Characterizing Teleoperator Behavior for Feedback Design and Performance Analysis

Simple teleoperator feedback schemes such as proportional-derivative control can be tuned based on intuition. More sophisticated feedback controllers, however, do not generally provide such intuitive parameters for tuning. In this paper, we examine a parameterization of teleoperator feedback design that reveals relationships between controller design and closed-loop performance. The four transfer function parameters we identify separate the feedback design into compensation of hardware dynamics and tuning of a virtual coupler between the master and slave. To demonstrate the utility of this parameterization, we show that the parameters are related in simple ways to measures of transparency and tracking performance. Interpretation of these expressions generates design directives that apply to all feedback designs. Furthermore, we prove bounds on a measure of transparency which are satisfied for a class of environment dynamics defined by their magnitude frequency response. Based on this result, we introduce a graphical tool we term a transparency diagram which reveals the aspect of the feedback design that limit transparency for given environment dynamics.