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譯文和原文
P3R3串行機(jī)械手移動(dòng)焊接機(jī)器人優(yōu)化設(shè)計(jì)和工作空間分析
摘要
本文介紹了基于工作空間分析的移動(dòng)焊接機(jī)器人的優(yōu)化設(shè)計(jì)。一個(gè)焊接機(jī)器人已經(jīng)被開(kāi)發(fā)用于船舶的雙層船身結(jié)構(gòu),而且展現(xiàn)了良好的焊接性能。但是優(yōu)化運(yùn)動(dòng)變量來(lái)保證在船舶里的焊接性能令人滿意是很有必要的。面向任務(wù)的工作區(qū),是工作區(qū)啟用特定的旋轉(zhuǎn),被定義驗(yàn)證機(jī)器人的焊接能力,并合并所需的旋轉(zhuǎn)功能。計(jì)算工作空間,一個(gè)同時(shí)考慮投球和偏航角度的幾何方法被采用。基于工作空間分析,一個(gè)方案是編譯考慮質(zhì)量減少,和一個(gè)帶有工作空間邊緣約束的在設(shè)計(jì)參數(shù)和工作區(qū)之間的一個(gè)比率。擬議的優(yōu)化過(guò)程是由粗細(xì)搜索兩個(gè)步驟組成。在粗搜索步驟中,一個(gè)滿足幾何設(shè)計(jì)約束的可行的參數(shù)區(qū)域(定期用量法)被定義,和獲得無(wú)任何考慮的目標(biāo)函數(shù)。在細(xì)搜索步驟,在整個(gè)的定期用量法中,使用優(yōu)化技術(shù)的共軛梯度法確定設(shè)計(jì)變量。這種建議的方法來(lái)計(jì)算面向任務(wù)的工作區(qū)和程序優(yōu)化設(shè)計(jì),將適用于一般工業(yè)機(jī)器人。
關(guān)鍵詞:工作區(qū)優(yōu)化;移動(dòng)焊接機(jī)器人;串行機(jī)械手;面向任務(wù)的工作區(qū)
1. 介紹
1.1在船舶建造工業(yè)中的焊接機(jī)器人
在過(guò)去的幾十年里,已經(jīng)有一大批試圖在造船過(guò)程中實(shí)現(xiàn)自動(dòng)化焊接。在這里,我們想介紹先進(jìn)的焊接機(jī)器人系統(tǒng)。表1-A展示了智能移動(dòng)焊接結(jié)構(gòu),這些結(jié)構(gòu)是由2個(gè)(表1-A(a),[1]或者3個(gè)(表1-A(b),[2])棱柱和2個(gè)轉(zhuǎn)動(dòng)關(guān)節(jié)組成。他們使用差動(dòng)驅(qū)動(dòng)輪定位在橫向方向。因此,如果一個(gè)特定的魯棒算法高定位精度并不存在,差動(dòng)驅(qū)動(dòng)由于滑動(dòng)不能保證在重復(fù)的多道焊中的平直度。
在一個(gè)開(kāi)放的區(qū),用開(kāi)銷龍門(mén)起重機(jī)可以將一個(gè)多軸鉸鏈機(jī)器人放置于此。DANDY [3],顯示在表1-B,已開(kāi)發(fā)和成功地用于大宇造船的船廠和韓國(guó)的海洋工程有限公司。當(dāng)機(jī)器人完成單一焊接任務(wù),機(jī)器人通過(guò)使用安裝在船的天花板上的開(kāi)銷龍門(mén)起重機(jī)移動(dòng)到第二焊接位置。因?yàn)殚_(kāi)銷起重機(jī)不能到達(dá)封閉區(qū)的內(nèi)部,所以適用于區(qū)域的機(jī)器人只能被限制在開(kāi)放區(qū)。此外,控制器位于開(kāi)放區(qū)的外面,因此需要大量的電纜從外面進(jìn)來(lái)。這就在封閉結(jié)構(gòu)中處理幾個(gè)電纜過(guò)程中產(chǎn)生了困難。還有更多由多軸機(jī)器人系統(tǒng)與一個(gè)高架起重機(jī)組成的當(dāng)前可用的系統(tǒng),,在[7,8]有相關(guān)描述。
在這一點(diǎn)上,我們想強(qiáng)調(diào)的是船舶建造環(huán)境中嵌入式控制器的重要性。在焊接中,一個(gè)電流用于在基本材質(zhì)和自耗電擊棒之間觸發(fā)電弧。在那一刻,眾所周知,電子的隨機(jī)運(yùn)動(dòng)攜帶電流發(fā)生,影響了連接在機(jī)器人和控制器之間的信號(hào)電纜。此外,很多機(jī)器人同時(shí)在同一個(gè)區(qū)域焊接。因此,可以認(rèn)為模塊化控制器有助于避免多種噪音對(duì)整個(gè)系統(tǒng)的消極影響。基于到目前為止已經(jīng)澄清了的事實(shí)可以知道,一個(gè)便攜式只焊接機(jī)器人的集成系統(tǒng)設(shè)計(jì),需要一個(gè)模塊化控制器和輔助運(yùn)輸設(shè)備,作為在封閉結(jié)構(gòu)中工作的移動(dòng)機(jī)器人的最終選擇,被大力提倡。
