Leaderless Consensus-based Formation Control of Multiple Nonholonomic Mobile Robots with Interconnecting Delays

The control objective in the leaderless consensus-based formation control is to ensure that the Cartesian positions of the nonholonomic mobile robots converge to a given position in a formation pattern and the barycentre of such formation is agreed, in a decentralized manner, by all the robots, while their orientations converge to a common value. The main problem behind this stabilization objective is that for robots that exhibit nonholonomic restrictions, due to the Brocket's condition, the controller has to be designed such that it is discontinuous or it is non-autonomous (time-varying). In this work we propose a simple Proportional plus damping (P+d) smooth controller that solves the aforementioned objective and we provide a sufficient condition on the damping gain to ensure robustness with respect to variable time-delays in the interconnection. Simulations are provided to show the effectiveness of our control proposal.