外文翻譯--自動(dòng)表面粗糙度同三維機(jī)器視覺和合作的機(jī)器人控制

1、<p>　　附錄錯(cuò)誤!未找到引用源。 外文翻譯</p><p>　　自動(dòng)表面粗糙度同三維機(jī)器視覺和合作的機(jī)器人控制</p><p>　　Chris Marshall, Robert Bicker and Paul Taylor</p><p>　　摘要：本文介紹了創(chuàng)新和務(wù)實(shí)的自動(dòng)檢測(cè)皮革表面粗糙度，利用結(jié)構(gòu)光三維機(jī)器視覺對(duì)物體輪廓的知覺和NURBS插補(bǔ)準(zhǔn)確

2、和平穩(wěn)軌跡生成。作為高壓噴砂用于粗加工，要考慮空間限制，在爆破庭額外的自由度介紹利用一個(gè)轉(zhuǎn)盤，它支持工件，協(xié)同控制是實(shí)施之間的一個(gè)六自由度機(jī)器人和轉(zhuǎn)臺(tái)盡量機(jī)器人動(dòng)作在滿足要求的變速控制，精確的軌跡跟蹤和定位控制。實(shí)驗(yàn)結(jié)果一致的業(yè)績(jī)已經(jīng)顯示出了該方法的有效性。</p><p>　　關(guān)鍵詞∶三維視覺；曲線曲面的非均勻有理B樣條內(nèi)插法；合作管理；機(jī)器人；表面粗糙度 </p><p><b&

3、gt;　　1 、引言</b></p><p>　　表面處理，特別適用于鞋類制造業(yè)，質(zhì)量關(guān)鍵的大問題是為行業(yè)的生產(chǎn)鞋用水泥粘結(jié)和直接注塑鞋底。一個(gè)主要因素在于完整的膠合面，這就意味著要充分清除材料的表面，以促進(jìn)市場(chǎng)的基本結(jié)構(gòu)，或者在發(fā)生天然皮革的表皮。目前，表面處理等兩種形式進(jìn)行，采用了氣缸鋼絲刷或磨料表面旋轉(zhuǎn)車輪或帶;這是做手工應(yīng)用的歷時(shí)鞋面的旋轉(zhuǎn)鋼絲刷，或自動(dòng)機(jī)適用該鞋面以鋼絲刷控制四個(gè)或五個(gè)軸，顯

4、然，手工操作，需要高超的技巧，是難以維持在一個(gè)良好的水準(zhǔn)，由于始終不斷注意經(jīng)營(yíng)者?？刂葡到y(tǒng)的自動(dòng)化進(jìn)程通常開環(huán)定位裝置和過程控制是有限事先調(diào)整刷特點(diǎn)，如絲的剛度和敏銳性，轉(zhuǎn)速和控制力量與毛筆適用。在過去十年中，研究工作已取得根本性改善的軌跡控制， 運(yùn)用傳感器和分析方法能夠檢測(cè)過程實(shí)時(shí)[1]，[2]，[3]，智能控制[4]，[5]的接觸力，轉(zhuǎn)速和進(jìn)給速度的鋼絲刷優(yōu)化材料去除和表面紋理。大多數(shù)的這些努力都局限于實(shí)驗(yàn)室示威由于有實(shí)際困難的調(diào)諧

5、有很大差異，在刷特色。因此，新工藝是可取推進(jìn)素質(zhì)表面處理技術(shù)。</p><p>　　磨料爆破和噴丸有效而廣泛采用的表面處理工藝去除縫針，提高強(qiáng)度和其它相關(guān)的表面制備應(yīng)用。一系列的皮革表面篩選試驗(yàn)采用噴砂機(jī)根據(jù)不同的條件下在我們的實(shí)驗(yàn)室最近表現(xiàn)一致的材料去除性能。相對(duì)于這些方法用接觸力控制，這是比較容易控制參數(shù)的噴砂工藝，如空氣壓力，速度砂粒流遷入表面距離噴嘴表面，而更重要表現(xiàn)較為一致，較不敏感的工藝參數(shù)變化。&l

6、t;/p><p>　　一個(gè)主要問題自動(dòng)鞋上摔打，是如何衡量可靠的三維剖面上，并確定適當(dāng)?shù)拇謴缴?，這使得機(jī)器人操縱粗工具加以引導(dǎo)沿著指定的速度。常規(guī)傳感器所不具備足夠的計(jì)算粗徑的上表面因復(fù)雜幾何概況，尤其是當(dāng)今許多女人的時(shí)尚鞋。機(jī)器視覺是最適當(dāng)?shù)母泄俜椒ǎ谌S測(cè)量，而且越來越便宜，為雙方研究和過程控制。以前的相關(guān)研究著作描述[6]，[7]在某種程度上成功地證明效力結(jié)構(gòu)光機(jī)視覺在自動(dòng)唯一和粘接上的應(yīng)用。然而，與其建立了

7、視覺系統(tǒng)的模型，固定價(jià)值尺度因素來計(jì)算鞋廓坐標(biāo)從圖像數(shù)據(jù)。本文將建立一個(gè)數(shù)學(xué)模型之間的圖像數(shù)據(jù)和世界的坐標(biāo)它可以大大提高精確度剖面測(cè)量。</p><p>　　測(cè)量結(jié)果，從機(jī)器視覺一般是離散的位置坐標(biāo)，從一個(gè)連續(xù)剖面上可重構(gòu)，經(jīng)分段直線段或通過復(fù)雜曲線插補(bǔ)。掃描數(shù)據(jù)是有限的分辨率，由于速度要求的裝配線，并花費(fèi)大量時(shí)間形象加工一幢醫(yī)科相機(jī)使用的建議視覺系統(tǒng)掃描決議排列為5毫米，在腳背面積和2.5毫米的腳趾和足跟區(qū)。大

8、多數(shù)工業(yè)機(jī)器人控制器的位置直流裝置內(nèi)置插值，使他們能夠處理斷面位置。然而，這些控制器通常采用串行通信傳輸數(shù)據(jù)和指令上位PC機(jī)和機(jī)器人控制器相對(duì)緩慢的更新率，它必然導(dǎo)致低精度和呆滯的動(dòng)態(tài)響應(yīng)。一個(gè)美洲豹760個(gè)工業(yè)機(jī)器人被重新利用多軸運(yùn)動(dòng)控制器與以太網(wǎng)通信和位置更新率 多達(dá)200余等高線模式，這可大大提高精度。鑒于先前的嵌入式插不再提供,非均勻有理B樣條插補(bǔ)應(yīng)用于重建順利連續(xù)軌跡由離散路徑坐標(biāo)。NURBS插補(bǔ)提供了一個(gè)統(tǒng)一的代表性分析和自

9、由型曲線，并明顯優(yōu)于線性插值常規(guī)數(shù)控機(jī)床和機(jī)器人通常使用。速度和加速度的連續(xù)性整個(gè)曲線是至關(guān)重要的特點(diǎn)，以避免急沖提案的機(jī)器人末端效應(yīng)。</p><p>　　表面噴砂進(jìn)行內(nèi)密封庭該機(jī)器人已在有限空間內(nèi)操控粗噴嘴。為減少運(yùn)動(dòng)造成的機(jī)器人手臂，額外自由度引入到工件使鞋上支撐平臺(tái)可以轉(zhuǎn)動(dòng)實(shí)時(shí)控制下。因此，協(xié)同控制算法所需要的7個(gè)自由度的冗余系統(tǒng)。保持一貫的表面處理性能，在某些砂?？諝饬髁浚忝骰蚓€速度的粗噴嘴相對(duì)的上表

10、面是至關(guān)重要的，這一目標(biāo)已經(jīng)實(shí)現(xiàn)，開發(fā)新穎的NURBS軌跡生成算法和插值方法。</p><p>　　2、三維機(jī)器視覺輪廓測(cè)量發(fā)達(dá)結(jié)構(gòu)光掃描系統(tǒng)顯示</p><p>　　如圖1;它包括一個(gè)模擬式攝像機(jī)，激光線發(fā)生器和步進(jìn)電機(jī)驅(qū)動(dòng)直線下滑提供掃描議案照相機(jī)和激光打印機(jī)。鞋將掃描是緊緊空氣鉗位在一個(gè)轉(zhuǎn)盤是位于45度角的水平面。這種配置可以減輕媒體爆破積累了放在桌上的噴砂工藝。照相機(jī)和激光線發(fā)生器

