【機械類畢業(yè)論文中英文對照文獻翻譯】ResQuake：遠程操作救援機器人【PDF英文11頁word中文翻譯3633字7頁】【有出處】,機械類畢業(yè)論文中英文對照文獻翻譯,PDF英文11頁,word中文翻譯3633字7頁,有出處,機械類,畢業(yè)論文,中英文,對照,對比,比照,文獻,翻譯,resquake,遠程,操作,救援,救濟,營救,機器人 附件1：外文資料翻譯譯文 ResQuake：遠程操作救援機器人 ResQuake作為一種遠程操作救援機器人，它的設計程序以及對其動態(tài)分析，生產過程，控制系統(tǒng)，防滑性能改進等一直被人們所探討。人們首先要探討的問題是規(guī)定機器人要完成的總任務以及組成機器人基本結構的各種機構。選擇適當?shù)臋C構、幾何尺寸、對質量進行定性分析以形成系統(tǒng)的運動學和動力學模型。其次是對每個構建的強度進行分析以最終定型并提出機構模型。接著對控制系統(tǒng)進行簡要的介紹，該控制系統(tǒng)包括用作主處理器的操作者的電腦以及安裝在機器人身上作為從處理器的便攜式電腦。最后通過實驗測試確定并驗證軌道滑移系數(shù)，以改善系統(tǒng)的跟蹤性能。 ResQuake已經參加幾個救援機器人聯(lián)賽。 關鍵詞：移動機器人，遠程操作，運動機制，控制結構，滑移估計 1 引言 由一個或多個操縱器平臺組成的移動操縱型機器人有無限的工作空間。因此，各種行走，輪式，履帶式和飛行系統(tǒng)已被提出并成功地付諸實踐。這種系統(tǒng)被廣泛用于消防，林業(yè)，排爆，有毒廢物清理，運輸材料，空間軌道維護等會危機到人類健康安全的領域 [1]。因此，可以預計，不管是自動運行的還是遠程操作的移動機器，都將會在人類生活的各個不同領域發(fā)揮更加重要的作用。但是，在移動機器人系統(tǒng)中，基于作用于反作用原理，動力會影響到基座與操縱器的運動。因此，運動學、動態(tài)，以及對這些系統(tǒng)的控制已經得到了廣泛的研究關注[2-5]。 地震是一種會威脅人類生命的自然事件。主震之后的余震會造成二次坍塌， 這會危及搜救人員的生命。為了盡量降低救援人員的風險，同時增加受害人生存機率，開發(fā)出一種能相互協(xié)作的機器救援隊不失為一種好的選擇。該種機器人及其操作者的任務是找到受害者并確定他們的情況，然后匯報目標在建筑物地圖上的方位[6,7]。這消息，會立即被發(fā)送至人類救援隊。對救援機器人的進一步預期，如能夠自主搜索倒塌建筑物，發(fā)現(xiàn)受害者和確定他們的環(huán)境，為幸存者提供生活用品和通信工具和布設傳感器(聲，熱，地震等)正處于課題研究中。然而，救援機器人的基本能力是它們在遭受破壞地區(qū)的機動性,這完全依賴于它們的運動系統(tǒng)和它們的維度。到目前為止已經設計并生產了各救援機器人[8,9]。 本文對Khaje Nasir Toosi大學（KNTU）的ResQuake項目進行了直觀的描述，如圖1所示。首先對移動機構的設計步驟進行詳細介紹，并確定系統(tǒng)尺寸和相關參數(shù)。然后是對系統(tǒng)運動學和動力學進行探討，并提出對每個機構部件應力分析問題。接著是敘述機器人控制系統(tǒng)。最后通過實驗測試確定并驗證軌道滑移系數(shù)，以改善系統(tǒng)的跟蹤性能。ResQuake有著友好的人機操作界面，它在非結構化環(huán)境、不光滑的路徑，甚至是在爬樓梯時都有很強的移動能力。它的性能已被如下事實證明：在2005年日本大阪機器人世界杯救援機器人聯(lián)賽中取得第二個最佳設計獎，2006年在德國不來梅機器人世界杯足球賽中取得最佳操作界面獎，以及2008年在中國蘇州機器人杯大賽中取得第二個最佳移動獎。 圖1 ResQuake在不同的環(huán)境中運動：(左)折疊路徑,(右)爬上不平斜坡可擴展軌跡 2 機構設計 以移動形式劃分，搜救機器人主要有三類，即輪式，履帶式和行走機器人。輪式機器人，可以在搜索平坦的區(qū)域時使用。由于動力簡單，開發(fā)這些自動系統(tǒng)相對容易。輪式機器人還能夠攀爬高度比車輪小的障礙物。履帶式機器人由于具有在崎嶇不平的地形上移動的超強能力而得到廣泛使用。圖2展示了輪式和履帶式系統(tǒng)面臨著同樣的障礙（樓梯）。可以看出，相對較小的履帶式機器人具有相同的越障能力。 圖2 兩種運動系統(tǒng)遇到相同障礙物 行走機器人通常具有高自由度(DOFs)，故而具有高機動性。因此，這種系統(tǒng)的動力學模型及其穩(wěn)定性要比前者復雜的多。此外，這種系統(tǒng)的運行需要大量的執(zhí)行機構和傳感器，所以他們的控制系統(tǒng)更昂貴。還應該提到的是兩輪和行走機構相結合的方式，這保留了兩個運動系統(tǒng)的優(yōu)點，而且避免了它們的缺點[10]。在輪式-行走混合機構中，輪式機構可以支撐行走機構的重量，而行走機構可以在崎嶇的地形上移動機器人。 不僅僅是運動系統(tǒng)類型，救援機器人的尺寸也是一個重要的問題。在一個遭受破壞的室內環(huán)境中，可能存在一些例如倒塌的墻壁或天花板一類的一般系統(tǒng)不能輕易通過的障礙。在這種情況下，機器人必須在障礙物之間尋找一條其他的路徑而不是爬過他們，這無疑取決于它的大小。一個相對較小的機器人能夠輕易地通過一條狹窄通道并繼續(xù)搜索。應當指出，樓梯是室內環(huán)境的一個不可分割的一部分。不管樓梯破壞與否，救援機器人都應該有能力上下樓梯以搜查整個地區(qū)。 為了在這兩個矛盾之間進行折衷，人們提出了一種具有高機動性的小機器人，履帶式機構已經被應用于ResQuake的研制。這種機制包括一個主體(基座)和兩個可擴展履帶(臂)。這一布置使機器人能根據(jù)它遇到的障礙調整自身大小。因此，相應的，履帶應該有一個最小長度以防止失去平衡，并且能夠在沒有額外震動的情況下能在連續(xù)的樓梯上穩(wěn)定的運動，如圖3(a)所示,。另一方面,長的履帶,例如那些簡單的履帶機器人需要一個較大的區(qū)域進行拐彎,如圖3(b)，這在遭受破壞的環(huán)境中很難滿足這一條件。 圖3 (a)履帶式機器人最小長度 (b)簡單的履帶式機器人最小拐彎半徑 2.1 可擴展履帶(臂) 圖4中顯示的結構,使得機器人可以擴大它的履帶長度以便通過障礙。另一方面,當機器人在穿過狹窄的通道以及需要較小體積時，其前端可以折疊。這也有助于減少轉彎半徑。最初的想法是在折疊工作臂上，以克服上述矛盾。 這個概念已經改進了在兩邊都有一對工作臂的車輛，如圖4(b) 所示，用折疊臂來減少機器人的長度或擴大其他長度來滿足其他要求。另一個優(yōu)點是對稱結構，該結構使得機器人在前進和后退時運動相似，這一布置便于在受限空間內轉彎。 其次，工作臂被布置在同一平面內以降低機器人寬度(圖5 (b))。最后，為了在工作臂折疊時使用額外的區(qū)域空間，在每個臂中安裝了連接件(圖5 (b))。因此,機器人兩邊的履帶都能伸展成三個平行層面,這提供了更有效的牽引力。 圖4 (a)前端履帶初步設計 (b)具有兩對臂的改進設計 (前端和后端) 圖5（a）使履帶共線以減少機器人寬度 (b)履帶最終結構 在系統(tǒng)中添加四個獨立的（主動）關節(jié)會增加執(zhí)行機構的數(shù)量從而增加系統(tǒng)的總價格。因此，人們用行星齒輪系來簡化每個臂上主連接件到次連接件的功率傳輸。每個臂上的兩個的旋轉是相互獨立的。通過分析兩個臂的輪廓可以得出齒輪傳動比；（i）完全伸展（ii）完全折疊，這樣，在那些具有兩個輪廓的預期平面上的臂就可以運動(圖6)。 圖6 臂的運動軌跡 如圖6所示，當工作臂的主體部分旋轉∏/ 2rad時，從屬部分的旋轉角度應該超過∏rad。具備這一性能的齒輪系應該是一個行星變速箱。第一個工作臂的主體部分在行星輪系中起著工作臂的作用，其動力由電動機直接提供。太陽輪連接在機器人上的主體之上，行星輪連接到在工作臂的從屬結構上。一對中間齒輪安裝在太陽輪和行星輪之間，該處齒輪的直徑不得超過履帶主輪直徑這一閾值（圖7）。這一機構的另一個優(yōu)點是工作臂的兩個連接點處的中心距離在旋轉時將保持不變。