表1-C(a)顯示的是已在日本的日立Zosen船廠被開(kāi)發(fā)的數(shù)控(NC)噴漆機(jī)器人[4]。一個(gè)6軸噴漆機(jī)器人,連同一個(gè)自動(dòng)駕駛裝置,用一個(gè)可擴(kuò)展的放置器放在了封閉區(qū)。然而,這種機(jī)器人系統(tǒng)需要一個(gè)800×1600平方毫米的出入孔。因?yàn)槌鋈肟椎某叽缗c船舶的設(shè)計(jì)安全條例密切相關(guān),任何擴(kuò)大措施都必需得到船的主人的許可,這幾乎是不可能實(shí)現(xiàn)的。這個(gè)機(jī)器人噴漆系統(tǒng)的另一個(gè)嚴(yán)重的問(wèn)題是,在封閉區(qū)域的內(nèi)部,它不能在橫向方向上自由移動(dòng)。在西班牙的工業(yè)自動(dòng)化研究所(IAI)開(kāi)發(fā)了一個(gè)機(jī)器人系統(tǒng)稱為槳手1,可以用在一個(gè)封閉的區(qū)域[5];這個(gè)機(jī)器人像一個(gè)蜘蛛一樣移動(dòng),有四條腿可以擴(kuò)展和收縮。它可以自主移動(dòng),因此可以克服很多在封閉區(qū)域中遇到的焊接障礙,,但它必須分解成七個(gè)模塊才可以放入一個(gè)封閉的區(qū)域,然后重新組裝起來(lái)。重組大約需要15分鐘,這是漫長(zhǎng)的足以嚴(yán)重影響系統(tǒng)的生產(chǎn)效率[9]。
最近被建立的SNU的RRX平臺(tái)[6],克服了以前機(jī)器人的所有缺點(diǎn),在超過(guò)一年的實(shí)地測(cè)試中,它的焊機(jī)和移動(dòng)性能得到驗(yàn)證。然而,值得一提的是這個(gè)系統(tǒng)在500×700平方毫米洞的出入仍然是相對(duì)困難的,盡管它滿足空間約束。主要的原因是它的尺寸相對(duì)工人來(lái)說(shuō)還是很大的。
1.2 機(jī)械手的優(yōu)化
運(yùn)動(dòng)設(shè)計(jì)已在機(jī)器人的機(jī)械手臂設(shè)計(jì)中占有重要的地位,因?yàn)楣ぷ骺臻g、速度和精度等系統(tǒng)的性能由它的幾何參數(shù)確定。特別的,確定維度的機(jī)械手的幾何參數(shù)主要受制于優(yōu)化非線性成本函數(shù),受到一組適當(dāng)?shù)募s束。作為評(píng)判機(jī)械手臂質(zhì)量的標(biāo)準(zhǔn),人們?cè)絹?lái)越感興趣的是機(jī)械手的運(yùn)動(dòng)學(xué)特性,如工作區(qū)特性,調(diào)節(jié)指數(shù),靈巧的標(biāo)準(zhǔn)。
1.2.1 工作空間
已經(jīng)有很多的研究來(lái)優(yōu)化機(jī)械手的工作空間[10,11]。Kumar 和 Waldron提出[12]了一個(gè)在可及的和靈巧的工作區(qū)上的優(yōu)化設(shè)計(jì)和分析,用于幾何優(yōu)化[13]。一個(gè)可達(dá)的工作空間是末端可以不考慮取向而達(dá)到的位置,一個(gè)靈巧的工作空間是末端可以擁有完整的旋轉(zhuǎn)能力而達(dá)到的位置。Haug等人提出了一個(gè)復(fù)合的工作區(qū),這個(gè)工作區(qū)在所有的部分的關(guān)節(jié)區(qū)都具有指定的工作能力[14,15],和一個(gè)依據(jù)等級(jí)缺陷決定工作空間邊界的雅克比方法。Pond和Carretero還提出依據(jù)雅克比矩陣的條件數(shù)決定工作空間的雅克比方法[16]。Bonev和Ryu提出了一個(gè)定向工作區(qū):一個(gè)末端所有可達(dá)到的取向都在一個(gè)固定點(diǎn)上[17]。
1.2.2. 調(diào)節(jié)和靈巧
另一方面,各種評(píng)估工作空間運(yùn)動(dòng)性能的有關(guān)性能指標(biāo)的研究在很長(zhǎng)一段時(shí)間被發(fā)表。Salibury和Craig[18]用雅克比矩陣的條件數(shù)作為評(píng)估工作空間性能的優(yōu)化標(biāo)準(zhǔn)。Yoshikawa [19]提出了將雅克比矩陣的行列式作為可操縱性的測(cè)量(MOM), 而Stoughton and Kokkinis [20] 用最低奇異值和條件數(shù)。
值得特別注意的一點(diǎn)是,先前有關(guān)工作空間的概念是任務(wù)獨(dú)立的:他們對(duì)于特定的任務(wù)不能保證最好的機(jī)械手。因此,任務(wù)特異性直接考慮在規(guī)定的轉(zhuǎn)動(dòng)能力,采用代表效果好確定工作空間邊界需要在特定的任務(wù)。并且MOM可以作為數(shù)學(xué)工具來(lái)驗(yàn)證到奇異點(diǎn)的距離,而條件數(shù)可以被用作一個(gè)實(shí)際測(cè)量的生病調(diào)節(jié)[21]的工作區(qū)和運(yùn)動(dòng)精度[22]的機(jī)械手在它整個(gè)工作區(qū)。因此,可操縱性測(cè)量的需要將從避免的可能性奇點(diǎn)在縮放操作臂的尺寸的角度在本文出現(xiàn)。
1.3 研究目的
在這項(xiàng)研究中,任務(wù)導(dǎo)向的工作區(qū)和它的部分工作區(qū)是至關(guān)重要的在有效地獲得最優(yōu)設(shè)計(jì)。因?yàn)槲覀冎恍枰?5°的轉(zhuǎn)動(dòng)能力,使一個(gè)Ushaped焊接任務(wù),一個(gè)面向任務(wù)的工作區(qū)(TOW)可以得到排除無(wú)用的方向的末端。在這里,拖可以被定義為一組機(jī)器人末端位置這樣可以達(dá)到末端用一個(gè)預(yù)定義的轉(zhuǎn)動(dòng)能力。即使我們只考慮規(guī)定的發(fā)展方向采用空間,工作空間搜索仍然是一個(gè)耗時(shí)程序。因此,為了減少計(jì)算成本,部分工作區(qū)(PW),它可以被視為一個(gè)橫截面積的牽引,提出了計(jì)算theTOWand之間距離的u形焊接部分沒(méi)有詳盡的搜索可能的職位候選人在完整的范圍的面向任務(wù)的工作區(qū)。一些研究提出的幾何處理機(jī)械手工作空間被發(fā)現(xiàn)在文學(xué);但是,這個(gè)話題似乎是值得的受調(diào)查,應(yīng)該是一個(gè)偉大的幫助在最優(yōu)設(shè)計(jì)。
