Minimum Mass for Haptic Display Simulations
2
J. Michael Brown
J. Edward Colgate
Proceedings of the ASME Interational Mechanical Engineering Congress and Exhibition
1998 ASME
http://lims.mech.northwestern.edu/mbrown-lib/imece98/imece98.pdf
http://lims.mech.northwestern.edu/mbrown-lib/imece98/imece98.ps
This paper addresses the issue of providing stability guarantees
during the implementation of multibody simulations for haptic display.
Within the framework of the virtual coupling, we discuss the passivity
of the haptic display.  Previous work has established that, if the
numerical methods used in the virtual environment are discrete time
passive, it is possible to decouple the stability of the device from
the virtual environment simulation.  In the present work, we prove
that discrete time passive operators must be implicit, making them
unlikely candidates for real time implementation.  Given restrictions
on environment parameters, however, passivity can sometimes be
preserved even when using explicit numerical methods.  An important
benchmark simulation is that of a point mass, and restrictions take
the form of a minimum mass that can be simulated passively.  This
minimum mass is derived for several simple numerical
integrator-virtual coupling pairs.