Stable region of a haptic device that is displaying a bilateral virtual wall.

Alpha = normalized virtual stiffness
Beta = normalized virtual damping
Delta = normalized physical damping
d = Time delay

References:

• Gil, J.J.; Sanchez, E.; Hulin, T.; Preusche, C.; Hirzinger, G.: Stability Boundary for Haptic Rendering: Influence of Damping and Delay, ICRA2007, April 2007, Rome - Italy
• Hulin, T.; Preusche, C.; Hirzinger, G.: Stability Boundary for Haptic Rendering: Influence of Physical Damping, IROS2006, Oct. 2006, Beijing - China