Virtual Mass Feedback for Rendering Stiff Virtual Springs

Rendering stiff virtual walls is of interest in the haptics domain. As one of the approaches, stiff springs can be rendered by adding virtual damping in an impedance controlled haptic interface. In this paper, we study the effect of incorporation of virtual mass on maximum renderable stiffness of a bilateral wall. The haptic interface is analyzed as a discrete time state-space system using exact discretization technique. Analytical stability boundary is obtained by solving for the roots of the characteristics polynomial. The main result of the paper shows that the maximum stiffness is rendered when the mass feedback is close to the mass of the device. For the devices with low inertia this means, at low frequencies, a high stiffness can be stably rendered with little compromise on the transparency of the system. Experiments performed on a single degree of freedom haptic interface validate the analytical results. The uncoupled stability of the interface is verified for the response of the device for initial displacement condition. The accuracy of displayed stiffness is validated when the user interacts with the wall. This further ensures the coupled stability of the device for the performed experiments. We show that the maximum stiffness achieved with virtual mass is about 2.5 times higher than that can be achieved with virtual damping.