全方位移动机器人运动控制及规划
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摘要
本论文以国家自然科学基金项目和国家863项目为背景,针对全方位移动机器人的执行存在偏差和时间最优轨迹规划等问题,系统的研究了全方位机器人的运动学和动力学模型以及轨迹规划问题,取得了如下具有创新性的研究成果：
1.提出一种基于神经网络的全方位移动机器人速度补偿算法。通过对全方位移动机器人的运动学和动力学模型详细分析,以及对万向轮中主动轮和从动轮的受力分析,本文发现万向轮中主动轮和从动轮之间的摩擦力是造成全方位移动机器人产生执行偏差的主要原因。根据模型分析的结果,建立一个基于神经网络的速度补偿模型,实验和实际使用证明该补偿模型可以将机器人的执行偏差从15%降低到5%。
2.提出一种基于bangbang控制的时间最优轨迹规划算法。该算法克服了以往bangbang轨迹规划方法只能处理目标状态末速度为零的缺陷。本文先重点研究了一维轨迹规划问题。根据机器人的初始状态和目标状态,提出一种新的分类标准,将一维轨迹规划问题分解为3个基本子问题。通过对这3个基本子问题,分别采用bangbang控制算法进行求解,从而完成目标状态速度为任意值的一维轨迹规划问题。在完成一维轨迹规划的基础上,进行时间同步处理,完成二维轨迹规划问题。
3.提出一种参数化最优控制轨迹规划算法。该算法结合全方位机器人特殊的运动能力,将参数化轨迹算法进行了有针对性的改进,从而能够更充分的发挥出全方位移动机器人的运动能力。对比实验证明,参数化轨迹规划算法得到的轨迹更加光滑流畅,轨迹执行时间更短。当初速度较大和初速度方向与位移方向夹角较大时,参数化算法得到的轨迹要比bangbang算法生成的轨迹快10%以上。
4.针对机器人执行复杂任务的规划问题,提出了一种基于PSO(粒子群优化算法)和神经网络的松弛边界条件轨迹规划算法。常规的轨迹规划算法主要是研究如何让机器人安全的从一个位置导航到另一个位置。在实际应用中,机器人执行的任务往往要比导航任务复杂。轨迹规划必须考虑在完成导航同时是否能有利于任务的完成。针对这类松弛边界条件轨迹规划问题,本文结合前面提出的固定边界条件轨迹规划算法,采用PSO优化算法进行离线寻优,并采用神经网络对寻优结果进行建模,以满足实时性的要求。
Supported by the National Natural Science funds projects and the863National projects, this thesis discusses some issues about motion control and plan of omnidirectional mobile robots. Detailed work are as follows:
1. A velocity compensation algorithm based on neural networks is proposed for omni-directional mobile robots. Through a comprehensive analysis of the omni-directional mobile robot kinematics and dynamics model, the executive deviation of robot is caused by the friction between the main wheel and the passive rollers. According to the results of the analysis model, A compensation algorithm based on a neural net-work model is presented. Experiment results and practical application show that the compensation model can improve the execution accuracy of the robot.
2. A time optimal trajectory generation algorithm using bangbang control principal is proposed. Most research on trajectory generation of omnidirectional robots assume the final velocities to be zero in order to avoid discontinuities when approaching the destination. By introducing a new time optimal control method, our algorithm can handle the discontinuities when approaching the destination. With the new algorithm, our system is capable of generating very complex trajectories, for example, finding an optimal trajectory passing more than2points. Our algorithm can be used as a part of high-level path planner.
3. A parameterized time optimal trajectory generation algorithm for omni-directional robots is proposed. The algorithm combines all of the special capability of omni-directional robots. It can make full use of the robots capability. The contrast experi-ments show that the trajectories generated by the parameterized algorithm are more smooth and efficiency than the one generated by the bangbang method. In some cases, the former is over10%faster than the latter.
4. For performing motion planning in complex environments that go beyond traditional navigation planning, the problem's boundary conditions sometimes are not closed. An open boundary trajectory generation algorithm based on PSO(Particle Swarm Optimal) and neural network is proposed for such problem. We use PSO to do the offline optimal, and neural network to perform on-line application.
1.提出一种基于神经网络的全方位移动机器人速度补偿算法。通过对全方位移动机器人的运动学和动力学模型详细分析,以及对万向轮中主动轮和从动轮的受力分析,本文发现万向轮中主动轮和从动轮之间的摩擦力是造成全方位移动机器人产生执行偏差的主要原因。根据模型分析的结果,建立一个基于神经网络的速度补偿模型,实验和实际使用证明该补偿模型可以将机器人的执行偏差从15%降低到5%。
2.提出一种基于bangbang控制的时间最优轨迹规划算法。该算法克服了以往bangbang轨迹规划方法只能处理目标状态末速度为零的缺陷。本文先重点研究了一维轨迹规划问题。根据机器人的初始状态和目标状态,提出一种新的分类标准,将一维轨迹规划问题分解为3个基本子问题。通过对这3个基本子问题,分别采用bangbang控制算法进行求解,从而完成目标状态速度为任意值的一维轨迹规划问题。在完成一维轨迹规划的基础上,进行时间同步处理,完成二维轨迹规划问题。
3.提出一种参数化最优控制轨迹规划算法。该算法结合全方位机器人特殊的运动能力,将参数化轨迹算法进行了有针对性的改进,从而能够更充分的发挥出全方位移动机器人的运动能力。对比实验证明,参数化轨迹规划算法得到的轨迹更加光滑流畅,轨迹执行时间更短。当初速度较大和初速度方向与位移方向夹角较大时,参数化算法得到的轨迹要比bangbang算法生成的轨迹快10%以上。
4.针对机器人执行复杂任务的规划问题,提出了一种基于PSO(粒子群优化算法)和神经网络的松弛边界条件轨迹规划算法。常规的轨迹规划算法主要是研究如何让机器人安全的从一个位置导航到另一个位置。在实际应用中,机器人执行的任务往往要比导航任务复杂。轨迹规划必须考虑在完成导航同时是否能有利于任务的完成。针对这类松弛边界条件轨迹规划问题,本文结合前面提出的固定边界条件轨迹规划算法,采用PSO优化算法进行离线寻优,并采用神经网络对寻优结果进行建模,以满足实时性的要求。
Supported by the National Natural Science funds projects and the863National projects, this thesis discusses some issues about motion control and plan of omnidirectional mobile robots. Detailed work are as follows:
1. A velocity compensation algorithm based on neural networks is proposed for omni-directional mobile robots. Through a comprehensive analysis of the omni-directional mobile robot kinematics and dynamics model, the executive deviation of robot is caused by the friction between the main wheel and the passive rollers. According to the results of the analysis model, A compensation algorithm based on a neural net-work model is presented. Experiment results and practical application show that the compensation model can improve the execution accuracy of the robot.
