基于一致性理论的航天器编队协同控制方法研究
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摘要
航天器编队系统通过多航天器协同工作以完成诸多单一航天器难以完成的空间任务,近十年来备受国际航天领域的广泛关注。编队协同控制是实现航天器编队飞行的关键技术之一,也是航天领域研究的热点与难点,尚没有完善成熟的解决方案。本文利用代数图论这一形式化数学工具,研究了基于变权无向图的二阶一致性算法,并将其应用于航天器编队初始化防碰撞协同控制和相对方位约束下的航天器编队姿态同步协同控制等问题,取得了以下创新研究成果:
为了提高基于加权无向图一致性算法的分布式协同控制系统的性能,针对二阶多智能体系统,提出了一类与状态变量相关加权一致性(SBWC: State-Based Weighted Consensus)算法,通过对其进行渐近一致性分析给出了此类状态相关变权系数的选取条件。分别针对无Leader和一个固定Leader这两种编队情况,基于人工势场法给出了与位置矢量相关的无向图加权策略,进而给出了相应的二阶一致性算法,同时基于LaSalle不变集原理证明了该算法的渐近一致性,并通过数值仿真验证了该算法的一致性。
针对航天器编队初始化协同控制任务,给出了基于匈牙利算法的顶层任务分配策略和基于SBWC的底层分布式协同控制策略相结合的分散式递阶控制结构。针对底层分布式协同控制,构造了与航天器相对位置矢量反相关的人工势函数,在此基础上给出了基于SBWC的航天器编队初始化协同控制算法,有效地解决了编队初始化过程中的碰撞问题。这也解决了多固定Leader下编队的一致性协同控制问题。最后,通过理论证明了该算法的渐近稳定性,通过数学仿真验证了该算法在编队构型初始化过程中的防碰撞性能。
针对基于激光或视觉等相对状态测量敏感器具有相对方位约束要求的问题,为了确保航天器编队姿态同步过程中相对方位满足该约束条件,构造了与航天器相对姿态正相关的人工势函数,给出了相对方位约束下的航天器编队姿态同步协同控制算法,基于LaSalle不变集原理证明了该算法的渐近稳定性,并通过数学仿真验证了其性能。
The spacecraft formation system which could enable large numbers of uncomplicated and inexpensive spacecrafts to work cooperatively to accomplish complex aerospace missions which a giant one even can’t has gotten the international aerospace academics’interest in resent decade. The most pivotal and difficult technology to achieve the spacecraft formation is the cooperative control on which there isn’t successful experience. A kind of state-based variable-weighted consensus algorithms whose weights could be designed for some specific purposes has been proposed in this dissertation by undirected graphs. This paper accomplished two aerospace missions considering collision avoidance during spacecraft formation initialization and limited opposite directions during synchronizing attitudes utilizing the consensus algorithms. The innovations this paper make are following.
A kind of stated-based weighted consensus (SBWC) algorithms has been proposed to improve the performance of the steady-weighted consensus algorithms for double-integrator dynamics systems. The demands of the weights have been given through the analysis of the system consensus. For a fixed Leader case and a Leaderless case, the double-integrator consensus algorithms have been proposed utilizing the artificial potential functions. The consensus has been proved by LaSalle’s Invariance principle. The simulation results are provided to demonstrate the algorithms’performance.
A distributed hierarchical control structure constituting of Hungarian algorithm based task assignment and SBWC based cooperative control for spacecrafts initialization has been proposed. A kind of artificial potential function anti-interrelated with spacecrafts’relative positions has been constructed. Then a SBWC based cooperative control law has been proposed to avoid the collision during spacecrafts initialization. Finally the collision avoidance mechanism has been demonstrated by simulation results.
There are constraint conditions of relative orientation in laser/vision based relative states measurement systems. To satisfy the constraint during spacecrafts attitudes synchronization, a SBWC based cooperative control law has been proposed and the weights interrelated with relative attitudes have been given. This law has been proved by LaSalle’Invariance principle and demonstrated by simulation results.
为了提高基于加权无向图一致性算法的分布式协同控制系统的性能,针对二阶多智能体系统,提出了一类与状态变量相关加权一致性(SBWC: State-Based Weighted Consensus)算法,通过对其进行渐近一致性分析给出了此类状态相关变权系数的选取条件。分别针对无Leader和一个固定Leader这两种编队情况,基于人工势场法给出了与位置矢量相关的无向图加权策略,进而给出了相应的二阶一致性算法,同时基于LaSalle不变集原理证明了该算法的渐近一致性,并通过数值仿真验证了该算法的一致性。
针对航天器编队初始化协同控制任务,给出了基于匈牙利算法的顶层任务分配策略和基于SBWC的底层分布式协同控制策略相结合的分散式递阶控制结构。针对底层分布式协同控制,构造了与航天器相对位置矢量反相关的人工势函数,在此基础上给出了基于SBWC的航天器编队初始化协同控制算法,有效地解决了编队初始化过程中的碰撞问题。这也解决了多固定Leader下编队的一致性协同控制问题。最后,通过理论证明了该算法的渐近稳定性,通过数学仿真验证了该算法在编队构型初始化过程中的防碰撞性能。
针对基于激光或视觉等相对状态测量敏感器具有相对方位约束要求的问题,为了确保航天器编队姿态同步过程中相对方位满足该约束条件,构造了与航天器相对姿态正相关的人工势函数,给出了相对方位约束下的航天器编队姿态同步协同控制算法,基于LaSalle不变集原理证明了该算法的渐近稳定性,并通过数学仿真验证了其性能。
The spacecraft formation system which could enable large numbers of uncomplicated and inexpensive spacecrafts to work cooperatively to accomplish complex aerospace missions which a giant one even can’t has gotten the international aerospace academics’interest in resent decade. The most pivotal and difficult technology to achieve the spacecraft formation is the cooperative control on which there isn’t successful experience. A kind of state-based variable-weighted consensus algorithms whose weights could be designed for some specific purposes has been proposed in this dissertation by undirected graphs. This paper accomplished two aerospace missions considering collision avoidance during spacecraft formation initialization and limited opposite directions during synchronizing attitudes utilizing the consensus algorithms. The innovations this paper make are following.
A kind of stated-based weighted consensus (SBWC) algorithms has been proposed to improve the performance of the steady-weighted consensus algorithms for double-integrator dynamics systems. The demands of the weights have been given through the analysis of the system consensus. For a fixed Leader case and a Leaderless case, the double-integrator consensus algorithms have been proposed utilizing the artificial potential functions. The consensus has been proved by LaSalle’s Invariance principle. The simulation results are provided to demonstrate the algorithms’performance.
A distributed hierarchical control structure constituting of Hungarian algorithm based task assignment and SBWC based cooperative control for spacecrafts initialization has been proposed. A kind of artificial potential function anti-interrelated with spacecrafts’relative positions has been constructed. Then a SBWC based cooperative control law has been proposed to avoid the collision during spacecrafts initialization. Finally the collision avoidance mechanism has been demonstrated by simulation results.
There are constraint conditions of relative orientation in laser/vision based relative states measurement systems. To satisfy the constraint during spacecrafts attitudes synchronization, a SBWC based cooperative control law has been proposed and the weights interrelated with relative attitudes have been given. This law has been proved by LaSalle’Invariance principle and demonstrated by simulation results.
引文
1王鹏基.卫星编队飞行相对动力学与队形控制方法及应用研究.哈尔滨工业大学博士学位论文, 2004.
2 Peter C E Robertson, Tom S Bowling, Stephen E Hobbs. Mustang: A Technology Demonstration for Formation Flying and Distributed Systems Technologies in Space. Proceedings of the 5th International Conference on Dynamics and Control of Structures and Systems in Space, Cambridge, England, 2002.
3 Didier Massonnet. Capabilities and Limitations of the Interferometric Cartwheel. IEEE Transactions on Geosciences and Remote Sensing, 2001, 39(3):507-520.
4 Kim Luu, Maurice Martin, et al. University Nanosatellite Distributed Satellite Capabilities to Support Techsat21. 13th AIAA/USU Conference on Small Satellite, AUG, 1999: 23-26.
5 Maurice Maritn, Howard Schlossverg, et al. University Nanosatellite Program: IAF Symposium Redondo Beach, CA, 1999.
6“The Micro-Arcsecond X-ray Imaging Mission,”http://maxim.gsfc.nasa.gov.
7“The Terrestrial Planet Finder Mission,”http://tpf.jpl.nasa.gov.
8“The Stellar Imager Mission,”http://hires.gsfc.nasa.gov/si.
9 Randal W Beard, Wynn Stilling, Rick Frost. A Hierarchal Coordination Scheme for Satellite Formation Initialization. AIAA Guidance, Navigation and Control, 1998, 17: 138-145.
10 W Kang, Andy Sparks, Siva Banda. Multi-satellite Formation and Reconfiguration: Proceedings of the American Control Conference, Chicago, Illinois, June 2000.
11 W Kang, N Xi, Andy Sparks. Theory and Applications of Formation Control in A Perceptive Reference Frame: Proceedings of the 39th IEEE Conference onDecision and Control, Sydney, Australia, December, 2000.
12 Wei Kang, Andy Sparks, Siva Banda. Coordinated Control of Multisatellite Systems. Journal of Guidance, Control, and Dynamics, 2001, 24(2):360-368
13 Mrak B Milam, Nicolas Prtit, Richard M Murry. Constrained Trajectory Generation for Micro-satellite Formation Flying. AIAA, 2001: 4030-4036.
14 Michael Tillerson, Gokhan nalhan, Jonnthan P How. Co-ordination and Control of Distributed Spacecraft Systems Using Convex Optimization Techniques. Int, J. Robust Nonlinear Control, 2002, 12: 207-242.
15 Rechard H Vassar. Formationkeeping for A Pair of Satellite in A Circular Orbit. Journal of Guidance, Control, and Dynamics, 1985, 8: 235-242.
16 Sparks A. Linear Control Spacecraft Formation Flying. AIAA Gudiance, Navigation, and Control Conference, Denver, CO, August, 2000: 4438.
17 Tamas Kormos, Phil Palmer, Martin Sweeting. Series of Satellite Encounters to Solve Autonomous Formation Assembly Problem: 16th AIAA/USU Small Satellite Conference, 2002. SSC, 2002,Ⅶ: 7.
18 Qi Guoyan. Nonlinear Dynamics and Output Feedback Control Control of Multiple Spacecraft in Elliptical Orbits, Proceeding of American Control Conference, Chicago, Illinois, 2000. 2000: 839-843.
19 Marcio S De Queiroz, Vikram Kapila, Qiguo Yan. Adaptive Nonlinear Control of Multiple Spacecraft Formation Flying. Journal of Guidance, Control and Dynamics, May-June, 2000, 23(3): 385-390.
20 His-Han Yeh. Nonlinear Tracking Control of Satellite Formation. Journal of Guidance, Control and Dynamics, 2002, 25(2):376-386.
21刘少然,曾国强.编队飞行航天器平均轨道根数分线性控制研究.中国空间科学技术,2005, 10, 25(5): 24-28.
22王兆魁,张育林.分布式卫星精确构型保持变结构控制.航天控制, 2005, 23(6):27-30.
23 Wang Zhaokui, Zhang Yulin. Sliding Mode Control for Satellite Formation Keeping Against J2 Perturbation: Proceedings of the 23rd Chinese ControlConferece, Wuxi, China, Aug. 2004, 2004: 1386-1390.
24 Hao Jigang, Zhang Yulin. Application of Phase-plane Method in the Co-plane Formation Maintenance of Formation Flying Satellite[. Proceedings of 25th Chinese Control Conferece, Harbin, Heilongjiang, China, 7-11 August, 2006.
25郝继刚,张育林.基于大气阻力的编队构形沿航迹模糊控制方法.国防科技大学学报, 2007, 29(3):6-10
26 Hanspeter K, Chatlotte K H. A Rtificial Fish Schools: Collective Effects of School Size, Body Size, and Body Form. A rtificial Life, 2003,(9): 237-253.
27 Smon H, Petro B, Svent, et al. A Model of the Formation of Fish School and Migrations of Fish. Ecological Modelling, 2004,(174) : 359-374.
