Stability Analysis of a Dual-Rate Haptic System: A New Closed-Form Solution

Haptic devices (HDs) play a vital role in simulating the sense of touch in various virtual environments (VEs). Ensuring stable interaction between the HD and the VE is critical, particularly when simulating stiff virtual objects. One approach to enhancing stability is increasing the sampling rate; however, excessively high rates can compromise velocity information, thereby reducing damping stability. Dual-rate haptic devices address this issue by sampling position at higher rates and velocity at lower rates. This paper presents a novel closed-form equation for predicting the stability boundary of a dual-rate HD without restrictions on time delay or virtual damping. The proposed equation, which depends on the physical parameters of the HD and VE, sampling times, and time delay, is validated through simulations and experiments.