This paper deals with the discrete-time connected coverage problem with the constraint that only local information can be utilized for each robot. In such distributed framework, global connectivity characterized by the second smallest eigenvalue of topology Laplacian is estimated through introducing distributed minimal-time consensus algorithm and power iteration algorithm. A self-deployment algorithm is developed to disperse the robots with the precondition that the estimated second smallest eigenvalue is positive at each time-step. Since thus connectivity constraint does not impose to preserve some certain edges, the self-deployment strategy developed in this paper reserves a sufficient degree of freedom for the motion of robots. Theoretical analysis demonstrates that each pair of neighbor robots can finally reach the largest objective distance from each other while the group keeps connected all the time, which is also shown by simulations.
The stretching process,as a key phase of web production system,pursues the target velocities of rollers and the web tensions of spans between the successive rollers to guarantee proper stretching ratios. This requires the stable velocities and velocity ratios of large number rollers separated throughout the workshop. To this goal,a distributed cooperative controller is designed to coordinate the velocities of the rollers to the desired values as well as the target ratios between the upper and lower rollers. During the whole evolution,only the neighbor rollers can exchange the working information,and neither global information nor central controller is required. It is proven that all the rollers asymptotically achieve the desired velocity ratios via the proposed control law,which is also demonstrated by numerical simulation.
