Stability Analysis of Decentralized PVFC Algorithm for Cooperative Mobile Robotic Systems

Passive velocity field control (PVFC) was previously developed for fully mechanical systems, in which the motion task was specified behaviorally in terms of a velocity field, and the closed-loop was passive with respect to a 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 method to apply a decentralized control algorithm to cooperative 3-wheeled mobile robots whose subsystem is under nonholonomic constraints and which 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 convergence to a scaled multiple of each desired velocity field for cooperative mobile robot systems.