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外文文獻(xiàn)翻譯
（屆）
New Steering Mechanism for Wheeled Mobile Robots
新創(chuàng)造的輪式督導(dǎo)機(jī)制移動(dòng)機(jī)器人
學(xué)生姓名
學(xué) 號(hào)
院 系
專(zhuān) 業(yè)
指導(dǎo)教師
完成日期
New Steering Mechanism for Wheeled Mobile Robots
Siaibe Marie Bernard, FU Yi-li, XU He, MA Yu-lin
(School of Mechanical and Electrical Engineering, Center of Advanced Manufacturing Technology,Harbin Institute of Technology Harbin 150001,China,E—mail：sidibebernard@yaho.Fr)
Abstract：A new castor wheel mechanism for Omni-directional mobile platform is presented. A motion of translation is transformed into a rotation to steer the wheel with the help of a helical path fits into a translation joint and three rollers whose axes are connected to the driving shaft of the wheel. When the path moves in translation it acts on the rollers for steering. The path-roller friction transmission. The wheel kinematics and the maneuverability have been analyzed.
Key words：castor wheel；helical path；friction；roller；maneuverability；mobility
CLC number：TP24 Document code：A Article ID：l0o5-9l13(2007)02-0184-05
Mobile platform has attracted various researches in robotic applications such as wheelchair,car-like-robotetc.Different categories of Omni-directional mobile platform s have been presented significantly over the last 20 years. Their mechanical structures are mainly differentiated and characterized by the wheel echanisms.which determine their mobility【1】.It has been shown that only robots equipped with three castor wheels or three universal wheels have fu兒mobility (homonymic and mni-directional）【5】.The universal wheels present several drawbacks such as low load capacity-Periodical bump leading to a vibration【8】.Their mechanism is usually complex ,with many parts increasing the weight of the mobile platform. The three castor-Wheeled mobile robot main drawbacks is that it needs at least four actuators (three for steering and at least one for drive).Some examples exist with six actuators, three driving and three steering actuators .This phenomenon leads to some singularities in control. But it has the advantage of carrying important load[9] .Up to now new researches are going on castor wheeled mobile robot【2.3】 , and most of mobile robots for manipulation have only conventional wheel[9],The interest of our research consists of a design of new type of castor wheel mechanism with a connection of elementary joints (spin, linear and screw joints).The interest of our work is the improvement of the maneuverability.
For that we have shown in Section 4 that an elementary linear displacement of the joint can produce an important steering angle of the wheel because the steering angle of our mechanism depends on the linear displacement of a joint. The kinematics is given in Section 2.
1 Wheel Architecture
1.1 Description
The computer model is represented in Figs.1—3 represent the kinematical chain of the wheel mechanism. It has 3 rollers (Fig.2) able to rotate freely about their axis. Each of them has a free revolute joint with a shaft. The three shafts are built in to each other and fit to the wheel shaft and the revolute joint4 (Figs.1 and 3)
So the ensemble of this connection constitutes the wheel link (wheel suspension) which can turn about the vertical axe passing trough the centers of joints 1,3 and 4 (Fig.3).The shaft divided into two different forms：cylindrical form at one side and prismatic at another one (Fig.1).
At the down side is a cylinder forming with the wheel link a revolute joint(joint4) and the upper side is prismatic built in the platform and forming with the cylinder of the helical path a translation joint1.The aim of the latest cited is to provide a translation motion to the helical path rea1ized around a cylinder(Fig.1,part with gold color)。
1.2 Kinematics Description
The kinematics representation of the mechanism is in Fig.3.In fact. the helical path and rollers connection can be considered as a screw joint. The path is a screw constrained in rotation about vertical axis by joint l and the rollers consist of a nut constrained in translation about the same axle by joint 4.Joint1 is actuated in translation. When it moves the path acts on the rollers. At their turn, animating by a rotation about the vertical axe. They react on the wheel link and finally on the wheel.
The eccentricity e and the height h remain constant whatever the posture of the platform. The use of rollers rolling without slipping inside the path is important to avoid coulomb friction even if they make the mechanism little bulky.
