Leader-follower Consensus of Unicycle-type Vehicles via Smooth Time-invariant Feedback

For a system of multiple vehicles with non-holonomic constraints and communicating under a directed spanning-tree graph, we solve the problem of full consensus, that is, convergence to a common unspecified value both in position and orientation. Remarkably, our controller is smooth time-invariant thanks to a polar-coordinates based model. Furthermore, the proposed control is quite simple, as it uses only relative information and achieves a more natural behaviour of the vehicles, making it well suited for practical applications. We establish (almost) global asymptotic convergence to the consensus manifold using the Lyapunov framework and cascaded systems theory.