Discovering principles of locomotion in complex terrain remains a challenge: how do organisms coordinate their enormous numbers of degrees of freedom to generate changes in body shape which lead to emergent robustness, stability and efficiency? Of interest to us in this project is limbless locomotion: snakes must coordinate the interaction of their flexible trunks with environmental heterogeneities (rocks, branches) to generate propulsion. We conjecture that snake motion in cluttered terrain is (and in future snake-like robots, should be) the result of an optimization procedure with the goal to minimize internal stresses, and likely energetic cost of transport. Led by Blekherman, snake locomotion will be modeled using applied algebraic geometry techniques, specifically as a series of polynomial optimization problems. The theory will be informed by data and insights from controlled laboratory animal experiments in Goldman’s group.