Stability and performance of haptic simulation involving interaction with non-passive virtual environment

Previous researches on analysis of stability of haptic simulation largely assume that the virtual environment is passive. But the virtual environment can become non-passive due to various reasons including discretization errors and interaction dynamics between virtual tools and objects. This paper provides an analysis of the stability and performance of the haptic simulation involving non-passive virtual environment. The dynamic interaction between the virtual tools and the objects is modeled using the two-port networks. The analysis is carried out using a velocity and force mapping matrix for six-DOF simulation. New stability condition resulting from the analysis is applied to an example simulation of a one-DOF virtual wall. Maximum stiffness satisfying the stability condition established in the previous literature, and the proposed condition is compared with the maximum stiffness experimentally determined with various time steps. The newly proposed stability condition manifests less standard deviation of errors than the widely applied absolute stability condition.