群体自主机器人系统分布式优化与一致性控制
|
摘要
群体自主机器人系统因其具有鲁棒性、可扩展性、适应性和经济性等方面的优势,成为近年来机器人领域的研究热点之一。本文以群体自主机器人系统一致性控制为切入点,以国家自然科学基金项目和研究生创新项目为依托,着重研究了群体系统对复杂环境的适应性、群体收敛速度的可控性以及群体系统性能的优化。具体如下：
1)设计了一种分布式协同控制策略来实现群体一致性行为对非线性环境的适应。利用具备有界梯度的特定势能函数对外部非线性环境信息进行描述,结合虚拟力和最近邻居原则的思想设计了基于局部信息交互的分布式协同控制策略,实现非线性环境下的群体一致性行为,并对群体收敛时间进行了估计。仿真结果表明了该控制策略的有效性和可行性,同时也体现出了群体系统的适应性和可扩展性。
2)针对障碍物环境设计了群体一致性行为的避障控制器,并进行了稳定性分析。考虑群体机器人系统中个体数量众多的优势,提出了一种基于改进传统人工势场法的群体机器人避障控制算法,并利用群体中虚拟领导者的引导作用使群体在感知到障碍物后,能够实现对障碍物的安全避碰,并同时完成协同一致任务。理论分析和仿真结果表明该算法克服了传统人工势场法中容易出现死锁现象的缺陷。
3)解决了在不破坏群体机器人系统局部交互规则的情况下群体速度的可控问题。利用“软控制”思想在群体中引入可控智能体,通过对可控智能体施加控制来实现整个群体的速度可控,对具有恒定期望速度的群体自治系统和具有时变期望速度的群体非自治系统,分别利用LaSalle不变性原理和Barbalat引理从群体速度可控性、群体结构稳定性以及群体收敛快速性的角度证明所设计控制器的有效性。
4)针对群体自主机器人系统一致性控制的综合性能优化问题进行了分析和研究。以群体速度误差、群体结构误差和通信量的优化为目标,以群体速度收敛时间最短为约束条件,利用粒子群优化算法得出了群体的最佳通信频率和通信半径,从而提高了群体系统可控状态的准确性、速度收敛的快速性以及通信成本的经济性。
综上所述,本文就群体自主机器人系统的一致性行为进行了一系列的理论研究,主要目的是实现群体系统的适应性、可控性和优化性,并通过仿真实验进行了相应的验证与分析。
For significant advantages on the robustness, adaptability, extendibility and economy of the swarm robots system, it has been an active research in the robot area in resent years. In this thesis, the main research work is the adaptability to the complex environment of swarm robots system, the controllability of swarm velocity and the optimization of system performance, which is based on the flocking control of swarm robots system. This work is supported by the National Nature Science Fund Project and Graduate Innovative Project. The main work in this paper is as follows:
Firstly, the distributed control strategy is designed to make the flocking behavior of swarm robots system adapt to nonlinear environment. And the nonlinear environment is described by a given potential function which is assumed to have finite bounded slopes. And based on the local information interaction distributed control algorithm is presented by using the idea of virtual force and nearest neighborhood law, which can realize the swarm flocking behavior in the nonlinear environment, and the finish time of flocking can be estimated. Simulation results are included to verify the distributed controller, and also show the adaptability and extendibility of swarm system.
Secondly, the controller is designed for swarm robot system in the environment with unknown obstacles and the stability of system is proved. The traditional artificial potential field method is improved to achieve obstacle avoidance based on the number advantage of the swarm. After perceiving obstacles the swarm can achieve safe avoidance with the obstacles and then finish flocking task by using the heading effect of virtual leader in swarm. To validate the proposed algorithm, the theory analysis and experimental simulation are performed. And the results show that the algorithm can make swarm avoid obstacles effectively, and overcome the defect that traditional artificial potential field method easy to deadlock.
Then, the velocity controllability problem of swarm flocking is solved without breaking the local interaction rules of swarm robots system. Controllable agents (one or more) are introduced to the swarm based on the idea of "soft control", and the velocity controllability of the swarm is realized through controlling the controllable agents. For the swarm autonomous system with constant expected speed and the swarm non-autonomous system with time-varying expected velocity, LaSalle invariance principle and Barbalat Lemma is adopted in analysis of system stability, so that we proof speed vector of all robots can converge to the desired value, the swarm will form a stable structure, and the more controllable agents are introduced, the faster the swarm convergence. So the results show that the designed control strategy is effective.
