多智能体机器人协调控制研究及稳定性分析
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摘要
多智能体机器人的集合运动问题引起了不同领域研究人员的极大兴趣。从物理学,生物学到计算机科学,再到控制科学,科学家们试图弄明白,自主运动的生物体,比如鸟群,鱼群,细菌群,人群,或人造自主移动智能体,如何能够在没有集中协调的情况下,通过局部的协调聚集成编队。这主要是由于多智能体机器人系统在无人机协调控制、多机器人编队控制、多智能体群集运动、分布式传感器网络、人造卫星群位姿调整及通信网络拥塞控制等领域的广泛应用。
本文主要研究了多智能体机器人的群集运动控制,多智能体机器人的一致性问题,多机器人编队的非线性模型。具体内容如下:
对具有二次积分动态模型的智能群体跟随领航者取得群集运动编队进行了研究。通过建立智能群体相互作用或通信的图论模型,提出了一类控制规则,使智能群体跟随领航者取得群集运动。在固定和动态的网络拓扑,分别运用传统的Lyapunov稳定性理论及非平滑分析理论进行了稳定性分析。
对具有二次积分动态的智能群体,在有向网络取得群集运动进行了研究。提出了一个分散控制方法对智能群体进行分散控制。理论分析显示,有向图的弱连通性及一种称为平衡图的有向图在系统的稳定性分析中扮演着关键角色。
对具有质点动态模型的智能群体在高维空间取得群集运动进行了研究。基于智能群体两个不同的中心(质心及重心)提出了4个不同的控制规则使智能群体取得群集运动编队。前2个控制规则是基于智能群体的质心,其余2个则基于智能群体的几何中心。引入了光滑的邻接矩阵及光滑的势场函数来克服理论分析的困难。在某种合理的假设下,得以从理论上建立系统的稳定性,即:聚集、避免碰撞、速度匹配。
提出了加权平均一致性的新概念。首先,对多智能体无向动态网络取得全局加权平均一致性问题进行了研究,提出了线性和非线性分布式协调控制规则以使多智能体系统取得加权平均一致性。其次,对多智能体有向网络的一致性问题进行了研究。基于一类分散协调控制器使多智能体网络在固定和切换的网络拓扑取得全局渐近加权平均一致性。从理论上证明了有向网络的强连通性及一类称为平衡图的有向图在解决加权平均一致性问题中扮演着关键角色。
对Vicsek模型进行了进一步的讨论。首先,对多智能体有向网络取得渐近一致性进行了研究。提出了多智能体协调的新规则——N近邻规则,基于N——近邻规则,应用分布式控制器使得多智能体网络取得渐近一致性。其次,基于简化的Vicsek模型,对自主移动多机器人的集合运动进行了研究。给出了自主移动多机器人基于最近邻规则在有向网络的集合动态行为的一个定性分析。提出了多机器人运动方向收敛到同一方向的一个充分必要图条件。互连图有一个全局可达的结点在系统的收敛性分析中扮演着关键角色。进一步,如果该全局可达的结点没有邻接成员,则作为特殊情形,该结点充当着群组的领航者。
对多机器人编队的一个非线性模型进行了研究。提出了一种非线性滑模控制器,协调一组非完整移动机器人以取得合乎要求的编队。在合理的假设下,从理论上证明了存在有界干扰情形下机器人编队的渐近稳定性,即所提出的滑模控制器使得相对距离误差、方位角误差及运动方向误差渐近稳定。
The problem of collective motion of multi-agent robots attracts attention of the scientists from different research fields. From physics, biology, computer science to control science, scientists try to understand how a group of moving creatures such as flocks of birds, schools of fish, colonies of bacteria, crowds of people, or man-made mobile autonomous agents, can cluster in formations only by local cooperative rule without centralized coordination. This is mainly due to broad applications of multi-agent robots systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control of multi-robot, flocking of multi-agent robots, distributed sensor networks, attitude alignment of clusters of satellites, and congestion control in communication networks.
This thesis mainly investigates flocking motion control of multi-agent robots, consensus problem of multi-agent robots and a nonlinear model for multi-robot formations. Details are as follows:
The multiple mobile agents with double integrator dynamics followed by a leader to achieve flocking motion formation is studied. We model the interaction and/or communication relationship between agents by algebraic graph theory. A class of control laws for a group of mobile agents is proposed. Stability analysis is achieved by using classical Lyapunov theory in fixed network topology, differential inclusions and nonsmooth analysis in switching network topology respectively.