這使得我們能夠補償主履帶和裝有另一履帶的工作臂之間的間隙。這種履帶的作用是將履帶主體部分上的動力傳遞至工作臂上的從屬履帶上。 圖7 個行星傳動鏈 斜齒輪由于剛度大且齒輪輪齒強度相比于直齒圓柱齒輪來說更強而被用在行星齒輪系中[11,12]。臂的角速度應低于2至4轉每分鐘，而電機的輸出速度為3000轉每分鐘。因此電機與連桿之間的速比約為1000。三級行星齒輪變速箱這以組合結構的每一級的比率皆為3：1 (推定直角在角速度相對較大電機軸處）的比例。傳動比為30:1的蝸輪系為受限空間提供了理想的傳動比（圖8）。機器人的兩側履帶都是直流電機驅動。 圖8 最終設計的布置 2.2 履帶 移動系統(tǒng)的牽引力在很大程度上依賴于機器人行走時履帶表面與接觸面之間的摩擦。因此履帶部件的材料和形狀就顯得尤為重要[13]。另一方面履帶應該承受適當?shù)膹埦o力。設計的履帶由兩個主要部件組成。鏈齒結構為系統(tǒng)提供了足夠的張緊力,由乳膠做成的齒形零部件則補償了鏈與接觸面之間的隙，從而得到所需的摩擦力。通過用長銷釘替換標準鏈中的銷釘對金屬鏈進行了修正。圖9展示了修正后的鏈以及履齒是如何安裝在這些銷釘上的。 當系統(tǒng)需要快速機動的穿過或是爬過某個斜坡時，產生了一個嚴重的問題，那就是由于基座運動而導致的不穩(wěn)定性及傾覆[14]。懸架結構具備兩個主要優(yōu)點。 懸架系統(tǒng)包括主體上的兩個表面，并將它們通過回轉副連接起來（圖9）。一對線性彈簧限制了旋轉角度，同時使得該系統(tǒng)在未受到額外施加的作用力時保持理想姿勢。在此指出一點，該系統(tǒng)不需要使用減震器，因為作為轉動副的滑動軸承產生的摩擦力足以限制彈簧的額外震動。 圖9 上圖：安裝在鏈上的乳膠零件；下圖：懸掛系統(tǒng)基本結構 2.3 最終尺寸 移動結構設計完成后開始進行尺寸設計。一些諸如金屬鏈和行星輪一類的零件作為標準間很容易得到，所以其他零件的尺寸應該與它們相匹配。除此之外，在計算時必須考慮機器人的整體尺寸和齒輪系的公式。由于大量的方程式共同決定著參數(shù)，人工計算無法得到最優(yōu)解。所以可以通過MATLAB來解方程得出最優(yōu)解。該過程需要考慮的尺寸列在圖10和表1中。 圖10 主要的長度確定其他維度 表1尺寸參數(shù)的機器人 … … 1 Robot e kinematic analyzed ol , and DOI: obots, 1 more ous posed, dif bombs, orbit endangered H208511H20852. So, it is expected that mobile robots, whether autonomous or tele-operative, play a more important role in dif- ferent fields of human life. However, in a mobile robotic system, dynamic based dynamics, research Aftershocks secondary and while collaborative robots their building man being victims communications thermal, less, mechanism is addressed. Then, the robot control system is de- scribed. Finally, slip coefficients are identified and validated by various tests to improve the system tracking performance. in manuscript by Journal Downloaded 02 Dec 2009 to 222.190.117.200. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm forces affect the motion of the base and the manipulators, on the action and reaction principle. Therefore, kinematics, and control of such systems have received extensive attention H208512–5H20852. Earthquake is a natural incident, which threatens human life. occurring a while after the main earthquake cause collapses and may take victims away from the search rescue personnel. In order to minimize the risks for rescuers, increasing victim survival rates, exploiting fielding teams of robots is a good alternative. The mission for the and their operators would be to find victims, determine situation, and then report their findings based on a map of the H208516,7H20852. This information will immediately be given to hu- rescue teams. Further expectations of rescue robots such as able to autonomously search collapsed structures, finding and ascertain their conditions, delivering sustenance and to the victims, and emplacing sensors H20849acoustic, seismic, etc.H20850 are ongoing research subjects. Neverthe- the basic capability of rescue robots is their maneuverability ResQuake has great capabilities for moving in unstructured envi- ronment, on rough trains, and even climbing stairs, with a user- friendly operative interface. Its performance has been demon- strated in the rescue robot league of RoboCup 2005 in Osaka, Japan, achieving the second best design award, RoboCup 2006 in Bremen, Germany, achieving the best operator interface award, and RoboCup 2008 in Suzhou, China, achieving the second best award for mobility. 