多自主移动机器人的编队控制及稳定性分析
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摘要
多自主机器人系统是目前控制和机器人研究领域的研究热点之一。多自主机器人系统通过模拟生物之间的某些群体行为从而完成特定的任务。在多自主机器人系统中,每个机器人按照预定规则检测周围环境,与其邻近机器人通讯,并根据自身获得的信息决定下一步的行动。虽然每个机器人只使用了其能获得的局部信息,但是整个系统却能实现一些全局性的任务。多机器人协作可以提高系统的效率,完成单个机器人无法完成的任务,在军事监测、抢险救援、空间及海洋开发、智能交通系统及其他自动化协作中有广泛的应用前景。多自主机器人的编队控制研究是多机器人协调控制的重要研究问题,非完整性约束下的多移动机器人编队控制更是具有非常重要的理论和实际意义。
论文的第一部分研究非完整性约束下的多移动机器人的分布式队形控制问题。本文提出了一个新的循环追踪的控制策略来实现多移动机器人的分布式队形控制。在这个策略中,每个移动机器人的前进速度和转弯速度分别正比于其追踪的目标机器人在其前进方向和侧向上的投影。运用这种策略,最终所有的机器人将会以恒定的速度等间隔地在一个圆周上运动。该控制策略可以确保机器人轨迹的最终有界性,且系统只有两个稳定平衡多边形。该控制器避免了其他循环追踪控制策略中可能出现的问题,如机器人的轨迹可能发散到无穷远,稳定多边形的个数会随着机器人数量而增加。文中采用伪线性化的方法证明了此控制策略可以保证系统的最终有界性。同时运用根轨迹分析方法,通过分析一个复数多项式得到了平衡点的稳定性和收敛性。
论文的第二部分研究非完整性约束下的多移动机器人的分布式集结问题。我们提出了一个分布式连续时不变的状态反馈控制器。在这个控制器下,每个移动机器人的前进速度和转弯速度分别正比于其相邻的机器人在其前进方向和侧向上的投影之和。利用图论的工具,我们证明了该控制器可以使机器人最终收敛到一点。与其他常见的不连续或(和)时变的控制策略相比,我们的控制器简单易于实现。本文还证明了对一大类典型的具有非线性特性的执行器,该控制策略仍然有效。接着同样采用伪线性化的方法,本文研究证明了动态图下系统轨迹的最终有界性。
论文的第三部分讨论非完整性约束的多移动机器人的主从式编队控制问题。文章讨论了两种控制策略。首先,我们提出了一种基于投影的控制策略并分别分析了当主机器人做直线运动和匀速直线运动时从机器人的运动。为了补偿因主车速度变化引起的队形几何变化,我们考虑一个积分控制器并证明了该控制器在特定的假设下可以实现预定的队形。
Multiple autonomous robot systems (MARS) have attracted many researchers from the control and robot community in recent years. Many ideas in MARS are inspired by collective animal behaviors observed in nature. In a MARS, like an individual animal, each robot is programmed to sense its local environment, communicate with its neighboring robots, and decide its next movement based on its available information, yet the whole group together can perform desired global tasks. The coordination of multi-robots can improve the performance and complete tasks which are too difficult for a single robot to perform alone. Due to this advantage, there exist numerous potential engineering applications in military surveillance, rescue missions, space and ocean explorations, intelligent transportation systems, and other automated collaborative operations. Among all the coordinated and cooperative control problems, formation control of multiple mobile robots, especially nonholonomic mobile robots is a key problem which is of both theoretical and practical significance.
In the first part of this thesis, we explore the distributed formation control of nonholonomic mobile robots. A new cyclic pursuit control law is proposed, where each robot's linear speed and angular speed are proportional to the projection of its prey's position on its forward direction and lateral direction, respectively. Through these interaction a cooperative behavior emerges and the robots eventually move at a constant speed on a circle with constant inter-robot spacings. The control scheme ensures ultimate boundedness and leads to only two stable equilibrium polygons formations. This contrasts with other cyclic pursuit control schemes, where the robots may diverge to infinity and there are more stable equilibrium polygons as the total number of robots increases. For this control scheme, ultimate boundedness is proved using the pseudo-linearization technique. Possible equilibrium polygons are analyzed and stability and convergence properties are established through root locus analysis of a complex characteristic polynomial.