Flock with double integrator dynamics to achieve flocking motion formation in directed networks is studied. A class of decentralized control laws for a flock of mobile agents is proposed. Theoretical analysis show that the weakly connectedness of directed graph and a class of directed graphs, called balanced graphs, play a crucial role in stability analysis.
A novel procedure is presented for control and analysis of multiple autonomous agents with point mass dynamics achieving flocking motion in high-dimensional space. Four distributed control laws are proposed for a group of autonomous agents to achieve flocking formations related to two different centers (mass center and geometric center) of the flock. The first two control laws are designed for flocking motion guided at mass center and the others for geometric center. Smooth adjacency matrix and smooth potential function are introduced to overcome the difficulties in theoretical analysis. Under some reasonable assumptions, theoretical analysis is established to indicate the stability (cohesiveness, collision avoidance and velocity matching) of the control systems.
A new notion, called weighted average-consensus, is proposed. Firstly, multi-agent achieving global weighted average-consensus in undirected dynamic networks is studied, linear and nonlinear distributed cooperative control laws are proposed for multi-agent systems to achieve weighted average-consensus. Secondly, the consensus problem in directed networks of multi-agent is studied. A class of distributed controller is applied to achieve global asymptotically weighted average-consensus in networks of multi-agent with fixed and switching topology. It is proved theoretically that the strongly connectedness of directed graph and a class of directed graphs, called balanced graphs, play a crucial role in solving weighted average-consensus problems.
Vicsek's model is further discussed. Firstly, multi-agent achieving consensus asymptotically in directed dynamic networks is studied. A new rule, N-nearest neighbors rule, is proposed for multi-agent coordination. Based on N-nearest neighbors rule, a class of distributed controllers is applied for multi-agent networks to reach consensus asymptotically. Secondly, based on simplified Vicsek's model, coordinated collective motion of groups of autonomous mobile robots is studied. A qualitative analysis for the collective dynamics of multiple autonomous robots with directed interconnected topology using nearest neighbor rules is given. A necessary and sufficient graphical condition is proposed to guarantee that the headings of all robots converge to the same heading. The graph having a globally reachable node plays a crucial role in convergence analysis. Furthermore, we show that the globally reachable node having no neighbors serves as a group leader as a special case.
A nonlinear model for multi-robot formations is studied. A nonlinear sliding mode controller is proposed to coordinate a group of nonholonomic mobile robots such that a desired formation can be achieved. We prove theoretically that under certain reasonable assumptions the formation is asymptotically stable even with bounded disturbances; that is, the proposed sliding mode controller can asymptotically stabilize the errors in relative distance, relative bearing and heading direction, respectively.
本文主要研究了多智能体机器人的群集运动控制,多智能体机器人的一致性问题,多机器人编队的非线性模型。具体内容如下:
对具有二次积分动态模型的智能群体跟随领航者取得群集运动编队进行了研究。通过建立智能群体相互作用或通信的图论模型,提出了一类控制规则,使智能群体跟随领航者取得群集运动。在固定和动态的网络拓扑,分别运用传统的Lyapunov稳定性理论及非平滑分析理论进行了稳定性分析。
对具有二次积分动态的智能群体,在有向网络取得群集运动进行了研究。提出了一个分散控制方法对智能群体进行分散控制。理论分析显示,有向图的弱连通性及一种称为平衡图的有向图在系统的稳定性分析中扮演着关键角色。
对具有质点动态模型的智能群体在高维空间取得群集运动进行了研究。基于智能群体两个不同的中心(质心及重心)提出了4个不同的控制规则使智能群体取得群集运动编队。前2个控制规则是基于智能群体的质心,其余2个则基于智能群体的几何中心。引入了光滑的邻接矩阵及光滑的势场函数来克服理论分析的困难。在某种合理的假设下,得以从理论上建立系统的稳定性,即:聚集、避免碰撞、速度匹配。
提出了加权平均一致性的新概念。首先,对多智能体无向动态网络取得全局加权平均一致性问题进行了研究,提出了线性和非线性分布式协调控制规则以使多智能体系统取得加权平均一致性。其次,对多智能体有向网络的一致性问题进行了研究。基于一类分散协调控制器使多智能体网络在固定和切换的网络拓扑取得全局渐近加权平均一致性。从理论上证明了有向网络的强连通性及一类称为平衡图的有向图在解决加权平均一致性问题中扮演着关键角色。
对Vicsek模型进行了进一步的讨论。首先,对多智能体有向网络取得渐近一致性进行了研究。提出了多智能体协调的新规则——N近邻规则,基于N——近邻规则,应用分布式控制器使得多智能体网络取得渐近一致性。其次,基于简化的Vicsek模型,对自主移动多机器人的集合运动进行了研究。给出了自主移动多机器人基于最近邻规则在有向网络的集合动态行为的一个定性分析。提出了多机器人运动方向收敛到同一方向的一个充分必要图条件。互连图有一个全局可达的结点在系统的收敛性分析中扮演着关键角色。进一步,如果该全局可达的结点没有邻接成员,则作为特殊情形,该结点充当着群组的领航者。
对多机器人编队的一个非线性模型进行了研究。提出了一种非线性滑模控制器,协调一组非完整移动机器人以取得合乎要求的编队。在合理的假设下,从理论上证明了存在有界干扰情形下机器人编队的渐近稳定性,即所提出的滑模控制器使得相对距离误差、方位角误差及运动方向误差渐近稳定。
