Maintaining visibility for leader-follower formations in obstacle environments

This paper addresses the problem of controlling a leader-follower (L - F) formation of two unicycle mobile robots moving under visibility constraints in a known obstacle environment. Visibility constraints are realized as inequality state constraints that determine a visibility set K. Maintaining visibility is translated into controlling the robots so that system trajectories starting in K always remain in K. We provide the conditions under which visibility is maintained, as well as a feedback control scheme that forces F to converge and remain into a set of desired configurations w.r.t. L while maintaining visibility. We also propose a cooperative control scheme for the motion of the formation in a known obstacle environment, so that both collision avoidance and maintaining visibility are ensured. The proposed control schemes are decentralized, in the sense that there is no direct communication between the robots. The efficacy of our algorithms is evaluated through simulations.