11、裝在步進(jìn)電機(jī)驅(qū)動(dòng)直線下滑，與激光線垂直的轉(zhuǎn)盤和一個(gè)夾角，照相機(jī)的光軸與激光線?？陀^的視覺系統(tǒng)，是提供一個(gè)三維輪廓的鉗位鞋基于坐標(biāo)系統(tǒng)定義的轉(zhuǎn)盤，邊鞋面，然后是發(fā)現(xiàn)和粗徑是指形匹配的上唯一的。經(jīng)過粗加工的道路，得到了 鞋鉗位的轉(zhuǎn)盤是運(yùn)到爆破廳通過直線滑機(jī)器人操縱噴砂處理。</p><p>　　圖1 結(jié)構(gòu)光視覺系統(tǒng)。</p><p>　　如圖2，存在兩個(gè)坐標(biāo)系，圖像坐標(biāo)系團(tuán)與物體坐標(biāo)系統(tǒng)哎喲，

12、它們之間的關(guān)系需要加以確定的物理位置和方向的對(duì)象點(diǎn)提取圖像數(shù)據(jù)。圖像坐標(biāo)系，是指與鏡頭的光軸作為ocz軸方向增加圖像連續(xù)坐標(biāo)ocy軸線，軸線的ocx決定用右手規(guī)則。物體坐標(biāo)系是指與該中心的轉(zhuǎn)盤出身，向下方向沿轉(zhuǎn)盤和平行的直線滑攜帶激光照相機(jī)作為owz軸截至方向垂直于轉(zhuǎn)盤作為owx軸線;owy可以定義方便用右手規(guī)則。結(jié)構(gòu)光三維掃描鉆機(jī)是精心，刻意設(shè)計(jì)，激光平面平行于xowy平面物體坐標(biāo)系，使每一個(gè)點(diǎn)上的激光線相交的對(duì)象有一個(gè)固定的Z坐標(biāo)對(duì)

13、象坐標(biāo)系因此，其他兩個(gè)部件坐標(biāo)X和Y可以單獨(dú)確定從二維圖像數(shù)據(jù)。</p><p>　　圖2 攝像機(jī)與世界坐標(biāo)系統(tǒng)。</p><p>　　數(shù)學(xué)關(guān)系的攝像機(jī)坐標(biāo)系與物體坐標(biāo)系中是不可或缺的連接二維 圖像數(shù)據(jù)與三維物體的坐標(biāo)。有很多方法[8]，[9]，[10]，[11]和[12]開發(fā)構(gòu)建數(shù)學(xué)模型的視覺系統(tǒng)，其中蔡明亮的方法[8]，是最常采用的。一般來說，模擬視覺系統(tǒng)分為兩階段相關(guān)參數(shù)的外在和內(nèi)在

14、參數(shù)。外在參數(shù)描述空間關(guān)系中的兩個(gè)坐標(biāo)系，如平移和旋轉(zhuǎn)變換的坐標(biāo)系中的物體坐標(biāo)系統(tǒng)可以映射到 攝像機(jī)坐標(biāo)系; 這些轉(zhuǎn)變可以在數(shù)學(xué)上表示為:</p><p><b>　?。?）</b></p><p>　　在這里，R是旋轉(zhuǎn)矩陣定義的歐拉角，由TAIPEI，烴厝翻譯沿新owx，owy和owz軸旋轉(zhuǎn)。分子RI在矩陣R可以表示為功能旋轉(zhuǎn)角度α，β，γ如下: </p>

15、;<p><b>　?。?）</b></p><p>　　成反比，歐拉角可確定由R:</p><p><b>　?。?）</b></p><p>　　第二階段的模擬進(jìn)程，是與照相機(jī)的內(nèi)在參數(shù):它是基于針孔相機(jī)的透視投影模型徑向變形及其它異?，F(xiàn)象的考慮。針孔相機(jī)的模式來改造點(diǎn)(圓度量，zc)在攝像機(jī)坐標(biāo)系奧委會(huì)