The problem of collective motion of multi-agent robots attracts attention of the scientists from different research fields. From physics, biology, computer science to control science, scientists try to understand how a group of moving creatures such as flocks of birds, schools of fish, colonies of bacteria, crowds of people, or man-made mobile autonomous agents, can cluster in formations only by local cooperative rule without centralized coordination. This is mainly due to broad applications of multi-agent robots systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control of multi-robot, flocking of multi-agent robots, distributed sensor networks, attitude alignment of clusters of satellites, and congestion control in communication networks.
This thesis mainly investigates flocking motion control of multi-agent robots, consensus problem of multi-agent robots and a nonlinear model for multi-robot formations. Details are as follows:
The multiple mobile agents with double integrator dynamics followed by a leader to achieve flocking motion formation is studied. We model the interaction and/or communication relationship between agents by algebraic graph theory. A class of control laws for a group of mobile agents is proposed. Stability analysis is achieved by using classical Lyapunov theory in fixed network topology, differential inclusions and nonsmooth analysis in switching network topology respectively.
Flock with double integrator dynamics to achieve flocking motion formation in directed networks is studied. A class of decentralized control laws for a flock of mobile agents is proposed. Theoretical analysis show that the weakly connectedness of directed graph and a class of directed graphs, called balanced graphs, play a crucial role in stability analysis.
A novel procedure is presented for control and analysis of multiple autonomous agents with point mass dynamics achieving flocking motion in high-dimensional space. Four distributed control laws are proposed for a group of autonomous agents to achieve flocking formations related to two different centers (mass center and geometric center) of the flock. The first two control laws are designed for flocking motion guided at mass center and the others for geometric center. Smooth adjacency matrix and smooth potential function are introduced to overcome the difficulties in theoretical analysis. Under some reasonable assumptions, theoretical analysis is established to indicate the stability (cohesiveness, collision avoidance and velocity matching) of the control systems.
A new notion, called weighted average-consensus, is proposed. Firstly, multi-agent achieving global weighted average-consensus in undirected dynamic networks is studied, linear and nonlinear distributed cooperative control laws are proposed for multi-agent systems to achieve weighted average-consensus. Secondly, the consensus problem in directed networks of multi-agent is studied. A class of distributed controller is applied to achieve global asymptotically weighted average-consensus in networks of multi-agent with fixed and switching topology. It is proved theoretically that the strongly connectedness of directed graph and a class of directed graphs, called balanced graphs, play a crucial role in solving weighted average-consensus problems.
Vicsek's model is further discussed. Firstly, multi-agent achieving consensus asymptotically in directed dynamic networks is studied. A new rule, N-nearest neighbors rule, is proposed for multi-agent coordination. Based on N-nearest neighbors rule, a class of distributed controllers is applied for multi-agent networks to reach consensus asymptotically. Secondly, based on simplified Vicsek's model, coordinated collective motion of groups of autonomous mobile robots is studied. A qualitative analysis for the collective dynamics of multiple autonomous robots with directed interconnected topology using nearest neighbor rules is given. A necessary and sufficient graphical condition is proposed to guarantee that the headings of all robots converge to the same heading. The graph having a globally reachable node plays a crucial role in convergence analysis. Furthermore, we show that the globally reachable node having no neighbors serves as a group leader as a special case.
A nonlinear model for multi-robot formations is studied. A nonlinear sliding mode controller is proposed to coordinate a group of nonholonomic mobile robots such that a desired formation can be achieved. We prove theoretically that under certain reasonable assumptions the formation is asymptotically stable even with bounded disturbances; that is, the proposed sliding mode controller can asymptotically stabilize the errors in relative distance, relative bearing and heading direction, respectively.
引文
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