2. A time optimal trajectory generation algorithm using bangbang control principal is proposed. Most research on trajectory generation of omnidirectional robots assume the final velocities to be zero in order to avoid discontinuities when approaching the destination. By introducing a new time optimal control method, our algorithm can handle the discontinuities when approaching the destination. With the new algorithm, our system is capable of generating very complex trajectories, for example, finding an optimal trajectory passing more than2points. Our algorithm can be used as a part of high-level path planner.
3. A parameterized time optimal trajectory generation algorithm for omni-directional robots is proposed. The algorithm combines all of the special capability of omni-directional robots. It can make full use of the robots capability. The contrast experi-ments show that the trajectories generated by the parameterized algorithm are more smooth and efficiency than the one generated by the bangbang method. In some cases, the former is over10%faster than the latter.
4. For performing motion planning in complex environments that go beyond traditional navigation planning, the problem's boundary conditions sometimes are not closed. An open boundary trajectory generation algorithm based on PSO(Particle Swarm Optimal) and neural network is proposed for such problem. We use PSO to do the offline optimal, and neural network to perform on-line application.
引文
[1]梅凤翔.非完整系统力学基础[M].北京工业学院出版社,1985.
[2]胡跃明.非线性控制系统理论及应用[M].国防工业出版社,2002.
[3]郭丙华.非完整移动机器人运动规划研究[D]. PhD thesis华南理工大学,2003.
[4]李胜.非完整系统若干控制问题的研究[D]. PhD thesis南京理工大学,2005.
[5]祝晓才.轮式移动机器人的运动控制[D]. PhD thesis国防科学技术大学,2006.
[6]杰格日达,索尔塔哈,梅凤翔(译).非完整系统的运动方程和力学的变分原理：新一类控制问题[M].北京理工大学出版社,2007.
[7]韩光信.控制受限的非完整轮式移动机器人运动控制研究[D]. PhD thesis吉林大学,2009.
[8]陈德玲.主动前轮转向系统的控制系统[D]. PhD thesis上海交通大学,2008.
[9]J.A.Kennedy-McGregor. Ship-cleaning apparatus. US Patent 3,876,2251907.
[10]J.Grabowiecki. Vehicle wheel. US Patent 1,303,535.1919.
[11]Doroftei T, Grosu V, Spinu V. Bioinspiration and Robotics:Walking and Climbing Robots[M]. I-Tech Education and Publishing,2007:511-528.
[12]B.E.Ilon. Wheels for a course stable self-propelling vehicle movable in any desired direction on the ground or some other base. US Patent 3,876,255.1975.
[13]J.F.Blumrich. Omnidirectional wheel. US Patent 244,519.1974.
[14]Byun K S, Song J B. Design and construction of continuous alternate wheels for an omnidirectional mobile robot[J]. Journal of Robotic Systems,2003,20(9):569--579.
[15]Rojas R, Forster A. Holonomic control of a robot with an omnidirectional drive[J]. Kunstliche Intelligenz,2006.
[16]Stonier D, Cho S H, Choi S L, et al. Nonlinear slip dynamics for an omniwheel mo-bile robot platform[C]//Robotics and Automation,2007 IEEE International Confer-ence on.2007:2367-2372.
[17]Williams R L, Carter B E, Gallina P, et al. Dynamic model with slip for wheeled omnidirectional robots[J]. Robotics and Automation, IEEE Transactions on,2002, 18(3):285-293.
118] Balakrishna R, Ghosal A. Modeling of slip for wheeled mobile robots[J]. Robotics and Automation, IEEE Transactions on Robotics and Automation,1995,11 (1):126--132.
[19]Oubbati M, Schanz M, Buchheim T, et al. Velocity control of an omnidirectional robocup player with recurrent neural networks[G]//RoboCup 2005:Robot Soccer World Cup IX. vol 4020. Springer Berlin/Heidelberg,2006:691-701.
[20]Kalmar-nagy T, Raffaello D A, Ganguly P. Near-optimal dynamic trajectory gen-eration and control of an omnidirectional vehicle.[J]. Robotics and Autonomous Systems,2004,46:47-64.
[21]熊蓉,张翮,褚健,何臻峰,吴永海,四轮全方位移动机器人的建模和最优控制[J].控制理论与应用,2006,24(2)：170--176.
[22]Rong X, He 2, Jian C. Modeling and optimal control of omni-directional mobile robots[J]. Control Theory Apllications,2005,23:93-98.
[23]Purwin O, Andrea R D. Trajectory generation and control for four wheeled omnidi-rectional vehicles[J]. Robtics and Autonomous Systems,2006,54:13--22.
[24]邓旭玥,易建强,赵冬斌.一种全方位移动机器人的运动学分析[J].机器人,2004,26(1)：419--53.
[25]Loh W, Low K, Leow Y. Mechatronics design and kinematic modelling of a sin-gularityless omni-directional wheeled mobile robot[C]//Robotics and Automation, 2003, Proceedings. ICRA'03. IEEE International Conference on. vol 3.2003:3237--3242.
[26]Liu Y, Wu X. Jim Zhu J. et al. Omni-directional mobile robot controller design by trajectory linearization[C]//American Control Conference,2003. Proceedings of the 2003. vol 4.2003:3423-3428.
[27]赵冬斌,易建强,邓旭碉.全方位移动机器人结构和运动分析[J].机器人,2003.25(5)：394--398.
