平面冗余機(jī)械手的運(yùn)動(dòng)學(xué)控制擴(kuò)展運(yùn)動(dòng)分配方案外文文獻(xiàn)翻譯、中英文翻譯、外文翻譯,平面,冗余,機(jī)械手,運(yùn)動(dòng)學(xué),控制,擴(kuò)展,運(yùn)動(dòng),分配,方案,外文,文獻(xiàn),翻譯,中英文 XXX 附錄一: 平面冗余機(jī)械手的運(yùn)動(dòng)學(xué)控制擴(kuò)展運(yùn)動(dòng)分配方案 機(jī)械工程系,浦項(xiàng)市科學(xué)技術(shù)研究所125年郵政信箱,浦項(xiàng)市790 - 600年(朝鮮) (最終形式收到:1991年4月28日) 摘要 數(shù)度的平面機(jī)械手的運(yùn)動(dòng)控制的冗余是一個(gè)困難的問題,因?yàn)橹赜?jì)算,維負(fù)擔(dān)或缺乏適當(dāng)?shù)募夹g(shù)。擴(kuò)展運(yùn)動(dòng)分配方案,基于平面冗余機(jī)械手分解為一系列n冗余當(dāng)?shù)匚淦骱头职l(fā)效應(yīng)器在關(guān)節(jié)的運(yùn)動(dòng)速度水平,本文提出了。配置指數(shù)被定義為未成年人的產(chǎn)品對(duì)應(yīng)雅可比矩陣,用于指導(dǎo)全球冗余機(jī)械手。提高方案的性能,自動(dòng)控制,負(fù)責(zé)內(nèi)部聯(lián)合運(yùn)動(dòng),不運(yùn)動(dòng)導(dǎo)致效應(yīng)器,可以使用可選保證全局最優(yōu)操縱。的重復(fù)性問題討論了冗余機(jī)械手使用方案。計(jì)算機(jī)模擬的結(jié)果顯示,詳細(xì)分析了平面特性和9-DOF操縱者,為例。 關(guān)鍵詞:運(yùn)動(dòng)控制;平面機(jī)械手;分配方案,配置指數(shù)。 1. 簡介 卓越的靈活性和多功能性,人類手臂展品在執(zhí)行各種任務(wù),主要?dú)w因于手臂的運(yùn)動(dòng)學(xué)冗余。機(jī)器人機(jī)械手叫做(動(dòng))冗余如果它具有更多的自由度(自由度)比是必要的來執(zhí)行指定的任務(wù)。額外的自由度的冗余機(jī)械手可以用來實(shí)現(xiàn)一些如避免奇點(diǎn),!避障、2或關(guān)節(jié)限制回避。3雖然一個(gè)或兩個(gè)冗余度可以用來滿足上述，變得非常有吸引力,因?yàn)樗氖褂渺`活性和敏捷運(yùn)動(dòng)在一定的任務(wù)在一個(gè)復(fù)雜的環(huán)境。然而,研究冗余機(jī)械手的運(yùn)動(dòng)控制冗余度大的尚未執(zhí)行廣泛因?yàn)槿狈m當(dāng)?shù)募夹g(shù)和/或計(jì)算負(fù)擔(dān)。 大部分的冗余機(jī)械手的運(yùn)動(dòng)控制方法專注于解決冗余運(yùn)用廣義逆或偽逆機(jī)械手基于性能函數(shù)可操縱性等措施,1條件數(shù),兼容性索引,7的機(jī)械手的雅可比矩陣。然而,大多數(shù)這樣的瞬時(shí)優(yōu)化方案是基于本地決策可能不能保證全局最優(yōu)。9 - 11最近幾個(gè)全局優(yōu)化方案被提出,但需要大量的計(jì)算,使實(shí)時(shí)應(yīng)用程序不現(xiàn)實(shí)的。這些偽逆的方法可用于控制平面冗余機(jī)械手不管偶數(shù)和奇數(shù)的自由度。然而,當(dāng)機(jī)械手等大型冗余自由度平面特性或9-DOF某個(gè)任務(wù)需要在復(fù)雜的環(huán)境中,偽逆的方法有很大的困難在制定性能函數(shù),發(fā)現(xiàn)其梯度向量甚至借助象征MACSYMA等計(jì)算。 另一個(gè)不同的概念,提出了由李等。12平面四自由度機(jī)械手,分解成兩個(gè)冗余機(jī)械手當(dāng)?shù)匚淦?稱為和前臂,在一個(gè)中間的手臂位置或任務(wù)點(diǎn)稱為肘部。即冗余機(jī)械手轉(zhuǎn)換為連續(xù)的雙臂系統(tǒng)合作,與合作由肘部。這個(gè)方案被稱為任務(wù)分配方案使用一個(gè)名為面向任務(wù)的可操縱性的新措施措施(湯米),代表任務(wù)之間的差異需求和機(jī)械手的可操縱性,全球指導(dǎo)任務(wù)執(zhí)行。然而,任務(wù)分配方案有以下限制: ? 適它只適用于連冗余機(jī)械手的自由度,因?yàn)闄C(jī)械手應(yīng)該分解為。因此該計(jì)劃變得很難被應(yīng)用到一個(gè)平面機(jī)械手單自由度,如平面五自由度或7自由度機(jī)械手。 ? 它并不傾向于保留重復(fù)性如果所需的奇異值向量對(duì)湯米不正確的選擇。 ? 湯米需要先驗(yàn)知識(shí)所需的奇異值和奇異向量的任務(wù)執(zhí)行,這在實(shí)踐中是相當(dāng)困難的。 本文提出一種新方案,可以應(yīng)用于任何平面冗余機(jī)械手通過擴(kuò)展和推廣上述任務(wù)分配方案。冗余機(jī)械手是把這里當(dāng)作系統(tǒng)多個(gè)冗余手臂串行連接在一起。這個(gè)計(jì)劃叫做擴(kuò)展運(yùn)動(dòng)分配方案摘要,因?yàn)樗ㄟ\(yùn)動(dòng)分配方法和解決運(yùn)動(dòng)方法。3雖然基本結(jié)構(gòu)類似于李等人工智能。2,控制方案和方法指導(dǎo)機(jī)器人運(yùn)動(dòng)的新方案在很大程度上不同于。使用冗余機(jī)械手的固有特性,可以可選地包括在自動(dòng)控制方案來提高可操縱性或獲得更理想的配置。靈巧指數(shù),稱為配置指數(shù),也是開發(fā)作為判據(jù)來確定執(zhí)行自動(dòng)控制和/或性能函數(shù)的最大化解決運(yùn)動(dòng)方法。 第二節(jié)提出了方案的結(jié)構(gòu),和第三節(jié)描述了控制由配置指數(shù)。在第四節(jié)中,數(shù)值模擬了平面8-00F和9-00F機(jī)械手來驗(yàn)證該方法的有效性與討論。結(jié)論在第五節(jié)。 2。擴(kuò)展運(yùn)動(dòng)分配方案 方案的基本結(jié)構(gòu)分解為一系列冗余機(jī)械手?；旧鲜?-link機(jī)械手模塊,但最后可以2自由度或機(jī)械手偶數(shù)和奇數(shù)自由度機(jī)械手,分別。