机器人外文翻译

第一篇：机器人外文翻译

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机 器 人

工业机器人是在生产环境中以提高生产效率的工具，它能做常规乏味的装配线工作，或能做那些对于工人来说是危险的工作，例如，第一代工业机器人是用来在 核电站中更换核燃料棒，如果人去做这项工作，将会遭受有害的放射线的辐射。工业机器人亦能工作在装配线上将小元件装配到一起，如将电子元件安放在电路印制板，这样，工人就能从这项乏味的常规工作中解放出来。机器人也能按程序要求用来拆除炸弹，辅助残疾人，在社会的很多应用场合下履行职能。

机器人可以认为是将手臂末端的工具、传感器和（或）手爪移到程序指定位置的一种机器。当机器人到达位置后，它将执行某种任务。这些任务可以是焊接、密封、机器装料、拆卸以及装配工作。除了编程以及系统的开停之外，一般来说这些工作可以在无人干预下完成。如下叙述的是机器人系统基本术语：

1.机器人是一个可编程、多功能的机械手，通过给要完成的不同任务编制各种动作，它可以移动零件、材料、工具以及特殊装置。这个基本定义引导出后续段落的其他定义，从而描绘出一个完整的机器人系统。

2.预编程位置点是机器人为完成工作而必须跟踪的轨迹。在某些位

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置点上机器人将停下来做某些操作，如装配零件、喷涂油漆或焊接。这些预编程点贮存在机器人的贮存器中，并为后续的连续操作所调用，而且这些预编程点想其他程序数据一样，可在日后随工作需要而变化。因而，正是这种编程的特征，一个工业机器 人很像一台计算机，数据可在这里储存、后续调用与编译。

3.机器手是机器人的手臂，它使机器人能弯曲、延伸和旋转，提供这些运动的是机器手的轴，亦是所谓的机器人的自由度。一个机器人能有3~16轴，自由度一词总是与机器人轴数相关。

4.工具和手爪不是机器人自身组成部分，但它们是安装在机器人手臂末端的附件。这些连在机器人手臂末端的附件可使机器人抬起工件、点焊、刷漆、电弧焊、钻孔、打毛刺以及根据机器人的要求去做各种各样的工作。

5.机器人系统还可以控制机器人的工作单元，工作单元是机器人执行任务所处的整体环境，该单元包括控制器、机械手、工作平台、安全保护装置或者传输装置。所有这些为保证机器人完成自己任务而必须的装置都包括在这一工作单元中。另外，来自外设的信号与机器人通讯，通知机器人何时装配工件、取工件或放工件到传输装置上。机器人系统有三个基本部件：机械手、控制器和动力源。

A.机械手

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机械手做机器人系统中粗重工作，它包括两个部分：机构与附件，机械手也用联接附件基座，图21-1表示了一机器人基座与附件之间的联接情况。

机械手基座通常固定在工作区域的地基上，有时基座也可以移动，在这种情况下基座安装在导轨回轨道上，允许机械手从一个位置移到另外一个位置。

正如前面所提到的那样，附件从机器人基座上延伸出来，附件就是机器人的手臂，它可以是直动型，也可以是轴节型手臂，轴节型手臂也是大家所知的关节型手臂。

机械臂使机械手产生各轴的运动。这些轴连在一个安装基座上，然后再连到拖架上，拖架确保机械手停留在某一位置。

在手臂的末端上，连接着手腕（图21-1），手腕由辅助轴和手腕凸缘组成，手腕是让机器人用户在手腕凸缘上安装不同的工具来做不同的工作。

机械手的轴使机械手在某一区域内执行任务，我们将这个区域为机器人的工作单元，该区域的大小与机械手的尺寸相对应，图21-2列举了一个典型装配机器人的工作单元。随着机器人机械结构尺寸的增加，工作单元的范围也必须相应的增加。

机械手的运动有执行元件或驱动系统来控制。执行元件或驱动系统

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允许各轴力经机构转变为机械能，驱动系统与机械传动链相匹配。由链、齿轮和滚珠丝杠组成的机械传动链驱动着机器人的各轴。

B.控制器

机器人控制器是工作单元的核心。控制器储存着预编程序供后续调用、控制外设，及与厂内计算机进行通讯以满足产品更新的需要。

控制器用于控制机械手运动和在工作单元内控制机器人外设。用户可通过手持的示教盒将机械手运动的程序编入控制器。这些信息储存在控制器的储存器中以备后续调用，控制器储存了机器人系统的所有编程数据，它能储存几个不同的程序，并且所有这些程序均能编辑。