2 Path-roller Friction
Let us consider a cylinder in a coordinate system (o X, Y, z) and free of rotation about its axle (Fig.4 (a)).The cylinder and its axle ale free to rotate about and a vertical ax le distant of R from the wheel. An inclined plan with angle 6 is in contact with the cylinder. When the plan translates with respect to axis .The contact line (cylinder—plan) moves with respect to axis Y and the cylinder rotates of angle about the vertical axle. This angle corresponds to the rotation angle of the contact line.
These different motions can be expressed as follow
Where displacement of the plan with respect to axis z and Y is is the linear displacement of the contact point with respect to axis Y.The linear displacement of R the cylinder is equivalent to y. Then Eq.(1) Becomes
The parameters of a screw (Fig.4(b)) are：the diameter 2R the thread inclination 6 and the pitch P.They are related by
Finally the relation between the steering and the displacement of the translation joint by a combination of Eq.(2) and (3)
Eq.(4)relates the linear displacement of the prismatic joint of the helical path to the steering angle of the wheel.
3 Kinematics
The kinematics of wheeled mobile robot can be found in Refs[6～7].In this section we have added to these results the changes required by our mechanism.
In Fig.5,OXY and P XI Y1 represent the world coordinate and the robot coordinate .The robot posture is defined in the world coordinate by：x ,Y and .
X, Y are the coordinate of the point P and 0 is the robot orientation
The rotation matrix expressing the orientation of OXY with respect to the platform frame PX1Y1 is given by
Wheel parameters are：e is the eccentricity of the whee1 .It represents the distance between the centers of the wheel B the rotation axe passing by point A of the platform. l and a are the polar coordinates of A with respect to PXIY1(Fig.5).The wheel radius is defined by r is and P is the pitch helical path of wheel mechanism. Wheel variables are and.
The posture of the translation joint is represented by z of wheel I with respect to axis (Fig.3). Represents the rotation angle of the wheel I about an axis passing by the wheel center B.
The kinematics constraints of a traditional castor wheel are obtained by the projection of the velocities of the robot and the wheel into the wheel plan and in a plane perpendicular to the wheel plane. They are
The constraints of our presented wheel mechanism are obtained by a combination of Esq..(4) And (7) and then (4) and (8)
The last two above equations represent only the constraints of only one wheel. If three of our wheel mechanism is implemented to a mobile robot, the total number of constraints will be six.
4 Examples
In this section, we consider an example of a typical car—like-robot,I.e.A mobile robot equipped with two Passives fixed standard wheels and one castor wheel of our type and each wheel are distant of Z to the origin P 0f the robot rame(Fig.6).We assume that all of the three wheels have the same radius r and the robot is steered and driving by the castor whee1.W e also assume that the ground is an horizontal plane and there is no sliding or friction between wheels and ground.
The fixed standard wheel parameters are represented in Fig.7.As f0r the castor wheel, its kinematics constraints are obtained by projecting of the different velocities in wheel plane and in a plane perpendicular to the wheel plane .They are
Due to the arrangement of the three wheels in Fig.6,we have the following values：
.With these values a system forming by Eq.(11)(i=1,2 for the two fixed standard wheels)and Eq.(9)(For the castor whee1) can be written as
A system forming by Eq(12)(i=1,2)(for the two fixed standard wheels)and Eq.(10)(For the castor wheel) can be written as
Eq. (13) and (14) represent the robot kinematics constraints. The helical path. This is the steering mechanism, intervenes only during the robot steering process. In this example we consider as in pure rotation process then the components x and y of matrixbecome zero. We also consider that the steering and driving angular velocities of whee1.3 are equal .After some calculations Esq..(13) And (14) become
By eliminating 3 in the last 2 equations and using values in Tab.1 we obtain the following relation
Which is represented in Fig.8.All couple (z, P) that vanish Eq. (1 7) will satisfy the assumption, which is considering the robot in pure rotation.
