<>html>
Experimental Results
Figures 10-13 show sixteen Z-width plots for one of the subjects.
Results for the other subjects are shown in Appendix B.
Figure 10. Results for Subject A with high resolution encoders and no
velocity filter.
Figure 10 shows the Z-width for Subject A for four device configurations (the
four with high resolution encoders and no velocity filter). By comparing these
configurations, we can see that physical damping improves the Z-width at both
high and low update rates. We can also see that higher update rates allow
stiffer virtual walls to be implemented, but at the cost of reduced virtual
damping.
Figure 11. Results for Subject A with low resolution encoders and no
velocity filter.
Figure 11 shows the Z-width for Subject A for four device configurations (the
four with low resolution encoders and no velocity filter). As in Figure 10, we
can see the effects of inherent mechanism damping and controller update rate on
Z-width. By comparing these results to Figure 10, we can see that encoder
resolution does not seem to affect the Z-width quantitatively in these
experiments. However, subjects noted significant qualitative improvements with
the use of high resolution encoders. Particularly disturbing about the low
resolution encoders was an occasional "deep rumbling" that subjects encountered
during their interactions with virtual walls. They also observed that the
low-resolution-encoder walls sometimes felt "gritty" due to spikes in endpoint
force. As these effects were observed for walls with high virtual damping, it
is likely that poor velocity resolution is the cause.
Figure 12. Results for Subject A with high resolution encoders and
velocity filtering.
In Figure 12, as well, we can see the benefit obtained from adding physical
damping to the mechanism, regardless of update rate. We can also see the
increase in maximum stiffness associated with higher update rates. By
comparing this plot to Figure 10, we can see the effect of using a first order
digital lowpass filter with the velocity estimation. While some sacrifice was
made in the magnitude of the maximum achievable stiffness (400 Nm/rad instead
of 530 Nm/rad), the value of virtual damping at which this maximum stiffness
occurred was shifted dramatically (from 0.5 Nm-sec/rad to 1.3 Nm-sec/rad).
Subjects consistently observed that the second wall (with the filtered velocity
signal) felt "better" than the first (with the unfiltered velocity signal). In
fact, the configuration with increased physical damping, high update rates,
high resolution encoders, and velocity filtering was judged by the subjects as
being the most "realistic". This result coincides with the notion that both
high stiffness and damping are necessary to make a virtual wall feel
realistic.
Figure 13. Results for Subject A with low resolution encoders and
velocity filtering.
Figure 13 also demonstrates the importance of mechanism damping on achieving
large Z-widths, regardless of update rate. Like the other figures, it shows
that high update rates are necessary to achieve high wall stiffness, but at the
cost of decreased wall damping due to poor velocity resolution. Comparison to
Figure 11 lets us see how a first order low pass digital velocity filter can
significantly improve the range of achievable damping, at the cost of lowering
the achievable stiffness.
-->