甚至當(dāng)平面冗余機(jī)械手的自由度,所有模塊和效應(yīng)器的運(yùn)動(dòng)是分發(fā)給每個(gè)按照下列運(yùn)動(dòng)分布的方法。 一個(gè)節(jié)點(diǎn)被定義為相鄰之間的聯(lián)合。圖1說明了平面冗余機(jī)械手表示為連續(xù)多個(gè)輔助臂合作制度。機(jī)械手的關(guān)節(jié)速度,可以表示為一個(gè)組合的聯(lián)合輔助臂速度： 圖1多個(gè)輔助臂系統(tǒng)在平面的情況下。 , （1） 輔助臂的數(shù)量。效應(yīng)器速度, 輔助臂生成的參照基礎(chǔ)構(gòu)架可以描述的，: 一致的笛卡爾速度的第i個(gè)節(jié)點(diǎn)，方程(2)表明,效應(yīng)器運(yùn)動(dòng)可以顯式地表示輔助臂的共同運(yùn)動(dòng)。在這個(gè)方程式中,，為奇異值,可以表示分解為： 正交矩陣為奇異值，和等級(jí)一組標(biāo)準(zhǔn)正交基向量z范圍是由 和，在，節(jié)點(diǎn)速度,可以用標(biāo)準(zhǔn)正交基向量的線性組合, 和作為： 中，因此可以被寫作 現(xiàn)在由運(yùn)動(dòng)分布的問題，找到一個(gè)加權(quán)K的最低標(biāo)準(zhǔn)的解決方案滿足方程(5)和最小化以下運(yùn)動(dòng)分布函數(shù)。擬議的運(yùn)動(dòng)分布函數(shù)G是： 運(yùn)動(dòng)控制 圖2可操縱性的第i個(gè)輔助臂橢球。 運(yùn)動(dòng)分布函數(shù)的物理意義是,所有的可操縱性橢圓體輔助臂應(yīng)該盡可能輪通過函數(shù)的最小化。更具體地說,一個(gè)節(jié)點(diǎn)的分解速度的權(quán)重， ，成為的軸， 和在第i個(gè)輔助臂選擇軸的長度的倒數(shù)第i個(gè)輔助臂的可操縱性橢球。這種分解是實(shí)現(xiàn)更高的可操縱性以上各向同性配置的可操縱性橢圓體輔助臂更圓。如圖2所示,可操縱性的軸或更多的各向同性配置的可操縱性橢圓體輔助臂更圓。如圖2所示,可操縱性的軸橢球配合 和主軸的長度等于奇異值,，與一致，j=1,2.除了在輔助臂里K的權(quán)重,權(quán)重的輔助臂對(duì)整個(gè)機(jī)械手是由運(yùn)動(dòng)分布標(biāo)準(zhǔn)為: 標(biāo)準(zhǔn)的分布效應(yīng)器運(yùn)動(dòng)子武器是由權(quán)重因素,,被稱為“圓度的因素,圓度因素應(yīng)基于: (1) 與成反比 爾(術(shù)語(2)有一個(gè)物理意義,它正比于規(guī)范化的雅可比行列式的絕對(duì)值,也就是說, 另一方面,這一術(shù)語的第i個(gè)輔助臂體積成正比的可操縱性橢圓體。大量的橢球意味著它的圓度。因此,可以說,較大的型號(hào)更圓的第i個(gè)輔助臂的可操縱性橢球。上述標(biāo)準(zhǔn)的目的是一個(gè),大圓度因子應(yīng)輔助臂細(xì)長上可操縱性橢球橢球更圓。如果我們仔細(xì)觀察權(quán)重的方式,它可以很容易地發(fā)現(xiàn),有一個(gè)一致性增加可操縱性。 (7) 在λl以2 X 1拉格朗日乘子向量。最小的必要條件的G(K),結(jié)果是 （8） （9） 假設(shè)我們可以從選擇2線性獨(dú)立的行,方程(9)可分為 (10) (11) 可以由2線性獨(dú)立的行,剩下的（n-2）,行分別，類似，可以通過選擇制定2 線性獨(dú)立的行對(duì)應(yīng)的行，確定從方程(10)和方程（11），得到 （ 現(xiàn)在,可以唯一確定K方程(8)和(12)。K,,獲得上面.S可以從方程（4)中獲得 ，可以從方程（4）和方程（13）中獲得單個(gè)的輔助臂面冗余機(jī)械手使用方程可以有效地指導(dǎo)，(14)當(dāng)所有輔助臂模塊。另外,因?yàn)樽钚』慕鉀Q方案K方程(6)方程(5)的主題是W最低標(biāo)準(zhǔn)方程(5)的解決方案,它可以獲得的 方程（15） （15） 當(dāng)機(jī)械手的自由度,最后一個(gè)(s-th)輔助臂 3聯(lián)系模塊。在整個(gè)環(huán)節(jié)中,理由選擇3-link模塊作為最后的子部門是輔助臂接近效應(yīng)器容易分配給執(zhí)行某一任務(wù),同時(shí)優(yōu)化性能的功能。最后3-link模塊的基本控制方法是解決運(yùn)動(dòng)方法已廣泛用于動(dòng)控制冗余機(jī)械手。然而,剩下的(s-1)輔助臂是由上面提到的運(yùn)動(dòng)分布法。這兩種方法將使用專門為了方便。擴(kuò)展運(yùn)動(dòng)分配方案平面機(jī)械手與奇怪的自由度可以概括為: 運(yùn)動(dòng)分布來解決運(yùn)動(dòng)的轉(zhuǎn)換方法如下執(zhí)行,反之亦然。然后解決運(yùn)動(dòng)方法應(yīng)用,否則運(yùn)動(dòng)分布方法的應(yīng)用。上述標(biāo)準(zhǔn)的物理意義是解決運(yùn)動(dòng)方法將用于“當(dāng)最后輔助臂比任何其他更有可能將容易在執(zhí)行一個(gè)給定的任務(wù)。 當(dāng)運(yùn)動(dòng)解決方案應(yīng)用到最后輔助臂，效應(yīng)器的運(yùn)動(dòng)只分配到最后也的輔助臂就是說, （16） 一般解決方法，在方程（17）中可以得到 （ 在，和相關(guān)跡象的最大化和最小化性能函數(shù),分別;I是一個(gè)3×3單位矩陣。方程的系數(shù)K(18)是一個(gè)積極的標(biāo)量常數(shù)和,梯度向量的,被描述為: (19) 一個(gè)合適的選擇K可能基于手臂配置,硬件限制關(guān)節(jié)速度和試探法。 擴(kuò)展運(yùn)動(dòng)分配方案包括運(yùn)動(dòng)分配方法和解決運(yùn)動(dòng)方法適用于一般冗余機(jī)械手，擴(kuò)展運(yùn)動(dòng)分配方案的流程圖偶數(shù)和奇數(shù)的自由度機(jī)械手是圖3和圖4中所示,分別。盡管上述方案可以指導(dǎo)操縱者圓滿,自動(dòng)控制的內(nèi)在屬性冗余機(jī)械手,另外也可以用于提高性能和將在下一節(jié)中討論。 3.自動(dòng)控制 擴(kuò)展運(yùn)動(dòng)在第二節(jié)分布方案已經(jīng)制定一個(gè)有效的技術(shù)來控制平面冗余機(jī)械手。然而,提供更理想的配置或執(zhí)行另一個(gè)任務(wù),如一個(gè)避障一個(gè)自動(dòng)控制也可以使用可選。此外,如果我們注意到運(yùn)動(dòng)控制的基礎(chǔ)上擴(kuò)展運(yùn)動(dòng)的局部最優(yōu)分配方案在某個(gè)瞬間的時(shí)候,我們需要自動(dòng)控制來保證全局最優(yōu)操縱。 為此,需要使用一些指數(shù)量化機(jī)器人線圈形狀來確定是否需要自動(dòng)控制。 一個(gè)名為配置的新靈巧指數(shù),指數(shù),負(fù)責(zé)的轉(zhuǎn)換方面的定義是: （20） 配置指數(shù)可以提供標(biāo)準(zhǔn)確定機(jī)械手是在全球范圍內(nèi)的配置合適的或不是因?yàn)檫@個(gè)指數(shù)間接表明可操縱性。當(dāng)配置指數(shù)惡化低于某一閾值,執(zhí)行特定的子任務(wù)被稱為自動(dòng)控制通過改變手臂配置到配置的絕對(duì)值 指數(shù)高于閾值增加。 特別是自動(dòng)控制應(yīng)用于通過第S第一輔助臂和第(s - 1) 的偶數(shù)和奇數(shù)自由度機(jī)械手。 于自動(dòng)內(nèi)部關(guān)節(jié)機(jī)械手的運(yùn)動(dòng),不運(yùn)動(dòng)導(dǎo)致效應(yīng)器,它應(yīng)該滿足零空間，約束的零空間機(jī)械手雅可比行列式,J. 這意味著引導(dǎo)時(shí)自動(dòng)配置指數(shù)低于某一閾值,所謂的參考聯(lián)合配置是作為參考的理想配置。特別是用參考聯(lián)合配置重新配置機(jī)手械,以避免障礙物或某一物體的周圍形成一個(gè)包裝結(jié)構(gòu)。的使機(jī)械手是通過控制節(jié)點(diǎn)位置的方式來驅(qū)動(dòng)輔助臂對(duì)參考聯(lián)合配置， （21） （22） 這個(gè)優(yōu)化問題是一樣的,前面討論的運(yùn)動(dòng)分布方案。因此,K的解決方案,在這里可以得到使用方程描述的類似的程序(7)-()2)。自動(dòng)的關(guān)節(jié)速度同樣由方程(14)。 除了它的使用作為全球標(biāo)準(zhǔn)的指導(dǎo)在自動(dòng)控制、配置索引也被用作性能功能最大化在過去的三自由度suba輔助臂在前面的擴(kuò)展運(yùn)動(dòng)分配方案。例如,配置指數(shù)平面五自由度機(jī)械手,性能函數(shù)H方程(18)的解決運(yùn)動(dòng)方法,成為 （23） 5.數(shù)值例子 在這個(gè)仿真、特性和9-DOF平面作為一個(gè)選擇帶有轉(zhuǎn)動(dòng)關(guān)節(jié)機(jī)械手示例顯示如何擴(kuò)展運(yùn)動(dòng)分布 方案可以應(yīng)用于控制平面冗余運(yùn)動(dòng)方法,控制平面冗余操縱者。 1．平面特性機(jī)械手 的平面特性操縱者8聯(lián)系(單位米)被選中的整個(gè)長度是3.9米。給定的任務(wù)就是從最初的位置沿著x坐標(biāo)的正方向與速度常數(shù)效應(yīng)器最后的位置的初始位置1日2日和3日節(jié)點(diǎn)為(0.8,0.5),(1.2,0.3),(1.4,1.4)。輔助臂的數(shù)量是4,也就是說。s = 4。圓度因子分別為0.05,0.05,0.1,和0.65根據(jù)第二節(jié)使用的標(biāo)準(zhǔn)。在配置指數(shù)閾值觸發(fā)自動(dòng)控制被選為0.002。為了方便起見,我們定義效應(yīng)器的向前運(yùn)動(dòng)的運(yùn)動(dòng)從一個(gè)內(nèi)部外部的位置。同樣,我們也向后運(yùn)動(dòng)定義為從外部的運(yùn)動(dòng)效應(yīng)器內(nèi)部位置。最初的關(guān)節(jié)角度向后運(yùn)動(dòng)將同最后聯(lián)合角度向前運(yùn)動(dòng)。當(dāng)然,效應(yīng)器向后運(yùn)動(dòng)速度是相反的方向,而其重要性是一樣向前運(yùn)動(dòng)。圖5和圖6的仿真結(jié)果說明向前和向后運(yùn)動(dòng)使用擴(kuò)展運(yùn)動(dòng)分配方案沒有自動(dòng)控制,特別是，值得注意的是,沒有自我運(yùn)動(dòng)控制的方案傾向于保留重復(fù)性這些數(shù)據(jù)所示,預(yù)計(jì)。相同的任務(wù)圖5和圖6可以做更好的定性當(dāng)我們使用配置索引自動(dòng)。向前運(yùn)動(dòng)的仿真結(jié)果使用擴(kuò)展運(yùn)動(dòng)分配方案與自動(dòng)控制如圖7所示的聯(lián)合運(yùn)動(dòng)平滑比圖5。這個(gè)事實(shí)可以看到在圖8配置指數(shù)的值顯示在運(yùn)動(dòng)。大配置高可操縱性指數(shù)表示,這是一個(gè)好跡象光滑的行為。向后運(yùn)動(dòng)的仿真結(jié)果與自動(dòng)省略了,因?yàn)樗男袨轭愃朴谙蚯斑\(yùn)動(dòng)。從這些結(jié)果,可以說,自動(dòng)提高可操縱性的運(yùn)動(dòng)學(xué)控制配置指數(shù)惡化低于閾值時(shí),雖然擴(kuò)展運(yùn)動(dòng)分配方案可以獨(dú)自引導(dǎo)冗余機(jī)械手。 圖5仿真結(jié)果的平面特性操縱(前進(jìn)運(yùn)動(dòng)沒有自動(dòng)控制)。 圖6仿真結(jié)果的平面特性操縱者(向后運(yùn)動(dòng)沒有自動(dòng)控制)。 圖7仿真結(jié)果的平面特性操縱(前進(jìn)運(yùn)動(dòng)沒有自動(dòng)控制)。 沒有自我運(yùn)動(dòng)控制的方案傾向于保留重復(fù)性這些數(shù)據(jù)所示,預(yù)計(jì)。相同的任務(wù)圖5和圖6可以做更好的定性當(dāng)我們使用配置索引自動(dòng)。向前運(yùn)動(dòng)的仿真結(jié)果使用擴(kuò)展運(yùn)動(dòng)分配方案與自動(dòng)控制如圖7所示的聯(lián)合運(yùn)動(dòng)平滑比圖5。這個(gè)事實(shí)可以看到在圖8配置指數(shù)的值顯示在運(yùn)動(dòng)。大配置高可操縱性指數(shù)表示,這是一個(gè)好跡象光滑的行為。