機器人在自然地形下爬行【中文6940字】【PDF+中文WORD】,中文6940字,PDF+中文WORD,機器人,自然,地形,爬行,中文,6940,PDF,WORD 【中文6940字】 機器人在自然地形下爬行 摘要：這篇文章展示了爬行機器人規(guī)劃準(zhǔn)靜態(tài)動作的一種大致構(gòu)造。把這種構(gòu)造具體化是為了計算一種三足機器人在垂直自然地形中的爬行動作。在這里我們展示了通過模擬環(huán)境路徑的例子。規(guī)劃問題是五個對機器人系統(tǒng)發(fā)展的挑戰(zhàn)中的一個，它可使機器人在自然地形上爬行。剩下的四個方面——硬件設(shè)計、控制、判斷、抓握——仍在討論中。 關(guān)鍵詞：動作規(guī)劃，爬行，機器人學(xué)，有足機器人，高危通道，自然地形 1 前言 這篇文章中描寫的機器人爬行是發(fā)展核心技術(shù)成果的一部分，該技術(shù)能使一個自動化機器人的設(shè)計執(zhí)行系統(tǒng)實現(xiàn)在垂直自然地形中的爬行。對我們而言，這種技術(shù)之前從未在機器人系統(tǒng)中得到證實。先前的方法能夠處理好在人工地形爬行的問題，那些方法不是用特殊的裝置吸附在地形表面，就是利用地形特殊的性質(zhì)或特點。 發(fā)展這種機器人爬行技術(shù)將使我們對人類為什么能執(zhí)行像在崎嶇地形上攀爬這種復(fù)雜任務(wù)的理解更上一層樓。在今后精密機器人系統(tǒng)的發(fā)展中，將會證明這非常有益。精密機器人系統(tǒng)能夠?qū)崿F(xiàn)救助或代替人們在復(fù)雜地形上進行危險作業(yè)。這樣的例子包括用機器人系統(tǒng)來搜救，偵察和探索行星。 在機器人能夠真正在真實、垂直的自然地形下爬行前，需要解決許多問題。這篇文章考慮了這些問題中五個最主要的方面：硬件設(shè)計、控制、判斷、規(guī)劃和抓握。其中一個的問題，行動規(guī)劃問題，被我們詳盡的描述。爬行機器人的大致構(gòu)造已經(jīng)展示。這種構(gòu)造被具體化來計算圖1中展示的三足機器人的爬行動作。本圖展示的是這個機器人在一種典型垂直環(huán)境下的模擬結(jié)果。 圖1 三足機器人相愛自然垂直表面爬行 2 動機 在這個領(lǐng)域中的研究結(jié)果會使很多應(yīng)用受益，也為一些相關(guān)的研究領(lǐng)域提供了幫助。 2.1 應(yīng)用 寫這篇文章是受到需要機器人系統(tǒng)有提供高危自然環(huán)境下的途徑的能力的激勵。 這樣的系統(tǒng)有很多陸上的用途，例如搜救，探索洞穴，輔助人類攀巖和靈活的城市任務(wù)。每個都需要上升、下降或通過陡峭的斜坡和峭壁，因此可聯(lián)想到的人類風(fēng)險。 一些空間應(yīng)用同樣受益于這些先進的機器人系統(tǒng)。例如火星位置具有潛在的高科技價值已經(jīng)在懸崖面上得到證實。通常，飛行機器人進入這些位置既不實際也不可行。因此，到達(dá)這些位置，機器人必須攀爬、下降或通過陡峭的斜坡。將來探索其它行星餓目標(biāo)也許會需要進入同樣崎嶇的地形。 2.2 關(guān)聯(lián) 為了進一步提高機器人在垂直自然地形上的發(fā)展，在這種領(lǐng)域中的研究結(jié)果能為一些相關(guān)領(lǐng)域提供重要的見解。例如，這項研究能引導(dǎo)使機器人走路或靈活的操作的更好的策略發(fā)展。人類攀巖者通常討論提高平衡和在日?；顒又袛U大活動范圍，因為他們會越來越精于運動。這種提高了的移動性通常被提及為“發(fā)現(xiàn)了新的自由”，并且與為極復(fù)雜的仿生機器人或數(shù)字化演員發(fā)現(xiàn)新的有用的機動性的想法有關(guān)。 同樣，規(guī)劃運算法則的發(fā)展對爬行機器人來說能產(chǎn)生一套更好的標(biāo)準(zhǔn)，是對這種類型機器人的設(shè)計的標(biāo)準(zhǔn)。這種運算法則能夠用于模擬決定機器人的能力的候補設(shè)計，主要由此來選擇設(shè)計。 3 主要問題 在陡峭的自然地形上爬行涉及5個主要問題：硬件設(shè)計、控制、判斷、規(guī)劃、抓握。誒過領(lǐng)域中需要做大量的工作來研發(fā)一個真正的爬行機器人。這個部分描述了最初的4個領(lǐng)域中的挑戰(zhàn)；規(guī)劃問題將在第四部分詳細(xì)的討論。 3.1 硬件設(shè)計 一個好的硬件設(shè)計能提升機器人的性能，并且常常會使其他的主要問題更容易解決。然而，過去硬件解決方法在維持平衡上的應(yīng)用導(dǎo)致在能夠通過餓地形受到限制。 有足的機器人已經(jīng)被用來攀爬達(dá)到50度傾斜的自然峭壁，從75度傾斜的峭壁走下來，在粗糙地形上爬越小障礙。這些系統(tǒng)不是用了像[12，14-16]中的積極中斷形式，就是如[1]繞繩下降。用有足繞繩的機器人[3，17]和類蛇機器人得到同樣的結(jié)果。 這些行者費力的通過的地形是令人印象深刻的，但在現(xiàn)有的系統(tǒng)中沒有一個顯示有能力在90度傾斜或更傾斜的自然峭壁爬行。有足的行者和類蛇機器人有一個天生的抓握缺陷，這使它們不能用于攀爬連續(xù)的幾乎垂直的自然峭壁，和從連續(xù)的過于垂直的自然峭壁上爬下?，F(xiàn)有的有足機器人系統(tǒng)沒有這種缺陷，但在通過纏繞繩子維持與峭壁的接觸這個問題上仍然走了彎路。依靠這些繩子阻止了最初的懸崖的攀爬，并且限制了從懸崖上下來的傾角低于90度的峭壁級別。 現(xiàn)在多種機器人實現(xiàn)了在人工垂直表面上爬行。大多數(shù)機器人為了更好的抓握而利用表面的一些屬性。例如，一些機器人用吸氣杯或永磁鐵來避免打滑[5-8]。其它的利用像陽臺上的扶手。然而，這些被機器人利用的表面特征通常在自然地形下不可用。 相比之下，[2，11]用的簡單的硬件設(shè)計沒有這種限制。人們期望像這篇文章提出的規(guī)劃問題的解決方法通過類似的系統(tǒng)允許爬基本的自然垂直地形，另外通過現(xiàn)有的系統(tǒng)爬管子，也期望解決方法會建議設(shè)計有更好性能的變體。 將來的研究可以解決其他類型的工具的應(yīng)用問題，這些工具用于垂直自然表面的抓握，如鉆孔用的工具或在巖石上安裝其它用具的工具。 利用這些工具可以幫助解決更多有挑戰(zhàn)性的爬壁問題，同樣這些“輔助”可以幫助人類攀巖者[18,19]。然而，這些工具帶來了新的問題，重量大，復(fù)雜，移動緩慢還有手限制的潛在應(yīng)用。 3.2 控制 一個爬壁機器人的控制問題主要喲偶3個方面：維持平衡，末端打滑控制和末端壓力控制。這3方面緊密相聯(lián)。為了保持平衡，機器人的重心和來自自然特征接觸的壓力都要控制。這些接觸的打滑控制與接觸壓力的大小和方向直接有關(guān)。 現(xiàn)有的控制技術(shù)，像那些基于操作空間程式的技術(shù)，可以形成一種對控制風(fēng)格設(shè)計的基本途徑，這種控制風(fēng)格是對爬壁機器人而言的。然而，這些技術(shù)可以延伸成大量不同的方法來得到更好的性能。例如，將來的研究可能解決末端打滑控制器的設(shè)計問題，末端打滑控制器穩(wěn)定與接觸面彎曲部分的反映有關(guān)，而與只有一點接觸的反應(yīng)無關(guān)。 3.3 判斷 對于控制和抓握來說，爬墻機器人必須具備根據(jù)重力方向、重心位置、來自于足間末端的接觸面相關(guān)位置及盡力與自然地形接觸的壓力來判斷自己身體的方向的能力。對于規(guī)劃，機器人必須能夠定位新的抓附點和產(chǎn)生對他們性質(zhì)的說明，這可能需要衡量接觸點打滑的程度。判斷器的集成是個具有挑戰(zhàn)性的問題，判斷器的集成是為了獲得并利用算法信息來進行控制、抓握和規(guī)劃。 現(xiàn)有可行的設(shè)計解決方法可以引導(dǎo)每種情況中的一種基本途徑的發(fā)展。例如，像在[21，22]中描述的判斷器能夠提供基本末端壓力和衡量打滑程度，一種慣性單元和磁性指針能提供位置信息，一種觀察系統(tǒng)可以提供大概的吸附位置和性質(zhì)的描繪，編碼器可以提供重心位置。然而每個判斷器的提升，如性能、減重和減少經(jīng)費，提出了供研究的開放領(lǐng)域。盡管在第4部分闡述的規(guī)劃框架的性能，用更好的判斷器信息會得到提升，但它并不依賴環(huán)境的完美模式。因為框架工作發(fā)展的很快，使在線供給器具和計劃能在新判斷器信息可用時合作。 