Geometric Control of Mechanical Systems

This talk will outline a comprehensive set of modeling, analysis and design techniques for a class of mechanical systems. We concern ourselves with simple mechanical control systems, that is, systems whose Lagrangian is kinetic energy minus potential energy. Example devices include robotic manipulators, aerospace and underwater vehicles, and mechanisms that locomote exploiting nonholonomic constraints. Borrowing techniques from nonlinear control and geometric mechanics, we propose a coordinateinvariant control theory for this class of systems. First, we take a Riemannian geometric approach to modeling systems dened on smooth manifolds, subject to nonholonomic constraints, external forces and control forces. We…