Time Domain Passivity Control for multi-degree of freedom haptic devices with time delay

This paper generalizes the Time Domain Passivity Control concept originally introduced by J.-H. Ryu et al. (2004) in order to work for multi-degree of freedom (DoF) haptic systems with time delay. Its energy computation (named passivity observer) factors in the phase shift caused by time delay, and is improved by an energy estimation. Moreover, the variable damping of the passivity controller is generalized such that weighting by the mass matrix of the haptic device is possible. This transformation takes into account the direction-dependent inertia of multi-DoF haptic devices. Furthermore, a stability boundary for this damping is introduced for one as well as for several DoF allowing for high energy dissipation. Additionally, it is briefly shown that one single multi-DoF Cartesian passivity controller is advantageous compared to independent single-DoF passivity controllers in each joint of the haptic device. Finally, the generalized Time Domain Passivity Controller is experimentally verified using the DLR light weight robot arm as haptic device.