Analysis of virtual fixture contact stability for telemanipulation

A forbidden-region virtual fixture (FRVF) is a constraint, implemented in software, that keeps the slave manipulator of a master/slave telemanipulation system from entering into a forbidden region of the workspace. In this paper, we consider the problem of unstable vibrations of the slave against the FRVF for a general class of telemanipulator control architectures. The master and slave equilibrium positions resulting from a constant human input force are found, and the system is evaluated around this equilibrium. We consider two methods of analyzing the stability of the system around this equilibrium point. The first method uses tools developed for analysis of two-port networks. The second method converts the system to its discrete state-space form, and then uses the position of the eigenvalues to analyze system stability. We find that the discrete state-space method agrees with simulations, and can be easily used to design and analyze the stability and transient behavior of the telemanipulator.