[28]张翮,熊蓉,褚健,丁冠英.一种全方位移动机器人的运动分析与控制实现[J].浙江大学学报(工学版),2004,38(12)：1650--1653.
[29]Kuo-Yang T, Shi-Chao L. Design and implementation of omni-directional soccer robots for robocup[C]//2006 IEEE International Conference on Systems, Man, and Cybernetics.2006.
[30]El-Shenawy A, Wellenreuther A, Baumgart A, et al. Comparing different holonomic mobile robots[C]//Systems, Man and Cybernetics,2007. ISIC. IEEE International Conference on.2007:1584-1589.
[31]Hofbaur M, Kob J, Steinbauer G, et al. Improving robustness of mobile robots using model-based reasoning [J]. Journal of Intelligent & Robotic Systems,2007, 48:37-54.
[32]聂晓璐,赵臣.全方位小型足球机器人的运动学分析[J].机械科学与技术,2007,26(11)：1408--1412.
[33]冷春涛,曹其新.四轮全方位移动机器人各向相异性研究[J].智能系统学报,2007,2(3)：45--51.
[34]梁延德,于华玉,何福本.全方位小型足球机器人运动特性分析[J].口设计与研究,2008,4：5--8.
[35]Sheng Y, Wu Y. Motion prediction in a high-speed, dynamic environment[C]//IC-TAI 2005:17th IEEE International Conference on Tools with Artificial Intelligence, ICTAI'05, November 14,2005-November 16,2005. vol 2005.2005:703--705.
[36]Ching-Chang W. Yu-Han L, Shin-An L. et al. Ga-based fuzzy system design in fpga for an omni-directional mobile robot[J]. Journal of Intelligent & Robotic Systems,2005,44:327-347.
[37]Dubins L E. On curves of minimal length with a constraint on average curvature,and with prescribed initial and terminal positions and tangents[J]. American Journal of Mathematics,1957,79(3):pp.497--516.
[38]Kanayama Y, Miyake N. Trajectory generation for mobile robots[C]//Proceedings of the International Symposium on Robotics Research.1985:16--23.
[39]Kanayama Y, Hartman B. Smooth local path planning for autonomous vehicls[C]// Proceedings of the International Conference on Robotics and Automation. vol 3. 1989:1265-1270.
[40]Komoriya K, Tanie K. Trajectory design and control of a wheel-type mobile robot using b-spline cureve[C]//In Proceedings of the IEE-RJ International Conference on Intelligent Robots and Systems.1989:398-405.
[41]Guan Y, Yokoi K, Stasse O, et al. On robotic trajectory planning using polynomial interpolations[C]//Robotics and Biomimetics (ROBIO).2005 IEEE International Conference on.2005:111-116.
[42]Howard T M, Kelly A. Trajectory and spline generation for all-wheel steering mo-bile robots[C]//Proceedings of the the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'06).2006:4827-4832.
[43]Gasparetto A., Zanotto V. Optimal trajectory planning for industrial robots[J]. Ad-vances in Engineering Software,2010,41(4):548--556.
[44]Baker D. Exact solutions to some minimum-time problems and theire behavior near inequality state constrains[J]. IEEE Transactions on Automatic Control,1989,34 (1):103--106.
[45]Delingette H. Hebert M, Ikeuchi K. Trajectory generation with curvature constraint based on energy minimization[C]//Proceedings 1991 IEEE/RSJ International Con-ference On Intelligent Robotic Systems (IROS'91).1991.
[46]Laumond J P. Nonholonomic motion planning via optimal control[C]//Proceedings of the workshop on Algorithmic foundations of robotics. Natick, MA, USA:1995: 227-238.
[47]Kelly A, Nagy B. Reactive nonholonomic trajectory generation via parametric op-timal control[J]. The International Journal of Robotics Research,2003,22(1):583--601.
[48]Howard T M, Kelly A. Terrain-adaptive generation of optimal continuous trajec-tories for mobile robots[C]//International Symposium on Artificial Intelligence, Robotics, and Automation in Space 2005 (iSAIRAS 05).2005.
[49]Howard T M, Kelly A. Trajectory generation on rough terrain considering actuator dynamics[C]//Field and Service Robotics 2005 (FSR 05). Port.2005.
[50]Howard T M, Kelly A. Constrained optimization path following of wheeled robots [C]//in Natural Terrain," ISER 2006:The Tenth International Symposium on Experimental Robotics.2006.
[51]Howard T M, Alonzo K. Optimal rough terrain trajectory generation for wheeled mobile robots[J]. International Journal of Robotics Research,2007,141-166.
[52]Urmson C, Anhalt J, Bagnell D. Autonomous driving in urban environments:Boss and the urban challenge[J]. The DARPA Urban Challenge,2009,1-59.
[53]Huang P, Liu G, Yuan J, et al. Multi-objective optimal trajectory planning of space robot using particle swarm optimization[G]//Advances in Neural Networks-ISNN 2008. vol 5264. Springer Berlin Heidelberg,2008:171-179.
[54]Kalmar-nagy T, Ganguly P. Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle[J]. Robotics and Autonomous Systems,2004,46:47--64.
[55]Sahraei A, Manzuri M, Razvan M, et al. Real-time trajectory generation for mobile robots[G]//AI*IA 2007:Artificial Intelligence and Human-Oriented Computing. vol 4733. Springer Berlin Heidelberg,2007:459--470.
[56]ZJUNLICT. http://nlict.zju.edu.cn/ssl/welcomepage.html.
[57]刘建良Robocup小型足球机器人视觉系统的构建[D]. Master's thesis浙江大学,2007.
[58]郭成果.全方位移动机器人视觉子系统的设计及实现[D]. Master's thesis浙江大学,2006.
[59]TSAI R Y. A versatile camera calibration technique for high-accuracy 3d machine vision metrology using-the-shelftv cameras and lenses[J]. IEEE Journal of Robotics and Automation,1987, RA-3(4).
[60]ODE. Open dynamics engine. http://www.ode.org.
[61]Microsoft. Robotics studio. http://www.microsoft.com/robotics.
[62]AGEIA. Physx. http://www.ageia.com.
[63]日本机器人学会.新版机器人技术手册[M].科学出版社,2005.
