Stable forbidden-region virtual fixtures for bilateral telemanipulation

There has been recent interest in novel human-machine collaborative control laws, called "virtual fixtures," which provide operator assistance for telemanipulation tasks. A forbidden-region virtual fixture is a constraint, implemented in software, that seeks to prevent the slave manipulator of a master/slave telemanipulation system front entering into a forbidden region of the workspace. In this paper we consider the problem of unstable vibrations of the slave and/or master against forbidden-region virtual fixtures for a general class of telemanipulator control architectures, including those with haptic feedback. To the best of the authors' knowledge, there has been no rigorous study of the stability, of forbidden-region virtual fixtures in previous work. The system is evaluated around the master and slave equilibrium position resulting from a constant desired humun input force, using a discrete state-space model. We present a method to analytically determine if instability is possible in the system. We thoroughly evaluate this method, experimentally, applying malicious user strategies that attempt to drive the system unstable. Our approach agrees with experimental results and can be used to design and analyze the stability and transient properties of a telemanipulator interacting with virtual fixtures. We show that the user can affect both slave- and master-side virtual fixture stability by modifying his or her impedance characteristics. However, the upper bound on stable slave-side virtual fixture stiffness does not depend on the particular user.