Chain formation control for a platoon of robots using time-gap separation

The main objective of this article is to present a controller capable of maintaining a chain formation of platooning type, among a set of non-holonomic mobile robots, keeping a time-gap separation between each pair of consecutive robots at the platoon. It is intended that the whole set of robots asymptotically follows any feasible trajectory described by the leader robot. Under these conditions, the distance between any pair of consecutive robots, that is, the i-th robot and the (i + 1)-th robot, depends on the velocity of the i -th robot. Only position measurements are available, such that, to avoid using approximate velocity estimations, the chain formation problem is solved by considering a delay observer strategy. Based on the measurements of the positions of the robots, along the platoon, a delay observer is built for the i -th robot that provides a virtual reference for the (i + 1)-th robot, and this reference corresponds to the i -th robot trajectory delayed specific units of time, corresponding to the desired time-gap separation. Convergence of the di _ 1_ -th robot to its desired delayed trajectory, which implies convergence of the chain formation, is formally proved by means of a Lyapunov stability approach and supported by numerical simulations and real-time experiments.