3.4 抓握 爬壁機器人的性能依賴于吸附的能力或陡峭自然表面的特性。現(xiàn)在已經(jīng)證明特殊的抓握項目依賴于地表的特殊性，如非常平滑的質(zhì)地或支持，它不能用于自然地形。涉及在自然地形上抓握的問題在這部分會進一步探討。 傳統(tǒng)的抓握研究致力于拾起目標(biāo)物或穩(wěn)穩(wěn)的抓住它。這個課題的研究可以追溯到1876年，這研究顯示用一個小的4點無摩擦約束就可以穩(wěn)穩(wěn)的抓到一個平的目標(biāo)物。更多近期這方面好的概述見[24，25]。在這領(lǐng)域有個重要的概念“壓力終止”，被定義為“如果在單邊接觸中應(yīng)用足夠大的壓力，能抵御目標(biāo)物各方面的移動”的抓握。幾乎所有抓握的研究都致力于選擇、特性化、最優(yōu)化的抓握，它有壓力終止的性能。 然而，對于爬行抓握來說不需要壓力終止。例如，一個機器人會發(fā)現(xiàn)像架子樣的扶手可能很容易爬上去，即使這個抓握完全不能抵御來自其它方面的壓力。鑒于這個原因，選擇、特性化、最優(yōu)化抓握的研究必須好好的發(fā)展來把它應(yīng)用到爬壁機器人上。 描繪包括檢測用于抓握的壓力和扭矩的大小和方向。例如，對于一個點上的一個手指抓握，這個信息的合理描繪就是一個摩擦體，它將被用于在第四部分描述的規(guī)劃運算法則。 描繪的想法還包括一個“質(zhì)量因素”。抓握質(zhì)量的措施已經(jīng)被廣泛研究，見于[26]。這項工作列出了8個靈活的措施，包括使連接角度的偏差最小，使最小單個抓握模型的價值最大化。其它的相關(guān)研究用了扭空間的概念。用這個概念，質(zhì)量被定義為最大的扭轉(zhuǎn)球，它可以滿足抓握扭轉(zhuǎn)單元。抓握扭轉(zhuǎn)空間的體積或更多的專業(yè)橢球任務(wù)，可以用來當(dāng)作質(zhì)量措施。這些想法擴展了，包括限制最大接觸壓力和應(yīng)用于抓握模擬器來計算用不同的三維手進行最好的抓握。 然而，抓握質(zhì)量這個概念對于抓握來說沒有定義好，沒有提供壓力終止。依靠一個攀巖者想走的方向，不同的抓握有不同的質(zhì)量。而且，抓握質(zhì)量一般包括安全或穩(wěn)定性概念，這兩個概念對于無壓力終止抓握來說也沒定義好。再者，依靠依靠應(yīng)用壓力的方向，抓握的安全性肯會改變。握住質(zhì)量的概念應(yīng)在有用的最優(yōu)化可能之前定義。同時，傳送信息到控制器或規(guī)劃器，有必要有一個高效的方法來完成爬壁任務(wù)。 不同類型抓握的分類已經(jīng)存在于人類攀登者的技巧中。在這個分類中，抓握首先被分成兩種，一種是對礦穴、邊緣和其它沒有縫隙的垂直巖面而言的，另一種是對連續(xù)的垂直裂縫而言。圖2中可以看到不同地貌和裂縫的抓握例子。對于如安全水平的條件，這種技巧讓人聯(lián)想到各種抓握的質(zhì)量和用途餓一個大概想法，轉(zhuǎn)矩可被施于一個手柄上，摩擦可被施于受力點。 不僅是在期待的直觀質(zhì)量上，同樣清楚的是人類攀巖者在特殊情況下需要用到別處的抓握。長久以來“有多種不同的手柄，就有多少種方法去抓住它們”。然而，這種直觀性是用來作為決定意義深遠(yuǎn)的定性標(biāo)準(zhǔn)的起點，這定性標(biāo)準(zhǔn)是為了抓握的選擇和優(yōu)化。 這種爬壁技巧與過去的機器人抓握規(guī)劃的比較揭示出這兩種應(yīng)用間的幾種其它主要不同之處，這對將來的研究很重要。例如很多爬壁手柄很小，所以爬壁抓握時的手指常常為了與目標(biāo)物而擁有大直徑。機器人抓握技巧首先認(rèn)同小直徑的手指也可抓目標(biāo)物的情況。另外，像圖2中展示的一些爬壁抓握姿勢，都是基于裂縫中的手指。這項技術(shù)與機器人拾起目標(biāo)物的技術(shù)有不同，它需要高靈活性和小自由度來使手指伸入裂縫。清楚的是，連續(xù)的爬壁機器人研究工作最終將引起更多的考慮抓握中的新問題。 (a) (b) (c) (d) 圖2 四種不同的人類攀登抓握在(a)無阻礙的抓握，(b)卷曲的抓握，(c)手指鎖住抓握和(d)夾縫中抓握。 4 規(guī)劃 規(guī)劃問題是爬壁機器人在自然地形爬行的第五個主要挑戰(zhàn)。這部分展示的移動規(guī)劃框架細(xì)節(jié)見[32]。 4.1 挑戰(zhàn) 爬壁機器人的規(guī)劃問題包括產(chǎn)生一條軌跡使機器人保持平衡的通過垂直地形。 這個問題對人類攀巖者來說也是個挑戰(zhàn)。攀巖長久以來被描述成一個“偉大的挑戰(zhàn)，每個攀巖路線的次序和方案都是獨特的，都是解決精力和體力問題的設(shè)計”。一個獨特路線包含大量不同的“移動”，其中一些移動見圖3.每個移動對保持平衡來說都是成熟技術(shù)。除了這些妙想，通過大量特殊身體位置的移動也許是爬行進步到最高的必要條件。 在實際爬行前Graydon和Hanson就已經(jīng)注意到規(guī)劃一系列移動的重要性，他們認(rèn)為攀巖者“在攀爬簽會鑒定和檢查不同的地貌，計劃好然后迅速的爬越它們”。人們這種做法的動機主要是為了使每次移動所耗能量達(dá)到最小和節(jié)省能量，因為大多數(shù)人沒有足夠的體力和耐力。 規(guī)劃問題對機器人來說是類似的。機器人裝有驅(qū)動裝置，這可以在短時間內(nèi)運用高轉(zhuǎn)矩，所以在爬行之前規(guī)劃好移動順序?qū)C器人系統(tǒng)而言同樣重要。同樣，爬壁機器人要受制于同樣困難的平衡限制，并且需要在類似的可能移動范圍內(nèi)選擇。因此，規(guī)劃算法的發(fā)展對一個自動化爬壁機器人來說是一個非常有挑戰(zhàn)性的問題。 (a) (b) (c) 圖3 三種不同的人類攀爬移動（a）撤步（b）逆向行進（c）向上行進 4.2 相關(guān)工作 爬壁機器人的搜索范圍是一個混合的范圍，包括連續(xù)的動作和分散的動作。通過連續(xù)動作范圍許多不同方法對移動規(guī)劃可行，包括電池分解。潛在領(lǐng)域和路線圖算法。分散動作可直接包括在這些方法中，例如路線圖算法中結(jié)擴展的水平，但這種方法一般會導(dǎo)致執(zhí)行的減緩，特別是對特殊系統(tǒng)。 為有腿機器人做的移動規(guī)劃的前期工作已經(jīng)開發(fā)出了解決一些系統(tǒng)混合搜索范圍的工具。無論是不是脫機作規(guī)劃，這項工作都可以分類，這是為了產(chǎn)生一種反應(yīng)性的步法或聯(lián)機，為了考慮到敏感環(huán)境下的無步移動。 步態(tài)規(guī)劃著認(rèn)為在平穩(wěn)的環(huán)境中可以創(chuàng)造一種預(yù)先定義的脫機走路方式。這種方式用到一組或行為來控制機器人聯(lián)機，這基于近期傳感器輸入的信息。[2，11]用到了步態(tài)規(guī)劃，例如，設(shè)計爬管子的方式。其它像[34]樣的方法是基于為了保持平衡的支撐三角形的想法。 穩(wěn)定標(biāo)準(zhǔn)如零狀態(tài)點已經(jīng)用于設(shè)計最優(yōu)步態(tài)。有活力的步態(tài)和跳躍已經(jīng)被證實了。近期的工作是試圖提供統(tǒng)一的精確的工具為了產(chǎn)生步態(tài)。每個規(guī)劃的運算法則在一部分自然爬行環(huán)境下很有效果，這自然爬行環(huán)境有連續(xù)的特色，如幾乎一樣寬的長垂直裂縫。然而，在不規(guī)則的環(huán)境下爬行，如這篇文章研究的環(huán)境，機器人爬行餓表面是有角度的，任意固定的表面需要更多的技巧。 費步態(tài)規(guī)劃著用于關(guān)于環(huán)境的相關(guān)信息來創(chuàng)造可行的聯(lián)機步態(tài)計劃。為有足機器人做的關(guān)于非步態(tài)行動的大部分前期工作專注于一個特別的系統(tǒng)樣式，蜘蛛機器人。蜘蛛機器人的足被假定成很輕的，這引起了它們自由空間的一流表現(xiàn)，為了基于支撐三角形的準(zhǔn)靜態(tài)動作[44,45]。然而，當(dāng)考慮到機器人不能滿足蜘蛛機器人的假設(shè)，這些方法中用到的分析方法就終止了。例如，在[46，47]中為人類機器人規(guī)劃非步態(tài)走路動作附加技術(shù)是必須的。這篇文章探究的是一個具有少量自由度的機器人在一個更加有條理的搜索空間，那里比用啟發(fā)式方法更有可能獲得更好的性能。盡管這算法意味著創(chuàng)造“真實”而不是嚴(yán)格可行的動作，在為性格特征設(shè)計行動規(guī)劃算法時，[48]呈現(xiàn)了類似的問題。 