向后運(yùn)動(dòng)的仿真結(jié)果與自動(dòng)省略了,因?yàn)樗男袨轭愃朴谙蚯斑\(yùn)動(dòng)。從這些結(jié)果,可以說,自動(dòng)提高可操縱性的運(yùn)動(dòng)學(xué)控制配置指數(shù)惡化低于閾值時(shí),雖然擴(kuò)展運(yùn)動(dòng)分配方案可以獨(dú)自引導(dǎo)冗余機(jī)械手。 平面9-DOF機(jī)械手的平面9-DOF操縱者9聯(lián)系?(整個(gè)長度是5.0米)選為擴(kuò)展運(yùn)動(dòng)分配方案的另一個(gè)例子。 圖8配置指數(shù)的平面特性機(jī)械手(移動(dòng))。 圖9仿真結(jié)果的平面9-DOF機(jī)械手(前進(jìn)運(yùn)動(dòng)沒有自動(dòng)控制)。 在配置指數(shù)閾值觸發(fā)自動(dòng)控制是1×10 - 6。圖9說明了前進(jìn)運(yùn)動(dòng)的仿真結(jié)果使用擴(kuò)展的動(dòng)態(tài)分配方案自動(dòng)控制向前運(yùn)動(dòng)的仿真結(jié)果使用擴(kuò)展運(yùn)動(dòng)分配方案與自動(dòng)控制圖10所示。的配置前進(jìn)運(yùn)動(dòng)指數(shù)并沒有自動(dòng)控制的方案是如圖11所示。同樣的評(píng)價(jià)的作用自動(dòng)控制,如平面特性的操縱者。 圖11配置指數(shù)的平面9-DOF機(jī)械手應(yīng)用,本文提出的方法可以(移動(dòng))。 6.結(jié)論 提出了擴(kuò)展的運(yùn)動(dòng)分布方案平面機(jī)械手的運(yùn)動(dòng)控制與幾個(gè)程度的冗余,無論其景深是奇數(shù)還是偶數(shù)。該方法被證明有效地通過運(yùn)動(dòng)實(shí)現(xiàn)本地機(jī)械手的運(yùn)動(dòng)任務(wù)分配方法和運(yùn)動(dòng)方法解決。這個(gè)方案的顯著優(yōu)勢(shì)甚至自由度機(jī)械手的方案傾向于保留，這里提出延長運(yùn)動(dòng)分配方案是概念上很簡單有效,適用于任何平面冗余機(jī)械手。 靈巧指數(shù),稱為配置指數(shù),被用作性能函數(shù)解決運(yùn)動(dòng)控制和標(biāo)準(zhǔn)指導(dǎo)自動(dòng)控制。全球任務(wù)執(zhí)行指導(dǎo)有效地通過控制自動(dòng)通過漸進(jìn)的關(guān)節(jié)運(yùn)動(dòng)時(shí)參考聯(lián)合配置配置指數(shù)惡化低于某個(gè)閾值。模擬演示的,配置指數(shù),隋,表保存方面反映,是一個(gè)很好的性能指標(biāo)在全球指導(dǎo)自動(dòng)控制。自動(dòng)的運(yùn)動(dòng)控制也顯示增加可操縱性。另一點(diǎn)要提到的是,這種自動(dòng)控制還可以方便地應(yīng)用于避障問題,正確使用引用聯(lián)合配置。 盡管該方法有一個(gè)缺點(diǎn),它不能直接應(yīng)用于空間機(jī)械手使用目前的結(jié)構(gòu),方案可以推廣到覆蓋空間機(jī)械手與修改,在這個(gè)問題上和工作正在進(jìn)行。對(duì)于實(shí)際的應(yīng)用程序,本文提出的方法可用于實(shí)時(shí)控制平面機(jī)器人與數(shù)度冗余,機(jī)器人在復(fù)雜環(huán)境中工作等靈巧操作和控制POSTECH 7-00F直接驅(qū)動(dòng)機(jī)器人。16進(jìn)一步的研究將集中在逆運(yùn)動(dòng)學(xué)問題的共同立場水平在關(guān)節(jié)速度級(jí)別(不)機(jī)械手有大量冗余。 參考文獻(xiàn) 1. T.Yoshikawa ,“分析和控制冗余機(jī)器人的“機(jī)器人技術(shù)研究:第一個(gè)國際研討會(huì)(M. Brady and R. Pauleds)(麻省理工學(xué)院出版社、劍橋、質(zhì)量)(1984)439 - 439。 2. A.A. Maciejewski and CA. Klein,“冗余機(jī)械手避障在動(dòng)態(tài)變化的環(huán)境中”。機(jī)器人研究1、3號(hào)109 - 117(1985)。 3. A. Liegeois, “自動(dòng)監(jiān)控的配置和多體的行為機(jī)制”IEEE反式。在系統(tǒng)中,人,Cybern。SMC-7,12號(hào),868 - 871(1977)。 4. G.S. Chirikjian and J.W. Burdick, “避障算法操縱者，機(jī)器人與自動(dòng)化,辛辛那提(1990年5月)第625 - 631頁。 5. J.K. Salisbury and J.J. Craig, “力控制和運(yùn)動(dòng)學(xué)問題”。機(jī)器人技術(shù)研第一4-17(1982)。 6. R. Dubey and J.Y.S. Luh,“更高的靈活性冗余機(jī)器人控制，機(jī)器人與自動(dòng)化,羅利(1987年3月),頁1066 - 1072。 7. K.W. Jeong, W.K. Chung, and Y. Youm, “發(fā)展POSTECH 7自由度直接驅(qū)動(dòng)機(jī)器人”3日ISRAM Conf . .溫哥華(7月.1990)頁577 – 582。 附錄二 Kinematic control of planar redundant manipulators by extended motion distribution scheme W.l. Chung, W.K. Chung and Y. Youm MechanicaL Engineering Department, Pohang Institute of Science and TechnoLogy, P.O. Box 125, Pohang 790-6()() (Korea) (Received: in Final Form April 28 , 1991) SUMMARY The kinematic control of a planar manipulator with several-degrees of redundancy has been a difficult problem because of the heavy computat,ional burden and/or lack of appropriate techniques. The extended motion distribution scheme, which is based on decomposing a planar redundant manipulator into a series of nonredundant/redundant local arms (referred to as subarms) and distributing the motion of an end-effector to subarms at the joint velocity level, is proposed in this paper. The configuration index , which is defined as the product of minors corresponding to subarms in the Jacobian matrix, is used to globally guide the redundant manipulators. To enhance the performance of the proposed scheme, a self-motion control, which handles the internal joint motion that does not contribute to the end-effector motion, can be used optionally to guarantee globally optimal manipulation . The repeatability problem for the redundant manipulators is discussed using the proposed scheme. The results of computer simulations are shown and analyzed in detail for planar 8-DOF and 9-DOF manipulators, as examples. KEYWORDS: Kinematic control ; Planar manipulators; Distribution scheme; Configuration index. 1. INTRODUCTION The remarkable dexterity and versatility that the human arm exhibits in performing various tasks can be attributed largely to the kinematic redundancy of the arm . A robotic manipulator is called (kinematically) redundant if it possesses more degrees of freedom (DOF) than is necessary for performing a specified task. The extra degrees of freedom of a redundant manipulator can be used to achieve some subgoaJs such as singularity avoidance ,! obstacle avoidance,2 or joint limit avoidance. 3 Although one or two degrees of redundancy can be used to satisfy the above subgoaJs, the use of hyper-redundancy4 becomes very attractive because of its flexibility and dexterity in motion for a certain task in a complex environment. However, the studies on the kinematic control of the redundant manipulators with large degrees of redundancy has not been performed extensively because of the lack of appropriate techniques and/or computational burdens. Most of the approaches to the kinematic control of a redundant manipulator focus on resolving redundancy by applying the generalized inverse or pseudo-inverse to manipulator lacobians based on performance function such as the manipulability measure condition number,5 manipulator-velocity-ratio,6 compatibility index ,7 the minors of the manipulator Jacobian matrix. Most of such instantaneous optimization schemes, however, are based on local decision which may not guarantee global optimality. Several global optimization schemes have been proposed recently ,9- 11 but require a large amount of computation which makes real-time applications unrealistic. These pseudo-inverse approaches can be used to control planar redundant manipulators regardless of even and odd degrees of freedom . However, when a manipulator with large redundant degrees of freedom such as a planar 8-DOF or 9-DOF is required for a certain task in complex environment , the pseudo-inverse approaches have great difficulty in formulating a performance function and finding its gradient vector even with the aid of symbolic calculations such as MACSYMA. Another different concept was proposed by Lee et al. 12 for a planar 4-DOF manipulator where the redundant manipulator is decomposed into two nonredundant local arms, referred to as the basearm and the forearm, at an intermediate arm location or task point called the elbow. That is, a redundant manipulator is transformed into a serially cooperating dual-arm system, with the cooperation between the subarms being carried out by the elbow. This scheme which is called the task distribution scheme used a new measure called Task Oriented Manipulability Measure (TOMM), which represents the discrepancy between the task requirements and the manipulator's manipulability, to globally guide the task execution. The task distribution scheme, however, has the following restrictions. ? It can be applied to only a redundant manipulator with even degrees of freedom because the manipulator should be decomposed into nonredundant subarms only. Thus the scheme becomes very difficult to be applied to a planar manipulator with odd degrees of freedom , such as planar 5-DOF or 7-DOF manipulators. ? It does not tend to preserve repeatability if the desired singular values and vectors for TOMM are not properly chosen . ? TOMM requires a priori knowledge of the desired singular values and singular vectors for task execution, which is rather difficult in practice. This paper presents a new scheme which can be applied to any planar redundant manipulator by extending and generalizing the above task distribution scheme. A redundant manipulator is treated here as a multi-subarm system where multiple nonredundant/redundant arms are serially linked together. The scheme is called the extended motion distribution scheme in this paper because it includes both the motion distribution method and the resolved motion method.3 Although the basic structure is similar to that of Lee et aI. , ' 2 both the control scheme and the way to guide the robot motion in the new scheme are largely different from those of Lee et al. To use the intrinsic property of redundant manipulators, a self-motion control can be optionally included in the proposed scheme to enhance manipulability or to obtain a more desirable configuration. A dexterity index, which is called the configuration index, is also developed to be used as a criterion to determine the execution of self-motion control and/or a performance function to be maximized in the resolved motion method.. Section 2 presents the structure of the proposed scheme, and Section 3 describes the seU-motion control guided by the configuration index. In Section 4, the numerical simulations are made for planar 8-00F and 9-00F manipulators to verify the effectiveness of the proposed method with discussions. Concluding remarks are made in Section 5. 