控制器要求能够在工作单元内与外设进行通信。例如控制器有一个输入端，它能标识某个机加工操作何时完成。当该加工循环完成后，输入端接通，告诉控制器定位机械手以便能抓取已加工工件，随后，机械手抓取一未加工件，将其放置在机床上。接着，控制器给机床发出开始加工的信号。

控制器可以由根据事件顺序而步进的机械式轮鼓组成，这种类型的控制器可用在非常简单的机械系统中。用于大多数机器人系统中的控制器代表现代电子学的水平，是更复杂的装置，即它们是由微处理器操纵的。这些微处理器可以是8位、16位或32位处理器。它们可以使得控制器在操作过程中显得非常柔性。

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控制器能通过通信线发送电信号，使它能与机械手各轴交流信息，在机器人的机械手和控制器之间的双向交流信息可以保持系统操作和位置经常更新，控制器亦能控制安装在机器人手腕上的任何工具。

控制器也有与厂内各计算机进行通信的任务，这种通信联系使机器人成为计算机辅助制造（CAM）系统的一个组成部分。

存储器。给予微处理器的系统运行时要与固态的存储装置相连，这些存储装置可以是磁泡，随机存储器、软盘、磁带等。每种记忆存储装置均能贮存、编辑信息以备后续调用和编辑。

C.动力源

动力源是给机器人和机械手提供动力的单元。传给机器人系统的动力源有两种，一种是用于控制器的交流电，另一种是用于驱动机械手各轴的动力源，例如，如果机器人的机械手是有液压和气压驱动的，控制信号便传送到这些装置中，驱动机器人运动。

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液压与气压系统

仅有以下三种基本方法传递动力：电气，机械和流体。大多数应用系统实际上是将三种方法组合起来而得到最有效的最全面的系统。为了合理地确定采取哪种方法。重要的是了解各种方法的显著特征。例如液压系统在长距离上比机械系统更能经济地传递动力。然而液压系统与电气系统相比，传递动力的距离较短。

液压动力传递系统涉及电动机，调节装置和压力和流量控制，总的来说，该系统包括：

泵：将原动机的能量转换成作用在执行部件上的液压能。阀：控制泵产生流体的运动方向、产生的功率的大小，以及到达执行部件流体的流量。功率大小取决于对流量和压力大小的控制。

执行部件：将液压能转成可用的机械能。

介质即油液：可进行无压缩传递和控制，同时可以润滑部件，使阀体密封和系统冷却。

联接件：联接各个系统部件，为压力流体提供功率传输通路，将液体返回油箱（贮油器）。

油液贮存和调节装置：用来确保提供足够质量和数量并冷却的液体。

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液压系统在工业中应用广泛。例如冲压`钢类工件的磨削几一般加工业、农业、矿业、航天技术、深海勘探、运输、海洋技术，近海天然气和石油勘探等行业，简而言之，在日常生活中有人不从液压技术中得到某种益处。

液压系统成功而又广泛使用的秘密在于它的通用性和易操作性。液压动力传递不会象机械系统那样受到机器几何形状的制约，另外，液压系统不会像电气系统那样受到材料物理性能的制约，它对传递功率几乎没有量的限制。例如，一个电磁体的性能受到钢的磁饱和极限的限制，相反，液压系统的功率仅仅受材料强度的限制。

企业为了提高生产率将越来越依靠自动化，这包括远程和直接控制生产操作、加工过程和材料处理等。液压动力之所以成为自动化的组成部分，是因为它有如下主要的特点：

1.控制方便精确

通过一个简单的操作杆和按扭，液压系统的操作者便能立即起动，停止、加减速和能提供任意功率、位置精度为万分之一英寸的位置控制力。图13-1是一个使飞机驾驶员升起和落下起落架的液压系统，当飞行向某方向移动控制阀，压力油流入液压缸的某一腔从而降下起落架。飞行员向反方向移动控制阀，允许油液进入液压缸的另一腔，便收回起落架。

2.增力 一个液压系统（没有使用笨重的齿轮、滑轮和杠杆）能简单

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有效地将不到一盎司的力放大产生几百吨的输出。

3.恒力或恒扭矩

只有液压系统能提供不随速度变化而变化的恒力或恒扭矩，他可以驱动对象从每小时移动几英寸到每分钟几百英寸，从每小时几转到每分钟几千转。

4.简便、安全、经济

总的来说，液压系统比机械或电气系统使用更少的运动部件，因此，它们运行与维护简便。这使得系统结构紧凑，安全可靠。例如 一种用于车辆上的新型动力转向控制装置一淘汰其他类型的转向动力装置，该转向部件中包含有人力操纵方向控制阀和分配器。因为转向部件是全液压的，没有方向节、轴承、减速齿轮等机械连接，使得系统简单紧凑。