28 Couzn I D, KRAUSE J, JAMESR, et al. Collective memory and spatial sorting in animal groups. Journal of Theoretical Biology, 2002,(218): 1-11.
29 Felipe C, Smale S Emergent Behavior in Flocks. IEEE Transactions on Automatic Control, 2007, 52(5): 852-862.
30 Couzin I D, Farnksn R. Self-organized Lane Formation and Optimized Traffic Flow in Army Ants. Proceedings of the Royal Society of London, 2003: 139-146.
31 Naday. Steering Mechanism of Fish Schools. Complexity International, 2001(1): 1-9.
32 Breder C M. Equations Descriptive of Fish Schools and Other Animal Aggregation. Ecology, 1954, 35(3): 361-370.
33 Reynolds C. Flocks, Birds, and Schools: a Distributed Behavioral Model. Computer Graphics, 1987,(21): 25-34.
34 Vicsek T, Czirok A , Ben-Jacob E , et al. Novel Type of Phase Transition in A System of Self-driven Particle. Physical Review letters, 1995, 75(6): 1226-1229.
35 Jadbbaiea, Lin J, Morse A S. Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules. IEEE Transactions on Automatic Control, 2003,(48): 988-1001.
36 Olfati-Saber R. Flocking for Multi-agent Dynamic System: Algorithms and Theory. IEEE Transaction on Automatic Control, 2006, 51(3): 401-420.
37 Chen X P, Serrani A, Ozbay H. Control of Leader-follower Formations of Terrestrial UAVs. Proceedings of the IEEE Conference on Decision and Control. USA: IEEE, 2003, 498-503.
38 Balch T, Arkin R C. Behavior-based Formation Control Formulti Robot Teams. IEEE Transactions on Robotics and Automation, 1998, 14(6): 926-939.
39 Ren W, Beard R W. A Decentralized Scheme for Spacecraft Formation Flying via Virtual Structure Approach. Proceedings of the American Control Conference. USA: IEEE, 2003, 1746-1751.
40 Leonard N E, Fiorelli E. Virtual leader, Artificial Potential and Coordinated Control of Groups. Proceedings of the IEEE Conference on Decision and Control. USA: IEEE, 2001, 2968-2973.
41 Tanner H G, Jadbabaie A. Pappas G I Stable flocking of Mobile Agents, PartⅠ: Fixed Topology. Proceedings of the IEEE Conference on Decision and Control. USA: IEEE, 2003, 2010-2015.
42 Olfati-Saber R, Murray R M. Consensus Problems in Networks of Agents with Switching Togology and Time-delays. IEEE Transactions on Automatic Control, 2004, 49(9): 1520-1533.
43 Jadbabaie A, Lin J, Morse A S. Coordination of Groups of Mobile Autonomous Agents Using Nearest Rules. IEEE Transactions on Automatic Control, 2003, 48(6): 988-1001.
44 Lawton J R T, Beard R W, Young B J. A Decentralized Approach to Formation Maneuvers. IEEE Transactions on Robotics and Automation, 2003, 19(6): 933-941.
45 Desai J P. A Graph Theoretic Approach for Modeling Mobile Robot Team Formations. J of Robotic Systems, 2002, 19(11): 511-525.
46 Fierro R, Das A K. A Modular Architecture for Formation Control. Proc of the 3rd Int Workshop on Robot Motion and Control. Poznan, 2002: 285-290.
47 Olifati-Saber R, Murray R M. Graph Rigidity and Distributed Formation Stabilization of Multi-vehicle Systems. 41st Conf on Decision and Control. Las Vegas, 2002, 3: 2965-2971.
48 Olifati-Saber R, Murray R M. Distributed Cooperative Control of Multiple Vehicle Formation Using Structural Potential Functions. Proc of the 15th IFAC World Congress. Barcelona, 2002.
49 Herbert G Tanner., George J. Pappas, Vijay Kuman Leader to Formation Stability. IEEE Trans on Robotics and Automation, 2004, 20(3): 443-455.
50 Fax J A, Murry R M. Information Flow and Cooperative Control of Vehcile Formation. IEEE Transaction on Automatic Control, 2004, 49(9): 1465-1476.