利用提出的幾何治療在機(jī)械手工作區(qū),我們同時(shí)考慮結(jié)構(gòu)質(zhì)量和設(shè)計(jì)效率作為目標(biāo)函數(shù)對(duì)最大化質(zhì)量降低和減少損失的設(shè)計(jì)效率。設(shè)計(jì)包括兩個(gè)步驟:粗和細(xì)搜索。在粗搜索步驟,我們找到可行的參數(shù)區(qū)域(存取)在預(yù)定義的約束是滿意的。在找到搜索一步,我們分析目標(biāo)函數(shù)在存取獲得最終的最優(yōu)參數(shù)集,提出兩步過(guò)程簡(jiǎn)化通過(guò)將最優(yōu)設(shè)計(jì)問(wèn)題的復(fù)雜約束條件和目標(biāo)函數(shù)。
一個(gè)更重要的方面是可操縱性優(yōu)化設(shè)計(jì)措施,詳見(jiàn)1.2節(jié)。實(shí)際上,可操縱性僅用于避免奇點(diǎn)在優(yōu)化設(shè)計(jì)程序。然而,由于可操縱性是非常重要的決定焊接過(guò)程的質(zhì)量,我們獨(dú)立分析可操作度在本文的末尾。確定最優(yōu)聯(lián)合的價(jià)值觀,例如由Zacharias et al.。[23],是還剩下一個(gè)問(wèn)題需要解決。
2. 問(wèn)題描述
本節(jié)描述了RRX移動(dòng)焊接機(jī)器人和運(yùn)動(dòng)學(xué)分析是計(jì)算中使用的工作區(qū)。這個(gè)實(shí)驗(yàn)結(jié)果的u形線焊接操作還描述了定義所需的旋轉(zhuǎn)。
2.1移動(dòng)焊接機(jī)器人:RRX
2.1.1 RXX系統(tǒng)描述
圖2(一個(gè))顯示的成分RRX焊接機(jī)器人,這是由三個(gè)子系統(tǒng)組成的移動(dòng)平臺(tái),一個(gè)連續(xù)式焊接機(jī)械手,嵌入式控制器。移動(dòng)平臺(tái)使機(jī)器人的移動(dòng)橫向和縱向方向就確信雙層船身內(nèi)部塊,和詳細(xì)過(guò)程的運(yùn)動(dòng)一直解釋說(shuō)之前的出版物[6]。在搬到前面的u型焊接線,移動(dòng)平臺(tái)是停在一個(gè)固定的位置,和焊接機(jī)械手操作。焊接機(jī)械手包括三個(gè)柱狀節(jié)理和三個(gè)轉(zhuǎn)動(dòng)關(guān)節(jié)使6自由度(自由度)空間運(yùn)動(dòng)。
第四版的RRX組裝焊接機(jī)器人,或RRX4因?yàn)樗环Q為,是顯示在圖2(b),它具有一些優(yōu)勢(shì)在前面的模型在其嵌入式控制器,減少噪聲級(jí),它的更好的密封特點(diǎn),也可在危險(xiǎn)環(huán)境中使用。然而,最優(yōu)設(shè)計(jì)運(yùn)動(dòng)參數(shù)仍然是一個(gè)尚未解決的問(wèn)題,成功的焊接性能就確信雙層船身結(jié)構(gòu)內(nèi)的船只。
2.1.2 焊接機(jī)械手的運(yùn)動(dòng)學(xué)分析
圖3顯示了運(yùn)動(dòng)學(xué)模型的焊接部分的RRX機(jī)器人系統(tǒng),它包括一個(gè)3 p3r機(jī)械手組成一個(gè)PPRPRR串行鏈,P,R表示棱鏡和轉(zhuǎn)動(dòng)關(guān)節(jié)分別?;顒?dòng)關(guān)節(jié)的棱鏡來(lái)標(biāo)示d1、d2和d4,參加革命活動(dòng)關(guān)節(jié),θ5θ3來(lái)標(biāo)示,和θ6。
被定義為一個(gè)問(wèn)題的正運(yùn)動(dòng)學(xué)問(wèn)題確定末端效應(yīng)的姿勢(shì)時(shí)關(guān)節(jié)值給定的,所以可以串行機(jī)器人正運(yùn)動(dòng)學(xué)輕松解決使用齊次變換矩陣(HTM),定義如下[24]:
Rii哪里?1和有價(jià)證券?1代表方向和位置(我)th框架,分別對(duì)(我?1)th幀。RRX效應(yīng)器的姿勢(shì)可以按順序計(jì)算乘HTM從基本幀(幀零)框架采用(第七框架),如情商。(2)。組件產(chǎn)生的矩陣如表2所示,在ci,si,cα,sα表示cos(θi),罪(θi),因?yàn)?α),和贖罪(α),分別。見(jiàn)[6]的詳細(xì)推導(dǎo)。
逆運(yùn)動(dòng)學(xué)問(wèn)題的問(wèn)題是找到共同價(jià)值觀的姿勢(shì)時(shí),采用了。一般來(lái)說(shuō),逆運(yùn)動(dòng)學(xué)問(wèn)題的系列機(jī)器人是一個(gè)非線性聯(lián)立方程,所以一些數(shù)值方法可以采用計(jì)算解決方案。然而,逆運(yùn)動(dòng)學(xué)的RRX平臺(tái)可以解決分析從HTM在情商。(2),聯(lián)合采用計(jì)算值HTM的組件,如情商。(3)。結(jié)果的逆運(yùn)動(dòng)學(xué)分析將被應(yīng)用于計(jì)算工作空間在第三節(jié)。
