1Stability of Haptic Rendering: Discretization, Quantization, Time-Delay and Coulomb Effects

Abstract — Rendering stiff virtual objects remains a core chal-lenge in the field of haptics. A study of this problem is presented, which relates the maximum achievable object stiffness to the elements of the control loop. In particular, we examine how the sampling rate, quantization, computational delay, and amplifier dynamics interact with the inertia, natural viscous, and Coulomb damping of the haptic device. Nonlinear effects create distinct stability regions and many common devices operate stably, yet in violation of passivity criteria. An energy based approach provides theoretical insights, supported by simulations, experimental data, and a describing function analysis. The presented results subsume previously known stability conditions