Transparency of Haptic Systems

The control \(C_{1}\) in Chap. 3 limits the change rate, \(\dot{k}_{{{\text{dis}}}}\) , and the maximum value of \(k_{{{\text{dis}}}}\) to satisfy the ISS criteria for stability. This chapter presents a complementary compensation method for rendering of increased stiffness and transparency. The compensation is designed to reduce the discretization effect. The compensation expands the ISS-satisfying region by reducing the negative damping and spring caused by the ZOH and sampler. A control \(C_{2}\) is designed to satisfy the ISS criteria by bounding the \(\dot{k}_{{{\text{dis}}}} \left( t \right)\) . The \(C_{2}\) ensures the stability, but does not limit the maximum value of \(k_{{{\text{dis}}}}\) . Experiments with nonlinear environments are shown to compare the haptic rendering performance with the previous methods.