Many interesting dynamic systems in science and engineering evolve on nonlinear or curved spaces that cannot be globally identified with a linear space. These nonlinear spaces are referred to as manifolds and appear in various mechanical systems, such as planar pendulums or complex robotic systems. However, the geometric structures of nonlinear manifolds have not been carefully incorporated into control system engineering. Conventional nonlinear control systems based on local coordinates of a manifold suffer from singularities, ambiguities, and complexities, which severely restrict control performance.
Taeyoung Lee,
The George Washington University
This talk summarizes recent advances in geometric approaches for four major topics in nonlinear dynamics and control: computational mechanics, optimization, feedback control, and estimation. It is shown that aggressive maneuvers of complex dynamic systems can be achieved in an intrinsic and elegant fashion by constructing control systems directly on a manifold. The desirable properties of geometric mechanics and controls are illustrated by both computational and experimental results involving several aerospace systems, including binary asteroids, satellite formation reconfiguration, tethered spacecraft, and quadrotor unmanned aerial vehicles.
Taeyoung Lee is a professor in the Department of Mechanical and Aerospace Engineering at The George Washington University, Washington, DC. He received his doctoral degree in aerospace engineering and his master’s degree in mathematics from the University of Michigan in 2008. His research interests include geometric mechanics, geometric control, optimization, estimation, and uncertainty propagation, with applications to aerospace systems and robotics. He is the author of a research monograph titled Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds.