基于Vicsek模型的自驱动集群动力学研究
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摘要
集群动力学是研究集群运动的一门新兴学科,近几年受到国内外学者的广泛关注。集群行为无处不在,遍及自然界、生物系统和人类社会。其中深具代表性并广为人们熟知的集群行为包括:在宏观上,生物界中的鸟群、鱼群、蚂蚁等的运动;在微观上,细菌等微生物以及人类的黑色素细胞等都在进行群体运动。研究这些集群运动不仅对人们的工作和生活具有重要的现实意义,对了解自然界和生物系统具有深远的科学意义。而且集群运动的研究具有广阔的应用前景:在工程方面,生物群体中的同步、避障机制可以有效地应用到分布式机器人集群、无人驾驶飞行器群以及卫星群的运动控制中。在信息管理方面,可以从生物群体如何形成有效决策的研究中得到启示,为管理机制的改进和管理效率的提高提供新的思想源泉。
研究集群运动的最终目的是了解集群系统具有怎样的集体动力学行为和如何干预控制应用这些系统。关于集群动力学的研究,物理学者主要是通过建立模型的方法来实现的。其中,典型的模型主要有以下几个: Vicsek Model、Three-Circle Model和Leader-follower Model.本文主要调研了基于Vicsek Model的近几年的各种研究。一般来说,所有的研究方法可以分为两类:一种是通过理论推导及应用已有的物理理论,试图去理解和解释集群行为形成的内在原因;另一种则是从实际的集群运动及个体生物特征出发,通过构造模型去发现实际集群运动中存在的规律。这里我们采取的是后者方法,通过充分的调研,我们在Vicsek模型的基础上提出一种有限视野角度模型,发现了最佳视野角度的存在,在最佳视野角度下系统既能快速达到同步又节省能量。
在本文中,我们提出了有限视角模型,即每个个体的视野角度为其向前运动时眼睛所能看到的一个扇形范围而非Vicsek模型中的全局角度。我们发现,系统的收敛时间与个体的视野角度是非线性关系的,即不是角度越大收敛越快,而是存在最佳视野角度,使系统可以最快地达到同步;我们进一步研究了周围个体的平均数与收敛时间的关系,我们发现个体间过多的通信有时反而阻止系统的同步效果。我们的模型与实践更接近,得到的结果一是有助于对Vicsek模型更深层次的理解,另一个就是,在对人工智能如无人驾驶车辆和机器人的设计与控制研究中,可以为其提供借鉴,使其节省能量并更好地达到控制目的。
以上研究成果已经发表于:Phy. Rev. E 79.052102 (2009).
Collective dynamics has been considered as an important approach for describing and understanding collective motions. In nature, collective motions of abundant organisms universally exist in biological flocks、swarms、schools, ranging from the behavior of groups of ants, colonies of bacteria and clusters of cells in the microcosmic scale, to migration of flocks of birds and schools of fish in the macroscopical scale. These different forms of collective behavior root in the different kinds of interactions among group members, and hence the investigation on the inter-individual interactions among self-driven swarms has attracted more and more attention among physicists, biologists, as well as social and systems scientists. Its value is to extract some generic rules from those natural systems, and apply them in other relevant industrial application realms, such as sensor network data fusion, load balancing, swarms/flocks, unmanned air vehicles (UAVs), attitude alignment of satellite clusters, congestion control of communication networks, multi-agent formation control, and so on.
The ultimate goal of studying collective dynamics is two-fold: (i) examine the nature of such collective behaviors among bio-groups; (ii) understand the nature of collective behaviors and apply them in other field. The synchronization of collective motion is an important issue. With the advent of large computers, the field of collective dynamics has been dominated by numerical models. The typical models are Vicsek Model、Three-Circle Model、Leader-follower Model etc. In this paper, the main job is research on the various studies based on the Vicsek Model in recent years. Generally speaking, all research methods can be divided into two categories: from theory to the actual situation and from the actual situation to the theoretical research. The former is derived through the theory and tries to understand and explain the nature of collective motion. In the latter case, physicist is modeling the collective phenomenon to find the law of collective motions. Here, we adopt the latter method and propose a new model with the restricted vision and find that there exists an optimal view angle.