16、相關(guān)位置圖像緩沖像素。這一階段共分三個(gè)轉(zhuǎn)變，第一次描述了變換從相機(jī)坐標(biāo)(XC細(xì)胞度量，ZC)的失真，以二維傳感器平面坐標(biāo)(徐鈺)由方程：</p><p><b>　　（5）</b></p><p>　　其中f是有效焦距的鏡頭。第二個(gè)層面的轉(zhuǎn)變反映了徑向幾何失真，這是造成的鏡頭，其實(shí)這點(diǎn)在不同徑向距離鏡頭軸線發(fā)生明顯放大。坐標(biāo)，在一個(gè)失真圖像傳感器飛機(jī)(徐鈺)，可從觀測(cè)

17、(扭曲)圖像坐標(biāo)(XD型，YD型) </p><p><b>　　（6）</b></p><p>　　在這里，是徑向距離觀測(cè)點(diǎn)的攝像機(jī)光軸，K1的是系數(shù)的徑向畸變。 最后的變換敘述關(guān)系的觀察陣地的圖像傳感器平面坐標(biāo)，在緩沖圖像幀，它被描述的:</p><p><b>　　（7）</b></p><p&g

18、t;　　而泰航與CY是像素坐標(biāo)相交光軸與傳感器平面，DX的鏑的有效培訓(xùn)中心之間的距離照相機(jī)的傳感器組成，在第十和昌方向分別S、X的，是一個(gè)尺度因子，以彌補(bǔ)任何不確定的數(shù)目比例分子傳感器關(guān)于CCD和象素?cái)?shù)目在照相機(jī)的幀緩沖X方向。所以關(guān)系的對(duì)象坐標(biāo)和圖像數(shù)據(jù)相結(jié)合，建立了有效性。(1)，(5)，(6)，(7)在一起。照相機(jī)的模型所述標(biāo)定需要確定的外部和內(nèi)部參數(shù)，然后它可以把圖像數(shù)據(jù)用來作為坐標(biāo)在轉(zhuǎn)臺(tái)坐標(biāo)系。用標(biāo)定目標(biāo)，并根據(jù)Tsai的方法

19、，建議的攝像系統(tǒng)標(biāo)定以及由此產(chǎn)生的參數(shù)有: </p><p><b>　　3、合作機(jī)器人控制</b></p><p>　　圖3顯示了成立機(jī)器人鞋上噴砂， 其中噴砂嘴，是他操縱的機(jī)器人末端微跟隨造成粗徑與某些方向。一個(gè)金屬盤，并采取適當(dāng)?shù)霓固兆鳛檠谀５穆窂礁?，以防止流砂?破壞以外地區(qū)的皮革表面。雙方軌跡跟蹤和定位控制的機(jī)器人末端效應(yīng)可引起較大規(guī)模的聯(lián)合運(yùn)動(dòng)。作為噴砂

20、會(huì)發(fā)生議事堂，機(jī)器人動(dòng)作應(yīng)限制在一個(gè)受約束的小空間。 為了減少機(jī)器人動(dòng)作，額外的自由度，旋轉(zhuǎn) 引入到鞋面支持轉(zhuǎn)臺(tái)，這不可避免地導(dǎo)致了冗余系統(tǒng)七個(gè)自由度。</p><p>　　圖3 機(jī)器人鞋上噴砂成立的。</p><p>　　一個(gè)簡(jiǎn)單的協(xié)同控制策略適用于轉(zhuǎn)盤和機(jī)器人系統(tǒng)，旨在減輕關(guān)節(jié)運(yùn)動(dòng)。算法是描圖。B和C是坐標(biāo)的粗徑產(chǎn)生NURBS插補(bǔ)，角度α，β，可據(jù)此計(jì)算，同樣的計(jì)算，可以做到對(duì)所有插值