2 Mechanism Design There are three major categories of search and rescue robots in terms of their locomotion system, i.e., wheeled, tracked, and 1 Corresponding author. Contributed by the Mechanism and Robotics Committee of ASME for publication the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 21, 2008; final received May 7, 2009; published online July 20, 2009. Review conducted Ashitava Ghosal. Fig. 1 ResQuake in different conditions; ?left… folded tracks, ?right… extended tracks climbing up a ramp uneven surface of Mechanical Design AUGUST 2009, Vol. 131 / 081005-1Copyright ? 2009 by ASME S. Ali A. Moosavian Associate Professor e-mail: moosavian@kntu.ac.ir Arash Kalantari Graduate Student e-mail: arash1362@ Hesam Semsarilar Graduate Student e-mail: hesam2k@ Ehsan Aboosaeedan Graduate Student e-mail: ehsanaboo@ Ehsan Mihankhah Graduate Student e-mail: ehsanmihankhah@ Advanced Robotics and Automated Systems (ARAS) Laboratory, Department of Mechanical Engineering, Khaje Nasir Toosi University of Technology, P.O. Box 19395-1999, Tehran 19991 43344, Iran ResQuake: Rescue The design procedur analysis, manufacturing improvement are discussed. fined, and various mechanisms Choosing the appropriate detailed to develop each component is sented. Then, the contr the master processor slip coefficients of tracks system tracking performance. cue robot leagues. H20851 Keywords: mobile r slippage estimation Introduction Mobile manipulators, which consist of a platform and one or manipulators, have an unlimited workspace. Therefore, vari- legged, wheeled, tracked, and flying systems have been pro- and successfully put into practice. Such systems are used in ferent kinds of fields such as fire fighting, forestry, deactivating toxic waste cleanup, transportation of materials, space on- services, and similar applications in which human health is A Tele-Operative of ResQuake as a tele-operative rescue robot and its dynamics procedure, control system, and slip estimation for performance First, the general task to be performed by the robot is de- to form the basic structure of the robot are discussed. mechanisms, geometric dimensions, and mass properties are and dynamic models for the system. Next, the strength of to finalize its shape, and the mechanism models are pre- system is briefly described, which includes the operator’s PC as the laptop installed on the robot as the slave processor. Finally, are identified and validated by experimental tests to improve the ResQuake has participated with distinction in several res- 10.1115/1.3179117H20852 tele-operative, locomotion mechanisms, control architecture, in destructed areas, which thoroughly depends on their locomo- tion system and their dimensions. Various rescue robots were de- signed and manufactured so far H208518,9H20852. This paper presents an illustrative description of the ResQuake project at Khaje Nasir Toosi University H20849KNTUH20850, as shown in Fig. 1. First, designing procedure for the locomotion mechanism will be detailed, and the system dimensions and related parameters are determined. Next, the system kinematics and dynamics is dis- cussed, and the sequence of stress analysis for each member of the legged flat due climbing T move systems smaller H20849 modeling the quires expensive. the comotion vented mechanism while rain. cue ronment, ceilings situations, the pends passageway ways destructed up of Fig. same of 081005-2 Downloaded 02 Dec 2009 to 222.190.117.200. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm robots. Wheeled robots could be considered for searching areas. Developing the autonomy for these systems is easier to their simple dynamics. A wheeled robot is also capable of obstacles with a height smaller than their wheels. racked robots are used mostly because of their great ability to on uneven terrains. Figure 2 shows wheeled and tracked facing the same obstacle H20849stairH20850. It can be seen that a tracked robot has the same capability. Legged robots usually possess high degrees of freedom DOFsH20850, and thus, high maneuverability. Consequently, dynamics and stability of such systems is more complicated than former types. Besides, implementation of such systems re- numerous actuators and sensors, so their control is more It should be also mentioned that with a combination of two wheeled and legged mechanisms, advantages of both lo- systems can be preserved while shortcomings are pre- H2085110H20852. In a hybrid wheel-legged mechanism, wheeled can support the weight of the legged mechanism, the legged mechanism can move the robot on a rough ter- Regardless of the type of locomotion system, the size of a res- robot is also an important issue. In a destructed indoor envi- some obstacles may exist such as collapsed walls or that cannot be easily passed by usual systems. In such the robot should search for a bypass or a way between obstacles rather than climbing over them; that definitely de- on its size. A relatively small robot can easily pass a narrow and continue its search. It should be noted that stair- are an inseparable part of an indoor environment. Whether or not, a rescue robot should have the ability to climb and down stairways in order to search the whole area. In order to compromise between the two contradictory aspects providing a small robot with high maneuverability, a tracked 2 Two types of locomotion systems encountering the obstacle Fig. 3 ?a… Minimum length for tracks radius of a simple track robot / Vol. 131, AUGUST 2009 mechanism has been developed for ResQuake. This mechanism includes a main body H20849baseH20850 with two expandable tracks H20849armsH20850. This arrangement enables the robot to resize depending on the situation it encounters. Accordingly, these tracks should have a minimum length to prevent loosing its balance, and having a steady movement on successive stairs without extra vibrations, as shown in Fig. 3H20849aH20850. On the other hand, lengthy tracks such as those of a simple track robot will require a wide area for turning, as shown in Fig. 3H20849bH20850, which is rarely available in a destructed environment. 2.1 Expandable Tracks (Arms). The structure shown in Fig. 4 enables the robot to expand the length of its tracks to pass through obstacles. On the other hand, when the robot is going through narrow passages and needs to be rather small, the front tracks can be folded. This helps with reducing the turning radius as well. Folding arms was the original idea, developed to over- come the aforementioned contradiction. This concept has been improved to a system with two pairs of arms at both sides of the vehicle, as shown in Fig. 4H20849bH20850, to reduce the length of the robot with folded arms while the expanded length fulfills other requirement. Another advantage would be the symmetry of the structure, which enables the robot to move equivalently in both forward and backward directions. This ar- the robot and ?b… minimum turning Fig. 4 ?a… Preliminary design of just front tracks ?arm… and ?b… improved design with two pairs of arms ?front and rear… Transactions of the ASME rangement width order H20849 stretched traction. increase of simply second dependent. configurations such these arm, chain main chain, be attached placed does main mechanism will gap track the small Fig. robot Journal Downloaded 02 Dec 2009 to 222.190.117.200. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm facilitates turning in a confined space. Next, the arms are placed in the same plane to reduce the robot H20849Fig. 5H20849aH20850H20850. Finally, another joint is added to each arm in to use an extra area between the arms when they are folded, Fig. 5H20849bH20850H20850. Therefore, the tracks on each side of the robot are into three parallel planes, which provide a more efficient Adding four independent H20849activeH20850 joints to the system would the number of actuators and consequently the total price the system. Therefore, a planetary gear set has been used to transmit the power of the main joint of each arm to its joint. So, rotation of the two parts for each arm will be The gear ratio is obtained, considering two desirable of the arms; H20849iH20850 fully stretched and H20849iiH20850 fully folded, that the arms can move, based on a desired plan between two configurations H20849Fig. 6H20850. As shown in Fig. 6, for a H9266/2 rad rotation of the main part of the second part should rotate more than H9266 rad. The gear with such performance should be a planetary gearbox. The part of the first arm plays the role of the arm in the planetary which is directly powered by a motor. The sun gear should attached to the main body of the robot, and the planet gear is to the second part of the arm. A pair of medium gears is between the sun and the planet where the diameter of gears not exceed a given threshold, which is the diameter of the wheels of the tracks H20849Fig. 7H20850. Another advantage of this is that the center distance of the two joints of the arm remain constant during its rotation. This enables us to fill the between the main track, and the arm with another track. This is used to transmit power from the main part of the tracks to second part on the arm. Helical gears are chosen for the planetary gear set, due to their backlash and higher strength of gear tooth comparing with 5 ?a… Making the tracks collinear to reduce the width of and ?b… final mechanism chosen for the tracks Fig. 6 The path for motion of the arms Fig. 7 Planetary gear chain of Mechanical Design spur gears H2085111,12H20852. The angular velocity of the arm should be less than 2–4 rpm. The motor’s output velocity is 3000 rpm. Hence, the velocity ratio between the motor and the link should be ap- proximately 1000. A combination of a three stage planetary gear- box H20849constructed right at the motor shaft where the angular veloc- ity is relatively highH20850 with a ratio of 3:1 at each stage, and a worm gear set with a ratio of 30:1 provides the desirable ratio in a limited available space H20849Fig. 8H20850. A dc motor drives the tracks at each side of the robot. 