5 The Interest of the Mechanism
Given two wheeled mobile robots of equal mobility but different maneuverability, the more maneuverable robot will typically be advantageous in cluttered environments. A vehicle’s maneuverability is characterized by its ability to perform movements that combine multi-Dle degrees of freedom [10].Three castor—wheeled mobile robot has good values of degree of mobility (6 =3)and degree of steeribilitybut the maneuverability is closely linked to its design. In theory it is easy to steer a castor wheel straight by an actuator. But during the steering process some frictions occur opposing forces .the torque sometime should be multiplied. A rapid reaction in steering is needed when decision is made to turn. This is maneuverability. These two situations are the reasons why the need of mechanism for steering a castor wheel. In our case, the steering angle is a function of the pitch P
For a fixed displacement of z = 10 mm.Fig.9 shows the values of B for the chose of p during design. The system is more maneuverable for any P mini corresponding to any B maxi.
6 Conclusions
Since the beginning of mechanics a lot of simple rolling mechanisms got a castor wheel .In the field of robotic systems it has a particular importance for transportation an exploration .This paper brings a new type of castor drive to this field .In this paper, we have examined the design of a new steering mechanism .Its kinematics and the maneuverability have been analyzed.
References：
[1] Myung-Jin Jung, JonG—Hwan Kwa.Mobility augmentation of conventional wheeled bases for omni.directional motion.IEEE Transaction on Robotics and Automation.2002.
[2] Dong—Sun Kim,Wook Hyun Kwon,Hong Sung Park.Geometric kinematics and applications of a mobile robot.International Journal of Control, Automation and Systems,2003：1598—6446.
[3] Haoyong Yu,Steven Dubonsky,Adam Skwersky.Omni—directional mobility using active split offset castors.ASME(American Society of Mechanical En~neers),2004.
[4] Ferriere L,Campion G,Raucent B.ROLLMOBS,a new drive system for omnimobile robots.ROBOTICA.2001.
[5] 1 Ferriere L,Raucent B,Campion G.Design of omnimobile robot wheels.Procedings of the 1996 IEEE on Robotics and Automation.1996.
[6] Campion Guy,Bastin G,D’And~a—Novel B.Structural properties and classification of kinematic and dynamic models of wheeled mobile robots.IEEE rransactions on Robotics and Automation.1 996.
[7] Tang C P,Bath R,Krovi V.Decentralized kinematics control of Payload transport by a system of mobile manipulators. Proceeding of IEEE on Robotics and Automation, 2004.
[8] Fisette P,Ferriere L,Raucent B,et a1.A muhibody approach for modeling universal wheels for mobile robots.Elsevier Mechanism and Machine Theorie,2000,35：329—351.
[9] Fu Yili,He Xu,Wang Shuoguo,et a1.Topological analysis and control on mobile robo t with partially.failed propulsive whee1.Proceedings of 2005 IEEE International Conference on Robotics and Automation(ICRA2005).Barcelona.Spain,2005.
新創(chuàng)造的輪式督導(dǎo)機(jī)制移動(dòng)機(jī)器人
（校機(jī)械與電氣工程中心,先進(jìn)制造技術(shù),哈爾濱市技術(shù)學(xué)院 哈爾濱150001,
電子郵箱： sidibebernard@yaho.fr ）
摘要：提出了一種新的蓖麻車(chē)輪機(jī)制,對(duì)全方位移動(dòng)平臺(tái)進(jìn)行了稱(chēng)述.議案的翻譯轉(zhuǎn)化輪流掌舵車(chē)輪與幫助一個(gè)螺旋路徑怎樣可以成為一個(gè)翻譯聯(lián)合和三輥軸連接到動(dòng)軸的車(chē)輪. 當(dāng)?shù)缆返呐e動(dòng),在翻譯它的行為,督導(dǎo)輥的運(yùn)動(dòng),對(duì)徑輥摩擦傳動(dòng),車(chē)輪運(yùn)動(dòng)學(xué)和可操作性進(jìn)行了分析。
關(guān)鍵詞：蓖麻車(chē)輪；螺旋路徑；摩擦；壓路機(jī)；機(jī)動(dòng)性；調(diào)動(dòng)性。
分類(lèi)號(hào)：文件編號(hào)：tp24 ,文章編號(hào)： l0o5 - 9113 （ 2007 ） 02-0184-05
移動(dòng)平臺(tái)吸引了各種研究機(jī)器人的應(yīng)用,如輪椅,汽車(chē)類(lèi),不同類(lèi)別的全方向移動(dòng)平臺(tái)的鋪陳大大超過(guò)過(guò)去20年.他們的主要機(jī)械結(jié)構(gòu),是有區(qū)別的,并用車(chē)輪機(jī)制。 其中10.1測(cè)定其流動(dòng)性,它已經(jīng)表明,只有機(jī)器人配備3腳輪或三個(gè)車(chē)輪的普及有富兒流動(dòng)性（完整和全方位）。普遍輪子,目前一些缺點(diǎn),如低負(fù)荷能力顛簸導(dǎo)致了振動(dòng),其機(jī)理通常是復(fù)雜的,具有許多零件增加重量的移動(dòng)平臺(tái)三個(gè)蓖麻輪式移動(dòng)機(jī)器人的主要缺點(diǎn)是它至少需要4個(gè)驅(qū)動(dòng)器（三位為指導(dǎo),并至少有一名為驅(qū)動(dòng)器）。一些例子,存在著6個(gè)作動(dòng)器,3名駕駛和3個(gè)督導(dǎo)作動(dòng),這現(xiàn)象導(dǎo)致一些奇異控制。但這樣做的好處是攜帶重要負(fù)荷[9],直至現(xiàn)在新的研究正在進(jìn)行當(dāng)中蓖麻輪式移動(dòng)滾裝博特等,和大多數(shù)的移動(dòng)機(jī)器人操縱的,只有常規(guī)輪[9] ,有興趣的,我們的研究包括一個(gè)設(shè)計(jì)的新型蓖麻車(chē)輪機(jī)制,以連接初等伸縮縫（自旋,線性和螺絲接頭） 。本港利益工作,是要提高機(jī)動(dòng)性。
