Collision Avoidance and Connectivity Preservation for Time-Varying Formation of Second-Order Multi-Agent Systems With a Dynamic Leader

In this paper, the problem of time-varying formation tracking control, with collision avoidance (CA) and connectivity preservation (CP), is studied for second-order multi-agent systems. Consider the unknown control input of virtual leader, an estimator is introduced to design a distributed time-varying formation tracking control protocol, while relaxing the condition the leader’s velocity is constant. Different from some existing results, relative velocity-based action function is designed such that both CA and CP with small negative effects on formation are achieved, and a simpler method is proposed to eliminate the large jump and discontinuity of potential field force. Furthermore, the Lyapunov-like approach is used for the stability analysis and the theoretical results are derived. Accordingly, it is demonstrated that velocity tracking errors can asymptotically converge to 0, and steady-state position tracking errors are bounded and related to initial state. Finally, two simulation examples verify the effectiveness of theoretical results.