Network Representation and Passivity of Delayed Teleoperation Systems Jordi Artigas, Jee-Hwan Ryu, Carsten Preusche, Gerd Hirzinger Abstract— The paper proposes a general network based analysis and design guidelines for teleoperation systems. The electrical domain is appealing because it enjoys proficient anal- ysis and design tools and allows a one step higher abstraction element, the network. Thus, in order to analyze the system by means of network elements the mechanical system must be first modeled as an electric circuit. Only then power ports become apparent and networks can be defined. This kind of analysis has been previously performed in systems with well defined causalities, specially in the communication channel. Indeed, a communication channel exchanging flow-like and effort-like signals, as for instance velocity and computed force, has a well defined causality and can thus be directly mapped as a two-port electrical network. However, this is only one of the many possible system architectures. This paper investigates how other architectures, including those with ambiguous causalities, can be modeled by means of networks, even in the lack of flow or effort being transmitted, and how they can be made passive for any communication channel characteristic (delay, package-loss and jitter). The methods are exposed in the form of design guidelines sustained with an example and validated with experimental results. I. INTRODUCTION The goal of the methods presented in this article is to facil- itate the design of any possible teleoperation architecture on a systematic way, without the burden of having to explicitly tackle typical channel related issues, as are communication time delay, jitter and package loss. The network analysis [1] is one of the most accounted modeling frameworks for teleoperation systems [2], [3], [4], [5]. A network masks an electrical circuit, i.e. a collection of electrical components which accomplish a specific task. Sometimes it is convenient to speak of an electrical circuit as a network, de-emphasizing the internals of the circuit while stressing the interconnectiv- ity medium, i.e. the port. Indeed, the port is a two-terminal interface which allows connectivity between networks and thus a transfer of energy. A power port is entirely represented by the pair of dual variables, current and voltage, whose product is power. Thus, the description of a system in terms of networks allows an energy based analysis and therefore allows to extract conclusions about passivity, a powerful tool for system stability. The designs presented in this paper take place in an ideal channel scenario, where master and slave robots behave as rigidly connected masses, the communication delay is null and their power exchange is lossless. Stability out of the Jordi Artigas, Carsten Preusche and Gerd Hirzinger are with the Institute of Robotics and Mechatronics at the German Aerospace Center, 82234 Wessling, Germany. J.H. Ryu is Faculty of the Biorobotics Laboratory, Korean University of Technology, Cheonan, Rep. of South Korea ideal scenario is then tackled in a systematic way, using the Time Domain Passivity Control Approach [4], [6], as a tool to render the communication channel passive. The methods presented can be regarded as a framework for designing teleoperation systems which allows any possible communication channel causalities and characteristics and, in general, is compatible with any control architecture, that is, of any number of channels [7], [8] and any coupling control method, e.g. [2], [4], [5], [9]. The paper generalizes previous work [6], [10], [11] con- ceived for specific teleoperation architectures but is aimed as a stand alone paper rather than incremental. The treatment of the communication channel has been matter of discussion in many publications. Indeed, a data channel linking two phys- ical systems, as is the case of teleoperation, has been proved to be a source of energy and thus a cause of system instability [2]. The reasons lay into the fact that such channels are used to link physical systems but they miss physical meaning themselves. By way of illustration, a very long flexible beam connecting one mass to another could not ever be- come unstable (unless both masses would actively be moved in order to excite resonance frequencies). Instead, typical data channels, exchanging positions and forces for instance, implicitly reproduce the behavior of an ideal weightless infinitely rigid bar, but with delay. This is an element which cannot be physically modeled and misses therefore coherence with the rest of the system, i.e. master, slave, etc. The secular work based on the scattering parameters [2], or the wave variables formulation [3], uses a lossless transmission line model for representing the communication channel. The data channel is thus given a physical meaning, i.e. a transmission line, and benefits from its physical characteristics, as is the passive nature of such elements, even in presence of time delay. The treatment given in this publication is based on a com- plete electrical representation of the system using lumped elements. Rather than considering part of the system as being composed by lumped electrical elements, as can be master, slave and controllers, and part as a transmission line, i.e. the channel with the scattering parameters formulation, the system communication channel is given the meaning of one or more electrical networks which can be directly connected to the rest of the system. The framework involves a) the process of identification and isolation of active networks in the electrical domain and b) passivation of those networks using common Time Domain Passivity -based controllers. An example is used across the sections to facilitate the exposition of the meth- ods and arguments presented. Section II shows how the 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems September 25-30, 2011. San Francisco, CA, USA 978-1-61284-456-5/11/$26.00 ©2011 IEEE 177