In this paper, we propose a distance-based formation control strategy for a group of mobile agents to achieve almost global convergence to a target formation shape provided that the formation is represented by a complete graph, and each agent is governed by a single-integrator model. The fundamental idea of achieving almost global convergence is to use a virtual formation of which the dimension is augmented with some virtual coordinates. We define a cost function associated with the virtual formation and apply the gradient-descent algorithm to the cost function so that the function has a global minimum at the target formation shape. We show that all agents finally achieve the target formation shape for almost all initial conditions under the proposed control law.

中文翻译：

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一般空间中几乎全局收敛的 $\mathcal {K}_{n}$ 编队的基于距离的控制


在本文中，我们提出了一种基于距离的编队控制策略，用于一组移动代理，以实现几乎全局收敛到目标编队形状，前提是编队由完整的图表示，并且每个代理由单个积分器控制模型。实现几乎全局收敛的基本思想是使用虚拟编队，其维度通过一些虚拟坐标来增强。我们定义与虚拟编队相关的成本函数，并将梯度下降算法应用于成本函数，以便该函数在目标编队形状处具有全局最小值。我们表明，在所提出的控制律下，所有智能体最终在几乎所有初始条件下都达到了目标编队形状。