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Motivated by applications involving soft-tissue manipulation such as robotic surgery, the transparency objectives in bilateral teleoperation are redefined to include monotonic nonlinear and linear-time-invariant filter mappings between the master/slave position and force signals. To demonstrate the utility of the new performance measures, a stiffness discrimination telemanipulation task of soft environments is considered. A nonlinear force mapping can enhance stiffness discrimination thresholds as shown through a set of psychophysics experiments. Lyapunov-based adaptive motion/force controllers are presented that can achieve the new transparency objectives in the presence of dynamic uncertainty in the master, slave, user, and environment and in the absence of time delay. Given a priori known bounds on unknown dynamic parameters, a framework for robust stability analysis is proposed that uses an off-axis circle criterion and the Nyquist envelope of interval plant systems. Nonlinear- and linear-filtered mappings are achieved in experiments with a two-axis teleoperation system.