Power Scaling in Port-Hamiltonian Telemanipulation over Packet Switched Networks

Passivity is a very suitable tool to stabilize a telemanipulator; in fact, implementing each part of a telerobotic system as a passive system and interconnecting them in a power preserving way it is possible to achieve an intrinsically passive system which is consequently characterized by a stable behavior. In [1] scattering theory has been exploited to build a communication channel that is passive independently of any constant transmission delay. In [11] the concept of wave variables, which allow to give a clear energetic interpretation of the scattering based communication strategy proposed in [1], is introduced. Several passivity based strategies have been proposed to control master and slave robots. In particular, in [20], the port-Hamiltonian framework ([21]) has been applied to telemanipulation: both master and slave robots, which can be modeled as port-Hamiltonian systems, are controlled by means of intrinsically passive port-Hamiltonian impedance controllers (IPC, [17]) which guarantee a stable interaction with any, possibly unknown, passive environment. In this way both master and slave sides can be modeled as passive port-Hamiltonian systems that are then interconnected by means of a scattering based communication channel that allows a passive exchange of information independently of any transmission delay. The resulting telemanipulation system is intrinsically passive and, therefore, characterized by a stable behavior. In [13, 19] the discrete nature of the controllers is considered and techniques presented in [18] are used to obtain passive discrete port-Hamiltonian controllers and to interconnect them in a power preserving way to the continuous plants. Furthermore, discrete scattering is defined and used to implement a packet switching transmission line that has been proven to be passive also when communication delay is variable and some packets are lost. For an overview of the various techniques proposed in the literature see e.g. [3]. In several tasks involving bilateral telemanipulators, such as telesurgery and telemanipulation of huge robotic arms for extra-vehicular activity in space applications, master and slave act at different power scales and therefore, it is necessary to scale velocities and forces that are exchanged in order to take into account for this difference. Ideally, the system should transmit to the human operator a scaled version of the environment impedance such that the dynamic