為此,我們已經(jīng)表明,在第4條中說(shuō),一個(gè)初等線性位移的聯(lián)合能產(chǎn)生的一個(gè)重要轉(zhuǎn)向角的車(chē)輪由于轉(zhuǎn)向角度,對(duì)我們的機(jī)制依賴(lài)于線性位移的聯(lián)合。
一 輪式結(jié)構(gòu)
1.1 說(shuō)明
計(jì)算機(jī)模型為代表的是在圖1-3,代表了運(yùn)動(dòng)鏈的車(chē)輪機(jī)制。它有3個(gè)滾子（圖2）能夠自由地轉(zhuǎn)動(dòng)自己的軸。他們都擁有一個(gè)自由旋轉(zhuǎn)聯(lián)合軸。這三個(gè)軸都內(nèi)建于對(duì)方,適合方向盤(pán)軸和旋轉(zhuǎn)軸聯(lián)合4 （圖1和3）。
所以就此構(gòu)成了車(chē)輪環(huán)線（車(chē)輪懸架） ,它可以把垂直斧頭及槽中心的關(guān)節(jié)1,3和4 （圖3）。豎井分成兩個(gè)不同形式：圓柱形式在一邊,棱柱形,在另一次（圖1）。往下看,一邊是圓柱形成與車(chē)輪連接在一起,旋轉(zhuǎn)聯(lián)合（聯(lián)合4）及上側(cè)是棱柱形,建于平臺(tái)并形成與缸的螺旋走這條路,翻譯聯(lián)合（聯(lián)合1） ,該公司最新舉的目的是,意識(shí)到要提供一個(gè)平移運(yùn)動(dòng),以螺旋路徑圍繞缸（圖1 ,部分黃金色）。
1.2 運(yùn)動(dòng)學(xué)描述
運(yùn)動(dòng)學(xué)代表該機(jī)制在圖3上.事實(shí)上螺旋路徑和滾筒方面,可以被視為一個(gè)螺絲釘關(guān)節(jié)路徑是一個(gè)螺絲釘?shù)募s束,在旋轉(zhuǎn)垂直軸線上的聯(lián)合L ,并輥構(gòu)成一個(gè)螺母受限于翻譯大約同一軸聯(lián)合4。聯(lián)合1是驅(qū)動(dòng)在翻譯.當(dāng)在移動(dòng)路徑與滾筒提議通道法案的時(shí)候,經(jīng)過(guò)一關(guān)于垂直斧,對(duì)輪連接,并最后對(duì)輪子上作出反應(yīng)。
偏心E和高度h保持恒定,無(wú)論姿態(tài)的平臺(tái)。使用的軋輥,即使他們的機(jī)制不是太笨重,重要的是要避免庫(kù)侖摩擦。
二 徑輥摩擦
讓我們考慮一個(gè)圓柱坐標(biāo)系（X , Y , Z ）的和自由的旋轉(zhuǎn)約其車(chē)軸（圖4 （ a ） ）。汽缸及軸的自由旋轉(zhuǎn)和車(chē)輪垂直。傾斜計(jì)劃與角六是在接觸調(diào)節(jié)器。當(dāng)計(jì)劃轉(zhuǎn)化方面的主軸。接觸線（圓柱計(jì)劃）的動(dòng)作與軸Y和汽缸旋轉(zhuǎn)的角度對(duì)車(chē)軸垂直。這個(gè)角度對(duì)應(yīng)于旋轉(zhuǎn)角度的接觸線。
這些不同的運(yùn)動(dòng)可以表示為
軸Z和Y是線性位移的接觸點(diǎn),R取代柱是等于y,式（ 1 ）變成
參數(shù)螺絲釘（圖4 （ b ） ）有：直徑為2 r把螺紋傾角6和瀝調(diào)子P是相關(guān)的,由
結(jié)合式（ 2 ）及（ 3 ）最后可得
三 運(yùn)動(dòng)學(xué)
在參[6?7〕,可以發(fā)現(xiàn),輪式移動(dòng)機(jī)器人的運(yùn)動(dòng)學(xué)。在本節(jié)中,我們已經(jīng)將所需要的機(jī)制加入到這些結(jié)果的變化。
在圖5 ,OXY和Px1y1代表世界坐標(biāo)與機(jī)器人坐標(biāo)。機(jī)器人的態(tài)度將在世界坐標(biāo)：X , Y ,及中定義。
圖中X , Y是坐標(biāo)點(diǎn), P和0是機(jī)器人方向。
轉(zhuǎn)動(dòng)矩陣，表示OXY的關(guān)于從PX1Y1站臺(tái)結(jié)構(gòu)得到方向
車(chē)輪的參數(shù)是：車(chē)輪的偏心是E,它代表著它們之間的距離為中心的車(chē)輪b和由A點(diǎn)的平臺(tái)之間的距離。 L與a是極坐標(biāo)pxiy1 （圖5）中的參數(shù)。車(chē)輪半徑是指由R是與P是螺距螺旋路徑車(chē)輪機(jī)制。輪式變數(shù)和。
連接處被代表經(jīng)過(guò)關(guān)于軸輪子i的z(Fig.3).三個(gè)代表旋轉(zhuǎn)角度的方向盤(pán)I關(guān)于一個(gè)軸途經(jīng)車(chē)輪中心B 。
