| Summary: | Haptic simulation of medical procedures is an active area of research in engineering and medicine. Analogous to flight simulators for pilots, surgery simulators can allow medical students and doctors to practice procedures in a risk free and well monitored virtual environment. The quality of interaction that a surgery simulator can generate is dependent upon many components. In this thesis, careful attention is paid to the haptic display of viscous effects. === Viscous terms, defined here as terms that are dependent upon velocity, are typically computed 'using a discrete time backwards difference estimation of the velocity. It is well known that differentation has the tendency to amplify high frequency noise, and as a result, the backwards difference estimation generates considerable errors when applied to the quantized position readings from a digital encoder. Prior to this work, the only feasible method to improve velocity estimation was to use a variety of observation or filtering techniques, all of which inevitably add phase delay. In this thesis, the backwards difference operation was analyzed in detail. It was found that feedback viscosity simulation is very non-robust to noise, and oscillations exist in the presence of quantization noise regardless of the physical parameters of the plant. === A typical haptic interface for surgery simulation consists of a mechanical linkage driven by electric motors. These linkages are controlled with a computer using a discrete-time force update law that generates a prescribed force given the user's position in the medical virtual environment. It is clear from the literature that a haptic interface must have some level of physical dissipation to enable a passive rendering due to the inherent instability associated with time delayed systems. However, dissipation in typical haptic interfaces is a byproduct of their design, and is neither controllable nor easily identifiable. A prototype haptic interface is presented in this thesis that uses eddy current brakes to add high bandwidth programmable dissipation to an existing motor linkage. The new hardware has been optimized experimentally to maximize damping and minimize inertia given conventional machining and available material constraints. === A new paradigm in the control of haptic interfaces is time-domain passivity control. Passive systems are desirable in haptics because a passive system is globally stable, passivity theory applies to linear and nonlinear systems alike, and a user cannot extract energy from a passive system. Passivity controllers monitor the energy flow in the device and add virtual damping to remove any energy that violates the passivity constraint. Unfortunately, the amount of virtual damping available to a given device is limited by the physical dissipation that it exhibits. If the device is directly driven and light, such as the pantograph, the available virtual damping is insufficient to maintain the passivity constraint. The eddy current brakes allow programmable physical damping to be used in place of virtual damping which has been shown with experiments to improve the stable impedance range of a haptic interface. === It is clear from the literature that most tissues in a human body exhibit viscoelastic behavior. Simulation of viscoelastic objects requires that the velocity of interaction be known. Because typical haptic interfaces use digital encoders to sample position, the estimated velocity signal is noisy, delayed or both. Eddy current brakes are viscous actuators by nature, as they generate a resistive force proportional to the velocity. To take advantage of this fact, viscoelastic decomposition algorithms were developed that can output viscous components to the eddy current brakes and elastic components to the motors. This technique reduces or eliminates the use of a velocity estimation signal in the feedback loop which improves passivity, reduces motor saturation effects, and allows for a wider stable range of mechanical impedances than conventional haptic interfaces can achieve.
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