另外，只需要输入很小的扭矩就能产生满足极其恶劣的工作条件所需的控制力，这对于因操作空间限制而需要小方向盘的场合很重要，这也是减轻司机疲劳度所必须的。

液压系统的其他优点包括双向运动、过载保护和无级变速控制，在已有的任何动力、系统中液压系统也具有最大的单位质量功率比。

尽管液压系统具有如此的高性能，但它不是可以解决所有动力传递问题的灵丹妙药。液压系统也有缺点，液压油有污染，并且泄露不可能完全避免，另外如果油液渗漏发生在灼热设备附近，大多数液压油能引起火灾。

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气压系统

气压系统是用压力气体传递和控制动力，正如名称所表明的那样，气压系统通常用空气（不用其他气体）作为流体介质，因为空气是安全、成本低而又随处可得的流体，在系统部件中产生电弧有可能点燃泄露物的场合下（使用空气作为介质）尤其安全。

在气压系统中，压缩机用来压缩并提供所需的空气。压缩机一般有活塞式、叶片式和螺旋式等类型。压缩机基本上是根据理想气体法则，通过减小气体体积来增加气体压力的。气压系统通常考虑采用大的中央空气压缩机作为一个无限量的气源，这类似于电力系统中只要将插头插入插座边可获得电能。用这种方法，压力气体可以总气体源输送到整个工厂的各个角落，压力气体可通过空气滤清器除去污物，这些污染可能会损坏气动组件的精密配合部件如阀和汽缸等，随后输送到各个回路中，接着空气流经减压阀以减小气压值适合某一回路使用。因为空气不是好的润滑油，气压系统需要一个油雾器将细小的油雾注射到经过减压阀减压空气中，这有帮助于减少气动组件精密配合运动件的磨损。

由于来自大气中的空气含不同数量的水分，这些水分是有害的，它可以带走润滑剂引起的过分磨损和腐蚀，因此，在一些使用场合中，要用空气干燥器来除去这些有还的水分。由于气压系统直接向大气排

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气，会产生过大的噪声，因此可在气阀和执行组件排气口安装销声器来降低噪声，以防止操作人员因接触噪声及高速空气粒子有可能引发的伤害。

用气动系统代替液压系统有以下几条理由：液体的惯性远比气体大，因此，在液压系统中，当执行组件加速减速和阀突然开启关闭时，油液的质量更是一个潜在的问题，根据牛顿运动定律，产生加速度运动油液所需的力要比加速同等体积空气所需的力高出许多倍。液体比气体具有更大的粘性，这会因为内摩擦而引起更大的压力和功率损失；另外，由于液压系统使用的液体要与大气隔绝，故它们需要特殊的油箱和无泄露系统设计。气压系统使用可以直接排到周围环境中的空气，一般来说气压系统没有液体系统昂贵。

然而，由于空气的可压缩性，使得气压系统执行组件不可能得到精确的速度控制和位置控制。气压系统由于压缩机局限，其系统压力相当低（低于250psi），而液压力可达1000psi之高，因此液压系统可以是大功率系统，而气动系统仅用于小功率系统，典型例子有冲压、钻孔、夹紧、组装、铆接、材料处理和逻辑控制操作等。

