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) to enhance directional transparency while guaranteeing stability for multiple-dof haptic interaction. It was observed that the passivity condition for multiple ports may lead to some oscillatory limit cycle behaviors 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 keeping each energy flow-in always positive. For guaranteeing passivity, which in turn, stability in each coordinates, the EBA is applied. For multiple-dof haptic interaction, however, the EBA in each coordinate may distort the direction of the force vector to be rendered since the EBA may cut down the magnitude of the force and torque vectors to be rendered in order to ensure the passivity. For avoiding this problem, a simple projection method is presented. The validity of the proposed algorithm is shown by several experiments.