51 Ln Z, Francis B, Maggiorem. Necessary and Sufficient Graphical Conditions for Formation Control of Unicycles. IEEE Transaction on Automatic Control, 2005, 50(1): 121-127.
52 Olfati-Saber R, Murray R M. Consensus Problems in Networks of Agents with Switching Topology and Time-delays. IEEE Trasaction on Automatic Control, 2004, 49(9): 1520-1533.
53 Ren W, Beard R W. Consensus Seeking in Multiagent Systems Under Dynamically Changing Interaction Topologies. IEEE Transaction on Automatic Control, 2005, 50(5): 655-661.
54 Olfati-Saber R, Fax J A, Murray R M. Consensus and Cooperation in Multi-agent Networked Systems. Proceedings of the IEEE, 2007, 95 (1): 215-233.
55 Moreau L. Stability of Multi Agent Systems with Time-dependent Communicati on Links. IEEE Transaction on Aut omatic Control, 2005, 50(2): 169-182.
56 Marshall J A, Broucke M E, Francis B A. Formations of Vehicles in Cyclic Pursuit. IEEE Transaction on Automatic Control, 2004, 49(11): 1963–1974.
57 Caughman J S, Lafferr Iere G, Veerman J J P, et al. Decentralized Contr ol of Vehicle Formations. System & Control Letters, 2005, 54(9): 899-910.
58 Michael Y. Li, James S. Muldowney. A Geometric Approach to Global-Stability Problems. Siam J. Math. Anal. 1996, 27(4):1070-1083.
59 Hongbin Guo, Michael Y.Li, Zhisheng Shuai. A Graph-Theoretic Approach to The Method of Global Lyapunov Functions. Proceedings of the American Mathematical Society, March 27, 2008, pp. 2793-2802.
60 B. Wie. Space Vehicle Dynamics and Control. AIAA Education Series, 1988.
61 Wei Ren. On consensus algorithms for double-integrator dynamics. IEEE Transactions on Automatic Control, 2008, 53(6):1503-1509
62 Meng Ji. Graph-based control of networked systems. PhD dissertation, Gerogia Institute of Technology, Gerogia, August 2007.
63 Wei Ren, Randal W. Beard, and Ella M. Athins. A survey of consensus problems in multi-agent coordination. 2005 American Control Conference June 8-10, 2005. Portland, OR, USA.
64张旭辉,朱宏辉,郑启忠.最优指派问题匈牙利算法的探讨与C++实现.物流技术,2004.
65 Vicsek T, CzirooK A, Ben-Jacob E, Cohen I, and Shochet O. Novel type of phase transition in a system of self-deriven particles. Physical Review Letter, 1995, 75(6): 1226-1229.
66 Jadbabaie A, Lin J, and Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions Automatic Control, 2003, 48(6): 988-1001.
67 Olfati-Saber R and Murray R M. Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions Automatic Control, 2004, 49(9): 1520-1533.
68 Fax J A. Optimal and cooperative control of vehicle formation. Doctoral Dissertation, Pasadena, CA: Control Dynamical System, California Institute of Technology, 2001.
69 Fax J A and Murray R M. Information flow and cooperative control of vehicle formations, IEEE Transactions Automatic Control, 2004, 49(9): 1465-1476.
70 Ren W and Beard R W. Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE Transactions Automatic Control, 2005, 50(5): 655-661.
71 Ren W, Beard R W, and Atkins E M. Information consensus in multivehicle cooperative control: Collective group behavior through local interaction. IEEE Control Systems Magazine, 2007, 27(2): 71-82.
72 Moreau L. Stability of multi-agent systems with time-dependent communication links. IEEE Transactions Automatic Control, 2005, 50(2): 169-182.
73 Moreau L. Stability of continuous-time distributed consensus algorithms. In Proc. Of the 43nd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, 2004, pp. 3998-4003.
2 Peter C E Robertson, Tom S Bowling, Stephen E Hobbs. Mustang: A Technology Demonstration for Formation Flying and Distributed Systems Technologies in Space. Proceedings of the 5th International Conference on Dynamics and Control of Structures and Systems in Space, Cambridge, England, 2002.
3 Didier Massonnet. Capabilities and Limitations of the Interferometric Cartwheel. IEEE Transactions on Geosciences and Remote Sensing, 2001, 39(3):507-520.