2.2定義任務(wù)的焊接,u形邊界
焊接任務(wù)的機(jī)器人,和工作環(huán)境,圖4所示。動(dòng)的RRX縱向加勁肋形式、和方法,u形焊接線。移動(dòng)平臺(tái)的RRX停止其運(yùn)動(dòng)在一個(gè)預(yù)定義的固定距離,焊接機(jī)械手開(kāi)始焊接,u形焊接線。焊接后段,RRX移動(dòng)到前面下一個(gè)u型線和簡(jiǎn)歷焊接。
的尺寸u形焊接線的不同就確信雙層船身類型的塊。尺寸的范圍是顯示在右邊的圖4。從給定的尺寸,所需的平行六面體形狀的位置工作空間定義焊接一個(gè)900×800×10毫米的體積,這是馬克斯(西城)××max(HL)馬克斯(WT),重量的寬度焊接珠,從橫向網(wǎng)絡(luò)地板。
在焊接過(guò)程中沿焊縫,焊接火炬,供給熱量、氣體和物質(zhì)的對(duì)象被焊接,應(yīng)該對(duì)焊點(diǎn)連續(xù)旋轉(zhuǎn)因此,一個(gè)更可靠的附加質(zhì)量,達(dá)到了焊接過(guò)程。一般來(lái)說(shuō),不同的旋轉(zhuǎn)角度在連續(xù)焊接過(guò)程,所以測(cè)量的旋轉(zhuǎn)角是必要的焊接塊沿著u形焊接線。因?yàn)橐粋€(gè)滾動(dòng)的運(yùn)動(dòng)不會(huì)影響焊接性能,必需的角度對(duì)俯仰和偏航運(yùn)動(dòng)對(duì)于基地框架應(yīng)該被定義。
一般來(lái)說(shuō),所需的偏航和節(jié)距角焊接由技術(shù)人員的經(jīng)驗(yàn),所以它是嗎很難定義精確的角度觀察人工處理操作。因此,RRX用于本研究獲得要求偏航和節(jié)距角,以便RRX操作執(zhí)行一個(gè)成功的焊接沿著u形線,旋轉(zhuǎn)角度的測(cè)量記錄的焊槍通過(guò)遠(yuǎn)期運(yùn)動(dòng)學(xué)關(guān)節(jié)角的。焊接結(jié)果是密切檢查經(jīng)驗(yàn)豐富的技術(shù)人員。自需要有一個(gè)比較大的利潤(rùn)率的角度,一個(gè)合適的解決辦法就是所需的火炬角通過(guò)使用向前運(yùn)動(dòng)關(guān)系從聯(lián)合角度來(lái)衡量這個(gè)編碼器。焊接的質(zhì)量,還會(huì)檢查的經(jīng)驗(yàn)豐富的技術(shù)人員。
圖5(一個(gè))顯示了運(yùn)動(dòng)的焊槍沿u形焊接線,框{ B }表示基礎(chǔ)構(gòu)架,和幀{ T }表示工具框架。最初的工具框架焊接過(guò)程{ T0 }定義為旋轉(zhuǎn)(90°,0°、114°)就幀{ B },為了有對(duì)稱偏航螺距角。測(cè)量偏航螺距角焊炬、與尊重到幀{ T0 },表示為長(zhǎng)度從原點(diǎn)的投影到y(tǒng)z平面,見(jiàn)圖5(b)。所需的yawpitch角度是確定為35°關(guān)于Z { T0 }在整個(gè)焊接過(guò)程。
執(zhí)行焊接工藝成功地,35°的偏航螺距轉(zhuǎn)動(dòng)能力應(yīng)該得到保證。因此,客觀的紙可以定義為優(yōu)化運(yùn)動(dòng)參數(shù)為了提高設(shè)計(jì)效率,同時(shí)滿足35°的轉(zhuǎn)動(dòng)能力。在優(yōu)化過(guò)程中,一種新的方法確定提出了面向任務(wù)的工作區(qū)第三節(jié)。
3.確定任務(wù)導(dǎo)向的工作區(qū)
3.1幾何方法考慮結(jié)合偏航螺距角
本節(jié)提出了一種新的方法來(lái)考慮方向計(jì)算一個(gè)面向任務(wù)的工作區(qū)對(duì)匯率操縱國(guó)。通常,一個(gè)機(jī)械手的方向被定義為一個(gè)旋轉(zhuǎn)矩陣,由空間定向矢量和這個(gè)旋轉(zhuǎn)矩陣變換乘法。然而,表示的工具框架{ T },通過(guò)使用通常的慣例,不直觀的確定組方向的嗎指定范圍從規(guī)定的任務(wù)。這是因?yàn)?約定利用旋轉(zhuǎn)矩陣受到一系列的三個(gè)通過(guò)正常的歐拉角旋轉(zhuǎn)。
在這種方法中,一個(gè)指定范圍的方向的工具幀{ T },就基本框架{ B },是產(chǎn)生的簡(jiǎn)單的向量的計(jì)算。該方法考慮了在一個(gè)固定方向的末端位置作為一組計(jì)算方向向量。這種方法更簡(jiǎn)單,更直觀比傳統(tǒng)的方法,它也有優(yōu)點(diǎn)的考慮兩個(gè)偏航和節(jié)距角在同一時(shí)間。
圖6顯示了程序計(jì)算了定向向量,采用一個(gè)固定的位置周圍的末端。首先,旋轉(zhuǎn)z軸方向向量的初始工具框架{ T0 },需要35°偏航螺距角在這個(gè)研究。然后,讓一組M×新西蘭軸方向向量的向量計(jì)算顯示在底部圖6。滾動(dòng)運(yùn)動(dòng)也被認(rèn)為是在每個(gè)方向向量的z軸嗎防止發(fā)生沖突和焊接機(jī)械手結(jié)構(gòu)。由此產(chǎn)生的方向向量代表一組需要旋轉(zhuǎn)在一個(gè)固定的位置,采用,所以只有位置用于確定面向任務(wù)的工作區(qū)。
