|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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