Analysis of Limit Cycle Oscillations in Dual-rate Haptic Rendering: Effect of Dual-rate Sampling. Issue 1 (2022) - Ganiny, Suhail; Koul, Majid H; Ahmad, Babar
Abstract: The onset of instability during virtual or remote haptic interaction is most often associated with the existence of limit cycles that are perceptible to a human operator's touch and even hearing. Time discretization due to sampling, position quantization due to ubiquitous use of optical encoders, and the device Coulomb friction are the main factors that contribute to the occurrence of limit cycles in haptic systems. The frequency and magnitude of such limit cycles are important as they limit the control gains that characterize the dynamics of the rendered environments. In earlier works, the effect of discrete sampling and position quantization on the behavior of limit cycles exhibited in uniform-rate haptics controllers has been studied but a similar analysis for multi-rate haptics controllers has not been reported yet. Towards this end, the present work explores how sampling of the position data at two distinct rates - dual-rate sampling - for implementation of stiff virtual walls affect the limit cycle behavior in a particular class of multi-rate haptics controllers. Specifically, we intend to evaluate the dependence of limit cycle frequency and magnitude on the dual-rate sampling rates. We utilize the non-linear control theory tool of describing function analysis along with numerical simulations to establish the same.