4 Kim Luu, Maurice Martin, et al. University Nanosatellite Distributed Satellite Capabilities to Support Techsat21. 13th AIAA/USU Conference on Small Satellite, AUG, 1999: 23-26.
5 Maurice Maritn, Howard Schlossverg, et al. University Nanosatellite Program: IAF Symposium Redondo Beach, CA, 1999.
6“The Micro-Arcsecond X-ray Imaging Mission,”http://maxim.gsfc.nasa.gov.
7“The Terrestrial Planet Finder Mission,”http://tpf.jpl.nasa.gov.
8“The Stellar Imager Mission,”http://hires.gsfc.nasa.gov/si.
9 Randal W Beard, Wynn Stilling, Rick Frost. A Hierarchal Coordination Scheme for Satellite Formation Initialization. AIAA Guidance, Navigation and Control, 1998, 17: 138-145.
10 W Kang, Andy Sparks, Siva Banda. Multi-satellite Formation and Reconfiguration: Proceedings of the American Control Conference, Chicago, Illinois, June 2000.
11 W Kang, N Xi, Andy Sparks. Theory and Applications of Formation Control in A Perceptive Reference Frame: Proceedings of the 39th IEEE Conference onDecision and Control, Sydney, Australia, December, 2000.
12 Wei Kang, Andy Sparks, Siva Banda. Coordinated Control of Multisatellite Systems. Journal of Guidance, Control, and Dynamics, 2001, 24(2):360-368
13 Mrak B Milam, Nicolas Prtit, Richard M Murry. Constrained Trajectory Generation for Micro-satellite Formation Flying. AIAA, 2001: 4030-4036.
14 Michael Tillerson, Gokhan nalhan, Jonnthan P How. Co-ordination and Control of Distributed Spacecraft Systems Using Convex Optimization Techniques. Int, J. Robust Nonlinear Control, 2002, 12: 207-242.
15 Rechard H Vassar. Formationkeeping for A Pair of Satellite in A Circular Orbit. Journal of Guidance, Control, and Dynamics, 1985, 8: 235-242.
16 Sparks A. Linear Control Spacecraft Formation Flying. AIAA Gudiance, Navigation, and Control Conference, Denver, CO, August, 2000: 4438.
17 Tamas Kormos, Phil Palmer, Martin Sweeting. Series of Satellite Encounters to Solve Autonomous Formation Assembly Problem: 16th AIAA/USU Small Satellite Conference, 2002. SSC, 2002,Ⅶ: 7.
18 Qi Guoyan. Nonlinear Dynamics and Output Feedback Control Control of Multiple Spacecraft in Elliptical Orbits, Proceeding of American Control Conference, Chicago, Illinois, 2000. 2000: 839-843.
19 Marcio S De Queiroz, Vikram Kapila, Qiguo Yan. Adaptive Nonlinear Control of Multiple Spacecraft Formation Flying. Journal of Guidance, Control and Dynamics, May-June, 2000, 23(3): 385-390.
20 His-Han Yeh. Nonlinear Tracking Control of Satellite Formation. Journal of Guidance, Control and Dynamics, 2002, 25(2):376-386.
21刘少然,曾国强.编队飞行航天器平均轨道根数分线性控制研究.中国空间科学技术,2005, 10, 25(5): 24-28.
22王兆魁,张育林.分布式卫星精确构型保持变结构控制.航天控制, 2005, 23(6):27-30.
23 Wang Zhaokui, Zhang Yulin. Sliding Mode Control for Satellite Formation Keeping Against J2 Perturbation: Proceedings of the 23rd Chinese ControlConferece, Wuxi, China, Aug. 2004, 2004: 1386-1390.
24 Hao Jigang, Zhang Yulin. Application of Phase-plane Method in the Co-plane Formation Maintenance of Formation Flying Satellite[. Proceedings of 25th Chinese Control Conferece, Harbin, Heilongjiang, China, 7-11 August, 2006.
