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In this paper, we use the notion of Möbius transformation to develop a chain-wise methodology for the analysis of coupled stability in a cascade of leader–follower networks. The methodology tracks the transmission of the load passivity unit disk through the cascade to the user network. It allows for networks in the cascade that are neither passive nor absolutely stable. Due to its modularity, the proposed methodology is more suitable for dynamic distributed systems in which a network block, such as virtual coupling or delay in the cascade, is modified, added or taken out. We also introduce the notion of "bounded- Γ absolute stability" to verify the coupled stability for any prescribed range of loads, denoted by circles in the scattering domain. To demonstrate the effectiveness of the proposed methodologies, numerical and experimental results for a position–force control architecture under constant time delays are provided. [ABSTRACT FROM AUTHOR]

Position resolution is a major problem in teleoperation applications with significant disparity between master and slave workspace. While rate mode control is suitable for slave free motion operations, it poses significant stability and performance challenges for task manipulation. In this paper, we propose a hybrid control scheme that offers seamless transition between position and rate control modes based on the environment location information collected from a range sensor. The system incorporates the strengths of position and rate control modes while masking their shortcomings. Experiments to determine the viability of this method are carried out on a single degree-of-freedom teleoperation test-bed. • A hybrid rate–position teleoperation system offering workspace expansion • The hybrid system offers seamless transition between position and rate control modes • A weighted mix of position and rate signals is provided in the transition region • Mode switch is based on the environment location collected from a range sensor • Stability and transparency analysis for the two-port network model is obtained [ABSTRACT FROM AUTHOR]