21、點(diǎn)的路徑。簡(jiǎn)單地轉(zhuǎn)動(dòng)轉(zhuǎn)盤角度，以α，β分別可以帶多點(diǎn)，B和C上的X軸為中心的A1，B1和C1組，同樣，所有坐標(biāo)的軌跡，這可以大大降低運(yùn)動(dòng)的機(jī)器人。理論上，有沒有運(yùn)動(dòng)，在y方向做一系列動(dòng)作，在X方向不會(huì)改變，小的方向變化的最終效應(yīng)在Z軸方向高度變化。</p><p><b>　　4、結(jié)論</b></p><p>　　本文描述了一種新的自動(dòng)皮革技術(shù)，它利用空氣助推噴砂表面

22、處理表面粗度，三維機(jī)器視覺物體輪廓測(cè)量，NURBS曲線插補(bǔ)軌跡重建和工業(yè)機(jī)器人的自動(dòng)操縱和控制。一個(gè)數(shù)學(xué)模型的形象，制度的建立及相關(guān)參數(shù)進(jìn)行了校準(zhǔn)，這大大提高了測(cè)量精度。平穩(wěn)軌跡的作品再現(xiàn)，由離散圖像數(shù)據(jù)的NURBS曲線插補(bǔ)基于這個(gè)原因，泰勒的二階逼近擴(kuò)張被用來執(zhí)行速度控制的機(jī)器人末端效應(yīng)。順利機(jī)器人準(zhǔn)確地跟蹤目標(biāo)。協(xié)同控制實(shí)施機(jī)器人與工件支持平臺(tái)，以最小的機(jī)器人動(dòng)作。實(shí)驗(yàn)結(jié)果一致的表面處理表現(xiàn)的效率的方法。 可以進(jìn)一步改進(jìn)，采用高幀頻

23、攝像機(jī)結(jié)合標(biāo)定的視覺系統(tǒng)登記的機(jī)器人末端微向工件平臺(tái)和工藝優(yōu)化。</p><p>　　附錄錯(cuò)誤!未找到引用源。 外文原文</p><p>　　Automatic surface roughing with 3D machine vision and cooperation robot control</p><p>　　Chris Marshall, Robert

24、Bicker and Paul Taylor</p><p><b>　　Abstract</b></p><p>　　This paper presents an innovative and practical strategy for automated leather surface roughing, using structured light 3D ma

25、chine vision for object profile perception, and NURBS interpolation for accurate and smooth trajectory generation. As high pressure grit blasting is used for roughing, considering the spacial constraints in the blasting

26、chamber, an additional degree of freedom is introduced using a rotary table, which supports the workpiece. Cooperative control is implemented between a 6-D</p><p>　　Keywords: 3D vision; NURBS interpolation;

27、Cooperative control; Robot; Surface roughing </p><p>　　1. Introduction </p><p>　　In surface treatment with particular application in the footwear manufacturing industry, the quality of sole bond

28、 is a major problem for the sectors that manufacture shoes with cement bonded and direct injection moulded soles. A main factor in the integrity of the sole bond is the preparation of the mating surfaces, which means to

29、remove the surface of the material adequately so as to facilitate a bond to the underlying structure of the upper material, or in the case of natural leather to the ep</p><p>　　Abrasive blasting and shot pee

30、ning are effective and widely used surface treatment processes for the removal of sharp edges, improvement of strength and other related surface preparation applications. A series of leather surface screening experiments

31、 using a grit blasting machine under distinct conditions undertaken in our laboratory recently have shown consistent material removal performance. Comparing with those methods using contact force control, it is much easi

32、er to control parameters of th</p><p>　　A major problem for automatic shoe-upper roughing is how to reliably measure the 3D profile of the upper, and define a proper roughing path on it, this enables the rob

33、ot manipulated roughing tool to be guided along the path with specified velocity. Conventional sensors are not sophisticated enough to calculate the roughing path on the upper surface due to the complex geometrical profi

34、le, particularly many of today’s women’s fashion shoes. Machine vision is the most appropriate sensory methodolog</p><p>　　Measurement results obtained from machine vision are generally discrete position coo

35、rdinates, from which a continuous profile can be reconstructed, either via piecewise straight line segments or through complex curve interpolation. Scan data are of limited resolution due to velocity requirements of the