3.2 計(jì)算的面向任務(wù)的工作區(qū)
面向任務(wù)的工作區(qū)可以由使用幾何的方法,提出了在前面的部分中。首先, 一組位置,采用的taskoriented作為候選人工作區(qū)是定義。為每一個(gè)位置,一個(gè)錐形的集所需的能力被定義為過(guò)程提出了在3.1節(jié)。在計(jì)算所需的活動(dòng)關(guān)節(jié)值通過(guò)逆運(yùn)動(dòng)學(xué)為每個(gè)位置,限制活動(dòng)關(guān)節(jié)中風(fēng)是用來(lái)作為判據(jù)來(lái)確定位置在面向任務(wù)的工作區(qū)或不是。詳細(xì)的流程圖計(jì)算任務(wù)導(dǎo)向工作區(qū)顯示在圖7。
圖5。測(cè)量偏航螺距角焊在u形線通過(guò)使用組裝RRX4及其表示的長(zhǎng)度在XY{ T0 }平面的投影。(一)焊接過(guò)程的一個(gè)標(biāo)準(zhǔn)塊模擬測(cè)量所需的旋轉(zhuǎn)角度。(b)測(cè)量的旋轉(zhuǎn)角度沿{ T0 }幀被表示為一個(gè)長(zhǎng)度從原點(diǎn)通過(guò)余弦函數(shù)。
圖6。錐形幾何表示包括旋轉(zhuǎn)角度和計(jì)算過(guò)程;α和β表示增量的迭代循環(huán)。
計(jì)算任務(wù)導(dǎo)向的工作區(qū),幾個(gè)旋轉(zhuǎn)角度,顯示在圖8,其中每個(gè)圖形在平面上表示預(yù)測(cè)計(jì)算的面向任務(wù)的工作區(qū)。隨著需要旋轉(zhuǎn)能力增加,體積的面向任務(wù)的工作區(qū)卻降低了。面向任務(wù)的工作區(qū)35°的轉(zhuǎn)動(dòng)能力,表示為紅色線。計(jì)算任務(wù)型工作空間相對(duì)大保證金與所需的900×800×工作區(qū)10毫米,因此有必要找出最佳的運(yùn)動(dòng)設(shè)計(jì)成本和重量參數(shù)效率。
4.結(jié)論
本文介紹了最優(yōu)設(shè)計(jì)的移動(dòng)焊接機(jī)器人,RRX,通過(guò)任務(wù)型工作空間。所需的轉(zhuǎn)動(dòng)角度探討了實(shí)驗(yàn)研究沿著u型線的焊接。幾何方法使用一個(gè)錐形的單位來(lái)確定任務(wù)型工作空間提出基于運(yùn)動(dòng)分析的機(jī)器人,這樣可以執(zhí)行所需的旋轉(zhuǎn)。運(yùn)動(dòng)學(xué)變量,這樣會(huì)減少一個(gè)多目標(biāo)函數(shù)組成的質(zhì)量機(jī)及其設(shè)計(jì)的效率,取決于一個(gè)二級(jí)優(yōu)化程序。因此,大規(guī)模減少優(yōu)化設(shè)計(jì)是13%,和損失的設(shè)計(jì)效率是4.9%。從這個(gè)預(yù)計(jì)的重量RRX可以會(huì)減少。重新設(shè)計(jì)RRX4后,機(jī)器人可以應(yīng)用在組裝線的船舶建造過(guò)程。擬議的優(yōu)化設(shè)計(jì)方法是將采用串行和并行機(jī)制的機(jī)器人。
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Optimal design and workspace analysis of a mobile welding robot with a 3P3R
serial manipulator
abstract
This paper presents the design optimization of a mobile welding robot based on the analysis of its workspace. A welding robot has been developed to be used inside the double-hull structure of ships, and it shows good welding functionality. But there is a need to optimize the kinematic variables ensuring that the required welding functions inside the ships are satisfied. The task-oriented workspace, which is the workspace enabling specific rotations, has been defined in order to validate the welding ability of the robot, and incorporating the required rotational capabilities. To calculate the workspace, a geometric approach is adopted which considers the pitching and yawing angles simultaneously. Based on the workspace