[64]Bemis S, Riess B, Nokleby S. Control of a novel omni-directional platform[C]// Electrical and Computer Engineering,2008. CCECE 2008. Canadian Conference on.2008:761--766.
[65]王仲民.移动机器人路径规划及轨迹跟踪问题研究[D]. PhD thesis河北工业大学,2006.
[66]史恩秀.轮式移动机器人的运动控制及定位方法研究[D]. PhD thesis西安理工大学,2006.
[67]王薇.轮式移动机器人的运动控制研究[D]. PhD thesis北京邮电大学,2009.
[68]Shin D H, Park K H. Velocity kinematic modeling for wheeled mobile robots[C]// 2001 IEEE International Conference on Robotics & Automation.2001,4:3516-3522.
[69]Chaoli Wang, Dalong Tan, Yuechao Wang. Stabilization of dynamic systems for multiple omni-directiona I mobile robots[J]. Journ al of Southeast University (En-glish Edition),2001.17(1):35-40.
[70]Ben-Israel A. Greville T, Greville T. Generalized Inverses:Theory and Applications [M]. books.google.com,2003.
[71]Zhao D, Yi J, Deng X. Motion regulation of redundantly actuated omni-directional wheeled mobile robots with internal force control [C]//Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.2007:3919-3924.
[72]杨新文,翟婉明.车轮扁疤激起的轮轨冲击噪声机理分析[J].震动与冲击,2009,28(8)：46--49.
[73]王建斌,邬平波,唐兆.车轮扁疤引发附加冲击力对车轴应力谱影响的研究[J].铁道学报,2006,28(1)：39--43.
[74]Vyas N S, Gupta A K. Modeling rail wheel-flat dynamics[G]//Engineering Asset Management. Springer London,2006:1222--1231.
[75]姜涛,孙守光,李强.车轮扁疤引起的车轴附加载荷的仿真研究[J].北方交通大学学报,1998,22(4)：61一65.
[76]翟婉明.铁路车轮扁疤的动力学效应[J].铁道车辆,1994,7：1--5.
[77]王其昌.车轮扁疤冲击分析[J].西南交通大学学报,1991,82(4)：45--48.
[78]Hecht-Nielsen R. Theory of the backpropagation neural network[C]//Neural Net-works,1989. IJCNN., International Joint Conference on. vol 1.1989:593--605.
[79]Hagan M T, Demuth H B, Beale M神经网络设计(Neural Network Design影响版)[M].机械工业出版社,2002.
[80]Haykin S,史忠植(译).神经网络原理[M].机械工业出版社,2004.
[81]Haykin S. Neural Networks and Leaning Machines[M]. Prentice Hall,2009.
[82]Dierks T, Jagannathan S. Neural network output feedback control of robot formations [J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on, 2010,40(2):383-399.
[83]Silva C, Tre, Lat E. Smooth regularization of bang-bang optimal control problems [J]. Automatic Control, IEEE Transactions on.2010,55(11):2488-2499.
[84]Peng Z, Yang Y, Huang L. Control elimination of time optimal bang-bang control with a class of input constraints[C]//Control and Automation (ICC A),2010 8th IEEE International Conference on.2010:1710-1715.
[85]Chang S, Huang T, Huang T. Fuzzy bang-bang controller for servo systems via optimal path estimation method[C]//Power Electronics and Drive Systems,1995., Proceedings of 1995 International Conference on.1995:208--211 vol.1.
[86]Glad T. The gain margin of optimal bang-bang control systems[C]//Decision and Control,1984. The 23rd IEEE Conference on. vol 23.1984:941-943.
[87]Luque E. Moreno L, Serra I. A time-optimal bang-bang control algorithm for mi-croprocessor control [C]//American Control Conference,1983.1983:750--751.
[88]Mohleji S, Thomas P. The design of optimal third-order bang-bang systems us-ing delayed switching[J]. Industrial Electronics and Control Instrumentation, IEEE Transactions on,1970, IECI-17(5):374--383.
[89]Dorato P, Hsieh C M, Robinson P. Optimal bang-bang control of linear stochastic systems with a small noise parameter[J]. Automatic Control, IEEE Transactions on, 1967,12(6):682--690.
[90]袁亚湘.最优化理论与方法[M].科学出版社,1997.
[91]蒋金山.最优化计算方法[M].华南理工大学出版社,2007.
[92]王晓陵.最优化方法与最优控制[M].哈尔滨工程大学出版社,2008.
[93]孙文瑜.最优化方法[M].高等教育出版社,2010.
[94]Howard T M. Green C J, Kelly A. Receding horizon model-predictive control for mobile robot navigation of intricate paths.
[95]Shi Y. Eberhart R. A modified particle swarm optimizer[C]//Proceedings of IEEE International Conference on Evolutionary Computation.1998:69--73.
[96]J. K, R. E. Particle swarm optimization[C]//Proceedings of IEEE International Con-ference on Neural Networks, vol Ⅳ.1995:1942--1948.
[97]Kennedy J. The particle swarm:social adaptation of knowledge[C]//Proceedings of IEEE International Conference on Evolutionary Computation.1997:303--308.
[98]Bratton D, Blackwell T. A simplified recombinant pso[J]. Journal of Artificial Evolution and Applications,2008.
[99]Carlisle A, Dozier G. An off-the-shelf pso[C]//Proceedings of the Particle Swarm Optimization Workshop.2001:1--6.
[100]van den Bergh F. An Analysis of Particle Swarm Optimizers[D]. PhD thesis. Uni-versity of Pretoria, Faculty of Natural and Agricultural Science,2001.
[101]Clerk M., Kennedy J. The particle swarm-explosion, stability, and convergence in a multidimensional complex space[J]. IEEE Transactions on Evolutionary Compu-tation,2002,6(1):58--73.
[102]Poli R. Analysis of the publications on the applications of particle swarm optimisa-tion[J]. Journal of Artificial Evolution and Applications,2008,1--10.
[103]Pedersen M. Tuning and Simplifying Heuristical Optimization[D]. PhD thesis. University of Southampton, School of Engineering Sciences, Computational Engi-neering and Design Group,2010.