在為有足運動、抓握和機器人操作的非步態(tài)動作規(guī)劃中存在類似之處，特別是在操作概念上[24,49-51]。兩種規(guī)劃都需要作出分散和連續(xù)的選擇。 所有現(xiàn)有的規(guī)劃技術(shù)都不足以解決甚至是在自然環(huán)境中最簡單的爬行問題。在自然環(huán)境中，準(zhǔn)靜態(tài)移動，準(zhǔn)確的信息和單指抓握一點手柄都被采用。如果準(zhǔn)靜態(tài)和準(zhǔn)確信息的采用是松懈的，考慮更多復(fù)雜的抓握，這個問題會越來越復(fù)雜。 4.3 規(guī)劃框架 在這部分，我們將描述圖上展示的一種特殊爬壁機器人的規(guī)劃框架。這個機器人有三條腿，每條腿有兩個關(guān)節(jié)，一個在機器人的中心，一個在腿的中點。動作被認(rèn)為是準(zhǔn)靜態(tài)的，伴隨重力發(fā)生在垂直平面。這種機器人運動學(xué)的低復(fù)雜性使它適合于研究爬行動作的規(guī)劃。 地形是垂直平面，附有一堆小的、有角度的平表面，叫做“手柄”，它們是任意分布的。每個機器人腿的末端都可以在每個手柄拉或推一個點，產(chǎn)生摩擦防止打滑。 機器人的爬行動作包括連續(xù)的步伐。任意兩個連貫的步伐之間，三個腿末端接觸到不同的支撐。每一個步伐中，腿從一個支撐移動到另一個支撐，另兩個末端仍可固定。機器人可以用兩個相當(dāng)?shù)哪_形成的連接中的自由度來維持準(zhǔn)靜態(tài)平衡和防止在兩個相當(dāng)?shù)闹伍g打滑。另外，走一步時，任意一個連接處的扭矩不能超過控制裝置的極限，腳之間也不能相互碰撞。這些限制決定了機器人每走一步的外形輪廓的可用子設(shè)備。這子設(shè)備中的一條路線決定了一步動作。 所有的計劃問題如下：一個給定的地形，依賴一對手柄和一個目標(biāo)支撐的最初的機器人外形產(chǎn)生了一系列一步的動作，這將使機器人在準(zhǔn)靜態(tài)平衡上從最初外形到最后外形，在最后外形下一腳的末端與目標(biāo)手柄接觸。 [32]中我們展示了解決這規(guī)劃問題的框架的細(xì)節(jié)。這個框架可簡說如下。 首先，我們展示了三足爬壁機器人的一步動作的詳盡的分析。連續(xù)結(jié)構(gòu)的屬性已經(jīng)設(shè)定了，將被用來定義機器人在每對支撐下的可用集。特別的，當(dāng)規(guī)劃一個二維的子空間時，機器人的4維連續(xù)可用范圍的連貫性可以保留。這個結(jié)果精簡了一步規(guī)劃問題的復(fù)雜程度并且導(dǎo)致了一個快捷聯(lián)機餓執(zhí)行實現(xiàn)。 然后，所有的規(guī)劃者將這種“本地規(guī)劃者”與靈活的搜索技術(shù)結(jié)合起來來決定對目標(biāo)支撐技術(shù)而言的最初外形的一系列支撐。這啟示性的方法來自于觀察人類攀巖者規(guī)劃他們的動作。 4.4 結(jié)果 [32]中展示的成果不是對特殊垂直環(huán)境模擬結(jié)果中的一組。這篇文章我們將展示在一個更具挑戰(zhàn)性的環(huán)境中的第二組結(jié)果。圖4中展示的環(huán)境，包括隨機固定的、有角的支撐。機器最先定位于這環(huán)境底部的兩個支撐，它被要求達(dá)到頂點的兩個支撐。 圖4 三足機器人在垂直環(huán)境爬行的例子 用一個450MHZ的處理器3秒內(nèi)就可以找到一個計劃，對一個包含50個支撐的環(huán)境來說非常典型。為更小的環(huán)境規(guī)劃時間。 圖5中展示了一個不同的連續(xù)結(jié)構(gòu)，來自于每個規(guī)劃次序的一步動作。許多這類的結(jié)構(gòu)明顯與人類的結(jié)構(gòu)相似。例如，圖5（a）中展示的結(jié)構(gòu)與圖3（b）展示的類似。另外，圖5（i）和（n）描述的結(jié)構(gòu)分別與圖3（a）中的“后退”和圖3（c）中的“高步”類似。 圖5中每個框架都展示了平衡區(qū)域，這是對機器人站立支撐而言的。這個區(qū)域機器人在不打滑情況下保持平衡重心可以移動，而且是一個對機器人平衡限制的完全說明書。注意在每個結(jié)構(gòu)展示中，機器人重心存在于平衡區(qū)域。 更多資訊，包括可視3動畫，請訪問http://arl.stanford.edu/~tbretl/ 圖5 展示的動作是機器人在圖4環(huán)境下動作。每幅圖中的園點是機器人的重心 5 結(jié)論 這篇文章描述了發(fā)展自動化爬壁機器人的挑戰(zhàn)，提出了解決規(guī)劃問題的框架。 近期的工作是解決對一個真實機器人系統(tǒng)而言的規(guī)劃框架的應(yīng)用。作為部分努力，這框架已經(jīng)擴展到處理額外的動作限制，更加復(fù)雜的機器人幾何系統(tǒng)，不理想的環(huán)境和三維地形。 以后的工作將解決其它4個主要問題——硬件設(shè)計、控制、判斷、抓握及它們對規(guī)劃問題的關(guān)系。 15 Climbing Robots in Natural TerrainTimothy Bretl,Teresa Miller,and Stephen RockJean-Claude LatombeAerospace Robotics LabRobotics LaboratoryDepartment of Aeronautics and AstronauticsComputer Science DepartmentStanford University,Stanford,CA 94305Stanford University,Stanford,CA 94305tbretl,tgmiller,rocksun-valley.stanford.edulatombecs.stanford.eduKeywordsMotion planning,climbing,robotics,legged robots,high-risk access,natural terrain.AbstractThis paper presents a general framework for plan-ning the quasi-static motion of climbing robots.Theframework is instantiated to compute climbing motionsof a three-limbed robot in vertical natural terrain.Anexample resulting path through a large simulatedenvironment is presented.The planning problem is oneof five fundamental challenges to the development ofreal robotic systems able to climb real natural terrain.Each of the four other areashardware design,control,sensing,and graspingis also discussed.1 IntroductionThe work described in this paper is part of an effortto develop critical technologies that will enable thedesign and implementation of an autonomous robotable to climb vertical natural terrain.To our knowl-edge,this capability has not been demonstratedpreviously for robotic systems.Prior approaches havedealt with artificial terrain,either using special“grasps”(e.g.,pegs,magnets)adapted to the terrainssurface or exploiting specific properties or features ofthe terrain(e.g.,ducts and pipes)1-12.Developing this