36、assembly line and the time spent on image processing. For a 25 fps camera used in the proposed vision system, the scan resolutions are arranged as 5 mm at the instep area and 2.5 mm at the toe and</p>

37、;<p>　　Surface grit blasting is carried out inside a sealed chamber, in which the robot has limited space to manipulate the roughing nozzle. In order to minimize motion of the robot arm, an additional degree of fr

38、eedom is introduced to the workpiece, so that the shoe-upper support platform can rotate under real time control. Therefore, cooperative control algorithms are necessary for the 7 degrees of freedom redundant system

39、. To maintain consistent surface treatment performance under certain air grit f</p><p>　　The rest of the paper is organized as follows: description of the 3D vision system for shoe upper profile measurement

40、is given in Section 2; NURBS interpolation for smooth trajectory reconstruction from discrete scan data is placed in Section 3; variable feed rate NURBS interpolator for the robot can be found in Section 4

41、; experimental grit blasting results is given in Section 5. </p><p>　　2. 3D machine vision for profile measurement </p><p>　　The developed structured light scanning system is shown in Fig.

42、 1; it consists of an analogue camera, laser line generator and stepper motor driven linear slide providing scanning motions for the camera and laser. The shoe to be scanned is tightly air clamped on a rotary table

43、which is located at an angle of 45 degrees to the horizontal plane. This configuration can alleviate blasting media accumulating on the table during the grit blasting process. The camera and laser line generator are moun

44、te</p><p>　　Fig. 1. Structured light vision system.</p><p>　　As illustrated in Fig. 2, there exist two coordinate systems, the image coordinate system OC and object coordinate sys

45、tem OW, between them a relationship needs to be established to determine the physical position and orientation of object points from extracted image data. The image coordinate system is defined with the camera’s optical

46、axis as OCZ axis, the direction of increasing image row coordinates as OCY axis, and OCX axis is decided using the right-hand rule. The object coordinate system i</p><p>　　Fig. 2. Camera and world

47、coordinate systems.</p><p>　　The mathematical relationship between the camera coordinate system and the object coordinate system is vital and essential which connects 2D image data with 3D object coordinates

48、. There are a number of methods [8], [9], [10], [11] and [12] developed to construct a mathematical model for the vision system, among which, Tsai’s methodology [8] is most commonly applied. In general, modelli

49、ng of a vision system consists of two stages related the extrinsic parameters and intrinsic parameters. The extr</p><p><b>　　(2)</b></p><p>　　here, R is the rotation matrix defined b

50、y the Euler Angles , TX,TY and TZ are translations along the new OwX, OwY and OwZ axis after rotation respectively. Elements ri in matrix R can be expressed as function of rotation angles α, β, and γ as follows: </p&g

51、t;<p><b>　　(3)</b></p><p>　　Inversely, Euler angles can be determined from R by: </p><p><b>　　(4)</b></p><p>　　The second stage of the modelling proce

52、ss is related to the camera’s intrinsic parameters: it is based on the pinhole camera’s perspective projection model with radial distortion and other aberrations taken into account. Pinhole camera’s model is used to tran

53、sform point (XC,YC,ZC) in the camera coordinates system OC to associated position (Xf,Yf) in the image buffer in pixels. This stage consists of three transformations, the first one describes the transform from camera coo

54、rdinates (XC,YC,ZC) t</p><p><b>　　(5)</b></p><p>　　where f is the effective focal length of lens. The second transformation reflects the geometric radial distortion of the lens, whic

55、h is caused by the fact that points at different radial distance from the lens axis undergo distinct magnifications. The coordinates in an undistorted image sensor plane (XU,YU) can be obtained from the observed (distort

56、ed) image coordinates (XD,YD) by </p><p><b>　　(6)</b></p><p>　　here, is the radial distance from the observed point to the camera optical axis, k1 is the coefficient of radial lens d

57、istortion. The final transformation describes the relation between observed positions on the image sensor-plane to coordinates (Xf,Yf) in the image frame buffer, which is described by: </p><p><b>　　(7)

58、</b></p><p>　　where CX and CY are the pixel coordinates of the intersection of the optical axis and the sensor-plane, dX and dY are the effective centre to centre distances between the camera’s sensor