In the second part of this thesis, a distributed feedback control strategy that drives a system of multiple nonholonomic robots to a rendezvous point in term of position is introduced. In this control scheme, each robot's linear speed and angular speed are proportional to the sum of the projection of its neighbor robots' positions on its forward direction and lateral direction, respectively. For this control scheme, convergence is proved with the aid of tools from graph theory. Comparing with other discontinuous or(and) time-varying control schemes, ours is easier to be realized from the engineering perspective. Moreover, we prove that our control scheme also works even though actuations might exist for the control inputs. At the end of this part, ultimate boundedness of the system under dynamic sensing graph is proved by pseudo-linearization technique.
The third part of this thesis investigates the leader-following formation control of multiple nonholonomic robots. A projection-based control law is proposed and the behavior of the following robot is analyzed. In addition, we use an integral control law to compensate the deformation caused by the acceleration and deceleration of the leading robot and prove that this control scheme can achieve the predesigned formation under certain assumptions.
论文的第一部分研究非完整性约束下的多移动机器人的分布式队形控制问题。本文提出了一个新的循环追踪的控制策略来实现多移动机器人的分布式队形控制。在这个策略中,每个移动机器人的前进速度和转弯速度分别正比于其追踪的目标机器人在其前进方向和侧向上的投影。运用这种策略,最终所有的机器人将会以恒定的速度等间隔地在一个圆周上运动。该控制策略可以确保机器人轨迹的最终有界性,且系统只有两个稳定平衡多边形。该控制器避免了其他循环追踪控制策略中可能出现的问题,如机器人的轨迹可能发散到无穷远,稳定多边形的个数会随着机器人数量而增加。文中采用伪线性化的方法证明了此控制策略可以保证系统的最终有界性。同时运用根轨迹分析方法,通过分析一个复数多项式得到了平衡点的稳定性和收敛性。
论文的第二部分研究非完整性约束下的多移动机器人的分布式集结问题。我们提出了一个分布式连续时不变的状态反馈控制器。在这个控制器下,每个移动机器人的前进速度和转弯速度分别正比于其相邻的机器人在其前进方向和侧向上的投影之和。利用图论的工具,我们证明了该控制器可以使机器人最终收敛到一点。与其他常见的不连续或(和)时变的控制策略相比,我们的控制器简单易于实现。本文还证明了对一大类典型的具有非线性特性的执行器,该控制策略仍然有效。接着同样采用伪线性化的方法,本文研究证明了动态图下系统轨迹的最终有界性。
论文的第三部分讨论非完整性约束的多移动机器人的主从式编队控制问题。文章讨论了两种控制策略。首先,我们提出了一种基于投影的控制策略并分别分析了当主机器人做直线运动和匀速直线运动时从机器人的运动。为了补偿因主车速度变化引起的队形几何变化,我们考虑一个积分控制器并证明了该控制器在特定的假设下可以实现预定的队形。
Multiple autonomous robot systems (MARS) have attracted many researchers from the control and robot community in recent years. Many ideas in MARS are inspired by collective animal behaviors observed in nature. In a MARS, like an individual animal, each robot is programmed to sense its local environment, communicate with its neighboring robots, and decide its next movement based on its available information, yet the whole group together can perform desired global tasks. The coordination of multi-robots can improve the performance and complete tasks which are too difficult for a single robot to perform alone. Due to this advantage, there exist numerous potential engineering applications in military surveillance, rescue missions, space and ocean explorations, intelligent transportation systems, and other automated collaborative operations. Among all the coordinated and cooperative control problems, formation control of multiple mobile robots, especially nonholonomic mobile robots is a key problem which is of both theoretical and practical significance.
In the first part of this thesis, we explore the distributed formation control of nonholonomic mobile robots. A new cyclic pursuit control law is proposed, where each robot's linear speed and angular speed are proportional to the projection of its prey's position on its forward direction and lateral direction, respectively. Through these interaction a cooperative behavior emerges and the robots eventually move at a constant speed on a circle with constant inter-robot spacings. The control scheme ensures ultimate boundedness and leads to only two stable equilibrium polygons formations. This contrasts with other cyclic pursuit control schemes, where the robots may diverge to infinity and there are more stable equilibrium polygons as the total number of robots increases. For this control scheme, ultimate boundedness is proved using the pseudo-linearization technique. Possible equilibrium polygons are analyzed and stability and convergence properties are established through root locus analysis of a complex characteristic polynomial.
In the second part of this thesis, a distributed feedback control strategy that drives a system of multiple nonholonomic robots to a rendezvous point in term of position is introduced. In this control scheme, each robot's linear speed and angular speed are proportional to the sum of the projection of its neighbor robots' positions on its forward direction and lateral direction, respectively. For this control scheme, convergence is proved with the aid of tools from graph theory. Comparing with other discontinuous or(and) time-varying control schemes, ours is easier to be realized from the engineering perspective. Moreover, we prove that our control scheme also works even though actuations might exist for the control inputs. At the end of this part, ultimate boundedness of the system under dynamic sensing graph is proved by pseudo-linearization technique.
The third part of this thesis investigates the leader-following formation control of multiple nonholonomic robots. A projection-based control law is proposed and the behavior of the following robot is analyzed. In addition, we use an integral control law to compensate the deformation caused by the acceleration and deceleration of the leading robot and prove that this control scheme can achieve the predesigned formation under certain assumptions.
引文
[1]J.A.Fax and R.M.Murray.Information flow and cooperative control of vehicle formations.IEEE Transactions on Automatic Control,49(9):1465-1476,2004.
[2]Z.Lin,B.Francis,and M.Maggiore.Getting mobile autonomous robots to rendezvous.Lecture Notes in Control and Information Sciences,329:119-137,2006.
[3]Z.Lin,B.Francis,and M.Maggiore.Necessary and sufficient graphical conditions for formation control of unicycles.IEEE Transactions on Automatic Control,50(1):121-127,2005.
[4]J.Cortes,S.Martinez,T.Karatas,and F.Bullo.Coverage control for mobile sensing networks.In Proceedings of 2002 IEEE Inernational Conference on Robotics and Automation,pages 1327-1332,2002.
[5]R.Olfati-Saber and R.M.Murray.Consensus problems in networks of agents with switching topology and time-delays.IEEE Transactions on Automatic Control,,49(9):1520-1533,2004.
[6]T.Arai,E.Pagello,and LE Parker.Guest editorial advances in multirobot systems.IEEE Transactions on Robotics and Automation,18(5):655-661,2002.
[7]Intelligent transportation society of america.
[8]T.Balch and R.C.Arkin.Behavior-based formation control for multirobot teams.IEEE Transactions on Robotics and Automation,14(6):926-939,1998.
[9]M.A.Lewis and K.H.Tan.High precision formation control of mobile robots using virtual structures.Autonomous Robots,4(4):387-403,1997.
[10]J.P.Desai,J.P.Ostrowski,and V.Kumar.Modeling and control of formations of nonholonomic mobile robots.IEEE transactions on Robotics and Automation,17(6):905-908,2001.
[11]W.B.Dunbar and R.M.Murray.Distributed receding horizon control for multi-vehicle formation stabilization.Automatica,42(4):549-558,2006.
[12]N.E.Leonard and E.Fiorelli.Virtual leaders,artificial potentials and coordinated control ofgroups.In Decision and Control,2001.Proceedings of the 40th IEEE Conference on,volume 3,2001.
[13]L.Consolini,F.Morbidi,D.Prattichizzo,and M.Tosques.On the control of a leader-follower formation of nonholonomic mobile robots.2006.
[14]H.G.Tanner,G.J.Pappas,and V.Kumar.Leader-to-formation stability.IEEE Transactions on Robotics and Automation,20(3):443-455,2004.
[15]D.J.T.Sumpter.The principles of collective animal behaviour.Philosophical Transactions of the Royal Society B:Biological Sciences,361(1465):5,2006.
[16]C.W.Reynolds.Flocks,Herds,and Schools:A Distributed Behavioral Model.Computer Graphics,21(4),1987.
[17]A.Bernhart.Polygons of pursuit.Scripta Mathematica,1959.
[18]A.M.Bruckstein,N.Cohen,and A.Efrat.Ants,crickets and frogs in cyclic pursuit.Technical report,Center for Intelligent Systems,Technion-Israel Inst.Technol.,Haifa,Israel,1991.
[19]Z.Lin,M.Broucke,and B.Francis.Local control strategies for groups of mobile autonomous agents.IEEE Transactions on Automatic Control,49(4):622-629,2004.
[20]M.Pavone and E.Frazzoli.Decentralized policies for geometric pattern formation and path coverage.Journal of Dynamic Systems,Measurement,and Control,129(5):633-643,2007.
[21]S.L.Smith,M.E.Broucke,and B.A.Francis.A hierarchical cyclic pursuit scheme for vehicle networks.Automatica,41(6):1045-1053,2005.
[22]E.W.Justh and P.S.Krishnaprasad.Equilibria and steering laws for planar formations.Systems(?) Control Letters,52(1):25-38,2004.
[23]I.Kolmanovsky and N.H.McClamroch.Developments in nonholonomic control problems.IEEE Control Systems Magazine,15(6):20-36,1995.
[24]D.M.Stipanovic,G.Inalhan,R.Teo,and C.J.Tomlin.Decentralized overlapping control of a formation of unmanned aerial vehicles.Automatica,40(8):1285-1296,2004.
[25]J.A.Marshall,M.E.Broucke,and B.A.Francis.Formations of vehicles in cyclic pursuit.IEEE Transactions on Automatic Control,49(11):1963-1974,2004.
[26]J.A.Marshall,M.E.Broucke,and B.A.Francis.Unicycles in cyclic pursuit.In Proceedings of 2004 IEEE American Control Conference,volume 6,pages 5344-5349,2004.
[27]A.Sinha and D.Chose.Generalization of nonlinear cyclic pursuit.Automatica,43(11):1954-1960,2007.
[28]J.Jeanne,NE Leonard,and D.Paley.Collective motion of ring-coupled planar particles.In Proceedings 44th IEEE Conference on Decision and Control and European Control Conference,pages 3929-3934,2005.
[29]F.Behroozi and R.Gagnon.Cyclic pursuit in a plane.Journal of Mathematical Physics,20(11):2212-2216,1979.
[30]M.S.Klamkin and D.J.Newman.Cyclic pursuit or "the three bugs problem".The American Mathematical Monthly,78(6):631-639,1971.
[31]T.Richardson.Non-mutual captures in cyclic pursuit.Annals of Mathematics and Artificial Intelligence,31(1):127-146,2001.
[32]T.Richardson.Stable polygons of cyclic pursuit.Annals of Mathematics and Artificial Intelligence,31(1):147-172,2001.
[33]Z.Lin.Distributed Control and Analysis of Coupled Cell Systems.VDM Verlag Dr.M(u|¨)ller,2008.
[34]S.L.Smith,M.E.Broucke,and B.A.Francis.Curve shortening and the rendezvous problem for mobile autonomous robots.IEEE transactions on automatic control,52(6):1154-1159,2007.
[35]A.Ganguli,J.Cortes,and F.Bullo.Multirobot rendezvous with visibility sensors in nonconvex environments.IEEE Transactions on Robotics,25(2):340-352,2006.
[36]D.V.Dimarogonas and K.J.Kyriakopoulos.On the rendezvous problem for multiple nonholonomic agents.IEEE Transactions on automatic control,52(5):916-922,2007.
[37]C.Godsil and G.Royle.Algebraic graph theory.Springer New York,2001.
[38]R.A.Horn and C.R.Johnson.Matrix Analysis.Cambridge university press,1985.
[39]Wikipedia.克罗内克积—wikipedia,自由的百科全书,2009.
[40]P.J.Davis.Circulant Matrices.American Mathematical Society,1994.
[41]H.K.Khalil.Nonlinear Systems.Prentice Hall,third edition,2002.
[42]J.A.Marshall,M.E.Broucke,and B.A.Francis.Pursuit formations of unicycles.Automatica,42(1):3-12,2006.
[43]J.A.Marshall.Coordinated Autonomy:Pursuit Formations of Multivehicle Systems.PhD thesis,University of Toronto,Toronto,Ontario,Canada,2005.
[44]A.K.Das,R.Fierro,V.Kumar,J.P.Ostrowski,J.Spletzer,and C.J.Taylor.A vision-based formation control framework.IEEE Transactions on Robotics and Automation,18(5):813-825,2002.
[45]J.A.Rogge and D.Aeyels.Stability of phase locking in a ring of unidirectionally coupled oscillators.Journal of Physics A-Mathematical and General,37(46):11135-11148,2004.
[2]Z.Lin,B.Francis,and M.Maggiore.Getting mobile autonomous robots to rendezvous.Lecture Notes in Control and Information Sciences,329:119-137,2006.
[3]Z.Lin,B.Francis,and M.Maggiore.Necessary and sufficient graphical conditions for formation control of unicycles.IEEE Transactions on Automatic Control,50(1):121-127,2005.
[4]J.Cortes,S.Martinez,T.Karatas,and F.Bullo.Coverage control for mobile sensing networks.In Proceedings of 2002 IEEE Inernational Conference on Robotics and Automation,pages 1327-1332,2002.
[5]R.Olfati-Saber and R.M.Murray.Consensus problems in networks of agents with switching topology and time-delays.IEEE Transactions on Automatic Control,,49(9):1520-1533,2004.
[6]T.Arai,E.Pagello,and LE Parker.Guest editorial advances in multirobot systems.IEEE Transactions on Robotics and Automation,18(5):655-661,2002.
[7]Intelligent transportation society of america.
[8]T.Balch and R.C.Arkin.Behavior-based formation control for multirobot teams.IEEE Transactions on Robotics and Automation,14(6):926-939,1998.
[9]M.A.Lewis and K.H.Tan.High precision formation control of mobile robots using virtual structures.Autonomous Robots,4(4):387-403,1997.
[10]J.P.Desai,J.P.Ostrowski,and V.Kumar.Modeling and control of formations of nonholonomic mobile robots.IEEE transactions on Robotics and Automation,17(6):905-908,2001.
[11]W.B.Dunbar and R.M.Murray.Distributed receding horizon control for multi-vehicle formation stabilization.Automatica,42(4):549-558,2006.
[12]N.E.Leonard and E.Fiorelli.Virtual leaders,artificial potentials and coordinated control ofgroups.In Decision and Control,2001.Proceedings of the 40th IEEE Conference on,volume 3,2001.
[13]L.Consolini,F.Morbidi,D.Prattichizzo,and M.Tosques.On the control of a leader-follower formation of nonholonomic mobile robots.2006.
[14]H.G.Tanner,G.J.Pappas,and V.Kumar.Leader-to-formation stability.IEEE Transactions on Robotics and Automation,20(3):443-455,2004.
[15]D.J.T.Sumpter.The principles of collective animal behaviour.Philosophical Transactions of the Royal Society B:Biological Sciences,361(1465):5,2006.
[16]C.W.Reynolds.Flocks,Herds,and Schools:A Distributed Behavioral Model.Computer Graphics,21(4),1987.
[17]A.Bernhart.Polygons of pursuit.Scripta Mathematica,1959.
[18]A.M.Bruckstein,N.Cohen,and A.Efrat.Ants,crickets and frogs in cyclic pursuit.Technical report,Center for Intelligent Systems,Technion-Israel Inst.Technol.,Haifa,Israel,1991.
[19]Z.Lin,M.Broucke,and B.Francis.Local control strategies for groups of mobile autonomous agents.IEEE Transactions on Automatic Control,49(4):622-629,2004.
[20]M.Pavone and E.Frazzoli.Decentralized policies for geometric pattern formation and path coverage.Journal of Dynamic Systems,Measurement,and Control,129(5):633-643,2007.
