Formation control of multiple groups of agents finds application in large
area navigation by generating different geometric patterns and shapes, and also
in carrying large objects. In this paper, Centroid Based Transformation (CBT)
\cite{c39}, has been applied to decompose the combined dynamics of wheeled
mobile robots (WMRs) into three subsystems: intra and inter group shape
dynamics, and the dynamics of the centroid. Separate controllers have been
designed for each subsystem. The gains of the controllers are such chosen that
the overall system becomes singularly perturbed system. Then sliding mode
controllers are designed on the singularly perturbed system to drive the
subsystems on sliding surfaces in finite time. Negative gradient of a potential
based function has been added to the sliding surface to ensure collision
avoidance among the robots in finite time. The efficacy of the proposed
controller is established through simulation results.Comment: 8 pages, 5 figure