My research addresses the interplay of geometric mechanics and nonlinear control theory in the arena of robotic locomotion. One goal of this work is a comprehensive modelling paradigm for aquatic and aerial vehicles. The bridge between mechanics and control informs vehicle designs and navigation strategies which inherit efficiency and robustness from underlying physical law. Techniques from geometric mechanics provide reduced-order models in the presence of symmetries and accomodate disparate actuation schemes consistently.
Geometric methods elucidate flow phenomena traditionally accessible only numerically.
Certain animals boast advantages in adaptability, propulsive efficiency, maneuverability, and stealth over conventional submarines and aircraft. Progress in this area could impact the development of sensors and actuators for other problems in flow control. Motion-planning techniques which acknowledge global nonlinearities complement robust linear control schemes targeting local stability. Differential-geometric techniques are particularly applicable to underactuated systems, for which global control results are presently lacking. Nonlinearities underlying mechanical systems often reflect physical principles which can motivate novel control concepts.