2.2 Tracks. The traction of the locomotion system strongly depends on the friction between the track pieces and the surface on which the robot moves. Therefore, the material and the shape of the track pieces are of great importance H2085113H20852. On the other hand, the tracks should also bear a reasonable tension. Designed tracks are made of two main parts. A basis of chain-sprocket pro- vides the system with sufficient tensile strength, and tooth shaped pieces made of latex fills the gap between the chain and the sur- face to create the required friction. Metal chains have been modi- fied by replacing pins of the standard chain with longer pins, and the latex grousers are mounted directly on them. Figure 9 shows modified chains and how the grousers are mounted on these pins. One of the most important problems caused by base movement, when the system undergoes a fast maneuver or tries to climb a slopped terrain, is the instability problem or tipping over H2085114H20852. Noting this, two major advantages are obtained by including a suspension mechanism. The suspension system was designed by containing two sur- faces on the main body, and then attaching them by a revolute joint H20849Fig. 9H20850. A pair of linear springs limits the angle of rotation and makes the system remain at a desired position when no extra forces are applied. It should be mentioned that the use of dampers Fig. 8 Final designed arrangement for the arms Fig. 9 Top: latex pieces fixed on the chain; bottom: basic structure of the suspension system AUGUST 2009, Vol. 131 / 081005-3 was the springs. mechanisms, components dard parts. the merous not used dimensions summarized 3 can in tioned the coordinate 11 lows: Parameter C CL C d d d d Gap1 Gap2 H H L L 081005-4 Downloaded 02 Dec 2009 to 222.190.117.200. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm not needed because the friction of the sliding bearings used as so-called joints was enough to limit any extra shaking of the 2.3 Final Dimensions. Finishing the design of locomotion the dimensions are to be determined. Some of the like metal chains and sprockets are available as stan- parts, so that other dimensions should match their counter- Besides, the overall size of the robot and the formulas on gear chains must be considered in the calculations. Since nu- equations govern these factors, an optimized solution is reachable by manual calculations. Thus, MATLAB has been to find the desired values from a set of equations. The main considered in this procedure are shown in Fig. 10 and in Table 1. Kinematics Analysis A mobile rigid platform has three DOF in a flat plane, which be defined either in the body coordinate frame c:H20853x,y,H9278H20854,or the inertial coordinate frame C:H20853X,Y,H9272H20854. It should be men- that the body coordinate frame is fixed to the main body of robot with the x axis along with the tracks, while the inertial frame is fixed to the plane of motion as shown in Fig. H2085115,16H20852. The direct kinematics is developed in the main frame as fol- Table 1 Dimensional parameters of robot Value H20849mmH20850 Description m 292.1 Center to center distance of main sprockets 127 Center to center distance of link a 106.2 Center to center distance of arm sprockets G1 43.9 Pitch diameter of the sun gear G2 43.9 Pitch diameter of the first medium gear G3 41.6 Pitch diameter of the second medium gear G4 39.3 Pitch diameter of the planet gear 5 Gap between folded arm and main body 9 Gap between folded arms track 14 Height of track parts total 260 Height of the robot total F 400 Length of the robot with folded arms total O 760 Length of the robot with open arms Fig. 10 Main lengths for determining / Vol. 131, AUGUST 2009 H20849X ˙ ,Y ˙ ,H9272˙H20850 =H9024H20849H9275 r ,H9275 l H20850H208491H20850 which relates the velocity components of the main body to the angular speeds of the right and left