In this paper, we have studied the effects of restricted vision of a group of self-propelled agents. The field of vision of every agent is only a sector of disc and the included arc represents the view angle. It is interesting to find that there exists an optimal angle resulting in the fastest direction consensus. The value of the optimal view angle increases as the increasing of sensor radius, while decreases as the increasing of swarm number, the absolute velocity or the noise strength. Another interesting phenomenon is that agents with optimal view angle have the least number of neighbors in the steady state. Our studies indicate the existence of superfluous communications in the Vicsek model, which indeed hinder the direction consensus. Moreover, our results may be useful in designing the man-made swarms such as autonomous mobile robots.
研究集群运动的最终目的是了解集群系统具有怎样的集体动力学行为和如何干预控制应用这些系统。关于集群动力学的研究,物理学者主要是通过建立模型的方法来实现的。其中,典型的模型主要有以下几个: Vicsek Model、Three-Circle Model和Leader-follower Model.本文主要调研了基于Vicsek Model的近几年的各种研究。一般来说,所有的研究方法可以分为两类:一种是通过理论推导及应用已有的物理理论,试图去理解和解释集群行为形成的内在原因;另一种则是从实际的集群运动及个体生物特征出发,通过构造模型去发现实际集群运动中存在的规律。这里我们采取的是后者方法,通过充分的调研,我们在Vicsek模型的基础上提出一种有限视野角度模型,发现了最佳视野角度的存在,在最佳视野角度下系统既能快速达到同步又节省能量。
在本文中,我们提出了有限视角模型,即每个个体的视野角度为其向前运动时眼睛所能看到的一个扇形范围而非Vicsek模型中的全局角度。我们发现,系统的收敛时间与个体的视野角度是非线性关系的,即不是角度越大收敛越快,而是存在最佳视野角度,使系统可以最快地达到同步;我们进一步研究了周围个体的平均数与收敛时间的关系,我们发现个体间过多的通信有时反而阻止系统的同步效果。我们的模型与实践更接近,得到的结果一是有助于对Vicsek模型更深层次的理解,另一个就是,在对人工智能如无人驾驶车辆和机器人的设计与控制研究中,可以为其提供借鉴,使其节省能量并更好地达到控制目的。
以上研究成果已经发表于:Phy. Rev. E 79.052102 (2009).
Collective dynamics has been considered as an important approach for describing and understanding collective motions. In nature, collective motions of abundant organisms universally exist in biological flocks、swarms、schools, ranging from the behavior of groups of ants, colonies of bacteria and clusters of cells in the microcosmic scale, to migration of flocks of birds and schools of fish in the macroscopical scale. These different forms of collective behavior root in the different kinds of interactions among group members, and hence the investigation on the inter-individual interactions among self-driven swarms has attracted more and more attention among physicists, biologists, as well as social and systems scientists. Its value is to extract some generic rules from those natural systems, and apply them in other relevant industrial application realms, such as sensor network data fusion, load balancing, swarms/flocks, unmanned air vehicles (UAVs), attitude alignment of satellite clusters, congestion control of communication networks, multi-agent formation control, and so on.
The ultimate goal of studying collective dynamics is two-fold: (i) examine the nature of such collective behaviors among bio-groups; (ii) understand the nature of collective behaviors and apply them in other field. The synchronization of collective motion is an important issue. With the advent of large computers, the field of collective dynamics has been dominated by numerical models. The typical models are Vicsek Model、Three-Circle Model、Leader-follower Model etc. In this paper, the main job is research on the various studies based on the Vicsek Model in recent years. Generally speaking, all research methods can be divided into two categories: from theory to the actual situation and from the actual situation to the theoretical research. The former is derived through the theory and tries to understand and explain the nature of collective motion. In the latter case, physicist is modeling the collective phenomenon to find the law of collective motions. Here, we adopt the latter method and propose a new model with the restricted vision and find that there exists an optimal view angle.
In this paper, we have studied the effects of restricted vision of a group of self-propelled agents. The field of vision of every agent is only a sector of disc and the included arc represents the view angle. It is interesting to find that there exists an optimal angle resulting in the fastest direction consensus. The value of the optimal view angle increases as the increasing of sensor radius, while decreases as the increasing of swarm number, the absolute velocity or the noise strength. Another interesting phenomenon is that agents with optimal view angle have the least number of neighbors in the steady state. Our studies indicate the existence of superfluous communications in the Vicsek model, which indeed hinder the direction consensus. Moreover, our results may be useful in designing the man-made swarms such as autonomous mobile robots.
引文
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