機器人路徑規(guī)劃畢業(yè)論文外文翻譯

1、<p><b>　　附件7： </b></p><p><b>　　本科畢業(yè)論文</b></p><p><b>　　外文文獻及譯文</b></p><p>　　文獻、資料題目：Space Robot Path Planning for</p><p>　　Colli

2、sion Avoidance </p><p>　　文獻、資料來源：Proceedings of the International MultiConference of Engineers and Computer Scientists 2009 Vol II IMECS 2009</p><p>　　文獻、資料發(fā)表（出版）日期：2009 </p>&

3、lt;p>　　院 （部）： 信息與電氣工程學(xué)院</p><p><b>　　專 業(yè)：</b></p><p><b>　　班 級：</b></p><p><b>　　姓 名： </b></p><p><b>　　學(xué) 號： </b

4、></p><p><b>　　指導(dǎo)教師： </b></p><p>　　翻譯日期： 2013年3月</p><p><b>　　外文文獻：</b></p><p>　　Space Robot Path Planning</p><p>　　for Collision

5、Avoidance</p><p>　　Yuya Yanoshita and Shinichi Tsuda</p><p>　　Abstract — This paper deals with a path planning of space robot which includes a collision avoidance algorithm. For the future space

6、 robot operation, autonomous and self-contained path planning is mandatory to capture a target without the aid of ground station. Especially the collision avoidance with target itself must be always considered. Once the

7、location, shape and grasp point of the target are identified, those will be expressed in the configuration space. And in this paper a potential meth</p><p>　　Laplace potential function is applied to obtain t

8、he path in the configuration space in order to avoid so-called deadlock phenomenon. Improvement on the generation of the path has been observed by applying path smoothing method, which utilizes the spline function interp

9、olation. This reduces the computational load and generates the smooth path of the space robot. The validity of this approach is shown by a few numerical simulations.</p><p>　　Key Words —Space Robot, Path Pla

10、nning, Collision Avoidance, Potential Function, Spline Interpolation</p><p>　　I. INTRODUCTION</p><p>　　In the future space development, the space robot and its autonomy will be key features of t

11、he space technology. The space robot will play roles to construct space structures and perform inspections and maintenance of spacecrafts. These operations are expected to be performed in an autonomous. </p><p

12、>　　In the above space robot operations, a basic and important task is to capture free flying targets on orbit by the robotic arm. For the safe capturing operation, it will be required to move the arm from initial post

13、ure to final posture without collisions with the target.</p><p>　　The configuration space and artificial potential methods are often applied to the operation planning of the usual robot. This enables the rob

14、ot arm to evade the obstacle and to move toward the target. Khatib proposed a motion planning method, in which between each link of the robot and the obstacle the repulsive potential is defined and between the end-effect

15、er of the robot and the goal the attractive potential is defined and by summing both of the potentials and using the gradient of this poten</p><p>　　In order to resolve the above issue, a few methods are pro

16、posed where the solution of Laplace equation is utilized. This method assures the potential fields without the local minimum, i.e., no deadlock. In this method by numerical computation Laplace equation will be solved and

17、 generates potential field. The potential field is divided into small cells and on each node the discrete value of the potential will be specified. </p><p>　　In this paper for the elimination of the above de

18、fects, spline interpolation technique is proposed. The nodal point which is given as a point of path will be defined to be a part of smoothed spline function. And numerical simulations are conducted for the path planning

19、 of the space robot to capture the target, in which the potential by solving the Laplace equation is applied and generates the smooth and continuous path by the spline interpolation from the initial to the final posture.