[104]Pedersen M, Chipperfield A. Simplifying particle swarm optimization[J]. Applied Soft Computing,2010,618-628.
[105]Shi Y, Eberhart R. Parameter selection in particle swarm optimization[C]//Proceed-ings of Evolutionary Programming, vol Ⅶ.1998:591--600.
[106]Eberhart R, Shi Y. Comparing inertia weights and constriction factors in particle swarm optimization[C]// Proceedings of the Congress on Evolutionary Computation. 2000: 84-88.
[107]Inane T, Bhattacharya R, Muezzinoglu M K. Use of parametric approximation in real-time nonlinear trajectory generation[C]// Proceedings of the 45th IEEE Con-ference on Decision & Control. 2006:6808-6813.
[108]Huang P, Xu Y. Pso-based time-optimal trajectory planning for space robot wflh dynamic constraints.[C]//ROBIO'06. 2006:1402-1407.
[109]Jadbabaie A, Lin J, Morse A. Coordination of groups of mobile autonomous agents using nearest neighbor rules[J]. Automatic Control, IEEE Transactions on, 2003,48 (6):988-1001.
[110]杨甜甜,刘志远,陈虹,裴润.移动机器人编队控制的现状与问题[J].智能系统学报,2007,2(4)：21--25.
[111]柳林,刘斐,季秀才,卢惠民,海丹,郑志强.全向移动机器人编队分布式控制研究[J].机器人,2007,29(1)：23--28.
1112] Sorensen N, Ren W. A unified formation control scheme with a single or multiple leaders[C]// American Control Conference, 2007. ACC '07. 2007:5412-5418.
[113]Chen X, Min W, Li Y. Formation control based on adaptive nn with time-varying interaction among robots[C]// Control Conference, 2008. CCC 2008.27th Chinese. 2008: 341-345.
[114]姚恩瑜,何勇,陈仕平.数学规划与组合优化[M].浙江大学出版社,2001：142--146.
[115]Olfati-Saber R. Flocking for multi-agent dynamic systems: algorithms and theory [J]. Automatic Control, IEEE Transactions on, 2006,51(3):401~420.
[116]Zhang Y, Zeng L, Li Y, et al. Multi-robot formation control using leader-follower for manet[C]// Robotics and Biomimetics (ROBIO), 2009 IEEE International Con-ference on. 2009:337-342.
[117]Zhang T, Li X. Zhu Y, et al. Formation and obstacle avoidance in the unknown environment of multi-robot system[C]//Robotics and Biomimetics (ROBIO),2009 IEEE International Conference on.2009:729-734.
[118]Sheng-Ven S, Kuo-Lan S, Chun-Chieh W, et al. Formation exchange of the mul-tiple mobile robot system[C]//Computer Communication Control and Automation (3CA),2010 International Symposium on. vol 2.2010:265-269.
[119]Liu S, TAN D, LIU G. Vision-based formation control of mobile robots[J]. Journal of Control Theory and Applications,2005,2:173-180.
[120]Wang W. Slotine J J. A theoretical study of different leader roles in networks[J]. Automatic Control, IEEE Transactions on,2006,51 (7):1156-1161.
[121]Xing-ce W, Guo-chang G, Ru-bo Z. Design of the multirobot intelligent team for-mation's control architecture and performance analysis of the systme[J]. Journal of Harbin Institute of Technology,2007,14:124-129.
[122]Kang H D, Kawk J H, Kim C H, et al. Multiple robot formation keeping and coop-erative localization by panoramic view[C]//ICCAS-SICE,2009.2009:3509-3513.
[123]Mead R, Long R, Weinberg J. Fault-tolerant formations of mobile robots[C]//Intel-ligent Robots and Systems,2009. IROS 2009. IEEE/RSJ International Conference on.2009:4805-4810.
[124]谢文龙.机器人系统运动规划与协调的研究[D]. PhD thesis上海交通大学,2008.
[125]Kuhn H W. The hungarian method for the assignment problem[J]. Naval Research Logistics Quarterly,1955,2(1-2):83--97.
[2]胡跃明.非线性控制系统理论及应用[M].国防工业出版社,2002.
[3]郭丙华.非完整移动机器人运动规划研究[D]. PhD thesis华南理工大学,2003.
[4]李胜.非完整系统若干控制问题的研究[D]. PhD thesis南京理工大学,2005.
[5]祝晓才.轮式移动机器人的运动控制[D]. PhD thesis国防科学技术大学,2006.
[6]杰格日达,索尔塔哈,梅凤翔(译).非完整系统的运动方程和力学的变分原理：新一类控制问题[M].北京理工大学出版社,2007.
[7]韩光信.控制受限的非完整轮式移动机器人运动控制研究[D]. PhD thesis吉林大学,2009.
[8]陈德玲.主动前轮转向系统的控制系统[D]. PhD thesis上海交通大学,2008.
[9]J.A.Kennedy-McGregor. Ship-cleaning apparatus. US Patent 3,876,2251907.
[10]J.Grabowiecki. Vehicle wheel. US Patent 1,303,535.1919.
[11]Doroftei T, Grosu V, Spinu V. Bioinspiration and Robotics:Walking and Climbing Robots[M]. I-Tech Education and Publishing,2007:511-528.
[12]B.E.Ilon. Wheels for a course stable self-propelling vehicle movable in any desired direction on the ground or some other base. US Patent 3,876,255.1975.
[13]J.F.Blumrich. Omnidirectional wheel. US Patent 244,519.1974.
[14]Byun K S, Song J B. Design and construction of continuous alternate wheels for an omnidirectional mobile robot[J]. Journal of Robotic Systems,2003,20(9):569--579.
[15]Rojas R, Forster A. Holonomic control of a robot with an omnidirectional drive[J]. Kunstliche Intelligenz,2006.
[16]Stonier D, Cho S H, Choi S L, et al. Nonlinear slip dynamics for an omniwheel mo-bile robot platform[C]//Robotics and Automation,2007 IEEE International Confer-ence on.2007:2367-2372.
[17]Williams R L, Carter B E, Gallina P, et al. Dynamic model with slip for wheeled omnidirectional robots[J]. Robotics and Automation, IEEE Transactions on,2002, 18(3):285-293.
