Synthesis and Analysis of Virtual Holonomic Constraints for Lagrangian Mechanical Systems

A Virtual Holonomic Constraint (VHC) is a relationship among the generalized coordinates of a mechanical system which is made invariant by feedback control. In the last decades, the VHC approach has emerged as a valuable tool in motion control problems. The main contribution of this thesis is twofold. First, it presents a new synthesis procedure that generates feasible VHCs whose constrained dynamics possess a stable limit cycle. Second, it frames VHCs in a coordinate free formalism, based on a Riemannian geometry setting. This reformulation allows to give a clear geometrical interpretation of the inverse Lagrangian problem for the constrained system.