20、</p><p>　　II. ROBOT MODEL</p><p>　　The model of space robot is illustrated in Fig.1.</p><p>　　The robot is mounted on a spacecraft and has two rotary joints which allow the in-plane

21、 motion of the end-effecter. In this case we have an additional freedom of the spacecraft attitude angle and this will be considered the additional rotary joint. This means that the space robot is three linked with 3 DOF

22、 (Degree Of Freedom). The length of each link and the angle of each rotary joint are given byand(i = 1,2,3) , respectively. In order to simplify the discussions a few assumptions are made in th</p><p>　　-the

23、 motion of the space robot is in-plane,i.e., two dimensional one.</p><p>　　-effect of robot arm motion to the spacecraft attitude is negligible.</p><p>　　-robot motion is given by the relation o

24、f static geometry and not explicitly depending on time.</p><p>　　-the target satellite is inertially stabilized.</p><p>　　In general in-plane motion and out-of-plane motion will be separately pe

25、rformed. So we are able to assume the above first one without loss of generality. The second assumption derives from the comparison of the ratio of mass between the robot arm and the spacecraft body. With respect to the

26、third assumption we focus on generating the path planning of the robot and this is basically given by the static nature of geometry relationship and is therefore not depending on the time explicitly. The last</p>

27、<p>　　Fig.1 Model of Two-link Space Robot</p><p>　　III. PATH PLANNING GALGORITHM</p><p>　　A. Laplace Potential Guidance</p><p>　　The solution of the Laplace equation (1) is cal

28、led a Harmonic potential function, and its and minimum values take place only on the boundary. In the robot path generation the boundary means obstacle and goal. Therefore inside the region where the potential is defined

29、, no local minimum takes place except the goal. This eliminates the deadlock phenomenon for path generation.</p><p><b>　?。?）</b></p><p>　　The Laplace equation can be solved numerical

30、ly. We define two dimensional Laplace equation as below:</p><p><b>　?。?）</b></p><p>　　And this will be converted into the difference equation and then solved by Gauss -Seidel method.

31、 In equation (2) if we take the central difference formula for second derivatives, the following equation will be obtained:</p><p><b>　　（3）</b></p><p>　　where ， are the step (cell) s

32、izes between adjacent nodes for each x, y direction. If the step size is assumed equal and the following notation is used:</p><p>　　Then equation (3) is expressed in the following manner:</p><p>

33、;<b>　　（4）</b></p><p>　　And as a result, two dimensional Laplace equation will be converted into the equation (5) as below:</p><p><b>　　（5）</b></p><p>　　In th

34、e same manner as in the three dimensional case, the difference equation for the three dimensional Laplace equation will be easily obtained by the following: </p><p><b>　?。?）</b></p><p&

35、gt;　　In order to solve the above equations we apply Gauss-Seidel method and have equations as follows:</p><p><b>　?。?）</b></p><p>　　where is the computational result from the ( n +1

36、 )-th iterative calculations of the potential.</p><p>　　In the above computations, as the boundary conditions, a certain positive number is defined for the obstacle and 0 for the goal. And as the initial co

37、nditions the same number is also given for all of the free nodes. By this approach during iterative computations the value of the boundary nodes will not change and the values only for free nodes will be varying. Applyi

38、ng the same potential values as the obstacle and in accordance with the iterative computational process, the small potential arou</p><p>　　Using the above potential field from 4 nodal points adjacent to the

39、node on which the space robot exists, the smallest node is selected for the point to move to. This procedure finally leads the space robot to the goal without collision.</p><p>　　B. Spline Interpolation</

40、p><p>　　The path given by the above approach does not assure the smoothly connected one. And if the goal is not given on the nodal point, we have to partition the cells into much more smaller cells. This will i

41、ncrease the computational load and time.</p><p>　　In order to eliminate the above drawbacks we propose the utilization of spline interpolation technique. By assigning the nodal points given by the solution t

42、o via points on the path, we try to obtain the smoothly connected path with accurate initial and final points.</p><p>　　In this paper the cubic spline was applied by using MATLAB command.</p><p>

43、;　　C. Configuration Space</p><p>　　When we apply the Laplace potential, the path search is assured only in the case where the robot is expressed to be a point in the searching space. The configuration space(

44、C-Space), where the robot is expressed as a point, is used for the path search. To convert the real space into the C-Space the calculation to judge the condition of collision is performed and if the collision exists, the

