Energy bounding algorithm based on passivity theorem for stable haptic interaction control

After a basic theory on the passivity condition for the sampled-data system has been reviewed, passivity conditions on each subsystem of haptic simulation have been investigated. In addition, the virtual wall simulation is analytically analyzed with the passivity conditions and derived the previously well known stability condition (b > KT/2 + B). Based on this, we propose a novel energy bounding algorithm for stable haptic interaction control. The proposed energy bounding algorithm restricts the energy that is generated by the zero-order hold within the energy consumable by the physical damping in a haptic device and makes the virtual environment and controller passive. This algorithm, therefore, guarantees the passivity condition of the haptic simulation. While the virtual coupling algorithm restricts the actuator force with respect to the penetration depth, the proposed energy bounding algorithm restricts the change of actuator force and eventually restricts generated energy by the zero-order hold. Therefore, much stiffer contact simulation can be implemented.