capability will further our under-standing of how humans perform such complex tasksas climbing and scrambling in rugged terrain.Thismay prove useful in the future development ofsophisticated robotic systems that will either aid orreplace humans in the performance of aggressive tasksin difficult terrain.Examples include robotic systemsfor such military and civilian uses as search-and-rescue,reconnaissance,and planetary exploration.Many issues need to be addressed before real robotscan climb real,vertical,natural terrain.This paperconsiders five of the most fundamental of these issues:hardware design,control,sensing,planning,andgrasping.One of these issues in particular,the motion-planning problem,is described in more detail.Ageneral framework for climbing robots is presentedand this framework is instantiated to compute climbingmotions of the three-limbed robot shown in Figure 1.Simulation results are shown for the robot in anexample vertical environment.2 MotivationThe results of research in this area will benefit anumber of applications and have implications forseveral related research areas.2.1ApplicationsThis paper is motivated by a need for robotic sys-tems capable of providing remote access to high-risknatural environments.There are many terrestrial applications for thesesystems,such as search-and-rescue,cave exploration,human assistance for rock and mountain climbing,andtactical urban missions.Each of these applicationsrequires climbing,descending,or traversing steepslopes and broken terrain,and thus involves consider-able human risk.Several space applications could also benefit fromthese aggressive robotic systems.For example,sites onMars with potentially high science value have beenidentified on cliff faces 13.Often,it is neitherpractical nor feasible for flying robots to access theseFig 1.A three-limbed climbing robot moving vertically on naturalsurfaces.locations.Therefore,to reach these sites,robots mustclimb,descend,or traverse steep slopes.Future goalsfor exploration on other planetary bodies may requireaccess to equally rugged terrain.2.2ImplicationsIn addition to furthering the development of aclimbing robot for vertical natural terrain,the results ofresearch in this area could provide fundamental insightinto several related research areas.For example,thisstudy could lead to the development of better strategiesfor robotic walking or dexterous manipulation.Humanclimbers often comment on an increase in balance andan expanded range of movement in everyday activityas they become more proficient at the sport.Thisenhanced mobility is often referred to as“discoveringnew degrees of freedom,”and is related to the idea ofdiscovering useful new modes of mobility for ex-tremely complicated humanoid robots or digital actors.Also,the development of planning algorithms forclimbing robots could lead to a better set of criteria forthe design of these types of robots.These algorithmscould be applied to candidate designs in simulation todetermine the capabilities of the resulting robots,andthus to select a design.3 Fundamental IssuesThere are five fundamental issues involved inclimbing steep natural terrain:hardware design,control,sensing,grasping,and planning.A substantialamount of work needs to be done in each of these areasin order to develop a real climbing robot.This sectiondescribes the challenges involved in the first four ofthese areas;the planning problem will be discussed inmore detail in Section 4.3.1Hardware DesignA good hardware design can increase the perform-ance of the robot,and often can make each of the otherfundamental issues easier to deal with.However,pastuse of hardware solutions in maintaining equilibriumgenerally resulted