A directionally transparent energy bounding approach for multiple degree-of-freedom haptic interaction

This paper presents a multiple degree-of-freedom (DOF) energy bounding approach (EBA) for enhancing directional transparency while concurrently guaranteeing stability during multi-DOF haptic interactions. It was observed that the passivity condition for multiple ports may lead to oscillatory limit cycle behavior in some coordinate directions even though the total sum of energy flow-in is positive, meaning that the system is passive. The passivity condition, therefore, needs to be applied to each coordinate in order to avoid oscillatory behavior by ensuring that each energy flow-in is always positive. The EBA is applied to guarantee passivity. For multi-DOF haptic interaction, however, the EBA in each coordinate may distort the direction of the rendered force vector since the EBA may reduce the magnitude of the rendered force and torque vectors. To resolve this problem, a simple projection method is subsequently proposed. The validity of the proposed algorithm is then experimentally confirmed, and a comparative study with previous research is presented.