45、 corresponding point in the C-space is regarded as the obstacle. In this paper when the potential field was </p><p>　　IV.NUMERICAL SIMULATIONS</p><p>　　Based on the above approach the path plann

46、ing for capturing a target satellite was examined using a space robot model. In this paper we assume the space robot with two dimensional and 2 DOF robotic arm as shown in Fig.1.</p><p>　　The length of each

47、link is given as follows:</p><p>　　l1 =1.4[m], l2 = 2.0[m], l3 = 2.0[m] ,</p><p>　　and the target satellite was assumed 1m square. The grasp handle, 0.1 m square, was located at a center of one

48、side of the target. So this handle is a goal of the path.</p><p>　　Let us explain the geometrical relation between the space robot and the target satellite. When we consider the operation after capturing the

49、 target, it is desirable for the space robot to have the large manipulability. Therefore in this paper the end-effecter will reach the target when the manipulability is maximized. In the 3DOF case, not depending on the s

50、pacecraft body attitude, the manipulability is measured by. And if we assume the end-effector of the space robot should be vertical to the t</p><p>　　As all the joints angles are determined, the relative pos

51、ition between the spacecraft and the target is also decided uniquely. If the spacecraft is assumed to locate at the origin of the inertial frame (0, 0), the goal is given by (-3.27, -2.00) in the above case. Based on the

52、se preparations, we can search the path to the goal by moving the arm in the configuration space.</p><p>　　Two simulations for path planning were carried out and the results are shown below.</p><p

53、>　　A. 2 DOF Robot</p><p>　　In order to simplify the situation, the attitude angle(Link 1 joint angle) is assumed to coincide with the desirable angle from the beginning. The coordinate system was assumed

54、as shown in Fig.2. </p><p>　　was taken into consideration for the calculation of the initial condition of the Link 2 and its goal angles:</p><p>　　Innitial condition:</p><p>　　Goal

55、condition: </p><p>　　In this case the potential field was computed for the C-Space with 180 segments. Fig.3 shows the C-Space and the hatched large portion in the center is given by the obstacle mapped by t

56、he spacecraft body. The left side portion is a mapping of the target satellite. Fig.4 shows a generated path and this was spline-interpolated curve by using alternate points of discrete data for smoothing.</p><

57、;p>　　Fig.3 2 DOF C-Space</p><p>　　Fig.4 Path in C-Space(2 DOF)</p><p>　　When we consider the rotation of spacecraft body, -180 degrees are equal to +180 degrees and, then, the state over -180

58、 degrees will be started from +180 degrees and again back to the C-Space. For this reason the periodic boundary condition was applied in order to assure the continuity of the rotation. For the simplicity to look at the p

59、ath, the mapped volume by the spacecraft body was omitted. Also for the simplicity of the path expression the chart which has the connection of -180 degrees in t</p><p>　　V. CONCLUSION</p><p>　　

60、In this paper a path generation method for capturing a target satellite was proposed. And its applicability was demonstrated by numerical simulations. By using interpolation technique the computational load will be decre

61、ased and smoothed path will be available. Further research will be recommended to incorporate the attitude motion of the spacecraft body affected by arm motion. </p><p><b>　　中文譯文：</b></p>

62、<p>　　空間機器人避碰路徑規(guī)劃</p><p>　　Yuya Yanoshita and Shinichi Tsuda</p><p>　　摘要：本文論述的是空間機器人路徑規(guī)劃，這種規(guī)劃主要運用的是避碰算法。對于未來的空間機器人操作，自主控制的路徑規(guī)劃方法可以受到固定指令的支配去捕獲目標(biāo)，不用一直受地面站的控制。尤其是從始至終要考慮到避免與目標(biāo)本身的碰撞，一旦地點、形狀和目標(biāo)

63、的控制點得到確認(rèn)，這些點將在配置空間中表示出來。為了避免死鎖現(xiàn)象的發(fā)生，本文利用了一種勢場域算法，也就是將拉普拉斯勢函數(shù)的應(yīng)用在配置空間中獲取路徑。通過利用平滑路徑的方法，我們已經(jīng)在路徑生成方面做了一定的改進。這種方法主要是利用樣條函數(shù)插值，它減少了計算負荷和產(chǎn)生空間機器人的平滑路徑，這種方法的有效性可通過幾個數(shù)字模擬來展現(xiàn)。</p><p>　　關(guān)鍵字：空間機器人、路徑規(guī)劃、避碰、勢函數(shù)、樣條內(nèi)插</p&

64、gt;<p><b>　　1 介紹</b></p><p>　　未來的空間發(fā)展中，空間機器人及其自主性能將成為航天科技的關(guān)鍵特征。這種空間機器人將在構(gòu)建空間站和執(zhí)行航天器的檢查和維護方面發(fā)揮重要的作用。這些機器人將以自主的形式取代航天員進行艙外活動。上述機器人運行的一個基本和重要的任務(wù)就是由機械臂捕獲在軌道上自由飛行的目標(biāo)，為了這項捕獲操作的正常進行，要求將機械臂從初始位置移動

65、到末位置而不與目標(biāo)發(fā)生碰撞。</p><p>　　這種空間配置和人工勢場的方法通常應(yīng)用于普通機器人的運行規(guī)劃當(dāng)中，使機器人的機械臂能夠回避障礙物和朝目標(biāo)移動。Khatib提出了一種運動規(guī)劃的方法，在這種方法中定義了障礙物與機器人的每個鏈接的排斥勢，還定義了機器人的末端執(zhí)行器與目標(biāo)的吸引勢，并通過計算勢場和勢場的梯度而生成了最優(yōu)路徑。根據(jù)這種實時操作的簡單性和適應(yīng)性，我們得知該方法是有效的。</p>

66、<p>　　但是在吸引勢場和排斥勢場的共同作用下會產(chǎn)生局部極值點，這將導(dǎo)致所謂的死鎖現(xiàn)象。為了解決上述問題，科研人員提出了一些方法，例如拉普拉斯算法的使用。這種方法保證了勢場域不存在局部極值點，即無死鎖現(xiàn)象。勢場域分為很多小格，勢場域的每個節(jié)點的離散值將被唯一確定。</p><p>　　本文對上述缺陷的消除，提出了樣條插值技術(shù)。給定的節(jié)點作為路徑的一部分將被定義為平滑樣條函數(shù)的一部分。為了捕獲到目標(biāo)，空

67、間機器人的路徑規(guī)劃運用了數(shù)字模擬技術(shù)，它是通過對勢場域求解拉普拉斯函數(shù)來實現(xiàn)的，并且從最初的位置到末尾位置的樣條插值來產(chǎn)生連續(xù)光滑的路徑。</p><p><b>　　2. 機器人模型</b></p><p>　　空間機器人的模型如圖1所示：機器人被安裝在航天器和兩個旋轉(zhuǎn)接頭上，這兩個旋轉(zhuǎn)接頭可以實現(xiàn)末端執(zhí)行器的平面運動。這種情況下，我們的航天器的姿態(tài)角有一個額外的自

68、由度，我們將這個額外的自由度視為額外的旋轉(zhuǎn)接頭。這意味著空間機器人有三個自由度的鏈接，每個鏈路的長度和每個旋轉(zhuǎn)關(guān)節(jié)角度，分別由 (i = 1,2,3)表示。為了簡化這個討論，本文做了一些假設(shè)：</p><p>　　（1）空間機器人的運動是平面的，即二維；</p><p>　?。?）機器人機械臂的運動對航天器姿態(tài)的影響是可以忽略的；</p><p>　?。?）機器人運

69、動給出了靜態(tài)幾何關(guān)系，并沒有明確的依賴時間；</p><p>　?。?）目標(biāo)衛(wèi)星在慣性的作用下是很穩(wěn)定的；</p><p>　　一般情況下，平面運動和空間運動將分別進行，所以我們可以假設(shè)上面的第一個不失一般性，第二個假設(shè)來自機械臂和航天器質(zhì)量比的比較，對于第三個假設(shè)，我們專注于生成機器人的路徑規(guī)劃，這基本上是由幾何關(guān)系的靜態(tài)性質(zhì)決定，因此并不依賴明確的時間，最后一個就是合作衛(wèi)星。</

70、p><p>　　圖1 雙鏈路空間機器人</p><p><b>　　3 路徑規(guī)劃算法</b></p><p>　　拉普拉斯勢場域?qū)б?lt;/p><p>　　的拉普拉斯方程求解稱為諧波的勢場域功能，并且最大值和最小值僅發(fā)生在邊界處，在生成的機器人路徑中，邊界處代表障礙物和目標(biāo)，因此在此范圍中定義勢場域，除了目標(biāo)處其他位置不會

71、發(fā)生局部極值點的問題，這為路徑的生</p><p><b>　　成消除了死鎖現(xiàn)象。</b></p><p><b>　　(1)</b></p><p>　　拉普拉斯方程可以數(shù)值求解，我們定義了二維拉普拉斯方程，如下公式所示：</p><p><b>　　(2)</b></

72、p><p>　　這將轉(zhuǎn)化成差分方程，并通過高斯-賽德爾方法求解，在方程(3)中，如果采用的二階導(dǎo)數(shù)的差分公式，可以得到以下的差分公式：</p><p><b>　　(4)</b></p><p>　　，的代數(shù)值代表每個相鄰節(jié)點的X、Y的方向，假設(shè)長度等同于使用以下符號：</p><p>　　然后，方程3用以下方程表達：<

73、;/p><p><b>　　(5)</b></p><p>　　結(jié)果二維拉普拉斯方程轉(zhuǎn)變?yōu)榉匠?，如下：</p><p><b>　　(6)</b></p><p>　　同樣的方式，在三維的情況下，三維的拉普拉斯方程的差分方程由下式易得：</p><p><b>　　(

74、7)</b></p><p>　　為了解決上述方程，我們應(yīng)用了高斯賽德爾算法和求解方程，如下：</p><p><b>　　(8)</b></p><p>　　表示勢場域的迭代計算結(jié)果。</p><p>　　在上述的計算中，作為邊界條件，定義特定的正數(shù)來表示障礙物和目標(biāo)。為保證初始條件相同，給所有的自由節(jié)點賦

75、同樣的數(shù)值。通過這種方法，在迭代計算的邊界節(jié)點獲得的的值將不會改變，而且自由節(jié)點的值是不同。我們應(yīng)用相同的域值作為障礙物，并且按照迭代計算方法，則目標(biāo)周圍較小的勢場域會像障礙物一樣緩慢的向周圍傳播，勢場域就是根據(jù)上述方法建立的。采用4節(jié)點相鄰的空間機器人存在的節(jié)點上的勢場，最小的節(jié)點選擇移動到另一點，這個過程最終引導(dǎo)機器人無碰撞的到達目標(biāo)的位置。</p><p><b>　　樣條內(nèi)插法：</b&g

76、t;</p><p>　　通過上述方法給出的路徑不能保證能夠與另一個目標(biāo)順利連接，如果節(jié)點上沒有給定目標(biāo)，我們會將柵格劃分成的更小，但這將增加計算量和所用時間。為了消除這些弊端，我們提出利用樣條插值技術(shù)。通過在將節(jié)點解給出的通過點的道路上，我們試圖獲得順利連接路徑與準(zhǔn)確獲取最初的和最后的點。本文主要是通過MATLAB命令應(yīng)用樣條函數(shù)。</p><p><b>　　配置空間：<

