Methods are provided for stabilizing a haptic interface of a computer-controlled one-port virtual-reality system or a two-port teleoperation system comprising a robot manipulator. "Stabilizing" means to reduce the sense of vibration in a haptic interface. A Passivity Observer is computed to measure the amount of energy produced at the haptic interface, and a Passivity Controller is calculated to damp or absorb excess energy which causes the sense of vibration. This invention also provides a "filter," i.e. a threshold function which returns zero velocity if the computed estimated velocity is less than a small predetermined value, which may be applied to estimated velocities determined in impedance-based methods of this invention so as to remove noise in the velocity estimate. To improve speed of reaction of the systems, this invention also provides methods for resetting the Passivity Observer to zero when it has been too positive for too long a period of time. Systems implementing these methods are also provided.