in a fundamental limitation on theterrain that could be traversed.Wheeled robotic systems have been used to ascendand traverse natural slopes of up to 50 degrees,todescend slopes of up to 75 degrees,and to climb oversmall obstacles in rough terrain.These systems eitheruse some form of active or rocker-bogie suspension asin 12,14-16,or use rappelling as in 1.Similarresults have been obtained using legged rappellingrobots 3,17 and a snake-like robot 4.The terrain that these rovers can traverse robustly isimpressive,but none of the existing systems has beenshown to be capable of climbing natural slopes of 90degrees or higher.Wheeled rovers and snake-likerobots have an inherent grasping limitation thatprevents their use in ascending sustained near-verticalor descending sustained past-vertical natural slopes.Existing legged robotic systems do not have thislimitation,but still have bypassed the issue of main-taining contact with the slope by using rappel tethers.Reliance on these tethers prohibits initial cliff ascent,and limits the slope grade on cliff descent to below 90degrees.A wide variety of robots capable of climbing verticalartificial surfaces is available.Most of these robotsexploit some property of the surface for easy grasping.For example,some of these robots use suction cups orpermanent magnets to avoid slipping 5-8.Others takeadvantage of features such as balcony handrails 9 orpoles 10.However,the surface properties that areexploited by these robots generally are not available innatural terrain.In contrast,the simpler hardware designs used by 2,11 had no such limitations.It is expected thatsolutions to the planning problem such as the onepresented in this paper will allow basic natural verticalterrain to be climbed by similar systems,in addition tothe ducts and pipes climbed by existing systems,andwill suggest design modifications for better perform-ance.Future studies could address the use of other types oftools for grasping vertical natural surfaces,such astools for drilling bolts or placing other types of gear inrock.The use of these tools would allow morechallenging climbs to be accomplished,in the sameway that“aid”helps human climbers 18,19.However,these tools bring an increase in weight andcomplexity,slowing movement and limiting potentialapplications.3.2ControlThere are three primary components of the controlproblem for a climbing robot:maintenance of equilib-rium,endpoint slip control,and endpoint force control.These three components are tightly related.In order tomaintain balance,both the location of the center ofmass of the robot and the forces from contacts withnatural features must be controlled.Control of slip atthese contacts is directly related to the direction andmagnitude of the contact forces.Existing control techniques such as those based onthe operational space formulation 20 could form abaseline approach to the design of a control architec-ture for a climbing robot.However,these techniquescould be extended in a number of different ways toachieve better performance.For example,futureresearch might address the design of an endpoint slipcontroller that is stable with respect to the curvature ofa contact surface,rather than with respect to a pointcontact only.3.3SensingFor control and grasping,the robot must be capableof sensing the orientation of its body with respect tothe gravity vector,the location of its center of mass,the relative location of contact surfaces from its limbendpoints,and the forces that it is exerting at contactswith natural features.For planning,the robot mustadditionally be able to locate new holds and generate adescription of their properties,possibly requiring ameasurement of levels of