25郝继刚,张育林.基于大气阻力的编队构形沿航迹模糊控制方法.国防科技大学学报, 2007, 29(3):6-10
26 Hanspeter K, Chatlotte K H. A Rtificial Fish Schools: Collective Effects of School Size, Body Size, and Body Form. A rtificial Life, 2003,(9): 237-253.
27 Smon H, Petro B, Svent, et al. A Model of the Formation of Fish School and Migrations of Fish. Ecological Modelling, 2004,(174) : 359-374.
28 Couzn I D, KRAUSE J, JAMESR, et al. Collective memory and spatial sorting in animal groups. Journal of Theoretical Biology, 2002,(218): 1-11.
29 Felipe C, Smale S Emergent Behavior in Flocks. IEEE Transactions on Automatic Control, 2007, 52(5): 852-862.
30 Couzin I D, Farnksn R. Self-organized Lane Formation and Optimized Traffic Flow in Army Ants. Proceedings of the Royal Society of London, 2003: 139-146.
31 Naday. Steering Mechanism of Fish Schools. Complexity International, 2001(1): 1-9.
32 Breder C M. Equations Descriptive of Fish Schools and Other Animal Aggregation. Ecology, 1954, 35(3): 361-370.
33 Reynolds C. Flocks, Birds, and Schools: a Distributed Behavioral Model. Computer Graphics, 1987,(21): 25-34.
34 Vicsek T, Czirok A , Ben-Jacob E , et al. Novel Type of Phase Transition in A System of Self-driven Particle. Physical Review letters, 1995, 75(6): 1226-1229.
35 Jadbbaiea, Lin J, Morse A S. Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules. IEEE Transactions on Automatic Control, 2003,(48): 988-1001.
36 Olfati-Saber R. Flocking for Multi-agent Dynamic System: Algorithms and Theory. IEEE Transaction on Automatic Control, 2006, 51(3): 401-420.
37 Chen X P, Serrani A, Ozbay H. Control of Leader-follower Formations of Terrestrial UAVs. Proceedings of the IEEE Conference on Decision and Control. USA: IEEE, 2003, 498-503.
38 Balch T, Arkin R C. Behavior-based Formation Control Formulti Robot Teams. IEEE Transactions on Robotics and Automation, 1998, 14(6): 926-939.
39 Ren W, Beard R W. A Decentralized Scheme for Spacecraft Formation Flying via Virtual Structure Approach. Proceedings of the American Control Conference. USA: IEEE, 2003, 1746-1751.
40 Leonard N E, Fiorelli E. Virtual leader, Artificial Potential and Coordinated Control of Groups. Proceedings of the IEEE Conference on Decision and Control. USA: IEEE, 2001, 2968-2973.
41 Tanner H G, Jadbabaie A. Pappas G I Stable flocking of Mobile Agents, PartⅠ: Fixed Topology. Proceedings of the IEEE Conference on Decision and Control. USA: IEEE, 2003, 2010-2015.
42 Olfati-Saber R, Murray R M. Consensus Problems in Networks of Agents with Switching Togology and Time-delays. IEEE Transactions on Automatic Control, 2004, 49(9): 1520-1533.
43 Jadbabaie A, Lin J, Morse A S. Coordination of Groups of Mobile Autonomous Agents Using Nearest Rules. IEEE Transactions on Automatic Control, 2003, 48(6): 988-1001.
44 Lawton J R T, Beard R W, Young B J. A Decentralized Approach to Formation Maneuvers. IEEE Transactions on Robotics and Automation, 2003, 19(6): 933-941.
45 Desai J P. A Graph Theoretic Approach for Modeling Mobile Robot Team Formations. J of Robotic Systems, 2002, 19(11): 511-525.
46 Fierro R, Das A K. A Modular Architecture for Formation Control. Proc of the 3rd Int Workshop on Robot Motion and Control. Poznan, 2002: 285-290.
47 Olifati-Saber R, Murray R M. Graph Rigidity and Distributed Formation Stabilization of Multi-vehicle Systems. 41st Conf on Decision and Control. Las Vegas, 2002, 3: 2965-2971.
48 Olifati-Saber R, Murray R M. Distributed Cooperative Control of Multiple Vehicle Formation Using Structural Potential Functions. Proc of the 15th IFAC World Congress. Barcelona, 2002.