第二篇：智能机器人外文翻译

Robot Robot is a type of mechantronics equipment which synthesizes the last research achievement of engine and precision engine, micro-electronics and computer, automation control and drive, sensor and message dispose and artificial intelligence and so on.With the development of economic and the demand for automation control, robot technology is developed quickly and all types of the robots products are come into being.The practicality use of robot products not only solves the problems which are difficult to operate for human being, but also advances the industrial automation program.At present, the research and development of robot involves several kinds of technology and the robot system configuration is so complex that the cost at large is high which to a certain extent limit the robot abroad use.To development economic practicality and high reliability robot system will be value to robot social application and economy development.With the rapid progress with the control economy and expanding of the modern cities, the let of sewage is increasing quickly: With the development of modern technology and the enhancement of consciousness about environment reserve, more and more people realized the importance and urgent of sewage disposal.Active bacteria method is an effective technique for sewage disposal，The lacunaris plastic is an effective basement for active bacteria adhesion for sewage disposal.The abundance requirement for lacunaris plastic makes it is a consequent for the plastic producing with automation and high productivity.Therefore, it is very necessary to design a manipulator that can automatically fulfill the plastic holding.With the analysis of the problems in the design of the plastic holding manipulator and synthesizing the robot research and development condition in recent years, a economic scheme is concluded on the basis of the analysis of mechanical configuration, transform system, drive device and control system and guided by the idea of the characteristic and complex of mechanical configuration, electronic, software and hardware.In this article, the mechanical configuration combines the character of direction coordinate and the arthrosis coordinate which can improve the stability and operation flexibility of the system.The main function of the transmission mechanism is to transmit power to implement department and complete the necessary movement.In this transmission structure, the screw transmission mechanism transmits the rotary motion into linear motion.Worm gear can give vary transmission ratio.Both of the transmission mechanisms have a characteristic of compact structure.The design of drive system often is limited by the environment condition and the factor of cost and technical lever.'The step motor can receive digital signal directly and has the ability to response outer environment immediately and has no accumulation error, which often is used in driving system.In this driving system, open-loop control system is composed of stepping motor, which can satisfy the demand not only for control precision but also for the target of economic and practicality.on this basis, the analysis of stepping motor in power calculating and style selecting is also given.The analysis of kinematics and dynamics for object holding manipulator is given in completing the design of mechanical structure and drive system.Kinematics analysis is the basis of path programming and track control.The positive and reverse analysis of manipulator gives the relationship between manipulator space and drive space in position and speed.The relationship between manipulator’s tip position and arthrosis angles is concluded by coordinate transform method.The geometry method is used in solving inverse kinematics problem and the result will provide theory evidence for control system.The f0unction of dynamics is to get the relationship between the movement and force and the target is to satisfy the demand of real time control.in this chamfer, Newton-Euripides method is used in analysis dynamic problem of the cleaning robot and the arthrosis force and torque are given which provide the foundation for step motor selecting and structure dynamic optimal ting.Control system is the key and core part of the object holding manipulator system design which will direct effect the reliability and practicality of the robot system in the division of configuration and control function and also will effect or limit the development cost and cycle.With the demand of the PCL-839 card, the PC computer which has a.tight structure and is easy to be extended is used as the principal computer cell and takes the function of system initialization, data operation and dispose, step motor drive and error diagnose and so on.A t the same time, the configuration structure features, task principles and the position function with high precision of the control card PCL-839 are analyzed.Hardware is the matter foundation of the control.System and the software is the spirit of the control system.The target of the software is to combine all the parts in optimizing style and to improve the efficiency and reliability of the control system.The software design of the object holding manipulator control system is divided into several blocks such as 2 system initialization block, data process block and error station detect and dispose model and so on.PCL-839 card can solve the communication between the main computer and the control cells and take the measure of reducing the influence of the outer signal to the control system.The start and stop frequency of the step motor is far lower than the maximum running frequency.In order to improve the efficiency of the step motor, the increase and decrease of the speed is must considered when the step motor running in high speed and start or stop with great acceleration.The increase and decrease of the motor’s speed can be controlled by the pulse frequency sent to the step motor drive with a rational method.This can be implemented either by hardware or by software.A step motor shift control method is proposed, which is simple to calculate, easy to realize and the theory means is straightforward.The motor' s acceleration can fit the torque-frequency curve properly with this method.And the amount of calculation load is less than the linear acceleration shift control method and the method which is based on the exponential rule to change speed.The method is tested by experiment.At last, the research content and the achievement are sum up and the problems and shortages in main the content are also listed.The development and application of robot in the future is expected.机器人

机器人是典型的机电一体化装置，它综合运用了机械与精密机械、微电子与计算机、自动控制与驱动、传感器与信息处理以及人工智能等多学科的最新研究成果，随着经济的发展和各行各业对自动化程度要求的提高，机器人技术得到了迅速发展，出现了各种各样的机器人产品。机器人产品的实用化，既解决了许多单靠人力难以解决的实际问题，又促进了工业自动化的进程。目前，由于机器人的研制和开发涉及多方面的技术，系统结构复杂，开发和研制的成本普遍较高，在某种程度上限制了该项技术的广泛应用，因此，研制经济型、实用化、高可靠性机器人系统具有广泛的社会现实意义和经济价值。

由于我国经济建设和城市化的快速发展，城市污水排放量增长很快，污水处理己经摆在了人们的议事日程上来。随着科学技术的发展和人类知识水平的提高，人们越来越认识到污水处理的重要性和迫切性，科学家和研究人员发现塑料制品在水中是用于污水处理的很有效的污泥菌群的附着体。塑料制品的大量需求，使得塑料制品生产的自动化和高效率要求成为经济发展的必然。

