Global Stabilization of a Fully Actuated Mechanical System on a Riemannian Manifold including Control Saturation Effects

In (Chaturvedi et al., 2006), we presented the structure of a general intrinsic controller for global stabilization of an arbitrary configuration of a fully actuated simple mechanical system, evolving on a Riemannian manifold. This requires the construction of an error function on the configuration space and a choice of parameter functions. In this paper we continue this development and present results that allow one to construct these error functions explicitly. Next, we determine conditions on the parameter functions, which yield a controller that can stabilize even in the presence of control saturation effects. We illustrate our design technique by explicitly deriving controllers that stabilize the inverted position of a spherical pendulum, sleeping position of a spinning top, and upright position of a planar two-link manipulator. In all cases, global results are obtained even in the presence of control saturation effect