analysis, a scenario is compiled for considering a mass reduction, and a ratio between the design parameters and the workspace, with constraints on the workspace margins. The proposed optimization procedure is composed of two steps of coarse and fine searching. In the coarse searching step, a feasible parameter region (FPR) is defined, which satisfies the geometrical design constraints, and can be obtained without any considerations of the objective functions. In the fine searching step, the design parameters are determined by using the optimization technique of the conjugate gradient method in the overall FPRs. The suggested approach to calculating the task-oriented workspace, and the procedure of optimal design, are expected to be applied to general industrial robots.
1. Introduction
1.1. Welding robots in ship-building industries
Over the last few decades, there have been a large number of attempts to automate welding in the shipbuilding process.Here, we would like to introduce the state of the art in welding robot systems. Table 1-A shows the intelligent mobile welding carriages. These carriages are composed of two (Table 1-A(a), [1]) or three (Table 1-A(b), [2]) prismatic (P) and two revolute (R) joints. They use differential driving wheels for positioning in the transverse direction. Thus, if a certain robust algorithm for high positioning accuracy does not exist, the differential driving cannot guarantee the straightness in repetitive multi-pass welding because of slippage. In the case of an open block, a multi-axis articulated robot can be placed into the open block by using overhead gantry cranes. DANDY [3], shown in Table 1-B, has been developed and
successfully used in the shipyard of Daewoo Shipbuilding and Marine Engineering Co. Ltd., Korea. After the robot finishes a single welding task, the robot is moved to the next welding location by using the overhead gantry crane installed in the ceiling of the shipyard. Since the overhead crane cannot approach the inside of the closed block, as shown in Fig. 1, the applicable area of the robot is limited to open blocks. Moreover, controllers are located at the outside of the open blocks, thus requiring a number of cables from the outside. This gives rise to difficulties in handling the several cables in the enclosed structures. There are also more examples of the currently available systems, which are a combination of a multi-axis robotic system with an overhead crane, as described in [7,8].
