A Criterion for the PassivitY of Haptic Devices

Rendering a stiff virtual wall remains a core challenge in the field of haptics. A passivity study of this problem is presented, which relates the maximum achievable wall stiffness to the system discretization and sampling delays, to the quantization of the encoder, to the inertia of the haptic device, as well as to both the natural viscous and Coulomb damping present in the haptic device. The resulting stability criterion generalizes previously known results. Its analytic derivation is verified in both simulation and experiments on a one degree of freedom testbed.