傳統(tǒng)運(yùn)動(dòng)學(xué)限制了的蓖麻輪推算的速度,機(jī)器人和輪式到車(chē)輪計(jì)劃，并在一個(gè)平面垂直于車(chē)輪飛機(jī),他們是
我們提出了車(chē)輪機(jī)制的局限,得到了由多種方法，由（4）及（7） ,然后再由（4）及（8）
過(guò)去兩年以上方程只代表制約,只有一個(gè)車(chē)輪,如果我們輪子機(jī)械裝置的三被向一活動(dòng)的,是實(shí)施以移動(dòng)機(jī)器人,其總的約束是6。
四 舉例
在本節(jié)中,我們考慮的一個(gè)例子,一個(gè)典型的汽車(chē)式機(jī)器人, i.e. a移動(dòng)機(jī)器人配備有兩個(gè)無(wú)源定額標(biāo)準(zhǔn)車(chē)輪和一個(gè)車(chē)輪蓖麻我們的類(lèi)型和每個(gè)車(chē)輪都是遙遠(yuǎn)的Z為由來(lái)取消p的,該機(jī)器人框（圖6 ）,我們假設(shè)所有的三個(gè)車(chē)輪有相同的半徑R和機(jī)器人是帶領(lǐng)和駕駛由蓖麻車(chē)輪 。瓦特e還以為地面是一個(gè)水平面,并有沒(méi)有滑動(dòng)或摩擦之間的車(chē)輪和地面。
定額標(biāo)準(zhǔn)車(chē)輪參數(shù)代表圖7.就像蓖麻車(chē)輪,它的運(yùn)動(dòng)學(xué)約束得到投射的不同速度在砂輪機(jī),并在一個(gè)平面垂直車(chē)輪飛機(jī),他們是
由于安排的三個(gè)車(chē)輪圖6,我們有以下幾點(diǎn)值為：,這些價(jià)值體系,形成由式（ 11 ） （I = 1,2為兩個(gè)固定的標(biāo)準(zhǔn)車(chē)輪）和式（ 9 ） （為蓖麻車(chē)輪 ） ,可以寫(xiě)
一個(gè)制度的形成是由式（12） （I = 1,2 ）, （為兩個(gè)固定的標(biāo)準(zhǔn)車(chē)輪）和式（10）（為蓖麻車(chē)輪）可以寫(xiě)
式（13）及（14）代表機(jī)器人運(yùn)動(dòng)學(xué)約束螺旋路徑。這督導(dǎo)機(jī)制的介入,只有在機(jī)器人的轉(zhuǎn)向過(guò)程,在這個(gè)例子中,我們認(rèn)為在純旋轉(zhuǎn)過(guò)程中,然后組成X和Y的矩陣變成零,我們也認(rèn)為,督導(dǎo)及車(chē)輪駕駛角速度3都是平等。經(jīng)過(guò)一番計(jì)算，式（13）和（14）成為
通過(guò)消除3 ,在過(guò)去2方程,并用價(jià)值觀tab.1我們得到如下關(guān)系
由圖8（z , p）可知,消去式（1 7）將符合假設(shè),這是考慮到機(jī)器人的純旋轉(zhuǎn)。
五 利益機(jī)制
鑒于兩輪式移動(dòng)機(jī)器人的平等流動(dòng),但不同的可操作性,更便于操作的機(jī)器人通常會(huì)帶來(lái)好處,在雜亂的環(huán)境中。車(chē)輛的機(jī)動(dòng)性,其特點(diǎn)是有能力執(zhí)行動(dòng)作結(jié)合起來(lái)。蓖麻輪式移動(dòng)機(jī)器人具有良好的價(jià)值觀念一定程度的流動(dòng)性（6 = 3）和自由程度 但可操作性是緊密相連的,其設(shè)計(jì)在理論上是容易引導(dǎo)對(duì)待車(chē)輪直由一個(gè)致動(dòng)器,但在督導(dǎo)過(guò)程中存在一些因摩擦而發(fā)生的抗力,扭矩在一段時(shí)間里成倍增加?？焖俜磻?yīng),在轉(zhuǎn)向時(shí),是需要做出決定,這是機(jī)動(dòng)性,這兩種情況的原因是 在必要的機(jī)制下,我們可以督導(dǎo)車(chē)輪的一個(gè)功能調(diào)子p的轉(zhuǎn)向角度，
一個(gè)固定位移的Z = 10 mm.fig.9顯示值B為選擇的P在設(shè)計(jì)制度更有可操作性，任何p的最小值對(duì)應(yīng)的b最大。
六 結(jié)論
從力學(xué)的開(kāi)頭起許多簡(jiǎn)單機(jī)械裝置被得到一個(gè)小腳輪輪子,在外地的機(jī)器人系統(tǒng),它有一個(gè)特別重要的交通探索。本文帶來(lái)了一種新型的蓖麻,并推動(dòng)這一領(lǐng)域的合作。在這篇文章中,我們?cè)芯吭O(shè)計(jì)一個(gè)新的督導(dǎo)機(jī)制,對(duì)它的運(yùn)動(dòng)學(xué)和可操作性進(jìn)行了分析。
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