In this report we study haptic interaction with slowly updated virtual environments (VEs).
Such systems can become unstable due to phase lag introduced in the control loop by the
delay of the VE simulation. Because of the unpredictable nature of the VEs, a force feedback
control framework is required that can guarantee the stability of the haptic interaction in the
absence of a model of the VE. In [1] a passivity condition for such a framework is presented,
based on multirate wave variable control and filter banks, however up to now no filter
design is presented which actually obeys these passivity conditions.
Our contribution is an optimization algorithm to derive filters which guarantee stability. The
goal is to present an optimization algorithm which gives an engineer freedom in designing
the filters. By doing this we are able to present a filter bank which has guaranteed stability,
while giving special attention to the boundaries in the human sensory system and the
rejection of measurement noise. We investigate performance by comparing transferred
admittance and stiffness; both analytically and experimentally.
We present an optimization algorithm which generates guaranteed stable filter banks. The
filter bank derived using the proposed optimization algorithm has superior performance
compared to previous derived filter banks.