77、;/b></p><p>　　當(dāng)我們在應(yīng)用拉普拉斯勢域的時候，路徑搜索只能在當(dāng)機器人在搜索空間過程中表示成一個點的情況下才能保證實現(xiàn)。配置空間(C空間)中機器人僅表示為一個點，主要是用于路徑搜索。將真正的空間轉(zhuǎn)換到C空間，必須執(zhí)行判斷碰撞條件的計算，如果碰撞存在,相應(yīng)的點在c空間被認(rèn)為是障礙。本文中，在生成勢場域時，所有現(xiàn)實空間的點的生成條件對應(yīng)于所有的節(jié)點都是經(jīng)過計算的。在構(gòu)成的機械臂和生成的節(jié)點的障礙物

78、出現(xiàn)判斷選擇時，該節(jié)點可以看作是在c空間的障礙點。</p><p><b>　　數(shù)值仿真：</b></p><p>　　基于上述方法對于捕獲目標(biāo)衛(wèi)星路徑規(guī)劃的檢查是使用空間機器人模型進行的。在本文中，我們假設(shè)空間機器人二維和2自由度機械手臂見圖1。每個鏈接的長度給出如下:</p><p>　　l1 =1.4[m], l2 = 2.0[m], l

79、3 = 2.0[m]</p><p>　　并假設(shè)目標(biāo)衛(wèi)星有1平方米。掌握處理1平方米的范圍，是以目標(biāo)中心的一側(cè)為中心的，所以這種處理方法就是最優(yōu)路徑的一個選擇。</p><p>　　我們來解釋一下空間機器人和目標(biāo)衛(wèi)星的幾何關(guān)系，在捕捉到目標(biāo)后，我們再回想一下整個操作過程，讓空間機器人有更大的可操作性是完全可行的。因此在本文中，可操作性最大化的情況下，末端執(zhí)行器將到達指定目標(biāo)位置。在3個自由

80、度的情況下，并不是根據(jù)航天器機體的角度，可操縱性由來衡量。如果我們假設(shè)空間機器人的末端應(yīng)垂直于目標(biāo),然后所有的關(guān)節(jié)角度是預(yù)先確定的，數(shù)值如下:</p><p>　　因為所有的關(guān)節(jié)角度是確定的，航天器之間的相對位置和目標(biāo)也唯一確定，如果飛船被認(rèn)為定位在原點的慣性坐標(biāo)系(0,0),目標(biāo)坐標(biāo)在上面的情況下是給出的(-3.27,-2.00)?；谶@些準(zhǔn)備，我們可以通過在配置空間中機械臂的移動搜索來到達目標(biāo)位置。</

81、p><p>　　為了簡化境況，一開始就假設(shè)姿態(tài)角(鏈接1關(guān)節(jié)角)符合理想情況。假定的坐標(biāo)系統(tǒng)圖2所示</p><p>　　圖2 2個自由度的路徑規(guī)劃問題</p><p>　　為計算初始條件的鏈接2和它的目標(biāo)角度，應(yīng)考慮的大小：</p><p><b>　　初始角度：</b></p><p><

82、b>　　目標(biāo)角度：</b></p><p>　　在這種情況下，勢場域分成180段計算成C空間。圖3顯示的C空間和計劃中的很大一部分的中心是由航天器本體映射的障礙了，左邊部分是目標(biāo)衛(wèi)星的映射。圖4顯示的是生成的路徑，這是通過利用離散數(shù)據(jù)點平滑交替生成的樣條插值曲線。當(dāng)我們考慮航天器本體的旋轉(zhuǎn)時，-180度相當(dāng)于+180度狀態(tài)，然后，狀態(tài)超過-180度時，它將從180度再次轉(zhuǎn)到C-空間當(dāng)中。正是由于

83、這個原因，為了保證旋轉(zhuǎn)的連續(xù)性，我們需要充分利用周期性的邊界條件。為方便觀察路徑，航天器機體的映射體積忽略不計。同時為了路徑表述的更加簡單，附有在方向上-180度范圍的連接的插圖，并做了說明。從圖中可以很容易看出在-180度的范圍內(nèi)，沿著路徑走向目標(biāo)C，B和C是走向相同的目標(biāo)點。</p><p>　　圖3 兩個自由度的C空間</p><p>　　圖4 C空間的路徑（2個自由度）</p