastest trajectories for simple models of robots have an interesting and elegant structure, and I'll discuss mathematical techniques for finding the fastest trajectories. I'll show movies of the world's first origami-folding robot, discuss a classification of origami by complexity, and give some surprising results about a simple model of a paper shopping bag.

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