Haptic interface through wave transformation using delayed reflection: application to a passive haptic device

From the viewpoint of passivity, it is well known that wave variables are robust to transmission delay of a system. During wave transformation for the sampled-data system, a unit delay arises due to causality of the reflection wave. This delay makes the wave transformation in the sampled-data system different from the standard one in the continuous-time system. The unit delay on the reflection wave occasionally becomes a passive element. From the passivity condition of the sampled-data system, the wave impedance can be designed such that wave transformation using delayed reflection provides the effect of positive damping and thus a stable haptic interface is achieved in the sampled-data system. For a passive haptic device, although it is always considered stable because of its passive nature, the oscillatory motion appears during the wall-following task with force approximation. Various experiments for a two-linked passive haptic device show that a stable haptic interface can be accomplished for the wall-following task through wave transformation using delayed reflection.