Finally, the synthesis performance optimization problem of consistency control for groups of autonomous robots system is analyzed and studied. Make the velocity error of swarm, the structure error of swarm and the traffic as optimization goal, and treat the minimum convergence time of swarm velocity as constraint, particle swarm optimization algorithm is used to obtain the best communication frequency and communication radius of swarm, in order to improve the accuracy of controlled state, the speed of swarm convergence, and the economy of communication costs.
In summary, a series of theoretical studies about the flocking behavior of swarm robots system are conducted in this thesis. The main purpose of this work is to realize the robustness, adaptability and extendibility of swarm flocking system. And then, Simulation experiments are performed for the purpose of related verification and analysis.
1)设计了一种分布式协同控制策略来实现群体一致性行为对非线性环境的适应。利用具备有界梯度的特定势能函数对外部非线性环境信息进行描述,结合虚拟力和最近邻居原则的思想设计了基于局部信息交互的分布式协同控制策略,实现非线性环境下的群体一致性行为,并对群体收敛时间进行了估计。仿真结果表明了该控制策略的有效性和可行性,同时也体现出了群体系统的适应性和可扩展性。
2)针对障碍物环境设计了群体一致性行为的避障控制器,并进行了稳定性分析。考虑群体机器人系统中个体数量众多的优势,提出了一种基于改进传统人工势场法的群体机器人避障控制算法,并利用群体中虚拟领导者的引导作用使群体在感知到障碍物后,能够实现对障碍物的安全避碰,并同时完成协同一致任务。理论分析和仿真结果表明该算法克服了传统人工势场法中容易出现死锁现象的缺陷。
3)解决了在不破坏群体机器人系统局部交互规则的情况下群体速度的可控问题。利用“软控制”思想在群体中引入可控智能体,通过对可控智能体施加控制来实现整个群体的速度可控,对具有恒定期望速度的群体自治系统和具有时变期望速度的群体非自治系统,分别利用LaSalle不变性原理和Barbalat引理从群体速度可控性、群体结构稳定性以及群体收敛快速性的角度证明所设计控制器的有效性。
4)针对群体自主机器人系统一致性控制的综合性能优化问题进行了分析和研究。以群体速度误差、群体结构误差和通信量的优化为目标,以群体速度收敛时间最短为约束条件,利用粒子群优化算法得出了群体的最佳通信频率和通信半径,从而提高了群体系统可控状态的准确性、速度收敛的快速性以及通信成本的经济性。
综上所述,本文就群体自主机器人系统的一致性行为进行了一系列的理论研究,主要目的是实现群体系统的适应性、可控性和优化性,并通过仿真实验进行了相应的验证与分析。
For significant advantages on the robustness, adaptability, extendibility and economy of the swarm robots system, it has been an active research in the robot area in resent years. In this thesis, the main research work is the adaptability to the complex environment of swarm robots system, the controllability of swarm velocity and the optimization of system performance, which is based on the flocking control of swarm robots system. This work is supported by the National Nature Science Fund Project and Graduate Innovative Project. The main work in this paper is as follows:
Firstly, the distributed control strategy is designed to make the flocking behavior of swarm robots system adapt to nonlinear environment. And the nonlinear environment is described by a given potential function which is assumed to have finite bounded slopes. And based on the local information interaction distributed control algorithm is presented by using the idea of virtual force and nearest neighborhood law, which can realize the swarm flocking behavior in the nonlinear environment, and the finish time of flocking can be estimated. Simulation results are included to verify the distributed controller, and also show the adaptability and extendibility of swarm system.
Secondly, the controller is designed for swarm robot system in the environment with unknown obstacles and the stability of system is proved. The traditional artificial potential field method is improved to achieve obstacle avoidance based on the number advantage of the swarm. After perceiving obstacles the swarm can achieve safe avoidance with the obstacles and then finish flocking task by using the heading effect of virtual leader in swarm. To validate the proposed algorithm, the theory analysis and experimental simulation are performed. And the results show that the algorithm can make swarm avoid obstacles effectively, and overcome the defect that traditional artificial potential field method easy to deadlock.
