This paper studies the problem of controlling a multi-robot system to achieve a polygon formation in a self-organized manner. Different from the typical formation control strategies where robots are steered to satisfy the predefined control variables, such as pairwise distances, relative positions and bearings, the foremost idea of this paper is to achieve polygon formations by injecting control inputs randomly to a few robots (say, vertex robots) of the group, and the rest follow the simple principles of moving towards the midpoint of their two nearest neighbors in the ring graph without any external inputs. In our problem, a fleet of robots is initially distributed in the plane. The socalled vertex robots take the responsibility of determining the geometric shape of the entire formation and its overall size, while the others move so as to minimize the differences with two direct neighbors. In the first step, each vertex robot estimates the number of robots in its associated chain. Two types of control inputs that serve for the estimation are designed using the measurements from the latest and the last two time instants respectively. In the second step, the self-organized formation control law is proposed where only vertex robots receive external information. Comparisons between the two estimation strategies are carried out in terms of the convergence speed and robustness. The effectiveness of the whole control framework is further validated in both simulation and physical experiments.

翻译：本文研究多机器人系统以自组织方式形成多边形编队的问题。不同于典型编队控制策略（即引导机器人满足预设控制变量，如成对距离、相对位置和方位角），本文的首要思想是通过对群体中少数机器人（即顶点机器人）随机注入控制输入来实现多边形编队，而其余机器人遵循简单原则——在环状图中向最近两个邻居的中点移动，无需任何外部输入。在我们的问题中，一组机器人初始分布在平面上。所谓顶点机器人负责确定整个编队的几何形状及其整体尺寸，而其他机器人则移动以最小化与两个直接邻机的差异。第一步，每个顶点机器人估计其关联链中的机器人数量。分别利用最新时刻和最近两个时刻的测量值，设计了两种用于估计的控制输入。第二步，提出自组织编队控制律，其中仅顶点机器人接收外部信息。从收敛速度和鲁棒性两方面对两种估计策略进行了比较，并通过仿真和实物实验进一步验证了整个控制框架的有效性。