Passive velocity field control (PVFC) was previously developed for fully mechanical systems, in which the motion task was specified by behaviors in terms of a velocity field and the closed-loop was passive with respect to the supply rate given by the environment input. However, the PVFC was only applied to a single manipulator. The proposed control law was derived geometrically and the geometric and robustness properties of the closed-loop system were also analyzed. In this paper, we propose a virtual passivity-based algorithm to apply decentralized control to multiple 3wheeled mobile robotic systems whose subsystems are under nonholonomic constraints and convey a common rigid object in a horizontal plain. Moreover, it is shown that multiple robot systems ensure stability and the velocities of augmented systems converge to a scaled multiple of each desired velocity field for cooperative mobile robot systems. Finally, the application of proposed virtual passivity-based decentralized algorithm via system augmentation is applied to trace a circle and the simulation results is presented in order to show effectiveness for the decentralized control algorithm proposed in this research.
