机器人在自然地形下爬行【中文6940字】【PDF+中文WORD】

机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,机器人,自然,地形,爬行,中文,6940,PDF,WORD 【中文6940字】 机器人在自然地形下爬行 摘要：这篇文章展示了爬行机器人规划准静态动作的一种大致构造。把这种构造具体化是为了计算一种三足机器人在垂直自然地形中的爬行动作。在这里我们展示了通过模拟环境路径的例子。规划问题是五个对机器人系统发展的挑战中的一个，它可使机器人在自然地形上爬行。剩下的四个方面——硬件设计、控制、判断、抓握——仍在讨论中。 关键词：动作规划，爬行，机器人学，有足机器人，高危通道，自然地形 1 前言 这篇文章中描写的机器人爬行是发展核心技术成果的一部分，该技术能使一个自动化机器人的设计执行系统实现在垂直自然地形中的爬行。对我们而言，这种技术之前从未在机器人系统中得到证实。先前的方法能够处理好在人工地形爬行的问题，那些方法不是用特殊的装置吸附在地形表面，就是利用地形特殊的性质或特点。 发展这种机器人爬行技术将使我们对人类为什么能执行像在崎岖地形上攀爬这种复杂任务的理解更上一层楼。在今后精密机器人系统的发展中，将会证明这非常有益。精密机器人系统能够实现救助或代替人们在复杂地形上进行危险作业。这样的例子包括用机器人系统来搜救，侦察和探索行星。 在机器人能够真正在真实、垂直的自然地形下爬行前，需要解决许多问题。这篇文章考虑了这些问题中五个最主要的方面：硬件设计、控制、判断、规划和抓握。其中一个的问题，行动规划问题，被我们详尽的描述。爬行机器人的大致构造已经展示。这种构造被具体化来计算图1中展示的三足机器人的爬行动作。本图展示的是这个机器人在一种典型垂直环境下的模拟结果。 图1 三足机器人相爱自然垂直表面爬行 2 动机 在这个领域中的研究结果会使很多应用受益，也为一些相关的研究领域提供了帮助。 2.1 应用 写这篇文章是受到需要机器人系统有提供高危自然环境下的途径的能力的激励。 这样的系统有很多陆上的用途，例如搜救，探索洞穴，辅助人类攀岩和灵活的城市任务。每个都需要上升、下降或通过陡峭的斜坡和峭壁，因此可联想到的人类风险。 一些空间应用同样受益于这些先进的机器人系统。例如火星位置具有潜在的高科技价值已经在悬崖面上得到证实。通常，飞行机器人进入这些位置既不实际也不可行。因此，到达这些位置，机器人必须攀爬、下降或通过陡峭的斜坡。将来探索其它行星饿目标也许会需要进入同样崎岖的地形。 2.2 关联 为了进一步提高机器人在垂直自然地形上的发展，在这种领域中的研究结果能为一些相关领域提供重要的见解。例如，这项研究能引导使机器人走路或灵活的操作的更好的策略发展。人类攀岩者通常讨论提高平衡和在日常活动中扩大活动范围，因为他们会越来越精于运动。这种提高了的移动性通常被提及为“发现了新的自由”，并且与为极复杂的仿生机器人或数字化演员发现新的有用的机动性的想法有关。 同样，规划运算法则的发展对爬行机器人来说能产生一套更好的标准，是对这种类型机器人的设计的标准。这种运算法则能够用于模拟决定机器人的能力的候补设计，主要由此来选择设计。 3 主要问题 在陡峭的自然地形上爬行涉及5个主要问题：硬件设计、控制、判断、规划、抓握。诶过领域中需要做大量的工作来研发一个真正的爬行机器人。这个部分描述了最初的4个领域中的挑战；规划问题将在第四部分详细的讨论。 3.1 硬件设计 一个好的硬件设计能提升机器人的性能，并且常常会使其他的主要问题更容易解决。然而，过去硬件解决方法在维持平衡上的应用导致在能够通过饿地形受到限制。 有足的机器人已经被用来攀爬达到50度倾斜的自然峭壁，从75度倾斜的峭壁走下来，在粗糙地形上爬越小障碍。这些系统不是用了像[12，14-16]中的积极中断形式，就是如[1]绕绳下降。用有足绕绳的机器人[3，17]和类蛇机器人得到同样的结果。 这些行者费力的通过的地形是令人印象深刻的，但在现有的系统中没有一个显示有能力在90度倾斜或更倾斜的自然峭壁爬行。有足的行者和类蛇机器人有一个天生的抓握缺陷，这使它们不能用于攀爬连续的几乎垂直的自然峭壁，和从连续的过于垂直的自然峭壁上爬下。现有的有足机器人系统没有这种缺陷，但在通过缠绕绳子维持与峭壁的接触这个问题上仍然走了弯路。依靠这些绳子阻止了最初的悬崖的攀爬，并且限制了从悬崖上下来的倾角低于90度的峭壁级别。 现在多种机器人实现了在人工垂直表面上爬行。大多数机器人为了更好的抓握而利用表面的一些属性。例如，一些机器人用吸气杯或永磁铁来避免打滑[5-8]。其它的利用像阳台上的扶手。然而，这些被机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]用的简单的硬件设计没有这种限制。人们期望像这篇文章提出的规划问题的解决方法通过类似的系统允许爬基本的自然垂直地形，另外通过现有的系统爬管子，也期望解决方法会建议设计有更好性能的变体。 将来的研究可以解决其他类型的工具的应用问题，这些工具用于垂直自然表面的抓握，如钻孔用的工具或在岩石上安装其它用具的工具。 利用这些工具可以帮助解决更多有挑战性的爬壁问题，同样这些“辅助”可以帮助人类攀岩者[18,19]。然而，这些工具带来了新的问题，重量大，复杂，移动缓慢还有手限制的潜在应用。 3.2 控制 一个爬壁机器人的控制问题主要哟偶3个方面：维持平衡，末端打滑控制和末端压力控制。这3方面紧密相联。为了保持平衡，机器人的重心和来自自然特征接触的压力都要控制。这些接触的打滑控制与接触压力的大小和方向直接有关。 现有的控制技术，像那些基于操作空间程式的技术，可以形成一种对控制风格设计的基本途径，这种控制风格是对爬壁机器人而言的。然而，这些技术可以延伸成大量不同的方法来得到更好的性能。例如，将来的研究可能解决末端打滑控制器的设计问题，末端打滑控制器稳定与接触面弯曲部分的反映有关，而与只有一点接触的反应无关。 3.3 判断 对于控制和抓握来说，爬墙机器人必须具备根据重力方向、重心位置、来自于足间末端的接触面相关位置及尽力与自然地形接触的压力来判断自己身体的方向的能力。对于规划，机器人必须能够定位新的抓附点和产生对他们性质的说明，这可能需要衡量接触点打滑的程度。判断器的集成是个具有挑战性的问题，判断器的集成是为了获得并利用算法信息来进行控制、抓握和规划。 现有可行的设计解决方法可以引导每种情况中的一种基本途径的发展。例如，像在[21，22]中描述的判断器能够提供基本末端压力和衡量打滑程度，一种惯性单元和磁性指针能提供位置信息，一种观察系统可以提供大概的吸附位置和性质的描绘，编码器可以提供重心位置。然而每个判断器的提升，如性能、减重和减少经费，提出了供研究的开放领域。尽管在第4部分阐述的规划框架的性能，用更好的判断器信息会得到提升，但它并不依赖环境的完美模式。因为框架工作发展的很快，使在线供给器具和计划能在新判断器信息可用时合作。 3.4 抓握 爬壁机器人的性能依赖于吸附的能力或陡峭自然表面的特性。现在已经证明特殊的抓握项目依赖于地表的特殊性，如非常平滑的质地或支持，它不能用于自然地形。