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Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory

机译：多代理动态系统的植绒：算法和理论

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摘要

In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called α-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or α-agents, and virtual agents associated with α-agents called β- and γ-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.
机译：在本文中，我们为分布式植绒算法的设计和分析提供了一个理论框架。考虑了两种情况：在自由空间中发生植绒并存在多个障碍物。我们提出了三种植绒算法：两种用于自由植绒，一种用于约束植绒。提供了对前两种算法的全面分析。我们证明了第一个算法体现了雷诺兹的所有三个规则。这是一种提取交互规则的正式方法，从而导致了集体行为的出现。我们表明，第一种算法通常会导致规则碎片，而第二种和第三种算法都会导致植绒。提供了一种构建植绒成本函数（或集体潜力）的系统方法。这些集体势力惩罚了与一类称为α晶格的晶格状物体的偏离。我们使用多物种框架构建集体势，该势由羊群成员或α代理以及与α代理相关的虚拟代理（称为β和γ代理）组成。我们表明，可以使用代理的对等网络来执行群迁移，即“群不需要领导者”。给出了与李雅普诺夫稳定性相似的粒子系统的植绒“通用”定义。提供了一些仿真结果，这些结果演示了使用所提出的算法对数百个特工执行2-D和3-D植绒，拆分/重新加入机动和挤压机动。

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