Second-Order Leader-Following Consensus of Multi-Robot Systems under Limited Visual Feedback

This paper proposes a second-order leader-following consensus formation control method under limited visual feedback, which ensures that followers can observe and track the leader under vision constraints, reduces the risk of the leader disappearing from followers’ vision range, and ensures collaboration among followers. In formations based on visual perception for localization, followers are constrained by their vision range and may lose sight of the leader. To address this, this paper defines a safety range within each follower’s vision range and designs the boundary constraint function for the distance and the bearing angle between the leader and each follower. Furthermore, two bounded functions, i.e., the bounded smooth piecewise function and the bounded saturation function are introduced to the collaboration information interaction among followers. The simulation result indicates that our proposed formation control method can reduce the leader’s movement time near the boundary of the follower’s vision range. It also decreases the maximum bearing angle and the maximum distance between the leader and the follower during the leader’s movement near the boundary of the follower’s vision range. Furthermore, our method reduces the curvature of followers’ trajectories, ensuring the formation’s smoothness and robustness under vision constraints.