At this point, we would like to emphasize the importance of the embedded controller in the shipbuilding environment. During welding, an electric current is used to strike an arc between the base material and the consumable electrode rod. At that moment, it is known that, as the parts are welded, random movement of the electrons carrying the current occurs, and this affects the signal cables connecting the robots and the controllers. Moreover, there are a number of robots welding simultaneously in the same block. Thus, it can be thought that modularized controllers help to
Table 1 Several types of autonomous welding system.
prevent negative influences on the entire system from the various noises. Based on these facts that have been clarified so far, the design of an integrated system of a portable welding-only robot, having a modularized controller and auxiliary transportation devices, as a final alternative to a mobile robot working inside of
the enclosed structures has been encouraged.
Table 1-C(a) shows the numerically controlled (NC) painting robot, which has been developed by the Hitachi Zosen shipyard in Japan [4]. A 6-axis painting robot, together with a self-driving carriage, is placed inside the closed block using an expandable placer. However, this robotic system requires a large access hole of size 800 × 1600 mm2. Since the size of the access hole is related to ship-design safety regulations, any enlargement requires the permission of the ship’s owner, and is almost impossible to achieve. Another serious problem of this robotic painting system is that it cannot move freely in the transverse direction inside an enclosed block. The Industrial Automation Institute (IAI) in Spain has developed a robotic system called ROWER 1, that can be used in a closed block [5]; the robot moves like a spider, and has four legs capable of extending and contracting. It can move autonomously and can thus overcome many of the welding obstacles encountered in a closed block, but it has to be disassembled into seven modules before it can be placed into a closed block, and then reassembled in situ. Reassembly takes approximately 15 min, which is long
enough to seriously affect the productivity of the system [9].