118] Balakrishna R, Ghosal A. Modeling of slip for wheeled mobile robots[J]. Robotics and Automation, IEEE Transactions on Robotics and Automation,1995,11 (1):126--132.
[19]Oubbati M, Schanz M, Buchheim T, et al. Velocity control of an omnidirectional robocup player with recurrent neural networks[G]//RoboCup 2005:Robot Soccer World Cup IX. vol 4020. Springer Berlin/Heidelberg,2006:691-701.
[20]Kalmar-nagy T, Raffaello D A, Ganguly P. Near-optimal dynamic trajectory gen-eration and control of an omnidirectional vehicle.[J]. Robotics and Autonomous Systems,2004,46:47-64.
[21]熊蓉,张翮,褚健,何臻峰,吴永海,四轮全方位移动机器人的建模和最优控制[J].控制理论与应用,2006,24(2)：170--176.
[22]Rong X, He 2, Jian C. Modeling and optimal control of omni-directional mobile robots[J]. Control Theory Apllications,2005,23:93-98.
[23]Purwin O, Andrea R D. Trajectory generation and control for four wheeled omnidi-rectional vehicles[J]. Robtics and Autonomous Systems,2006,54:13--22.
[24]邓旭玥,易建强,赵冬斌.一种全方位移动机器人的运动学分析[J].机器人,2004,26(1)：419--53.
[25]Loh W, Low K, Leow Y. Mechatronics design and kinematic modelling of a sin-gularityless omni-directional wheeled mobile robot[C]//Robotics and Automation, 2003, Proceedings. ICRA'03. IEEE International Conference on. vol 3.2003:3237--3242.
[26]Liu Y, Wu X. Jim Zhu J. et al. Omni-directional mobile robot controller design by trajectory linearization[C]//American Control Conference,2003. Proceedings of the 2003. vol 4.2003:3423-3428.
[27]赵冬斌,易建强,邓旭碉.全方位移动机器人结构和运动分析[J].机器人,2003.25(5)：394--398.
[28]张翮,熊蓉,褚健,丁冠英.一种全方位移动机器人的运动分析与控制实现[J].浙江大学学报(工学版),2004,38(12)：1650--1653.
[29]Kuo-Yang T, Shi-Chao L. Design and implementation of omni-directional soccer robots for robocup[C]//2006 IEEE International Conference on Systems, Man, and Cybernetics.2006.
[30]El-Shenawy A, Wellenreuther A, Baumgart A, et al. Comparing different holonomic mobile robots[C]//Systems, Man and Cybernetics,2007. ISIC. IEEE International Conference on.2007:1584-1589.
[31]Hofbaur M, Kob J, Steinbauer G, et al. Improving robustness of mobile robots using model-based reasoning [J]. Journal of Intelligent & Robotic Systems,2007, 48:37-54.
[32]聂晓璐,赵臣.全方位小型足球机器人的运动学分析[J].机械科学与技术,2007,26(11)：1408--1412.
[33]冷春涛,曹其新.四轮全方位移动机器人各向相异性研究[J].智能系统学报,2007,2(3)：45--51.
[34]梁延德,于华玉,何福本.全方位小型足球机器人运动特性分析[J].口设计与研究,2008,4：5--8.
[35]Sheng Y, Wu Y. Motion prediction in a high-speed, dynamic environment[C]//IC-TAI 2005:17th IEEE International Conference on Tools with Artificial Intelligence, ICTAI'05, November 14,2005-November 16,2005. vol 2005.2005:703--705.
[36]Ching-Chang W. Yu-Han L, Shin-An L. et al. Ga-based fuzzy system design in fpga for an omni-directional mobile robot[J]. Journal of Intelligent & Robotic Systems,2005,44:327-347.
[37]Dubins L E. On curves of minimal length with a constraint on average curvature,and with prescribed initial and terminal positions and tangents[J]. American Journal of Mathematics,1957,79(3):pp.497--516.
[38]Kanayama Y, Miyake N. Trajectory generation for mobile robots[C]//Proceedings of the International Symposium on Robotics Research.1985:16--23.
[39]Kanayama Y, Hartman B. Smooth local path planning for autonomous vehicls[C]// Proceedings of the International Conference on Robotics and Automation. vol 3. 1989:1265-1270.
[40]Komoriya K, Tanie K. Trajectory design and control of a wheel-type mobile robot using b-spline cureve[C]//In Proceedings of the IEE-RJ International Conference on Intelligent Robots and Systems.1989:398-405.
[41]Guan Y, Yokoi K, Stasse O, et al. On robotic trajectory planning using polynomial interpolations[C]//Robotics and Biomimetics (ROBIO).2005 IEEE International Conference on.2005:111-116.
[42]Howard T M, Kelly A. Trajectory and spline generation for all-wheel steering mo-bile robots[C]//Proceedings of the the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'06).2006:4827-4832.
[43]Gasparetto A., Zanotto V. Optimal trajectory planning for industrial robots[J]. Ad-vances in Engineering Software,2010,41(4):548--556.
[44]Baker D. Exact solutions to some minimum-time problems and theire behavior near inequality state constrains[J]. IEEE Transactions on Automatic Control,1989,34 (1):103--106.
[45]Delingette H. Hebert M, Ikeuchi K. Trajectory generation with curvature constraint based on energy minimization[C]//Proceedings 1991 IEEE/RSJ International Con-ference On Intelligent Robotic Systems (IROS'91).1991.
[46]Laumond J P. Nonholonomic motion planning via optimal control[C]//Proceedings of the workshop on Algorithmic foundations of robotics. Natick, MA, USA:1995: 227-238.
[47]Kelly A, Nagy B. Reactive nonholonomic trajectory generation via parametric op-timal control[J]. The International Journal of Robotics Research,2003,22(1):583--601.
[48]Howard T M, Kelly A. Terrain-adaptive generation of optimal continuous trajec-tories for mobile robots[C]//International Symposium on Artificial Intelligence, Robotics, and Automation in Space 2005 (iSAIRAS 05).2005.
