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1、基于多机器人协调的船体分段对接系统的运动学及对接精度研究1) 国家“863”计划资助项目（编号：992103）.景奉水 谭民 侯增广 梁自泽 王云宽（中国科学院自动化研究 北京 100080）摘 要: 本文研究了基于多机器人协调的船体分段对接系统的运动学和对接精度问题。根据船体分段对接工艺特点，提出了了机器人的轨迹规划算法和对接控制方案。在此基础上，讨论了几种误差因素对系统对接精度的影响。理论分析和仿真结果都表明，在对接平台结构尺寸存在显著误差的情况下，采用本文提出的方法仍可以保证船体分段对接精度。关键词: 多机器人协调；移动机器人；对接精度；运动学中图分类号:TP13文献标志码：BSTUDY
2、 ON THE KINEMATICS AND MERGING PRECISION OF A SHIP BLOCK MERGING SYSTEM BASED ON MULTI-ROBOT COORDINATIONJING Feng-Shui TAN Min HOU Zeng-Guang LIANG Zi-Ze WANG Yun-Kuan(Institute of Automation, Chinese Academy of Sciences, Beijing 100080)Abstract: This paper has studied the kinematics and the precis
3、ion of a ship block merging system based on the multi-robot coordination. In coordination with the characteristics of the blocks merging technology, the boat blocks trajectory planning method and merging control scheme were presented. After that, we discussed a number of error factors, which may aff
4、ect the system precision. The simulation results and theoretical analysis show that, the merging systems precision can be guaranteed with the proposed the proposed methods even there are significant dimensional errors of the system structure.Key words: multi-robot coordination, mobile robots, mergin
5、g precision, kinematics1 引言(Introduction)多机器人协调（Multi-Robot Coordination）的研究起源于20世纪80年代初期。在任务本身复杂的情况下，如搬运大型物体，单个机器人难以完成；而多个机器人由于其内在分布特性，通过共享资源（信息、知识、物理装置等）可弥补单个机器人能力的不足，扩大能力范围，往往就可以获得满意效果。另外，设计若干简单的机器人比为具体任务设计功能强大的单个机器人容易、经济，且在容错性、柔性等方面具有优越性1。目前对多机器人协调的研究已引起普遍重视 2, 3。受多机器人协调搬运大型物体的启发 4, 5, 6, 7，本文对多
6、机器人协调对接大型船体分段进行了研究。第2节说明对接系统的结构；第3节研究对接系统的逆运动学和轨迹规划算法；第4节给出分段对接的控制方案，并讨论尺寸误差对系统精度的影响；第5节对全文的结果做出总结。2 对接系统结构(Merging system architecture)如图1所示，多个置于轨道上移动机器人的手部分别固定在两根刚性纵梁上，在纵梁之上再铺设横梁，从而构成托起移动段的平台。每个移动机器人的手部具有上下、左右和前后三个垂直方向上的运动自由度。系统依靠多个机器人协调运动，调整移动段的位姿，完成与基准段的对接。YbXpYpZR1XR1OR1ORnYRnxRnOpYR1基准段XbO0ObZ
7、0Y0X0H轨道移动段测量标志横梁纵梁移动机器人ZpDZb图 1船体分段对接系统Fig.1 Ship block merging system3 运动学与轨迹规划(Kinematics and trajectory planning)3.1移动段的运动模型由于船体分段重量较大，在进行调整时，已通过横梁和木桩压紧了纵梁，使得从纵梁到分段范围内的所有物体可以看作一个整体刚体。另外，机器人移动段的上下、左右平移，以及绕3个轴的转动都是由液压伺服驱动，而液压缸的有效行程同分段或纵梁尺寸相比，可视为小位移。因此，移动段的运动可以作为刚体小位移运动模型来处理。3.2移动段的逆运动学算法和轨迹规划算法分段的
8、对接是利用逆运动学算法，由移动段同基准段的位姿偏差求出各机器人关节位移，而后进行轨迹规划，最后由机器人伺服系统执行以消除或缩小移动段与基准段偏差的过程。为描述逆运动学算法，首先建立以下参考坐标系：1) 基准段坐标系。如图1所示，坐标系原点O0为基准段几何形心，X0轴、Y0轴在水平面上，Z0轴按右手系处于铅垂面内。2) 移动段坐标系。如图1所示，坐标系原点Ob为移动段的几何形心，Xb轴、Yb轴在移动段水平面上，Zb轴按右手系处于移动段铅垂面内。移动段坐标系原点同基准段坐标系原点沿Y0方向相隔距离为D。当移动段与基准段对正时，二者的水平面重合，垂直面平行。3) 平台坐标系。在移动段调整时，可以认为