Then, the velocity controllability problem of swarm flocking is solved without breaking the local interaction rules of swarm robots system. Controllable agents (one or more) are introduced to the swarm based on the idea of "soft control", and the velocity controllability of the swarm is realized through controlling the controllable agents. For the swarm autonomous system with constant expected speed and the swarm non-autonomous system with time-varying expected velocity, LaSalle invariance principle and Barbalat Lemma is adopted in analysis of system stability, so that we proof speed vector of all robots can converge to the desired value, the swarm will form a stable structure, and the more controllable agents are introduced, the faster the swarm convergence. So the results show that the designed control strategy is effective.
Finally, the synthesis performance optimization problem of consistency control for groups of autonomous robots system is analyzed and studied. Make the velocity error of swarm, the structure error of swarm and the traffic as optimization goal, and treat the minimum convergence time of swarm velocity as constraint, particle swarm optimization algorithm is used to obtain the best communication frequency and communication radius of swarm, in order to improve the accuracy of controlled state, the speed of swarm convergence, and the economy of communication costs.
In summary, a series of theoretical studies about the flocking behavior of swarm robots system are conducted in this thesis. The main purpose of this work is to realize the robustness, adaptability and extendibility of swarm flocking system. And then, Simulation experiments are performed for the purpose of related verification and analysis.
引文
[1]Dorigo M, Sahin E. Special Issue:Swarm Robotics [J]. Autonomous Robots.2004.17: 111-113.
[2]Bayindir L, Sahin E. A Review of Studies in Swarm Robotics [J]. Turkish Journal of Electrical Engineering and Computer Sciences,2007,15(2):115-147.
[3]Bonabeau E, Dorigo M, Theraulaz G. Swarm Intelligence:From Natural to Artificial Systems [M]. USA:Oxford University Press,1999.
[4]C. W. Reynolds, Flocks, birds, and schools:a distributed behavioral model[C]. Proc. Of ACM Computer Graphics (SIGGRAPH'87). New York, USA, July 1987,21(4):25-34.
[5]Vicsek T, Czirook A, Ben-Jacob E, Cohen I, and Shochet O. Novel type of phase transition in a system of self-driven particles [J]. Physical Review Letter,1995,75(6): 1226-1229.
[6]Jadbabaie A, Lin J, and Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules [J]. IEEE Transactions Automatic Control,2003, 48(6):988-1001.
[7]Olfati-Saber R and Murray R M. Consensus problems in networks of agents with switching topology and time-delays [J]. IEEE Transactions Automatic Control,2004, 49(9):1520-1533.
[8]Fax J A. Optimal and cooperative control of vehicle formations [D]. Pasadena, CA: Control Dynamical System, California Institute of Technology,2001.
[9]Fax J A and Murray R M. Information flow and cooperative control of vehicle formations [J]. IEEE Transactions Automatic Control,2004,49(9):1465-1476.
[10]Moreau L. Stability of continuous-time distributed consensus algorithms[C]. Proc. of the 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, 2004:3998-4003.
[11]Moreau L. Stability of multi-agent systems with time-dependent communication links [J]. IEEE Transactions Automatic Control,2005,50(2):169-182.
[12]Cortes J. Distributed algorithms for reaching consensus on general functions [J]. Automatic,2008,44(3):726-737.
[13]Ren W and Beard R W. Consensus seeking in multi-agent systems under dynamically changing interaction topologies[J], IEEE Transactions Automatic Control,2005,50(5): 655-661.
[14]Ren W. Multi-vehicle consensus with a time-varying reference state [J]. Systems and Control Letters,2007,56(7-8):474-483.
[15]Ren W. On consensus algorithms for double-integrator dynamics [J]. IEEE Transactions on Automatic Control,2008,53(6):1503-1509.
[16]Ren W, Beard R W, Atkins E M. Information consensus in multi vehicle cooperative control:Collective group behavior through local interaction [J]. IEEE Control Systems Magazine,2007,27(2):71-82.
[17]Kinfston D B and Ren W. Consensus algorithms are input-to-state stable[C]. Proceedings of the American Control Conference, Portland, June 2005,3:1686-1690.
[18]Ren W and E.M. Atkins. Distributed multi-vehicle coordinated control via local information exchange [J]. International Journal of Robust and Nonlinear Control,2007, 17(10):1002-1033.
[19]Ren W, Kevin L. Moore, and Yang Quan Chen. High-Order and Model Reference Consensus Algorithms in Cooperative Control of Multi-Vehicle Systems [J]. ASME Journal of Dynamic Systems, Measurement, and Control,2007,129(5):678-688.
[20]Ren W and Beard R W. Multi-agent Kalman consensus with relative uncertainty[C]. Proceedings of American Control Conference, June Portland,2005,3:1865-1870.