slip at contact points.Sensorintegration,in order to acquire and use this informationwith algorithms for control,grasping,and planning,isa challenging problem.Existing engineering solutions are available whichcan lead to the development of a baseline approach ineach case.For example,sensors such as those de-scribed in 21,22 can provide basic endpoint forceand slip measurements,an inertial unit and magneticcompass can provide position information,an on-boardvision system can provide a rough characterization ofhold locations and properties,and encoders canprovide the location of the center of mass.However,the improvement of each of these sensorsin terms ofperformance,mass reduction,or cost reduc-tionpresents an open area for research.Although the performance of the planning frame-work that will be presented in Section 4 would beimproved with better sensor information,it does notdepend on a perfect model of the environment a priori.Since the framework leads to fast,online implementa-tion,plans can be updated to incorporate new sensorinformation as it becomes available.3.4GraspingThe performance of a climbing robot is dependenton its ability to grasp“holds,”or features on a steepnatural surface.It has already been noted that special-ized grasping schemes,relying on specific propertiesof the surface such as very smooth textures,pegs,orhandles,cannot be used for grasping arbitrary naturalfeatures.The problems involved in grasping naturalholds will be examined further in this section.Traditionally grasp research has been interested ineither picking up an object or holding it immobile(alsocalled“fixturing.”)Research in this subject dates as farback as 1876 it was shown that a planar object couldbe immobilized using a minimum of four frictionlesspoint constraints 23.Good overviews of more recentwork can be found in 24,25.In this field an impor-tant concept is“force-closure,”defined as a grasp that“can resist all object motions provided that the end-effector can apply sufficiently large forces at theunilateral contacts.”25 Nearly all research on graspshas focused on selecting,characterizing,and optimiz-ing grasps that have the property of force-closure.However,for the task of climbing a grasp need notachieve force-closure to be a useful grasp.Forexample,a robot may find a shelf-like hold veryeffective for pulling itself up,even though this graspwould be completely unable to resist forces exerted inother directions.For this reason,the techniques forselecting,characterizing,and optimizing grasps mustbe expanded significantly to apply to climbing robots.Characterization involves examining the directionand magnitudes of forces and torques(also calledwrenches)that can be exerted by the grasp.Forexample,for one-finger grasps on point holds,anadequate representation of this information is a frictioncone,which will be used for the planning algorithmdescribed in Section 4.The idea of characterization also encompasses a“quality factor.”Measures of grasp quality have beenresearched extensively and are well reviewed in 26.This work lists eight dexterity measures that includeminimization of joint angle deviations and maximiza-tion of the smallest singular value of the grasp matrix.Other relevant research has been done using theconcept of the wrench space.Using this concept,quality is defined as the largest wrench space ball thatcan fit within the unit grasp wrench space 27.Thevolume of the grasp wrench space,or of morespecialized task ellipsoids,could be used as a qualitymeasure 28.These ideas have been expanded toinclude limiting maximum contact force and applied ina grasp simulator to compute optimal grasps withvarious hands in 3D 29,30.However,the concept