Discussion of experimental results and limitations

3.4 Discussion of experimental results and limitations

The results presented in Section 3.3 make it clear that physical damping plays a pivotal role in increasing the Z-width of a haptic display, for many different configurations of the device. In all cases, the addition of physical damping increased both the maximum achievable stiffness and the maximum achievable damping. The figures also show that in order to achieve high stiffness, high update rate is needed. However, high update rates exacerbate noise due to differentiation of the position signal, making large damping coefficients difficult to achieve. To achieve higher damping, the update rate can be slowed down (at the expense of stiffness) or a digital filter can be used to attenuate high frequency noise. With the proper digital filter, the velocity signal can be smoothed out to allow large damping with only a slight reduction in achievable stiffness.

As stated previously, we have used the virtual wall as a benchmark problem for haptic display, and used it to explore the effect of various factors on stability. It is not clear, however, how this information can be generalized to more complicated virtual environments. The passivity analysis of Section 2.3 cannot be relied upon to provide quantitative predictions of system stability, since it idealizes the behavior of the human operator, sensors and actuators. Inclusion of these effects makes the model unwieldy (i.e. highly non-linear), reducing its effectiveness. Thus, we can only use its current incarnation to provide guidelines for stability of interactions between humans and virtual environments. The benefit of this research, however, is that it clarifies the mechanical design issues for the manipulandum of a haptic display.

What this research doesn't provide is guidelines for the design of virtual environments. Even assuming that the mechanical configuration of the device is held constant, we still have no way of knowing whether a given virtual environment will be stable until we conduct a thorough parameter search. For the example of the 1 DOF virtual wall, such a search is feasible because there are only a handful of parameters (stiffness, damping, filter cutoff frequency, update rate, etc.) However, as the number of degrees of freedom in the virtual environment increases, this process becomes extremely inconvenient. Our current research is focused on reducing the parameter space which must be explored to guarantee stability.

At the end of Section 2.3, we raised the question of whether or not adding physical damping to the manipulandum detracts from its ability to display low impedances. The passivity theory discussed in that section indicates that, indeed, negative virtual damping could be used to help the human operator move the motor shaft through the viscous fluid. In practice, this "cancellation" of damping is difficult to achieve. In Section 4, we will outline some of the practical difficulties encountered in the successful display of low impedances with a damped haptic display, along with the concept of "frequency-dependent damping" as a means of overcoming these challenges.

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