9、机器人的手部中心始终处于同一平面，称为移动平台面，这一平面与移动段的水平面平行且相距H；取移动段坐标系的Zb轴与该平面的交点为平台坐标系的原点Op， Xp轴、Yp轴在移动平台面上，按右手系取Zp轴，如图1所示。4) 机器人末端坐标系。机器人末端坐标系的原点ORi位于机器人手部中心，ZRi轴竖直向上，与主缸上移方向一致；XRi轴水平向右，与副缸右移方向一致，按右手系取轴YRi，i=1,2n。n 为机器人数目。记T(x, f), T(y, a), T(z, q)表示绕x, y, z轴旋转齐次变换矩阵，Tran(px, py, pz)为平移齐次变换矩 阵，px，py，pz分别为移动段绕X0, Y0,
10、 Z0轴转角以及沿X0 ,Y0, Z0轴的位移，则第i个机器人坐标系到基准坐标系的齐次变化矩阵为：(1)由(1)式可得到第i个机器人坐标系原点，即其手部在基准坐标系的齐次坐标(2)将=0，px=py=pz=0代入(2)式，得到移动段处于对正位姿时，机器人坐标系原点在基准坐标系中的齐次坐标(3)机器人坐标系原点的位置与其手部位置一致，因此(2)式减去(3)式，得到移动段偏离对正位姿，做，旋转和px，py，pz平动时，机器人各关节需要移动的位移，即为机器人逆运动学解法；反之，(3)减去(2) 式，得到移动段从偏离位置回到对正位姿时机器人各关节需要的位移量，即机器人在对正调整时各关节的运动轨迹：主缸
11、位移 (4)副缸位移 (5)行走位移(6)式中，S表示正弦函数，C表示正弦函数，以下同。由于py项仅影响移动段与基准段的间距，即只影响分段的对接，而不影响分段的对正；而且移动段沿平直轨道与基准段对接时，不会影响分段原有的姿态和对正结果。利用这一点，可将分段的对接分成两个阶段：分段位姿对正和分段对接。在分段位姿对正完成后，分段对接只是简单的多机器人同步行走任务。以下只考虑分段位姿对正问题。令py=0，并忽略关于S，S，S，px， pz的2阶以上项，整理式(4)(6)，得到机器人各关节在分段位姿对正时的运动轨迹：(7)(8)(8)(9)3.3 移动段偏移，px，pz的计算以上公式中都是以移动段的旋
12、转角位移和平动线位移为自变量的。这些值难以在现场直接测量得到，但可以通过测量移动段定位点偏移的方法间接获得。如图1所示，在分段首尾端分别设置4个共圆定位点，且上下4个定位点处于同一平面，称为分段铅垂面；左右4个标志点也在同一平面，称为分段水平面。对正的目标即是要求移动段的上下标志点位于基准段的铅垂面上，左右标志点位于基准段的水平面上。引入记号Uf，Df，Lf，Rf，Ub，Db，Lb，Rb来表示分段8个定位点的偏移值，U，D，L，R代表上、下、左、右；下标f, b代表移动段的前后端面。它们共同说明标志点所在位置。偏移的正负号依坐标轴的正负方向定义，即向上偏移、向右偏移为正，反之为负。用Wf，Wb
13、来记前后端面定位园的直径，E来表示移动段长度。现说明如何由偏差测量值计算移动段偏移px，pz，。因为是小位移，易由各量间的几何关系和三角函数关系得到下列位移计算方法。1）前端面的平移量pxf，pzf和绕Y轴角位移f , ，或(10)2）后端面的平移量pxb，pzb和绕Y轴角位移b, 或 (11)3）移动段偏移px，pz，, , ， ,(12)4 控制方案和精度分析(Control scheme and procision analysis) 定位点偏差计算px，pz， 机器人轨迹规划执行机构基准段位姿比较移动段位姿图2 分段位姿对正的控制方案Fig.2 Control scheme of th
14、e posture aligning of ship blocks前面给出的船体分段位姿对正时的轨迹规划算法，并没有考虑模型误差。一般情况下，不能仅靠一次调整就能达到对接精度要求，往往需要多次调整才能达到对正的目标，我们采用了图2所示控制方案。另外，图1所展示的多机器人协调对接平台的结构是庞大且相对松散的，由于制造精度、弹塑性变形、测量精度等原因，各种结构尺寸实际值和名义值之间必然存在误差，而且数值往往远大于对接精度（典型的对接精度要求定位点偏差在1mm左右）。因此必须研究结构尺寸误差对于对接精度和系统稳定性的影响。从式(7)(9)容易看出，结构尺寸误差直接影响机器人轨迹规划结果。令, ,m为
15、机器人关节位移矢量，v平台结构尺寸矢量。由式(7)(9)可得到，(13)式中，J 为m 对v 的Jacobian 矩阵，反映了v的变化对m的影响程度，即有如下关系，(14)J内元素均是关于，函数，不难看出，在小位移前提下，J近为零矩阵。换言之，m对v的变化不敏感，不会对图2所示控制系统的稳定性产生大的影响。不失一般性，考察由4个3自由度移动机器人构成的船体分段对接平台。两纵梁的名义长度LB=20000.00mm, 名义间距SB=20000.00mm。各机器人分布在平台左右两根纵梁的两端，其手部坐标系原点在平台坐标系坐标(xRi，yRi)分别为(-SB/2，LB/2), (-SB/2，-LB/2
16、), (SB/2，LB/2), (SB/2，-LB/2)。移动段前后端面的定位圆直径Wf = Wb=10000.00mm，移动段长度 E=15000.00mm，移动段水平面与平台移动面名义距离H=12000.00mm。偏差测量数据为Uf=-4.99mm，Df=-205.02mm，Lf=225.02mm，Rf=24.99mm，Ub=145.02mm，Db=-55.01mm，Lb=75.01mm，Rb=-125.01mm。假设由于各种原因，使得LB, SB , H的实际值偏离了名义值，变化范围为10。表1显示了当按LB, SB , H名义值计算机器人关节位移，而按实际值计算移动段位姿时，均方差表1
17、 仿真结果Table 1 Simulation results平台结构实际值LB=20000, SB=20000,H =12000 LB=22000, SB=20000,H =12000LB=20000, SB=20000,H =13200LB=22000, SB=22000,H =13200调整前s131.636131.636131.636131.636调整1次后s2.1217.122417.08211.543调整2次后s0.0000.6200.0031.035调整3次后s0.0000.0560.0000.094随位姿对正次数增加而变化的情况（表1中的数据单位为mm）。从表1可以看出，即使结