[49]Howard T M, Kelly A. Trajectory generation on rough terrain considering actuator dynamics[C]//Field and Service Robotics 2005 (FSR 05). Port.2005.
[50]Howard T M, Kelly A. Constrained optimization path following of wheeled robots [C]//in Natural Terrain," ISER 2006:The Tenth International Symposium on Experimental Robotics.2006.
[51]Howard T M, Alonzo K. Optimal rough terrain trajectory generation for wheeled mobile robots[J]. International Journal of Robotics Research,2007,141-166.
[52]Urmson C, Anhalt J, Bagnell D. Autonomous driving in urban environments:Boss and the urban challenge[J]. The DARPA Urban Challenge,2009,1-59.
[53]Huang P, Liu G, Yuan J, et al. Multi-objective optimal trajectory planning of space robot using particle swarm optimization[G]//Advances in Neural Networks-ISNN 2008. vol 5264. Springer Berlin Heidelberg,2008:171-179.
[54]Kalmar-nagy T, Ganguly P. Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle[J]. Robotics and Autonomous Systems,2004,46:47--64.
[55]Sahraei A, Manzuri M, Razvan M, et al. Real-time trajectory generation for mobile robots[G]//AI*IA 2007:Artificial Intelligence and Human-Oriented Computing. vol 4733. Springer Berlin Heidelberg,2007:459--470.
[56]ZJUNLICT. http://nlict.zju.edu.cn/ssl/welcomepage.html.
[57]刘建良Robocup小型足球机器人视觉系统的构建[D]. Master's thesis浙江大学,2007.
[58]郭成果.全方位移动机器人视觉子系统的设计及实现[D]. Master's thesis浙江大学,2006.
[59]TSAI R Y. A versatile camera calibration technique for high-accuracy 3d machine vision metrology using-the-shelftv cameras and lenses[J]. IEEE Journal of Robotics and Automation,1987, RA-3(4).
[60]ODE. Open dynamics engine. http://www.ode.org.
[61]Microsoft. Robotics studio. http://www.microsoft.com/robotics.
[62]AGEIA. Physx. http://www.ageia.com.
[63]日本机器人学会.新版机器人技术手册[M].科学出版社,2005.
[64]Bemis S, Riess B, Nokleby S. Control of a novel omni-directional platform[C]// Electrical and Computer Engineering,2008. CCECE 2008. Canadian Conference on.2008:761--766.
[65]王仲民.移动机器人路径规划及轨迹跟踪问题研究[D]. PhD thesis河北工业大学,2006.
[66]史恩秀.轮式移动机器人的运动控制及定位方法研究[D]. PhD thesis西安理工大学,2006.
[67]王薇.轮式移动机器人的运动控制研究[D]. PhD thesis北京邮电大学,2009.
[68]Shin D H, Park K H. Velocity kinematic modeling for wheeled mobile robots[C]// 2001 IEEE International Conference on Robotics & Automation.2001,4:3516-3522.
[69]Chaoli Wang, Dalong Tan, Yuechao Wang. Stabilization of dynamic systems for multiple omni-directiona I mobile robots[J]. Journ al of Southeast University (En-glish Edition),2001.17(1):35-40.
[70]Ben-Israel A. Greville T, Greville T. Generalized Inverses:Theory and Applications [M]. books.google.com,2003.
[71]Zhao D, Yi J, Deng X. Motion regulation of redundantly actuated omni-directional wheeled mobile robots with internal force control [C]//Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.2007:3919-3924.
[72]杨新文,翟婉明.车轮扁疤激起的轮轨冲击噪声机理分析[J].震动与冲击,2009,28(8)：46--49.
[73]王建斌,邬平波,唐兆.车轮扁疤引发附加冲击力对车轴应力谱影响的研究[J].铁道学报,2006,28(1)：39--43.
[74]Vyas N S, Gupta A K. Modeling rail wheel-flat dynamics[G]//Engineering Asset Management. Springer London,2006:1222--1231.
[75]姜涛,孙守光,李强.车轮扁疤引起的车轴附加载荷的仿真研究[J].北方交通大学学报,1998,22(4)：61一65.
[76]翟婉明.铁路车轮扁疤的动力学效应[J].铁道车辆,1994,7：1--5.
[77]王其昌.车轮扁疤冲击分析[J].西南交通大学学报,1991,82(4)：45--48.
[78]Hecht-Nielsen R. Theory of the backpropagation neural network[C]//Neural Net-works,1989. IJCNN., International Joint Conference on. vol 1.1989:593--605.
[79]Hagan M T, Demuth H B, Beale M神经网络设计(Neural Network Design影响版)[M].机械工业出版社,2002.
[80]Haykin S,史忠植(译).神经网络原理[M].机械工业出版社,2004.
[81]Haykin S. Neural Networks and Leaning Machines[M]. Prentice Hall,2009.
[82]Dierks T, Jagannathan S. Neural network output feedback control of robot formations [J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on, 2010,40(2):383-399.
[83]Silva C, Tre, Lat E. Smooth regularization of bang-bang optimal control problems [J]. Automatic Control, IEEE Transactions on.2010,55(11):2488-2499.
[84]Peng Z, Yang Y, Huang L. Control elimination of time optimal bang-bang control with a class of input constraints[C]//Control and Automation (ICC A),2010 8th IEEE International Conference on.2010:1710-1715.
[85]Chang S, Huang T, Huang T. Fuzzy bang-bang controller for servo systems via optimal path estimation method[C]//Power Electronics and Drive Systems,1995., Proceedings of 1995 International Conference on.1995:208--211 vol.1.
[86]Glad T. The gain margin of optimal bang-bang control systems[C]//Decision and Control,1984. The 23rd IEEE Conference on. vol 23.1984:941-943.
[87]Luque E. Moreno L, Serra I. A time-optimal bang-bang control algorithm for mi-croprocessor control [C]//American Control Conference,1983.1983:750--751.
[88]Mohleji S, Thomas P. The design of optimal third-order bang-bang systems us-ing delayed switching[J]. Industrial Electronics and Control Instrumentation, IEEE Transactions on,1970, IECI-17(5):374--383.