涉及在自然地形上抓握的问题在这部分会进一步探讨。 传统的抓握研究致力于拾起目标物或稳稳的抓住它。这个课题的研究可以追溯到1876年，这研究显示用一个小的4点无摩擦约束就可以稳稳的抓到一个平的目标物。更多近期这方面好的概述见[24，25]。在这领域有个重要的概念“压力终止”，被定义为“如果在单边接触中应用足够大的压力，能抵御目标物各方面的移动”的抓握。几乎所有抓握的研究都致力于选择、特性化、最优化的抓握，它有压力终止的性能。 然而，对于爬行抓握来说不需要压力终止。例如，一个机器人会发现像架子样的扶手可能很容易爬上去，即使这个抓握完全不能抵御来自其它方面的压力。鉴于这个原因，选择、特性化、最优化抓握的研究必须好好的发展来把它应用到爬壁机器人上。 描绘包括检测用于抓握的压力和扭矩的大小和方向。例如，对于一个点上的一个手指抓握，这个信息的合理描绘就是一个摩擦体，它将被用于在第四部分描述的规划运算法则。 描绘的想法还包括一个“质量因素”。抓握质量的措施已经被广泛研究，见于[26]。这项工作列出了8个灵活的措施，包括使连接角度的偏差最小，使最小单个抓握模型的价值最大化。其它的相关研究用了扭空间的概念。用这个概念，质量被定义为最大的扭转球，它可以满足抓握扭转单元。抓握扭转空间的体积或更多的专业椭球任务，可以用来当作质量措施。这些想法扩展了，包括限制最大接触压力和应用于抓握模拟器来计算用不同的三维手进行最好的抓握。 然而，抓握质量这个概念对于抓握来说没有定义好，没有提供压力终止。依靠一个攀岩者想走的方向，不同的抓握有不同的质量。而且，抓握质量一般包括安全或稳定性概念，这两个概念对于无压力终止抓握来说也没定义好。再者，依靠依靠应用压力的方向，抓握的安全性肯会改变。握住质量的概念应在有用的最优化可能之前定义。同时，传送信息到控制器或规划器，有必要有一个高效的方法来完成爬壁任务。 不同类型抓握的分类已经存在于人类攀登者的技巧中。在这个分类中，抓握首先被分成两种，一种是对矿穴、边缘和其它没有缝隙的垂直岩面而言的，另一种是对连续的垂直裂缝而言。图2中可以看到不同地貌和裂缝的抓握例子。对于如安全水平的条件，这种技巧让人联想到各种抓握的质量和用途饿一个大概想法，转矩可被施于一个手柄上，摩擦可被施于受力点。 不仅是在期待的直观质量上，同样清楚的是人类攀岩者在特殊情况下需要用到别处的抓握。长久以来“有多种不同的手柄，就有多少种方法去抓住它们”。然而，这种直观性是用来作为决定意义深远的定性标准的起点，这定性标准是为了抓握的选择和优化。 这种爬壁技巧与过去的机器人抓握规划的比较揭示出这两种应用间的几种其它主要不同之处，这对将来的研究很重要。例如很多爬壁手柄很小，所以爬壁抓握时的手指常常为了与目标物而拥有大直径。机器人抓握技巧首先认同小直径的手指也可抓目标物的情况。另外，像图2中展示的一些爬壁抓握姿势，都是基于裂缝中的手指。这项技术与机器人拾起目标物的技术有不同，它需要高灵活性和小自由度来使手指伸入裂缝。清楚的是，连续的爬壁机器人研究工作最终将引起更多的考虑抓握中的新问题。 (a) (b) (c) (d) 图2 四种不同的人类攀登抓握在(a)无阻碍的抓握，(b)卷曲的抓握，(c)手指锁住抓握和(d)夹缝中抓握。 4 规划 规划问题是爬壁机器人在自然地形爬行的第五个主要挑战。这部分展示的移动规划框架细节见[32]。 4.1 挑战 爬壁机器人的规划问题包括产生一条轨迹使机器人保持平衡的通过垂直地形。 这个问题对人类攀岩者来说也是个挑战。