On velocity field control of mechanical systems

In this paper, we propose control schemes that stabilize the system´s behavior to the desired velocity field. In particular, we seek schemes that are divided into a dissipative component and an active component with respect to kinetic energy. We considered two cases: one in which both the dissipative and the active components are available for manipulation, and the other in which the active component is given, but not manipulable. It is shown that in the first case, a space varying damping control is sufficient, and in the second case, a dynamic damping control based on a fictitious manipulator is proposed