[21]刘志新,郭雷.Vicsek模型的连通与同步[J].中国科学E辑：信息科学,2007,37(8)：979-988.
[22]唐共国,郭雷.线性化Vicsek模型的同步性分析[C].第25届中国控制会议论文集,哈尔滨,2006：379-382.
[23]Zhixin Liu, Lei Guo. Synchronization of Vicsek Model with Large Population[C]. Proceedings of the 26th Chinese Control Conference, Zhangjiajie,2007:673-677.
[24]Lin Wang, Zhixin Liu, and Lei Guo. Robust Consensus of Multi-agent Systems with Noise[C]. Proceedings of the 26th Chinese Control Conference, Zhangjiajie,2007: 737-741.
[25]刘成林,田玉平.具有不同通信时延的多个体系统的一致性[J].东南大学学报(自然科学版),2008,38(1)：170-174.
[26]Tian Yu-Ping, Liu Cheng-Lin. Consensus of multi-agent systems with diverse input and communication delays [J]. IEEE Transaction on Automatic and Control,2008,53: 2122-2128.
[27]Tian Yu-Ping, Liu Cheng-Lin. Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations [J]. Automatic,2009,45(5): 1347-1353.
[28]Fangcui Jiang and Long Wang. Finite-time Information Consensus for Multi-agent Systems with Fixed and Switching Topologies [J]. Physica D,2009,238:1550-1560.
[29]Feng Xiao and Long Wang. Asynchronous Consensus in Continuous-Time Multi-agent Systems with Switching Topology and Time-varying Delays [J]. IEEE Transaction on Automatic and Control,2008,53(8):1804-1816.
[30]Yuan Gong Sun and Long Wang. Consensus of Multi-agent Systems in Directed Networks with Nonuniform Time-Varying Delays [J]. IEEE Transaction on Automatic and Control,2009,54(7):1607-1613.
[31]Guangming Xie, Huiyang Liu, Long Wang and Yingmin Jia. Consensus in Networked Multi-agent Systems via Sampled Control:Switching Topology Case [C]. Proceedings of the American Control Conference. St. Louis, MO, USA,2009:4525-4530.
[32]Fangcui Jiang, Long Wang and Yingmin Jia. Consensus in Leaderless Networks of High-Order-Integrator agents [C]. Proceedings of the American Control Conference. St. Louis, MO, USA,2009:4458-4463.
[33]Zonggang Li, Yingmin Jia, Junping Du, and Shiying Yuan, Flocking for Multi-agent Systems with Switching Topology in a Noisy Environment [C]. Proceedings of the American Control Conference. Seattle, Washington, USA,2008:111-116.
[34]Peng Lin, Yingmin Jia, Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies[J], Automatica, 2009,45:2154-2158.
[35]Yang Liu, Yingmin Jia, Junping Du and Shiying Yuan. Dynamic Output Feedback Control for Consensus of Multi-agent Systems:An H∞ Approach[C]. Proceedings of the American Control Conference,2009:4470-4475.
[36]Couzin I D, Krause J, Franks N R, Levin S A. Effective leadership and decision making in animal groups on the move. Nature.2005,433(7025):513-516.
[37]R.Olfati-Saber. Flocking for Multi-agent Dynamic Systems:Algorithms and Theory [J]. IEEE Transactions on Automation and Control,2006,51(3):401-420.
[38]Huosheng Su, Xiao fan Wang, and Zongli Lin. Flocking of Multi-Agent with a Virtual Leader [J]. IEEE Transactions on Automation and Control,2009,54(2):293-306.
[39]Dongbing Gu, Zongyao Wang. Leader-Follower Flocking:Algorithms and Experiments [J]. IEEE Transactions on Control Systems Technology,2009,17(5):1211-1219.
[40]Zongyao Wang, Dongbing Gu. Distributed Leader-Follower Flocking Control [J]. Asian Journal of Control,2009,11(4):396-406.
[41]Dongbing Gu, Huosheng Hu. Using Fuzzy Logic to Design Separation Function in Flocking Algorithms [J]. IEEE Transactions on Fuzzy System,2008,16(4):826-838.
[42]Wenwu Yu, Guanrong Chen, Ming Cao. Distributed Leader-Follower Flocking Control for Multi-Agent Dynamical Systems with Time-Varying Velocities [J]. Systems & Control Letters,2010,59:543-552.