攀岩长久以来被描述成一个“伟大的挑战，每个攀岩路线的次序和方案都是独特的，都是解决精力和体力问题的设计”。一个独特路线包含大量不同的“移动”，其中一些移动见图3.每个移动对保持平衡来说都是成熟技术。除了这些妙想，通过大量特殊身体位置的移动也许是爬行进步到最高的必要条件。 在实际爬行前Graydon和Hanson就已经注意到规划一系列移动的重要性，他们认为攀岩者“在攀爬签会鉴定和检查不同的地貌，计划好然后迅速的爬越它们”。人们这种做法的动机主要是为了使每次移动所耗能量达到最小和节省能量，因为大多数人没有足够的体力和耐力。 规划问题对机器人来说是类似的。机器人装有驱动装置，这可以在短时间内运用高转矩，所以在爬行之前规划好移动顺序对机器人系统而言同样重要。同样，爬壁机器人要受制于同样困难的平衡限制，并且需要在类似的可能移动范围内选择。因此，规划算法的发展对一个自动化爬壁机器人来说是一个非常有挑战性的问题。 (a) (b) (c) 图3 三种不同的人类攀爬移动（a）撤步（b）逆向行进（c）向上行进 4.2 相关工作 爬壁机器人的搜索范围是一个混合的范围，包括连续的动作和分散的动作。通过连续动作范围许多不同方法对移动规划可行，包括电池分解。潜在领域和路线图算法。分散动作可直接包括在这些方法中，例如路线图算法中结扩展的水平，但这种方法一般会导致执行的减缓，特别是对特殊系统。 为有腿机器人做的移动规划的前期工作已经开发出了解决一些系统混合搜索范围的工具。无论是不是脱机作规划，这项工作都可以分类，这是为了产生一种反应性的步法或联机，为了考虑到敏感环境下的无步移动。 步态规划着认为在平稳的环境中可以创造一种预先定义的脱机走路方式。这种方式用到一组或行为来控制机器人联机，这基于近期传感器输入的信息。[2，11]用到了步态规划，例如，设计爬管子的方式。其它像[34]样的方法是基于为了保持平衡的支撑三角形的想法。 稳定标准如零状态点已经用于设计最优步态。有活力的步态和跳跃已经被证实了。近期的工作是试图提供统一的精确的工具为了产生步态。每个规划的运算法则在一部分自然爬行环境下很有效果，这自然爬行环境有连续的特色，如几乎一样宽的长垂直裂缝。然而，在不规则的环境下爬行，如这篇文章研究的环境，机器人爬行饿表面是有角度的，任意固定的表面需要更多的技巧。 费步态规划着用于关于环境的相关信息来创造可行的联机步态计划。为有足机器人做的关于非步态行动的大部分前期工作专注于一个特别的系统样式，蜘蛛机器人。蜘蛛机器人的足被假定成很轻的，这引起了它们自由空间的一流表现，为了基于支撑三角形的准静态动作[44,45]。然而，当考虑到机器人不能满足蜘蛛机器人的假设，这些方法中用到的分析方法就终止了。例如，在[46，47]中为人类机器人规划非步态走路动作附加技术是必须的。这篇文章探究的是一个具有少量自由度的机器人在一个更加有条理的搜索空间，那里比用启发式方法更有可能获得更好的性能。尽管这算法意味着创造“真实”而不是严格可行的动作，在为性格特征设计行动规划算法时，[48]呈现了类似的问题。 在为有足运动、抓握和机器人操作的非步态动作规划中存在类似之处，特别是在操作概念上[24,49-51]。两种规划都需要作出分散和连续的选择。 所有现有的规划技术都不足以解决甚至是在自然环境中最简单的爬行问题。在自然环境中，准静态移动，准确的信息和单指抓握一点手柄都被采用。如果准静态和准确信息的采用是松懈的，考虑更多复杂的抓握，这个问题会越来越复杂。 4.3 规划框架 在这部分，我们将描述图上展示的一种特殊爬壁机器人的规划框架。