tracks. The speed of the right track is calculated by V r = rH9275 r H208491?i r H20850 = rH9275 r i ˉ r H208492H20850 where r is the driving wheel radius, H9275 r is the angular speed, and i r is the slip coefficient of the right track that is defined as i r = V t ? V rr V t =1? V rj V t H208493H20850 where V t is the theoretical speed, and V rr is the real speed of the right track. Equations H208492H20850 and H208493H20850 can be similarly rewritten for the left track. On the other hand, the velocity components for a point like F on the robot’s axis of symmetry can be obtained as x˙ = cbH20851H9275 r i ˉ r +H9275 l i ˉ l H20852 y˙ = l G H9278 ˙ ? cbH20851H9275 r i ˉ r +H9275 l i ˉ l H20852 · tanH20849H9251H20850 H9278 ˙ = cH20851H9275 r i ˉ r ?H9275 l i ˉ l H20852H208494H20850 where b is equal to the half width of the robot, c is a constant equal to r/2b, and H9251 is the slip angle of the robot, which has a the other dimensions Fig. 11 The robot moving on a circular path Transactions of the ASME nonzero value in the presence of side slippage. Lateral or side slippage happens mainly due to the centrifugal force exerted to the robot when moving on a curved path with a relatively high speed. Maximum ceed Besides, results robot glected, It terclockwise the From Replacing which grated configuration tion Substituting sented where Keeping rotation It second Journal Downloaded 02 Dec 2009 to 222.190.117.200. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm longitudinal speed of the chosen platform does not ex- 0.3 m/s, which will result in a negligible centrifugal force. the design of the track’s treads, as explained in Sec. 2.2, in a large lateral friction force, which in turn helps the to not slip laterally. Therefore, the lateral slippage is ne- and Eq. H208494H20850 is rewritten as x˙ = cbH20851H9275 r i ˉ r +H9275 l i ˉ l H20852H208495aH20850 y˙ = l G H9278 ˙ H208495bH20850 H9278 ˙ = cH20851H9275 r i ˉ r ?H9275 l i ˉ l H20852H208495cH20850 should be mentioned that Eq. H208495cH20850 yields a positive H9278 ˙ for coun- rotations. These components can be transferred into inertial frame F as X ˙ = x˙ cos H9278? y˙ sin H9278 H208496aH20850 Y ˙ = x˙ sin H9278+ y˙ cos H9278 H208496bH20850 H9278 ˙ =H9278 ˙ H208496cH20850 Eq. H208496H20850 we can write Y ˙ cos H9278? X ˙ sin H9278= y˙ H208497H20850 from Eq. H208495H20850 in Eq. H208497H20850, yields ? X ˙ sin H9278+ Y ˙ cos H9278? l G H9278 ˙ =0 H208498H20850 describes a nonholonomic constraint. It cannot be inte- analytically to result in an algebraic constraint between the variables of the platform, namely x, y, and H9278. Equa- H208498H20850 can be written in the matrix form AH20849qH20850q˙ =0 H208499aH20850 A = H20851? sin H9278 cos H9278 ? l G H20852 H208499bH20850 Eq. H208495H20850 into Eq. H208496H20850, direct kinematics can be pre- as d dtH20900 X Y H9272 H20901 = J H20875 H9275 r H9275 l H20876 H2084910H20850 J isa3H110032 Jacobian matrix as J = H20900 ri ˉ r 2 H20873cos H9278? 2l G sin H9278 B H20874 ri ˉ l 2 H20873cos H9278+ 2l G sin H9278 B H20874 ri ˉ r 2 H20873sin H9278+ 2l G cos H9278 B H20874 ri ˉ l 2 H20873sin H9278? 2l G cos H9278 B H20874 r B i ˉ r ? r B i ˉ l H20901 H2084911H20850 the first two equations of Eq. H2084910H20850 and displaying the matrix explicitly, we can write H20875 X ˙ Y ˙ H20876 = H20875 cos H9278 ? sin H9278 sin H9278 cos H9278 H20876 H20900 ri ˉ r 2 ri ˉ l 2 ri ˉ r l G B ? ri ˉ l l G B H20901 H20875 H9275 r H9275 l