[43]Hong Shi, Long Wang, Tianguang Chu and Minjie Xu. Flocking Control of Multiple Interactive Dynamic Agents with Switching Topology via Local Feedback [J]. Lecture Notes in Computer Science,2005,3630:604-613.
[44]Jing Han, Ming Li and Lei Guo. Soft Control on Collective Behavior of a Group of Autonomous agent y a Shill agent [J]. Journal of Systems Science and Complexity 2006, 19(1):54-62.
[45]万文军.优化算法及火电厂若干优化问题的研究[D].南京：东南大学博士论文,2005.
[46]Doctor S, Venayagamoorthy G and Gudise V. Optimal PSO for Collective Robotic Search Applications[C]. Proceedings of the IEEE Congress on Evolutionary Computation. Portland,2004:1390-1395.
[47]Pugh J, Martinoli A. Distributed Adaptation in Multi-robot Search Using Particle Swarm Optimization [J]. Lecture Notes in Computer Science,2008,5040:393-403.
[48]Pugh J, Martinoli A, Zhang Y. Particle Swarm Optimization for Unsupervised Robotic Learning[C]. Proceedings of the 2005 IEEE Swarm Intelligence Symposium. Pasadena, 2005:92-99.
[49]James M. Hereford. A Distributed Particle Swarm Optimization Algorithm for Swarm Robotic Applications [C]. Proc. of the IEEE Congress on Evolutionary Computation S. Vancouver,2006:1678-1685.
[50]王冬梅.群集运动控制及其相关特性的研究[D].武汉：华中科技大学博士学位论文,2009.
[51]雷斌.群体机器人系统合作控制问题研究[D].武汉：武汉理工大学博士学位论文,2009.
[52]杨永明.群体机器人系统协同行为研究[D].长春：吉林大学博士学位论文,2009.
[53]杨茂.群体机器人系统分布式协同控制方法与协同行为分析[D].长春,吉林大学博士学位论文,2010.
[54]刘宗春.群体机器人系统协同一致行为控制算法设计与仿真研究[D].长春,吉林大学硕士学位论文,2011.
[55]蓝艇,刘士荣.受生物群体智能启发的多机器人系统研究[J].机器人,2007,29(3)：298-304.
[56]楚天广,杨正东,邓魁英,王龙等.群体动力学与协同控制研究中的若干问题[J]控制理论与应用,2010,27(1)：86-93.
[57]H. G. Tanner, A. Jadbabaie, G. J. Pappas. Stable flocking of mobile agents-Part I:fixed topology [C]. Proceedings of the 42nd IEEE Conference on Decision and Control. Piscataway,2003:2010-2015.
[58]H. G. Tanner, A. Jadbabaie, G. J. Pappas. Stable flocking of mobile agents-Part II: dynamic topology [C]. Proceedings of the 42nd IEEE Conference on Decision and Control. Piscataway,2003:2016-2021.
[59]V. Gazi and K. M. Passino. A class of attraction/repulsion functions for stable swarm aggregations [C], Proc. of Conference on Decision Control, Los Vegas, NV, Dec 2002: 2842-2847.
[60]V. Gazi and K. M. Passino. Stability analysis of swarms in an environment with an attractant/repellent profile [C]. Proc. of the American Control Conference, Anchorage, AK, May 2002:1819-1824.
[61]V. Gazi and K. M. Passino. Stability analysis of social foraging swarms:combined effects of attractant/repellent profiles [C]. Proceedings of Conference on Decision Control, Las Vegas, NV, Dec 2002:114-123.
[62]V. Gazi and K. M. Passino. Stability analysis of social foraging swarm [J], IEEE Trans. on Systems, Man and Cybernetics-Part B:Cybernetics, Feb 2004,34(1):539-557.
[63]Dan Jin, Lixin Gao. Stability analysis of a double integrator swarm model related to position and velocity [J].Transactions of the Institute of Measurement and Control 2008. 30(3-4):275-293.
[64]Xiaohai Li, Jizong Xiao. Stable Flocking of Swarms Using Local Information [C]. Proceedings of Conference on Systems, Man and Cybernetics, Oct.2005,4:3921-3926.
[65]Reza Olfati-Saber, Richard M. Murray. Flocking with Obstacle Avoidance: Cooperation with Limited Communication in Mobile Networks[C]. Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii USA, December 2003:2022-2028.
[66]Herbert G. Tanner. Flocking with Obstacle Avoidance in Switching Networks of Interconnected Vehicles[C]. Proceedings of the 2004 IEEE International Conference on Robotics & Automation, New Orleans, LA,2004:3006-3011.
