abstract
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The performance index in teleoperation, transparency, is often defined as linear scaling of force and position between the master/ operator and slave/ environment. Motivated by applications involving soft tissue manipulation such as robotic surgery, the transparency objective is generalized in this thesis to include static nonlinear and linear-time-invariant filter mappings between the master I slave position and force signals. Lyapunov-based adaptive motion/ force controllers are proposed to achieve the generalized transparency objectives. Using Lyapunov stability theory the mapped position and force tracking errors are shown to converge in the presence of dynamic uncertainty in the master I slave robots and user I environment dynamics. Given a priori known bounds on unknown dynamic parameters, a framework for robust stability analysis is proposed that uses stability of Lur'ePostinkov systems and Nyquist/Bode envelopes of interval plant systems. Methods for finding the required Nyquist/Bode envelopes are presented in this thesis. A comprehensive stability analysis is performed under different sets of generalized mappings. For nonlinear mapping of either position or force, robust stability depends on stability of an equivalent Lur'e-Postinikov system. Stability results of such systems are discussed in this thesis. In particular, the on and off-axis circle theorems are utilized. Using these theorems, sufficient teleoperation stability regions are obtained that are far less conservative than those obtained from passivity. In the special case of LTI filtered force and position mappings the exact robust stability regions are obtained by showing stability of the relevant closed-loop characteristic polynomial. The proposed robust stability test uses the phase values of a limited set of extremal polynomials.
To demonstrate the utility of the generalized performance measures, a stiffness discrimination tele-manipulation task is considered in which the user compares and contrasts the stiffness of soft environments via haptic exploration in the presence and absence of visual feedback. Using adaptive psychophysical perception experiments a nonlinear force mapping is shown to enhance stiffness discrimination thresholds. The design guidelines for this enhanced nonlinear force mapping are reported in this thesis. Generalized nonlinear and linear filtered mappings are achieved in experiments with a two-axis teleoperation system where the details of implementation are given.