The RRX platform of SNU [6], which overcomes all the disadvantages of the previous robots, has recently been established, and its performances of welding and mobile functions have been verified through field testing over a period of one year. However, points of note are that this system is still relatively hard to handle for placing in, and withdrawing from, the 500×700mm2 access hole, even though it satisfies the dimensional constraints. The main reason for this is its relatively large size compared to the size of human workers.
1.2. Manipulator optimization
Kinematic design has occupied an important position in robotic manipulator design because the performance of a system in terms of workspace, velocity, and accuracy is dominated by its geometrical characteristics. In particular, determination of the dimensions of the geometric parameters of a manipulator is primarily concerned by optimizing a nonlinear cost function, subject to a set of appropriate constraints. As criteria for judging a manipulator’s quality, there has been an increasing interest in the kinematic properties of a manipulator, such as workspace feature, conditioning index, and dexterity criteria.
1.2.1. Workspace
There has been much research to optimize the workspace of manipulators [10,11]. Kumar and Waldron [12] proposed
Fig. 1. Double-hulled ship wall.
an optimal design and analysis on reachable and dexterous workspaces, which was used for geometric optimization by Kumar et al. [13]. A reachable workspace is a position set of end-effectors in which an end-effector can reach without considering orientation, and a dexterous workspace is a position set of end-effectors in which an end-effector can reach with a full rotational capability. Haug et al. proposed a composite workspace that requires a specified working capability in joint space for all sets of points [14,15], and a Jacobian approach that determines the workspace boundary in terms of rank deficiency. Pond and Carretero also proposed a Jacobian approach that determines the workspace in terms of the condition number of the Jacobian matrix [16]. Bonev and Ryu proposed the orientation workspace: the set of all attainable orientations of an end-effector about a fixed point [17].
1.2.2. Conditioning and dexterity
On the other hand, various research on performance indices for evaluating the kinematic quality of the workspace has also been published over a long period. Salibury and Craig [18] used the condition number of the Jacobian matrix as an optimization criterion to evaluate the workspace quality. Yoshikawa [19] proposed the determinant of the Jacobian matrix as a measure of manipulability (MOM), whereas Stoughton and Kokkinis [20] used the minimum singular value and the condition number.
A point where special attention should be paid is that the previous concepts of the workspace are task independent: they do not guarantee the best manipulator for a specific task. Thus, task specificity of a direct consideration on the prescribed rotational capability of the end-effector represents good performance in determining the workspace boundary required in the specific tasks. And the MOM can be used as a mathematical tool to verify the distance from singularities, whereas the condition number can be used as a practical measure of the ill-conditioning [21] of the workspace and kinematic accuracy [22] of a manipulator over its whole workspace. Hence, the need for a manipulability measure will arise in this paper in terms of avoiding the likelihood of the singularity under a scaling of the manipulator dimensions.
1.3. Objective of the research
In this study, the task-oriented workspace and its partial workspace are crucial in efficiently obtaining the optimal design. Since we need only 35° of rotational capability to enable a U-shaped welding task, a task-oriented workspace (TOW) can be obtained by excluding useless orientations of the end-effector. Here, the TOW can be defined as a position set of the end-effector such that the end-effector can reach with a predefined rotational capability. Even if we only consider prescribed orientations in the end-effector space, workspace searching is still a time-consuming procedure. Thus, in order to reduce the computational cost, a partial workspace (PW), which can be considered as across-sectional area of the TOW, is proposed to calculate the distance between the TOW and the U-shaped welding part without exhaustively searching the possible position candidates in the full range of task-oriented workspace. Few studies on the proposed geometric treatments for the manipulator workspace were found in the literature; however, this topic seems to be a worthwhile subject to investigate, and should be a great help in the optimal design.
Using the proposed geometric treatments on the manipulator workspace, we simultaneously considered structural mass and design efficiency as objective functions with respect to maximizing the mass reduction and minimizing the loss of design efficiency. The design involves two steps: coarse and fine searches. In the coarse search step, we find feasible parameter regions (FPRs) where the predefined constraints are satisfied. In the find search step, we analyze the objective function in the FPRs to obtain the final optimal parameter set. The proposed two-step procedure simplifies the optimal design problem by separating the complicated constraints and the objective function.
A further important aspect of the optimal design is the manipulability measure, as discussed in Section 1.2. Actually, manipulability is only used to avoid singularity during the optimal design procedure. However, since manipulability is very important for determining the quality of a welding process, we independently analyze the manipulability at the end of this paper. Determining the optimal joint values, such as performed by Zacharias et al. [23], is also a remaining p