Stability Analysis of a Dual-Rate Haptic System: A New Closed-Form Solution
Ahmad Mashayekhi, Oumaima Akhif, Amin Khorasani, Tom Verstraten
AI summary
Problem
High sampling rates in haptic devices improve stiffness rendering but cause noisy velocity estimation and instability. Prior dual-rate stability analyses lack closed-form solutions valid for arbitrary time delays and damping.
Approach
The authors derive a closed-form stability boundary equation by analyzing the system's characteristic transfer function, incorporating physical device parameters, dual sampling rates, and time delays.
Key results
- Derivation of a closed-form stability boundary equation for dual-rate haptic systems
- Equation validity across all time delays and virtual damping ranges without iteration
- Theoretical boundaries accurately match MATLAB Simulink simulations
- Experimental validation confirms predicted stability limits on a physical dual-motor haptic device
Why it matters
Provides haptic engineers with a fast, exact tool to design stable high-stiffness virtual environments without computationally heavy simulations.
Abstract
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, particu- larly when simulating stiff virtual objects. One approach to enhanc- ing 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.