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This paper studies the target circumnavigation problem by multiple second-order agents under directed topology. All agents need to surround the target with prescribed formation and circular velocity. Firstly, according to the control objectives, the cooperative circumnavigation problem is converted into the stability problem of the corresponding error system. Then, the error system is divided into two second-order subsystems, and a distributed controller comprised of two parts is delivered. The stability analysis of the whole system is given by the employing cascaded control theory. One key merit of the proposed controller is that the prescribed formation is an extensive case and unlimited, including different tracking radii and angular spacing. Another merit is that the communication topology among agents only needs to have a directed spanning tree. Furthermore, the controller can be implemented by each agent in its local frame so that only local information is utilised without knowing global information. These all extend the scope of practical application, the controller is more universal. Finally, the simulations validate the effectiveness of the proposed controllers.

Cooperative circumnavigation by multiple second-order agents with prescribed formations