18、构尺寸的实际值偏离名义值高达10，在增加少量调节次数条件下，仍可保证对接精度，这与前面分析的结论一致。5 结语(Conclusion) 一个相对松散的分布式系统，在存在大的结构尺寸误差的情形下，通过采用恰当的建模方法和控制策略，可达到精密对接的目标，是本文的一个重要结果。此外, 文中的机器人轨迹规划算法与机器人的数量无关，可以根据移动段的重量和尺寸来决定参与操作的机器人个数，使系统具有柔性和适应能力，显示出多机器人系统的优越性。参考文献(References)1 谭民. 机器人群体协作与控制的研究. 见： 863计划自动控制领域发展战略研讨会论文集， 北京: 1999, 185 - - 190
19、2 王越超，谈大龙. 协作机器人学的研究现状与发展. 机器人，1998，20(1)：69 753 Cao.Y, Fukunaga. A., Kahng. A. Cooperative mobile robotic: antecedents and directions. Autonomous Robotics . 1997, 4(1):7274 M. Hashimoto and F. Oba. Dynamic control approach for motion coordination of multiple wheeled mobile robots transporting a sin
20、gle object. In IEEE/RSJ IROS, 1993, 1944-19515 Johnson, P.J., Bay, J.S., Distributed control of simulated autonomous mobile-robot collective in payload transportation. Autonomous Robots , 1995, 2(1):43-636 Z.-D. Wang, E. Nakano, and T. Matsukawa. Cooperating multiple behavior based robots for object
21、 manipulation. In IEEE/RSJ IROS, 1994, 1524-1531.7 D. J. Stillwell and J. S. Bay. Toward the development of a material transport system using swarms of ant-like robots. In IEEE ICRA, volume 6, 1993, 766-771, 8 Fukuda, T, Iritani, G. Construction mechanism of group behavior with cooperation. In Proce
22、edings of the 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems, Pennsylvania, USA: 1995, 535-542作者简介景奉水 男，1969年生，博士研究生。研究领域为机器人控制和机器人视觉。谭民 男，1962年生，研究员，博士生导师。研究领域为机器人控制等。侯增广 男，1969年生，副研究员。研究领域为移动机器人。梁自泽 男，1962年生，副研究员。研究领域为机电伺服控制。王云宽 男，1966年生，副研究员。研究领域为机电伺服控制。Editors note: Jud
23、son Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static
24、 from space hear the faint beeps of the worlds first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled
25、 the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under
26、my desk. Im anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.Its like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack
27、 of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line we would be go
28、 for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a l
29、evel I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the
30、 ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgart
31、ner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The ball
32、oon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.1
33、7 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I
34、would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end
35、of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer t
36、o Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude
37、of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free f
38、all at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.