[67]王冬梅,方华京.全局未知环境下智能群体集群运动与避障控制[J].系统工程与电子技术,2008,30(9)：1744-1747.
[68]俞辉.多智能体机器人协调控制研究及稳定性分析[D].武汉：华中科技大学博士论文,2007.
[69]HONG Yiguang, HU Jiangping, GAO Linxin. Tracking control for multi-agent consensus with an active leader and variable topology [J]. Automatica 2006,42: 1177-1182.
[2]Bayindir L, Sahin E. A Review of Studies in Swarm Robotics [J]. Turkish Journal of Electrical Engineering and Computer Sciences,2007,15(2):115-147.
[3]Bonabeau E, Dorigo M, Theraulaz G. Swarm Intelligence:From Natural to Artificial Systems [M]. USA:Oxford University Press,1999.
[4]C. W. Reynolds, Flocks, birds, and schools:a distributed behavioral model[C]. Proc. Of ACM Computer Graphics (SIGGRAPH'87). New York, USA, July 1987,21(4):25-34.
[5]Vicsek T, Czirook A, Ben-Jacob E, Cohen I, and Shochet O. Novel type of phase transition in a system of self-driven particles [J]. Physical Review Letter,1995,75(6): 1226-1229.
[6]Jadbabaie A, Lin J, and Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules [J]. IEEE Transactions Automatic Control,2003, 48(6):988-1001.
[7]Olfati-Saber R and Murray R M. Consensus problems in networks of agents with switching topology and time-delays [J]. IEEE Transactions Automatic Control,2004, 49(9):1520-1533.
[8]Fax J A. Optimal and cooperative control of vehicle formations [D]. Pasadena, CA: Control Dynamical System, California Institute of Technology,2001.
[9]Fax J A and Murray R M. Information flow and cooperative control of vehicle formations [J]. IEEE Transactions Automatic Control,2004,49(9):1465-1476.
[10]Moreau L. Stability of continuous-time distributed consensus algorithms[C]. Proc. of the 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, 2004:3998-4003.
[11]Moreau L. Stability of multi-agent systems with time-dependent communication links [J]. IEEE Transactions Automatic Control,2005,50(2):169-182.
[12]Cortes J. Distributed algorithms for reaching consensus on general functions [J]. Automatic,2008,44(3):726-737.
[13]Ren W and Beard R W. Consensus seeking in multi-agent systems under dynamically changing interaction topologies[J], IEEE Transactions Automatic Control,2005,50(5): 655-661.
[14]Ren W. Multi-vehicle consensus with a time-varying reference state [J]. Systems and Control Letters,2007,56(7-8):474-483.
[15]Ren W. On consensus algorithms for double-integrator dynamics [J]. IEEE Transactions on Automatic Control,2008,53(6):1503-1509.
[16]Ren W, Beard R W, Atkins E M. Information consensus in multi vehicle cooperative control:Collective group behavior through local interaction [J]. IEEE Control Systems Magazine,2007,27(2):71-82.
[17]Kinfston D B and Ren W. Consensus algorithms are input-to-state stable[C]. Proceedings of the American Control Conference, Portland, June 2005,3:1686-1690.
[18]Ren W and E.M. Atkins. Distributed multi-vehicle coordinated control via local information exchange [J]. International Journal of Robust and Nonlinear Control,2007, 17(10):1002-1033.
[19]Ren W, Kevin L. Moore, and Yang Quan Chen. High-Order and Model Reference Consensus Algorithms in Cooperative Control of Multi-Vehicle Systems [J]. ASME Journal of Dynamic Systems, Measurement, and Control,2007,129(5):678-688.
[20]Ren W and Beard R W. Multi-agent Kalman consensus with relative uncertainty[C]. Proceedings of American Control Conference, June Portland,2005,3:1865-1870.
[21]刘志新,郭雷.Vicsek模型的连通与同步[J].中国科学E辑：信息科学,2007,37(8)：979-988.
[22]唐共国,郭雷.线性化Vicsek模型的同步性分析[C].第25届中国控制会议论文集,哈尔滨,2006：379-382.
[23]Zhixin Liu, Lei Guo. Synchronization of Vicsek Model with Large Population[C]. Proceedings of the 26th Chinese Control Conference, Zhangjiajie,2007:673-677.