[21]S.L.Smith,M.E.Broucke,and B.A.Francis.A hierarchical cyclic pursuit scheme for vehicle networks.Automatica,41(6):1045-1053,2005.
[22]E.W.Justh and P.S.Krishnaprasad.Equilibria and steering laws for planar formations.Systems(?) Control Letters,52(1):25-38,2004.
[23]I.Kolmanovsky and N.H.McClamroch.Developments in nonholonomic control problems.IEEE Control Systems Magazine,15(6):20-36,1995.
[24]D.M.Stipanovic,G.Inalhan,R.Teo,and C.J.Tomlin.Decentralized overlapping control of a formation of unmanned aerial vehicles.Automatica,40(8):1285-1296,2004.
[25]J.A.Marshall,M.E.Broucke,and B.A.Francis.Formations of vehicles in cyclic pursuit.IEEE Transactions on Automatic Control,49(11):1963-1974,2004.
[26]J.A.Marshall,M.E.Broucke,and B.A.Francis.Unicycles in cyclic pursuit.In Proceedings of 2004 IEEE American Control Conference,volume 6,pages 5344-5349,2004.
[27]A.Sinha and D.Chose.Generalization of nonlinear cyclic pursuit.Automatica,43(11):1954-1960,2007.
[28]J.Jeanne,NE Leonard,and D.Paley.Collective motion of ring-coupled planar particles.In Proceedings 44th IEEE Conference on Decision and Control and European Control Conference,pages 3929-3934,2005.
[29]F.Behroozi and R.Gagnon.Cyclic pursuit in a plane.Journal of Mathematical Physics,20(11):2212-2216,1979.
[30]M.S.Klamkin and D.J.Newman.Cyclic pursuit or "the three bugs problem".The American Mathematical Monthly,78(6):631-639,1971.
[31]T.Richardson.Non-mutual captures in cyclic pursuit.Annals of Mathematics and Artificial Intelligence,31(1):127-146,2001.
[32]T.Richardson.Stable polygons of cyclic pursuit.Annals of Mathematics and Artificial Intelligence,31(1):147-172,2001.
[33]Z.Lin.Distributed Control and Analysis of Coupled Cell Systems.VDM Verlag Dr.M(u|¨)ller,2008.
[34]S.L.Smith,M.E.Broucke,and B.A.Francis.Curve shortening and the rendezvous problem for mobile autonomous robots.IEEE transactions on automatic control,52(6):1154-1159,2007.
[35]A.Ganguli,J.Cortes,and F.Bullo.Multirobot rendezvous with visibility sensors in nonconvex environments.IEEE Transactions on Robotics,25(2):340-352,2006.
[36]D.V.Dimarogonas and K.J.Kyriakopoulos.On the rendezvous problem for multiple nonholonomic agents.IEEE Transactions on automatic control,52(5):916-922,2007.
[37]C.Godsil and G.Royle.Algebraic graph theory.Springer New York,2001.
[38]R.A.Horn and C.R.Johnson.Matrix Analysis.Cambridge university press,1985.
[39]Wikipedia.克罗内克积—wikipedia,自由的百科全书,2009.
[40]P.J.Davis.Circulant Matrices.American Mathematical Society,1994.
[41]H.K.Khalil.Nonlinear Systems.Prentice Hall,third edition,2002.
[42]J.A.Marshall,M.E.Broucke,and B.A.Francis.Pursuit formations of unicycles.Automatica,42(1):3-12,2006.
[43]J.A.Marshall.Coordinated Autonomy:Pursuit Formations of Multivehicle Systems.PhD thesis,University of Toronto,Toronto,Ontario,Canada,2005.
[44]A.K.Das,R.Fierro,V.Kumar,J.P.Ostrowski,J.Spletzer,and C.J.Taylor.A vision-based formation control framework.IEEE Transactions on Robotics and Automation,18(5):813-825,2002.
[45]J.A.Rogge and D.Aeyels.Stability of phase locking in a ring of unidirectionally coupled oscillators.Journal of Physics A-Mathematical and General,37(46):11135-11148,2004.