This paper focuses on the trajectory tracking problem for a swarm of mobile agents. A kinematic model describing the interactions and evolutions of the swarm members is proposed and its main properties are analyzed emphasizing that the agents centroid is ensured to track in finite-time a given reference trajectory and that the agents reach an aggregation in finite-time in a hyper-ball moving around the centroid path. One of the main characteristics of the model is the presence of an interaction matrix, between agents coordinates, which allows to define some properties of the swarm allowing the creation of different forms of agents aggregations, i.e., spheres, ellipsoids, straight lines, etc. Indeed swarm properties related to the agents configuration around the performed path along with agents interactions and absence of collisions are analyzed depending on the chosen interaction matrix.

中文翻译：

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群体有限时间轨迹跟踪的运动学模型


本文重点研究一群移动代理的轨迹跟踪问题。提出了描述群体成员相互作用和演化的运动学模型，并分析了其主要性质，强调确保智能体质心在有限时间内跟踪给定的参考轨迹，并保证智能体在有限时间内达到聚合。围绕质心路径移动的超级球。该模型的主要特征之一是代理坐标之间存在交互矩阵，它允许定义群体的一些属性，从而允许创建不同形式的代理聚合，即球体、椭球体、直线等。事实上，根据所选择的交互矩阵，分析与所执行路径周围的代理配置以及代理交互和不存在碰撞相关的群体属性。