ep18 - Naomi Ehrich Leonard, Part I: Geometric Control on Lie Groups, Underwater Vehicles and Collective Motion, Coordination in Animal Groups, Decision Making in Honeybees and Bifurcation Theory

Control theory provides a powerful framework for understanding complex systems, from the geometric mechanics of rigid bodies in fluids to the collective decision-making processes of biological swarms. Naomi Ehrich Leonard, Chair of Mechanical and Aerospace Engineering at Princeton, details how Lie groups and controlled Lagrangians enable the stabilization of underwater vehicles, such as autonomous gliders used for oceanographic sampling. These mathematical tools extend to biological systems, where principles like bifurcation theory explain how honeybees and fish schools achieve consensus through local interactions and stop signaling. By abstracting these natural behaviors into dynamical models, researchers can design robust, decentralized control strategies for robotic swarms, demonstrating that effective collective intelligence emerges from simple, local rules rather than centralized oversight. This interdisciplinary approach bridges the gap between theoretical control design and real-world environmental monitoring.