Centralized multi-user multi-rate haptic cooperation using wave transformation

This paper proposes a multi-rate control strategy for multi-user haptic cooperation. In the proposed architecture, the virtual environment simulation runs on a central server to which all users are connected as clients. Users send position commands to and receive forces from the centralized virtual object that they cooperatively manipulate via wave-based controllers. After deriving the passivity condition for the multi-rate wave transformation, the paper investigates the stability of the cooperation between two users within a multi-rate discrete-time state space framework. The analysis predicts that clients can cooperatively manipulate much stiffer centralized virtual objects when connected to the server using wave transformations than when connected using virtual coupling. Experiments performed in a 1 degree of freedom (DOF) virtual environment confirm the analytical results.