Stiffness-reflecting energy-bounding approach for improving transparency of delayed haptic interaction systems

The ultimate objective of this study is to produce an interaction system haptically transparent to the human operator while guaranteeing interaction stability. In delayed haptic interaction systems (HIS) such as the bilateral teleoperation system (TS) and networked haptic virtual environments (NHVE), time delay over networks is a major cause of instability and transparency degradation. It has been proved that the passivity based energybounding approach (EBA) can guarantee robust stable interaction of the delayed HIS. However, transparency of the EBA has not been fully addressed, especially in terms of environment stiffness. This paper analyzes EBA transparency for the delayed HIS followed by experimental validation. This study demonstrates that the EBA in the delayed HIS can transparently display the environment stiffness regardless of the time delay by setting the second control parameter in the EBA to the environment stiffness value if the environment stiffness is less than the stable displayable stiffness by the EBA. For a very short period of initial contact with the very stiff environments, the stable displayable impedance range of the EBA can also be significantly increased by using the time-varying first control parameter. Experimental results show the effectiveness of the proposed approach.