2. EXTENDED MOTION DISTRIBUTION SCHEME The basic structure of the scheme is to decompose the redundant manipulator into a series of subarms. The subarm is basically a 2-link manipulator module, but the last subarm can be either a 2-link or 3-link manipulator for even and odd degrees of freedom manipulators, respectively. When a planar redundant manipulator has even degrees of freedom, all of the subarms are 2-link modules and the motion of an end-effector is distributed to each subarm according to the following motion distribution method.. A node is defined as a joint between adjacent subarms. Figure 1 illustrates a planar redundant Fig1. Multi-subarm system in planar case manipulator represented as a serially cooperative multi-subarm system. The joint velocity of the manipulator, iJ Em", can be expressed as a combination of the joint velocities of subarms: , （1） where s is the number of subarms. The end-effector velocity, xn generated by the subarms with reference to the base frame can be described in terms of iJa; for i=1,2, ... ,s: ，: (2) where J; E m2X2 and x e; are the submatrix of the Jacobian 2XfI matrix, J E m, coresponding to iJa;, and the Cartesian velocity of the i-th node, respectively. The equation (2) indicates that the end-effector motion can be explicitly represented in terms of the joint motions of subarms. In this equation, J; for i = 1, 2, ... , s can be expressed by the singular value decomposition13 as: with the singular values 'a, ~'02 and rank (J;) = 2. A set of orthonormal basis vectors of rangeof J;, r!Il(J;) is formed by 'u, and 'U2 where 'U= ['U,'U2]. The node velocity, Xe;, can be represented by a linear combination of orthonormal basis vectors, ;u, and ;U2, as: ， Hence x~ can be written as The problem of motion distribution now consists of finding a weighted minimum norm solution of K satisfying equation (5) and minimizing the following motion distribution function. The proposed motion distribution function, Gis: （6） Fig. 2. Manipulability ellipsoid of the i-th subarm. The physical meaning of the motion distribution function is that all of the manipulability ellipsoids for subarms should be as round as possible through the minimization of the function. To be more specific, the weightings for the decomposition of a node velocity, X'i ' into the principal axes of Ji, i.e., iU1 and iU2 , within the i-th subarm are chosen to be the reciprocals of the lengths of the principal axes of the i-th subarm's manipulability ellipsoid.1 This decomposition is to achieve higher manipulability or more isotropic configuration by making the manipulability ellipsoids of subarms more round. As shown in Figure 2, the principal axes of the manipulability ellipsoid coincide