Leader–follower formation with reduction of the off-tracking and velocity estimation under visibility constraints

This article addresses the time-varying leader–follower formation control problem for nonholonomic mobile robots, under communication and visibility constraints. Although the leader–follower formation control under visibility constraints has been studied, the elimination of the off-tracking effect has not been widely addressed yet. In this work, a new method to eliminate the off-tracking effect, considering the time-invariant formation as a tractor–trailer system, for unknown and circular tractor paths, taking into account the visibility constraints, is proposed. For a time-varying formation with not circular tractor’s path, the proposed method significantly reduces the off-tracking. Only the relative position and the relative orientation, provided by the on board monocular camera, are required. Thus, both the leader robot’s absolute position and the leader robot’s velocities are not needed. Furthermore, to avoid explicit communication among the robots, an extended state observer is implemented to estimate both the translational and the rotational leader’s velocity. In this way, the desired tasks are executed and achieved in a decentralized manner. For a time-varying formation, with constant leader robot’s velocities, the proposed control strategy, based on the kinematic model, guarantees that the formation errors asymptotically converge to the origin. Based on the Lyapunov theory, the stability proof of the formation errors dynamics is shown. Simulation results, considering time-varying leader robot’s velocities, show the efficiency of the proposed scheme.