Optimal Topology Recovery Scheme for Multi-robot Formation Control

In applications of formation control, maintaining the original topology is of vital importance, e.g., military surveillance. How to recover the original topology based on the robotic mobility is currently an open issue. In this paper, therefore, a distance-based topology recovery scheme for multi-robot formation control is proposed to tackle this problem. First, we derive the novel motion model of a robot, where the model parameters can be estimated based on the classic least square method (LSM). Thus, the historical data is exploited to estimate a leader's motion, so that its follower can still track it even when the link fails. Then, we provide theoretical guarantees for successful topology recovery. Both minimum-time and minimum-distance controllers are designed for the follower to reconnect with its leader, given different velocity constraints and different relative distance and bearing of the two robots. Furthermore, the successful recovery probability is obtained when the proposed velocity and relative position conditions cannot be satisfied. Simulations illustrate the effectiveness of the proposed topology recovery scheme.