of grasp quality is ill definedfor grasps that do not provide force-closure.Depend-ing on the direction that a climber wishes to go,different grasps may be of higher quality.Furthermore,grasp quality generally includes a concept of securityor stability,and this too is ill defined for non-force-(a)(b)(c)(d)Fig.2.Four different human climbing grasps,the(a)open grip,(b)crimp,(c)finger-lock,and(d)hand jam.closure grasps.Again,depending on the direction ofapplied forces,the security of a grasp may change.Theconcept of hold quality must be defined before usefuloptimization is possible.Also,an efficient way oftransmitting this information to a controller or planneris necessary to accomplish the climbing task.A qualitative classification of different types ofgrasps already exists in the literature for humanclimbers 19,31.In this classification,grasps are firstbroken into two categories,those meant for pockets,edges,and other imperfections on otherwise unbrokenvertical rock faces,and those meant for sustainedvertical cracks.Several examples of different face andcrack grasps are shown in Figure 2.The literaturegives a rough idea of the quality and use of each typeof grasp in terms of criteria such as a perceived levelof security,the amount of torque that can be exerted ona hold,and the amount of friction at the“power point.”Not only is this expert intuition qualitative,but alsoit is clear that human climbers need to performadditional grasp planning for specific cases.As put byLong,“There are as many different kinds of holds asthere are ways to grab them 31.”However,thisintuition can be used as a starting point for determiningmeaningful quantitative criteria for grasp selection andoptimization.A comparison of the climbing literature with pastwork on robotic grasp planning reveals several otherfundamental differences between the two applicationsthat may become important in future research.Forexample,many climbing holds are very small,so thefingers used in a climbing grasp often have largediameters relative to the object to be grasped.Litera-ture on robotic grasping primarily considers the casewhere the fingers have small diameters relative to theobject.In addition,some climbing grasps,as men-tioned above and shown in Figure 2,are based onjamming fingers in a crack.This technique is verydifferent from one a robot might use to pick up anobject,and requires a high degree of flexibility andsmall degrees-of-freedom in order to“un-jam”thefingers.Clearly,continued work on climbing robotseventually will lead to the consideration of a wealth ofnew issues in grasping.4 PlanningThe planning problem is the fifth fundamentalchallenge for climbing robots in natural terrain.Detailsof the motion-planning framework presented in thissection are given in 32.4.1ChallengesThe planning problem for a climbing robot consistsof generating a trajectory that moves the robot througha vertical environment while maintaining equilibrium.This problem is challenging even for human climb-ers!Climbing is described by Long as a“singular(a)(b)(c)Fig.3.Three different human climbing“moves,”the(a)back-step,(b)stem,and(c)high-step.challenge,where each route up the rock is a mentaland physical problem-solving design whose sequenceand solution are unique.Every climb is different 31.”Much of the sequence for a particular route might becomposed of one of a variety of different types of“moves,”such as a back-step,stem,mantel,high-step,counterbalance,counterforce,lie-back,down-pressure,or under-cling.Some of these moves are shown inFigure 3.Each“move”is a learned technique formaintaining balance that may seem counterintuitive.Inaddition to these heuristics,movement through a largenumber of other