The Generalized Scattering Transformaton for Stable Teleoperation with Communication Unreliabilities

A teleoperation system allows the human to manipulate in remote/inaccessible/dangerous or scaled environments. From a control point of view, the haptic control loop, where motion and force data are exchanged between the master and the slave manipulator, is very challenging as it is closed over a communication network, e.g. the Internet. The communication network introduces unreliabilities such as (time-varying) time delay and packet loss, which are not only distorting the human haptic perception of the remote environment but can destabilize the overall system. In recent years control approaches based on the passivity framework and the scattering transformation have been developed in order to stabilize the teleoperation system in the presence of such communication unreliabilities, see e.g. [1,2]. The major reason for the success of the passivity formalism in teleoperation is that it can cope with the largely unknown, nonlinear and time-varying human arm and environment dynamics, which, however, can assumed to be passive. The scattering transformation transforms passive systems into finite gain L2-stable systems with a L2 gain γ ≤ 1 and guarantees the finite gain L2-stability of the overall teleoperation system for all communication network operators that are small gain, e.g. constant time delay but also appropriately handled packet loss [2]. However, the passivity framework is known to be conservative resulting in a distorted display of the remote environment properties. Current research is concentrating on relaxing this conservatism. In this work we will use the approximate knowledge on damping properties of the human arm, the controlled manipulators and the environment. In fact, we can show that these subsystems are QSR-dissipative [4], which will be exploited to the benefit of transparency in teleoperation architectures. The approach is based on the generalized scattering transformation [3] which applies to QSR-dissipative systems, ensuring finite gain L2-stability for arbitrary small gain network operators in the closed loop, analogously to the standard scattering transformation. A dynamical system Σ : ẋ = f(x, u), y = h(x, u), x ∈ <, u, y ∈ < is called QSR-dissipative if there exist a positive semi-definite function V : < → <+ such that for each admissible u and each t ≥ 0 V (x(t))− V (x(0)) ≤ ∫ t