这个机器人有三条腿，每条腿有两个关节，一个在机器人的中心，一个在腿的中点。动作被认为是准静态的，伴随重力发生在垂直平面。这种机器人运动学的低复杂性使它适合于研究爬行动作的规划。 地形是垂直平面，附有一堆小的、有角度的平表面，叫做“手柄”，它们是任意分布的。每个机器人腿的末端都可以在每个手柄拉或推一个点，产生摩擦防止打滑。 机器人的爬行动作包括连续的步伐。任意两个连贯的步伐之间，三个腿末端接触到不同的支撑。每一个步伐中，腿从一个支撑移动到另一个支撑，另两个末端仍可固定。机器人可以用两个相当的脚形成的连接中的自由度来维持准静态平衡和防止在两个相当的支撑间打滑。另外，走一步时，任意一个连接处的扭矩不能超过控制装置的极限，脚之间也不能相互碰撞。这些限制决定了机器人每走一步的外形轮廓的可用子设备。这子设备中的一条路线决定了一步动作。 所有的计划问题如下：一个给定的地形，依赖一对手柄和一个目标支撑的最初的机器人外形产生了一系列一步的动作，这将使机器人在准静态平衡上从最初外形到最后外形，在最后外形下一脚的末端与目标手柄接触。 [32]中我们展示了解决这规划问题的框架的细节。这个框架可简说如下。 首先，我们展示了三足爬壁机器人的一步动作的详尽的分析。连续结构的属性已经设定了，将被用来定义机器人在每对支撑下的可用集。特别的，当规划一个二维的子空间时，机器人的4维连续可用范围的连贯性可以保留。这个结果精简了一步规划问题的复杂程度并且导致了一个快捷联机饿执行实现。 然后，所有的规划者将这种“本地规划者”与灵活的搜索技术结合起来来决定对目标支撑技术而言的最初外形的一系列支撑。这启示性的方法来自于观察人类攀岩者规划他们的动作。 4.4 结果 [32]中展示的成果不是对特殊垂直环境模拟结果中的一组。这篇文章我们将展示在一个更具挑战性的环境中的第二组结果。图4中展示的环境，包括随机固定的、有角的支撑。机器最先定位于这环境底部的两个支撑，它被要求达到顶点的两个支撑。 图4 三足机器人在垂直环境爬行的例子 用一个450MHZ的处理器3秒内就可以找到一个计划，对一个包含50个支撑的环境来说非常典型。为更小的环境规划时间。 图5中展示了一个不同的连续结构，来自于每个规划次序的一步动作。许多这类的结构明显与人类的结构相似。例如，图5（a）中展示的结构与图3（b）展示的类似。另外，图5（i）和（n）描述的结构分别与图3（a）中的“后退”和图3（c）中的“高步”类似。 图5中每个框架都展示了平衡区域，这是对机器人站立支撑而言的。这个区域机器人在不打滑情况下保持平衡重心可以移动，而且是一个对机器人平衡限制的完全说明书。注意在每个结构展示中，机器人重心存在于平衡区域。 更多资讯，包括可视3动画，请访问http://arl.stanford.edu/~tbretl/ 图5 展示的动作是机器人在图4环境下动作。每幅图中的园点是机器人的重心 5 结论 这篇文章描述了发展自动化爬壁机器人的挑战，提出了解决规划问题的框架。 近期的工作是解决对一个真实机器人系统而言的规划框架的应用。作为部分努力，这框架已经扩展到处理额外的动作限制，更加复杂的机器人几何系统，不理想的环境和三维地形。 以后的工作将解决其它4个主要问题——硬件设计、控制、判断、抓握及它们对规划问题的关系。 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 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