very specific body positions might benecessary to progress towards the top of a climb.The importance of planning a sequence of movesbefore actually climbing is emphasized by Graydonand Hanson 19,who recommend that climbers“identify and examine difficult sections before theyget to them,make a plan,and then move through themquickly.”The human motivation for this approach isprimarily to minimize the effort required for eachmove and to conserve energy,since most people havehard strength and endurance limits.The planning problem for a climbing robot is quitesimilar.The robot likely will be equipped withactuators that can exert high torques only for shortamounts of time,so planning a sequence of movesbefore climbing is important for a robotic system aswell.Likewise,a climbing robot will be subject to thesame hard equilibrium constraints,and will need toselect between a similarly wide range of possiblemotions.Therefore,the development of a planningalgorithm for an autonomous climbing robot is a verychallenging problem.4.2Related WorkThe search space for a climbing robot is a hybridspace,involving both continuous and discrete actions.Many different methods are available for motionplanning through continuous spaces,including celldecomposition,potential field,and roadmap algo-rithms 33.Discrete actions can be included in thesemethods directly,for example at the level of nodeexpansion in roadmap algorithms,but this approachgenerally leads to a slow implementation that isspecific to a particular system.Previous work on motion planning for legged robotshas developed tools for addressing these hybrid searchspaces for some systems.This work can be categorizedby whether or not the planning is done offline,in orderto generate a reactive gait,or online,in order to allownon-gaited motion specific to a sensed environment.Gaited planners generate a predefined walkingpattern offline,assuming a fairly regular environment.This pattern is used with a set of heuristics or behav-iors to control the robot online based on current sensorinput.Gaited planning was used by 2,11,forexample,to design patterns for climbing pipes andducts.Other methods such as 34 are based on thenotion of support triangles for maintaining equilib-rium.Stability criteria such as the zero-moment-pointhave been used to design optimal walking gaits 35.Dynamic gaiting and bounding also have beendemonstrated 36-38.Recent work 39,40 hasattempted to provide unifying mathematical tools forgait generation.Each of these planning algorithmswould be very effective in portions of a naturalclimbing environment with a sustained feature such asa long vertical crack of nearly uniform width.How-ever,something more is needed for irregular environ-ments such as the one studied in this paper,where thesurfaces on which the robot climbs are angled andplaced arbitrarily.Non-gaited planners use sensed information aboutthe environment to create feasible motion plans online.Most previous work on non-gaited motion planning forlegged robots has focused on a particular systemmodel,the spider robot.The limbs of a spider robot areassumed to be massless,which leads to elegantrepresentations of their free space for quasi-staticmotion based on support triangles 41-43.Thesemethods have been extended to planning dynamicmotions over rough terrain 44,45.The analysis usedin these methods breaks down,however,whenconsidering robots that do not satisfy the spider-robotassumption.For example,additional techniques werenecessary in 46,47 to plan non-gaited walkingmotions for humanoids,which clearly do not satisfythis assumption.To address the high number ofdegrees of freedom and the high branching factor ofthe discrete search through