Two distributed singleton formation avoidance strategies for noncooperative target fencing

The cooperative fencing control problem has been extensively studied mainly in the context of multiple pursuers, also called agents, and one single evader usually called the target. The most popular scenario in the literature is, that the pursuers move in a circular formation to encircle and track the target. The requirement of the circular formation imposes a heavy burden on the distributed coordination among the pursuers. Fortunately, a novel cooperative fencing control framework proposed in [1] only drives the pursuers to form an arbitrary convex hull that could change over time. However, this cooperative fencing control framework also has a drawback in that, the collinear singleton formation could happen and result in ineffective fencing. In [1], a centralized singleton formation avoidance strategy requires that the target information is known to all pursuers. Besides, it fails in more complex settings, for example, the noncooperative target case. By means of a novel rotational term, this paper improves the singleton formation avoidance strategy in [1]. First, we trim the original rotational term and drive only two pursuers to break the singleton formation. Meanwhile, we use only distances between neighboring pursuers to impose additional restrictions on the collision avoidance function, which turns out to be fully distributed. Moreover, the target studied here is noncooperative under a bounded unknown velocity input. The novel strategies together with the nonsmooth cooperative fencing control algorithm are supported by rigorous theoretical analysis. Numerical simulations are conducted to demonstrate the effectiveness of our novel design.