Stable haptic rendering with detailed energy-compensating control

Sampled-data system nature is the main factor for a haptic system to exhibit non-passive behaviors or instabilities through “energy leaks”, especially for stiff objects rendering. A detailed energy-compensating method is presented aiming to improve the haptic system's performance based on the concept of “doing work”. Using an ideal continuous-time haptic system as a reference, we calculate the “work difference” between interactions in the sampled-data haptic system and the counterparts in the real world. An “energy-compensating controller” (ECC) is then designed to compensate for, in every sampling period, the “energy leaks” caused by “work difference”. The “work difference” exists both in entering and leaving periods of interaction contacts, which means the ECC not only removes the unwanted “extra work” from the virtual environment to eliminate potential non-passive system behaviors, but also compensates for the “deficient work” that should be done by the human operator to guarantee the intended rendering stiffness. The proposed method was tested and demonstrated on six human subjects with the implementation of a stiff-wall prototype haptic system via a Delta haptic device.