[24]Lin Wang, Zhixin Liu, and Lei Guo. Robust Consensus of Multi-agent Systems with Noise[C]. Proceedings of the 26th Chinese Control Conference, Zhangjiajie,2007: 737-741.
[25]刘成林,田玉平.具有不同通信时延的多个体系统的一致性[J].东南大学学报(自然科学版),2008,38(1)：170-174.
[26]Tian Yu-Ping, Liu Cheng-Lin. Consensus of multi-agent systems with diverse input and communication delays [J]. IEEE Transaction on Automatic and Control,2008,53: 2122-2128.
[27]Tian Yu-Ping, Liu Cheng-Lin. Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations [J]. Automatic,2009,45(5): 1347-1353.
[28]Fangcui Jiang and Long Wang. Finite-time Information Consensus for Multi-agent Systems with Fixed and Switching Topologies [J]. Physica D,2009,238:1550-1560.
[29]Feng Xiao and Long Wang. Asynchronous Consensus in Continuous-Time Multi-agent Systems with Switching Topology and Time-varying Delays [J]. IEEE Transaction on Automatic and Control,2008,53(8):1804-1816.
[30]Yuan Gong Sun and Long Wang. Consensus of Multi-agent Systems in Directed Networks with Nonuniform Time-Varying Delays [J]. IEEE Transaction on Automatic and Control,2009,54(7):1607-1613.
[31]Guangming Xie, Huiyang Liu, Long Wang and Yingmin Jia. Consensus in Networked Multi-agent Systems via Sampled Control:Switching Topology Case [C]. Proceedings of the American Control Conference. St. Louis, MO, USA,2009:4525-4530.
[32]Fangcui Jiang, Long Wang and Yingmin Jia. Consensus in Leaderless Networks of High-Order-Integrator agents [C]. Proceedings of the American Control Conference. St. Louis, MO, USA,2009:4458-4463.
[33]Zonggang Li, Yingmin Jia, Junping Du, and Shiying Yuan, Flocking for Multi-agent Systems with Switching Topology in a Noisy Environment [C]. Proceedings of the American Control Conference. Seattle, Washington, USA,2008:111-116.
[34]Peng Lin, Yingmin Jia, Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies[J], Automatica, 2009,45:2154-2158.
[35]Yang Liu, Yingmin Jia, Junping Du and Shiying Yuan. Dynamic Output Feedback Control for Consensus of Multi-agent Systems:An H∞ Approach[C]. Proceedings of the American Control Conference,2009:4470-4475.
[36]Couzin I D, Krause J, Franks N R, Levin S A. Effective leadership and decision making in animal groups on the move. Nature.2005,433(7025):513-516.
[37]R.Olfati-Saber. Flocking for Multi-agent Dynamic Systems:Algorithms and Theory [J]. IEEE Transactions on Automation and Control,2006,51(3):401-420.
[38]Huosheng Su, Xiao fan Wang, and Zongli Lin. Flocking of Multi-Agent with a Virtual Leader [J]. IEEE Transactions on Automation and Control,2009,54(2):293-306.
[39]Dongbing Gu, Zongyao Wang. Leader-Follower Flocking:Algorithms and Experiments [J]. IEEE Transactions on Control Systems Technology,2009,17(5):1211-1219.
[40]Zongyao Wang, Dongbing Gu. Distributed Leader-Follower Flocking Control [J]. Asian Journal of Control,2009,11(4):396-406.
[41]Dongbing Gu, Huosheng Hu. Using Fuzzy Logic to Design Separation Function in Flocking Algorithms [J]. IEEE Transactions on Fuzzy System,2008,16(4):826-838.
[42]Wenwu Yu, Guanrong Chen, Ming Cao. Distributed Leader-Follower Flocking Control for Multi-Agent Dynamical Systems with Time-Varying Velocities [J]. Systems & Control Letters,2010,59:543-552.
[43]Hong Shi, Long Wang, Tianguang Chu and Minjie Xu. Flocking Control of Multiple Interactive Dynamic Agents with Switching Topology via Local Feedback [J]. Lecture Notes in Computer Science,2005,3630:604-613.
[44]Jing Han, Ming Li and Lei Guo. Soft Control on Collective Behavior of a Group of Autonomous agent y a Shill agent [J]. Journal of Systems Science and Complexity 2006, 19(1):54-62.
[45]万文军.优化算法及火电厂若干优化问题的研究[D].南京：东南大学博士论文,2005.
