Abstract
We address the problem of tracking control of multiple mobile robots advancing in formation along straight-line paths. We use a leader-follower approach, and hence, we assume that only one swarm leader robot has the information of the reference trajectory. Then, each robot receives information from one intermediary leader only. Therefore, the communications graph forms a simple spanning directed tree. As the existence of a spanning tree is necessary to achieve consensus, it is the minimal configuration possible to achieve the formation-tracking objective. From a technological viewpoint, this has a direct impact on the simplicity of its implementation; e.g., less sensors are needed. Our controllers are partially linear time-varying with a simple added nonlinearity satisfying a property of persistency of excitation, tailored for nonlinear systems. Structurally speaking, the controllers are designed with the aim of separating the tasks of position-tracking and orientation. Our main results ensure the uniform global asymptotic stabilization of the closed-loop system, and hence, they imply robustness with respect to perturbations. All these aspects make our approach highly attractive in diverse application domains of vehicles' formations such as factory settings.