with iU1 and iU2 and the length of a principal axis is equal to the singular value, iOj , corresponding to iUj for j = 1, 2. In addition to this weighting of K within subarms, the weighting of each subarm for the whole manipulator is determined by the motion distribution criterion as: Criterion The distribution of an end-effector motion to sub arms is determined by weighting factors, a/s for i =1, 2, ... , s, called the "roundness factors" . The roundness factors should be given based on: (1) E~= l (l'i = 1. (2) (l'i is inversely proportional to Isin 0 2il. The Isin 0Zil term in (2) has a physical meaning that it is proportional to the absolute value of the normalized determinant of the Jacobian Ji, that is, On the other hand, the term Idet (Ji)1 is proportional to the volume of the i-th subarm's manipulability ellipsoidl. The large volume of the ellipsoid means its roundness. Thus, it can be said that the larger Isin 02il the more round the i-th subarm's manipulability ellipsoid. The purpose of the above criterion is that a ,large roundness factor should be given to the subarm with a slender manipulability ellipsoid to make its ellipsoid more round. If we observe carefully the way of weighting, it can be easily found that there is a consistency to increase manipulability. To obtain K minimizing G(K) subject to xe = UK, let us define the Lagrangian function L(K) as follows. where l is a 2 X 1 Lagrangian multiplier vector. The necessary conditions for the minimum of G(K), aL/al=O and aL/aK=O, result in (8) （9） respectively. Assuming that we can select 2 linearly independent rows from UT, equation (9) can be divided into where U[ E m2x 2 and iffE m(n-2) X2 can be formulated by 2 linearly independent rows of UT and the remaining respectively. Similarly, can be formulated by selecting 2 rows of W corresponding to 2 linearly independent rows of UT , and selecting the remaining (n -2) rows of W, respectively. Determining l from equation (10) and substituting into equation (11), we have Now, K can be uniquely determined by equations (8) and (12). With K, K = [KiK[ ... K}Y obtained above, Xei for i = 1, 2, . . . , s can be obtained from equation (4) as: The individual subarm of the planar redundant manipulator can be effectively guided by using equation (14) when all of the subarms are 2-link modules. Alternatively, since the solution K which minimizes equation (6) subject to equation (5) is the W-weighted minimum norm solution of equation (5), it can be obtained by When the manipulator has odd degrees of freedom , the last (s-th) subarm is a 3-link module. Among the whole links, the reason to choose the 3-link module as a last sub arm is that the subarm close to an end-effector C3n be easily assigned to perform a certain task while optimizing a performance function. The basic control method for the last 3-link module is the resol