49 Herbert G Tanner., George J. Pappas, Vijay Kuman Leader to Formation Stability. IEEE Trans on Robotics and Automation, 2004, 20(3): 443-455.
50 Fax J A, Murry R M. Information Flow and Cooperative Control of Vehcile Formation. IEEE Transaction on Automatic Control, 2004, 49(9): 1465-1476.
51 Ln Z, Francis B, Maggiorem. Necessary and Sufficient Graphical Conditions for Formation Control of Unicycles. IEEE Transaction on Automatic Control, 2005, 50(1): 121-127.
52 Olfati-Saber R, Murray R M. Consensus Problems in Networks of Agents with Switching Topology and Time-delays. IEEE Trasaction on Automatic Control, 2004, 49(9): 1520-1533.
53 Ren W, Beard R W. Consensus Seeking in Multiagent Systems Under Dynamically Changing Interaction Topologies. IEEE Transaction on Automatic Control, 2005, 50(5): 655-661.
54 Olfati-Saber R, Fax J A, Murray R M. Consensus and Cooperation in Multi-agent Networked Systems. Proceedings of the IEEE, 2007, 95 (1): 215-233.
55 Moreau L. Stability of Multi Agent Systems with Time-dependent Communicati on Links. IEEE Transaction on Aut omatic Control, 2005, 50(2): 169-182.
56 Marshall J A, Broucke M E, Francis B A. Formations of Vehicles in Cyclic Pursuit. IEEE Transaction on Automatic Control, 2004, 49(11): 1963–1974.
57 Caughman J S, Lafferr Iere G, Veerman J J P, et al. Decentralized Contr ol of Vehicle Formations. System & Control Letters, 2005, 54(9): 899-910.
58 Michael Y. Li, James S. Muldowney. A Geometric Approach to Global-Stability Problems. Siam J. Math. Anal. 1996, 27(4):1070-1083.
59 Hongbin Guo, Michael Y.Li, Zhisheng Shuai. A Graph-Theoretic Approach to The Method of Global Lyapunov Functions. Proceedings of the American Mathematical Society, March 27, 2008, pp. 2793-2802.
60 B. Wie. Space Vehicle Dynamics and Control. AIAA Education Series, 1988.
61 Wei Ren. On consensus algorithms for double-integrator dynamics. IEEE Transactions on Automatic Control, 2008, 53(6):1503-1509
62 Meng Ji. Graph-based control of networked systems. PhD dissertation, Gerogia Institute of Technology, Gerogia, August 2007.
63 Wei Ren, Randal W. Beard, and Ella M. Athins. A survey of consensus problems in multi-agent coordination. 2005 American Control Conference June 8-10, 2005. Portland, OR, USA.
64张旭辉,朱宏辉,郑启忠.最优指派问题匈牙利算法的探讨与C++实现.物流技术,2004.
65 Vicsek T, CzirooK A, Ben-Jacob E, Cohen I, and Shochet O. Novel type of phase transition in a system of self-deriven particles. Physical Review Letter, 1995, 75(6): 1226-1229.
66 Jadbabaie A, Lin J, and Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions Automatic Control, 2003, 48(6): 988-1001.
67 Olfati-Saber R and Murray R M. Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions Automatic Control, 2004, 49(9): 1520-1533.
68 Fax J A. Optimal and cooperative control of vehicle formation. Doctoral Dissertation, Pasadena, CA: Control Dynamical System, California Institute of Technology, 2001.
69 Fax J A and Murray R M. Information flow and cooperative control of vehicle formations, IEEE Transactions Automatic Control, 2004, 49(9): 1465-1476.
70 Ren W and Beard R W. Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE Transactions Automatic Control, 2005, 50(5): 655-661.
71 Ren W, Beard R W, and Atkins E M. Information consensus in multivehicle cooperative control: Collective group behavior through local interaction. IEEE Control Systems Magazine, 2007, 27(2): 71-82.
72 Moreau L. Stability of multi-agent systems with time-dependent communication links. IEEE Transactions Automatic Control, 2005, 50(2): 169-182.
73 Moreau L. Stability of continuous-time distributed consensus algorithms. In Proc. Of the 43nd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, 2004, pp. 3998-4003.