  In this work we present a constructive method to design a family of virtual
contraction based controllers that solve the standard trajectory tracking
problem of flexible-joint robots (FJRs) in the port-Hamiltonian (pH) framework.
The proposed design method, called virtual contraction based control (v-CBC),
combines the concepts of virtual control systems and contraction analysis. It
is shown that under potential energy matching conditions, the closed-loop
virtual system is contractive and exponential convergence to a predefined
trajectory is guaranteed. Moreover, the closed-loop virtual system exhibits
properties such as structure preservation, differential passivity and the
existence of (incrementally) passive maps.
