Passive Multirate Wave Communications for Haptic Interaction in Slow Virtual Environments

Haptic interaction in slow virtual environments (VEs) can become unstable due to the phase lag introduced in the control loop by the slow update rate of the VE. Increasing the physical damping and/or limiting the contact stiffness rendered to users can mitigate the destabilizing effect of the low VE update rate. However, large physical damping and compliant virtual contacts decrease the sense of presence in VEs, especially during interaction with rigid virtual objects. To increase the maximum virtual contact stiffness that can be rendered to users without increasing the interface damping, this paper proposes a control strategy based on multirate wave communications between a haptic interface and a VE updated at a slow and fixed rate. The multirate wave communications are shown to be guaranteed passive only if the decrease of the wave sampling rate at the connection between the haptic interface and the VE does not cause aliasing. Therefore, an antialiasing low-pass filter is placed before the wave rate drop in the communications. The passivity condition is verified analytically and numerically for multirate haptic interaction in VEs with various contact stiffnesses and update rates. The transparency of haptic interaction in slow VEs to which users connect via passive multirate wave communications is investigated analytically in the frequency domain. Experiments validate that passive multirate wave communications can render stiffer contact in slow VEs than conventional direct coupling, and illustrate the destabilizing effect of the aliasing caused by the sampling rate drop in the communications.