[89]Dorato P, Hsieh C M, Robinson P. Optimal bang-bang control of linear stochastic systems with a small noise parameter[J]. Automatic Control, IEEE Transactions on, 1967,12(6):682--690.
[90]袁亚湘.最优化理论与方法[M].科学出版社,1997.
[91]蒋金山.最优化计算方法[M].华南理工大学出版社,2007.
[92]王晓陵.最优化方法与最优控制[M].哈尔滨工程大学出版社,2008.
[93]孙文瑜.最优化方法[M].高等教育出版社,2010.
[94]Howard T M. Green C J, Kelly A. Receding horizon model-predictive control for mobile robot navigation of intricate paths.
[95]Shi Y. Eberhart R. A modified particle swarm optimizer[C]//Proceedings of IEEE International Conference on Evolutionary Computation.1998:69--73.
[96]J. K, R. E. Particle swarm optimization[C]//Proceedings of IEEE International Con-ference on Neural Networks, vol Ⅳ.1995:1942--1948.
[97]Kennedy J. The particle swarm:social adaptation of knowledge[C]//Proceedings of IEEE International Conference on Evolutionary Computation.1997:303--308.
[98]Bratton D, Blackwell T. A simplified recombinant pso[J]. Journal of Artificial Evolution and Applications,2008.
[99]Carlisle A, Dozier G. An off-the-shelf pso[C]//Proceedings of the Particle Swarm Optimization Workshop.2001:1--6.
[100]van den Bergh F. An Analysis of Particle Swarm Optimizers[D]. PhD thesis. Uni-versity of Pretoria, Faculty of Natural and Agricultural Science,2001.
[101]Clerk M., Kennedy J. The particle swarm-explosion, stability, and convergence in a multidimensional complex space[J]. IEEE Transactions on Evolutionary Compu-tation,2002,6(1):58--73.
[102]Poli R. Analysis of the publications on the applications of particle swarm optimisa-tion[J]. Journal of Artificial Evolution and Applications,2008,1--10.
[103]Pedersen M. Tuning and Simplifying Heuristical Optimization[D]. PhD thesis. University of Southampton, School of Engineering Sciences, Computational Engi-neering and Design Group,2010.
[104]Pedersen M, Chipperfield A. Simplifying particle swarm optimization[J]. Applied Soft Computing,2010,618-628.
[105]Shi Y, Eberhart R. Parameter selection in particle swarm optimization[C]//Proceed-ings of Evolutionary Programming, vol Ⅶ.1998:591--600.
[106]Eberhart R, Shi Y. Comparing inertia weights and constriction factors in particle swarm optimization[C]// Proceedings of the Congress on Evolutionary Computation. 2000: 84-88.
[107]Inane T, Bhattacharya R, Muezzinoglu M K. Use of parametric approximation in real-time nonlinear trajectory generation[C]// Proceedings of the 45th IEEE Con-ference on Decision & Control. 2006:6808-6813.
[108]Huang P, Xu Y. Pso-based time-optimal trajectory planning for space robot wflh dynamic constraints.[C]//ROBIO'06. 2006:1402-1407.
[109]Jadbabaie A, Lin J, Morse A. Coordination of groups of mobile autonomous agents using nearest neighbor rules[J]. Automatic Control, IEEE Transactions on, 2003,48 (6):988-1001.
[110]杨甜甜,刘志远,陈虹,裴润.移动机器人编队控制的现状与问题[J].智能系统学报,2007,2(4)：21--25.
[111]柳林,刘斐,季秀才,卢惠民,海丹,郑志强.全向移动机器人编队分布式控制研究[J].机器人,2007,29(1)：23--28.
1112] Sorensen N, Ren W. A unified formation control scheme with a single or multiple leaders[C]// American Control Conference, 2007. ACC '07. 2007:5412-5418.
[113]Chen X, Min W, Li Y. Formation control based on adaptive nn with time-varying interaction among robots[C]// Control Conference, 2008. CCC 2008.27th Chinese. 2008: 341-345.
[114]姚恩瑜,何勇,陈仕平.数学规划与组合优化[M].浙江大学出版社,2001：142--146.
[115]Olfati-Saber R. Flocking for multi-agent dynamic systems: algorithms and theory [J]. Automatic Control, IEEE Transactions on, 2006,51(3):401~420.
[116]Zhang Y, Zeng L, Li Y, et al. Multi-robot formation control using leader-follower for manet[C]// Robotics and Biomimetics (ROBIO), 2009 IEEE International Con-ference on. 2009:337-342.
[117]Zhang T, Li X. Zhu Y, et al. Formation and obstacle avoidance in the unknown environment of multi-robot system[C]//Robotics and Biomimetics (ROBIO),2009 IEEE International Conference on.2009:729-734.
[118]Sheng-Ven S, Kuo-Lan S, Chun-Chieh W, et al. Formation exchange of the mul-tiple mobile robot system[C]//Computer Communication Control and Automation (3CA),2010 International Symposium on. vol 2.2010:265-269.
[119]Liu S, TAN D, LIU G. Vision-based formation control of mobile robots[J]. Journal of Control Theory and Applications,2005,2:173-180.
[120]Wang W. Slotine J J. A theoretical study of different leader roles in networks[J]. Automatic Control, IEEE Transactions on,2006,51 (7):1156-1161.
[121]Xing-ce W, Guo-chang G, Ru-bo Z. Design of the multirobot intelligent team for-mation's control architecture and performance analysis of the systme[J]. Journal of Harbin Institute of Technology,2007,14:124-129.
[122]Kang H D, Kawk J H, Kim C H, et al. Multiple robot formation keeping and coop-erative localization by panoramic view[C]//ICCAS-SICE,2009.2009:3509-3513.
[123]Mead R, Long R, Weinberg J. Fault-tolerant formations of mobile robots[C]//Intel-ligent Robots and Systems,2009. IROS 2009. IEEE/RSJ International Conference on.2009:4805-4810.
[124]谢文龙.机器人系统运动规划与协调的研究[D]. PhD thesis上海交通大学,2008.
[125]Kuhn H W. The hungarian method for the assignment problem[J]. Naval Research Logistics Quarterly,1955,2(1-2):83--97.