59、elements in the XC and YC directions respectively, and SX is a scaling factor to compensate for any uncertainty in the ratio between the number of sensor elements on theCCD and the number of pixels in the camera’s frame

60、buffer in the X direction. Therefore the relationship between the object coordinates and imag</p><p>　　The camera’s model described above need calibration to identify the exterior and interior parameters bef

61、ore it can be used to convert image data (Xf,Yf) into coordinates in the rotary table coordinate system. Using a calibration target and according to Tsai’s method, the proposed camera system is calibrated and resulting p

62、arameters are: </p><p>　　To calculate 3D object’s coordinate from 2D image data (Xf,Yf) using the vision system’s model constructed above, the constraint imposed on the ZW coordinate when the laser line inte

63、rsects with the object is used together with model Eq. (1) to determine a unique world coordinate (xw,yw,zw). For simplicity, in this design, the laser beam is adjusted to be critically vertical to the rotary table or pa

64、rallel to YWOWZW plane, so that all ZW coordinates of intersection points on the laser line are co</p><p><b>　　(8)</b></p><p>　　Discrete shoe profile coordinates are obtained by imag

65、e processing to find the edge points and conformal matching of the shoe upper and sole for further fine trim, two angles that define the shoe upper surface are also calculated from neighbouring edge points and individual

66、 scan line. Detailed description of the strategy can be found in [13] published by the authors. Fig. 3 shows an example 3D shoe profile consists of discrete points extracted from the laser scanning process. <

67、;/p><p>　　Fig. 3. Measurement of shoe upper contour trajectory.</p><p>　　3. NURBS interpolation for trajectory production </p><p>　　3.1. NURBS curve interpolation </p>

68、<p>　　NURBS is an acronym for Non-Uniform Rational B-Splines, they provide a single precise mathematical method for describing common analytical shapes including lines, planes, conic curves, free-form curves, quadr

69、atic and sculptured surfaces. The one dimension B-Spline curve is defined over a free parameter 0≤u≤1 by the following equation: </p><p><b>　　(9)</b></p><p>　　The point on the curve

70、at the parameter value u is denoted by P(u), which is a weighted average of all the control points denoted by Pi, the blending function or basis function Ni,k(u) decides the extent to which a particular control point con

71、trols the curve at a particular parameter value u. </p><p>　　The basis function Ni,k(u) depends on the parameter value u and the order of the curve k, and is recursively defined as follows: </p><p

72、><b>　　(11)</b></p><p>　　the constants [u0,…,un+k], called knot values, are specific instances of the parametric value u, and are strictly in nondecreasing order. The order of a NURBS curve def

73、ines the number of nearby control points that influence any given control point, generally, high order interpolation leads to smoother curve recreation. If the knot values are decided so that u1?u0=u2?u1==un+k?un+k?1, th

74、en all the basis functions are of identical shape and every control point has identical effect on the resulting </p><p>　　Introducing an additional term, weight of the control point, will allow B-spline to r

75、epresent conics and any other free-form curves and surfaces, and have more control over the shapes. The resulting curves, with a weight for each control point, are called rational curves. Therefore, a Non-Uniform Rationa

76、l B-spline curve is defined by the formula: </p><p><b>　　(13)</b></p><p>　　where Ri,k(u) is the single rational B-spline, which denotes the extent to which the control point has cont

77、rol over the curve. </p><p>　　NURBS curve interpolation, combined with basic approximation principles for parametric curves such as first and second order Taylor series expansion, has successfully been utili

78、sed in real time CNC variable feed rate command generation [14], [15], [16], [17] and [18], robot control [19], [20], [21] and [22] and computer graphics. In this work it is used for the reconstruction of a con

79、tinuous profile model from discrete scan data; Fig. 4 shows the result of a 12th order NURBS interpolation of sho</p><p>　　Fig. 4. 3D trajectory from NURBS curve interpolation.</p><

80、p>　　Fig. 5. Velocity plot from 3 order NURBS interpolation.</p><p>　　3.2. Command generator for robot controller </p><p>　　By using NURBS interpolation, smooth trajectory has been a