[46]Doctor S, Venayagamoorthy G and Gudise V. Optimal PSO for Collective Robotic Search Applications[C]. Proceedings of the IEEE Congress on Evolutionary Computation. Portland,2004:1390-1395.
[47]Pugh J, Martinoli A. Distributed Adaptation in Multi-robot Search Using Particle Swarm Optimization [J]. Lecture Notes in Computer Science,2008,5040:393-403.
[48]Pugh J, Martinoli A, Zhang Y. Particle Swarm Optimization for Unsupervised Robotic Learning[C]. Proceedings of the 2005 IEEE Swarm Intelligence Symposium. Pasadena, 2005:92-99.
[49]James M. Hereford. A Distributed Particle Swarm Optimization Algorithm for Swarm Robotic Applications [C]. Proc. of the IEEE Congress on Evolutionary Computation S. Vancouver,2006:1678-1685.
[50]王冬梅.群集运动控制及其相关特性的研究[D].武汉：华中科技大学博士学位论文,2009.
[51]雷斌.群体机器人系统合作控制问题研究[D].武汉：武汉理工大学博士学位论文,2009.
[52]杨永明.群体机器人系统协同行为研究[D].长春：吉林大学博士学位论文,2009.
[53]杨茂.群体机器人系统分布式协同控制方法与协同行为分析[D].长春,吉林大学博士学位论文,2010.
[54]刘宗春.群体机器人系统协同一致行为控制算法设计与仿真研究[D].长春,吉林大学硕士学位论文,2011.
[55]蓝艇,刘士荣.受生物群体智能启发的多机器人系统研究[J].机器人,2007,29(3)：298-304.
[56]楚天广,杨正东,邓魁英,王龙等.群体动力学与协同控制研究中的若干问题[J]控制理论与应用,2010,27(1)：86-93.
[57]H. G. Tanner, A. Jadbabaie, G. J. Pappas. Stable flocking of mobile agents-Part I:fixed topology [C]. Proceedings of the 42nd IEEE Conference on Decision and Control. Piscataway,2003:2010-2015.
[58]H. G. Tanner, A. Jadbabaie, G. J. Pappas. Stable flocking of mobile agents-Part II: dynamic topology [C]. Proceedings of the 42nd IEEE Conference on Decision and Control. Piscataway,2003:2016-2021.
[59]V. Gazi and K. M. Passino. A class of attraction/repulsion functions for stable swarm aggregations [C], Proc. of Conference on Decision Control, Los Vegas, NV, Dec 2002: 2842-2847.
[60]V. Gazi and K. M. Passino. Stability analysis of swarms in an environment with an attractant/repellent profile [C]. Proc. of the American Control Conference, Anchorage, AK, May 2002:1819-1824.
[61]V. Gazi and K. M. Passino. Stability analysis of social foraging swarms:combined effects of attractant/repellent profiles [C]. Proceedings of Conference on Decision Control, Las Vegas, NV, Dec 2002:114-123.
[62]V. Gazi and K. M. Passino. Stability analysis of social foraging swarm [J], IEEE Trans. on Systems, Man and Cybernetics-Part B:Cybernetics, Feb 2004,34(1):539-557.
[63]Dan Jin, Lixin Gao. Stability analysis of a double integrator swarm model related to position and velocity [J].Transactions of the Institute of Measurement and Control 2008. 30(3-4):275-293.
[64]Xiaohai Li, Jizong Xiao. Stable Flocking of Swarms Using Local Information [C]. Proceedings of Conference on Systems, Man and Cybernetics, Oct.2005,4:3921-3926.
[65]Reza Olfati-Saber, Richard M. Murray. Flocking with Obstacle Avoidance: Cooperation with Limited Communication in Mobile Networks[C]. Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii USA, December 2003:2022-2028.
[66]Herbert G. Tanner. Flocking with Obstacle Avoidance in Switching Networks of Interconnected Vehicles[C]. Proceedings of the 2004 IEEE International Conference on Robotics & Automation, New Orleans, LA,2004:3006-3011.
[67]王冬梅,方华京.全局未知环境下智能群体集群运动与避障控制[J].系统工程与电子技术,2008,30(9)：1744-1747.
[68]俞辉.多智能体机器人协调控制研究及稳定性分析[D].武汉：华中科技大学博士论文,2007.
[69]HONG Yiguang, HU Jiangping, GAO Linxin. Tracking control for multi-agent consensus with an active leader and variable topology [J]. Automatica 2006,42: 1177-1182.