Leader-follower consensus formation control of differential-drive nonholonomic vehicles with time-varying delays

In this paper is addressed the problem of formation set-point control of mobile robots, exchanging information over a network affected by communication delays. It is assumed, moreover, that the latter may be time-varying which is commonly the case of wireless networks. On the other hand, the autonomous robots are modelled as second-order mechanical systems with nonholonomic constraints; in particular, as differential-drive vehicles. The control objective is to ensure that all the robots coordinate their motion and acquire a formation pattern located at a desired position. Furthermore, they are all required to synchronize their orientations to the leader's. The control approach exploits the structural properties of the system. Being second-order mechanical systems, we design decentralized controllers of the proportional-derivative (PD) type, endowed with a time-varying vanishing term that excites all the system's modes to render the whole space reachable in spite of the nonholonomic constraints (nonholonomic systems are not stabilizable to a point via smooth time-invariant feedback). We provide theoretical justification of our main result and illustrate our findings via numerical simulations.