Virtual Holonomic Constraints and the Synchronization of Euler-Lagrange Control Systems

A virtual holonomic constraint (VHC) for an Euler-Lagrange Control System is a smooth relation between the configuration variables that can be made invariant through application of suitable feedback. In this thesis we investigate the role played by VHCs in the synchronization of Euler-Lagrange systems. We focus on two problems. For $N$ underactuated cart-pendulums, we design a smooth feedback that fully synchronizes the cart-pendulums while simultaneously stabilizing a periodic orbit corresponding to a desired oscillation for the pendulums. A by-product of our results is the ability to simultaneously synchronize the pendulums and stabilize the unstable upright equilibrium. The second synchronization problem investigated in this thesis is bilateral teleoperation, whereby a master robot is operated by a human while a slave robot synchronizes to the master. For two identical planar manipulators, we develop a methodology to achieve teleoperation in the presence of a hard surface, with simultaneous force control.MAS