Control of Haptic Systems with Time-varying Delay: a Novel Approach

This paper addresses the stable implementation of high stiffness interactions of objects in the virtual environment. The virtual wall is modeled as a mechanical system including a linear spring characterized by a virtual stiffness and a damper with a virtual damping in parallel. A novel approach for improving the stability of discrete-time haptic systems in the case of time-varying delay is proposed by using an augmented state observer instead of the traditional backward finite differentiator. Based on Lyapunov's stability theory, the delay-dependent asymptotic stability condition expressed in terms of LMI for choosing the virtual-wall parameters is presented. The numerical simulation results in the case of the PHANTOM 1.0 haptic devices are included in order to prove the effectiveness of the proposed method.