81、chieved from discrete image data, which is represented in parametric form in three-dimension space in terms of a free parameter u: </p><p><b>　　(14)</b></p><p>　　The redesigned robot

82、 controller consists of several-position servo devices, which control each robot joint according to position increments received from the command generator. Velocity control of the robot end-effector is critical not only

83、 because it is essential formaterial removal control during the grit blasting process, but also because significant acceleration changes will cause mechanical vibrations. For simplicity, the robot dynamics was not consid

84、ered in this work, based on the assumpti</p><p>　　The key to velocity control of the robot end effector is to provide appropriate position increments in the cartesian coordinate during each sampling interval

85、 such that the ratio of the position increment and the sampling time equal to the prescribed velocity, based on NURBS interpolation of the desired trajectory and prescribed velocity profile of robot end effector. Althoug

86、h the NURBS curve is parametric and has continuous first and second order derivatives over parameter u, there is not a line</p><p><b>　　(15)</b></p><p><b>　　and </b></

87、p><p><b>　　(16)</b></p><p>　　Therefore, solution to parameter u for a specified line velocity along the curve can be found via the equation below: </p><p><b>　　(17)&l

88、t;/b></p><p>　　However, a solution to the above equation is difficult in the general case; a computational efficient solution of Eq. (17) based on Taylor’s expansion approximation is used. The Taylor’s ex

89、pansion up to second order is given by: </p><p><b>　　(18)</b></p><p>　　In the case that the sample time T is little, and the trajectory does not have a small radius of curvature, the

90、 first order approximation is usually adequate. However, considering the high curvature of the shoe upper particularly at the toe and heel areas, two terms of Taylor’s expansion were used to provide approximation of high

91、er precision. Second order derivative of parameter u over time: </p><p><b>　　(19)</b></p><p><b>　　here </b></p><p><b>　　(20)</b></p><p

92、>　　if substituting Eq. (16) into (19): </p><p><b>　　(21)</b></p><p>　　If substituting Eqs. (17) and (21) into (18): </p><p><b>　　(22)</b></p><p

93、>　　here, K=0,1,…n, indicating the kth segmented curve. Using the velocity profile derived in the first section, the next command parameter can be calculated using the above equation. </p><p>　　3.3. Veloci

94、ty control for NURBS generated trajectory </p><p>　　A trapezoidal velocity profile was used as the desired motion profile to achieve smooth motion of the robot end effector, enabling more accurate path track

95、ing. The PUMA 760 robot controller was upgraded using a GALIL multi-axis motion controller with Ethernet communication for data communication between a host computer and the robot controller. The sampling rate for robot

96、command updating depends mainly on the motion controller’s servo update rate which is an order of 2 ms. Here the robot comman</p><p>　　4. Cooperative robot control </p><p>　　Fig. 7 sho

97、ws the set-up for robotic shoe-upper grit blasting, in which the blasting nozzle is manipulated by the robot end-effector to follow the created roughing path with certain orientations. A metal disc is mounted and properl

98、y orientated as a mask during the path tracking to prevent grit flow from damaging the outside areas of the leather surface. Both trajectory tracking and orientation control of the robot end-effector can cause relatively

99、 large-scale joint movements. As grit blasting wil</p><p>　　Fig. 7. Robotic shoe-upper grit blasting set-up.</p><p>　　A simple cooperative control strategy was applied to the rotary ta

100、ble and robot system, aiming at minimizing joint movements. The algorithm is depicted in Fig. 8, points A, B and C are coordinates on the roughing path generated from NURBS interpolation, angles α,β and can be calcu

101、lated accordingly, the same calculation can be done to all interpolated points on the path. Simply rotating the rotary table with angles α,β and respectively can bring points A, B and C onto the X axis as points A1, B1 &

102、lt;/p><p>　　6. Conclusion </p><p>　　This paper describes a novel methodology for automatic leather surface roughing, which uses air-propelled grit blasting for surface treatments, 3D machine vision

103、 for object profile measurement, NURBS curve interpolation for trajectory reconstruction and an industrial robot for automatic manipulation and control. A mathematical model for the image system was established and relat