本文结合塑料一次挤出成型机和塑料抓取机械手的研制过程中出现的问题，综述近几年机器人技术研究和发展的状况，在充分发挥机、电、软、硬件各自特点和优势互补的基础上，对物料抓取机械手整体机械结构、传动系统、驱动装置和控制系统进行了分析和设计，提出了一套经济型设计方案。采用直角坐标和关节坐标相结合的框架式机械结构形式，这种方式能够提高系统的稳定性和操作灵活性。传动装置的作用是将驱动元件的动力传递给机器人机械手相应的执行机构，以实现各种必要的运动，传动方式上采用结构紧凑、传动比大的蜗轮蜗杆传动和将旋转运动转换为直线运动的螺旋传动。机械手驱动系统的设计往往受到作业环境条件的限制，同时也要考虑价格因素的影响以及能够达到的技术水平。由于步进电机能够直接接收数字量，响应速度快而且工作可靠并无累积误差，常用作数字控制系统驱动机构的动力元件，因此，在驱动装置中采用由步进电机构成的开环控制方式，这种方式既能满足控制精度的要求，又能达到经济性、实用化目的，在此基础上，对步进电机的功率计一算及选型问题经行了分析。

在完成机械结构和驱动系统设计的基础上，对物料抓取机械手运动学和动力学进行了分析。运动学分析是路径规划和轨迹控制的基础，对操作臂进行了运动学正、逆问题的分析可以完成操作空间位置和速度向驱动空间的映射，采用齐次坐标变换法得到了操作臂末端位置和姿态随关节夹角之间的变换关系，采用几何法分析了操作臂的逆向运动学方程求解问题，对控制系统设计提供了理论依据。机器人动力学是研究物体的运动和作用力之间的关系的科学，研究的目的是为了4 满足是实时性控制的需要，本文采用牛顿-欧拉方法对物料抓取机械手动力学进行了分析，计算出了关节力和关节力矩，为步进电机的选型和动力学分析与结构优化提供理论依据。

控制部分是整个物料抓取机械手系统设计关键和核心，它在结构和功能上的划分和实现直接关系到机器人系统的可靠性、实用性，也影响和制约机械手系统的研制成本和开发周期。在控制主机的选用上，采用结构紧凑、扩展功能强和可靠性高的PC工业控制计算机作为主机，配以PCL-839卡主要承担系统功能初始化、数据运算与处理、步进电机驱动以及故障诊断等功能;同时对PCL-839卡的结构特点、功能原理和其高定位功能等给与了分析。硬件是整个控制系统以及极限位置功能赖以存在的物质基础，软件则是计算机控制系统的神经中枢，软件设计的目的是以最优的方式将各部分功能有机的结合起来，使系统具有较高的运行效率和较强的可靠性。在物料抓取机械手软件的设计上，采用的是模块化结构，分为系统初始化模块、数据处理模块和故障状态检测与处理等几部分。主控计算机和各控制单元之间全部由PCL-839卡联系，并且由该卡实现抗干扰等问题，减少外部信号对系统的影响。

步进电机的启停频率远远小于其最高运行频率，为了提高工作效率，需要步进电机高速运行并快速启停时，必须考虑它的升，降速控制问题。电机的升降速控制可以归结为以某种合理的力一式控制发送到步进电机驱动器的脉冲频率，这可由硬件实现，也可由软件方法来实现。本文提出了一种算法简单、易于实现、理论意义明确的步进电机变速控制策略:定时器常量修改变速控制方案。该方法能使步进电机加速度与其力矩——频率曲线较好地拟合，从而提高变速效率。而且它的计算量比线性加速度变速和基于指数规律加速度的变速控制小得多。通过实验证明了该方法的有效性。

最后，对论文主要研究内容和取得的技术成果进行了总结，提出了存在的问题和不足，同时对机器人技术的发展和应用进行了展望。

第三篇：机器人算法外文翻译

Improved Genetic Algorithm and Its Performance Analysis

Abstract: Although genetic algorithm has become very famous with its global searching, parallel computing, better robustness, and not needing differential information during evolution.However, it also has some demerits, such as slow convergence speed.In this paper, based on several general theorems, an improved genetic algorithm using variant chromosome length and probability of crossover and mutation is proposed, and its main idea is as follows : at the beginning of evolution, our solution with shorter length chromosome and higher probability of crossover and mutation;and at the vicinity of global optimum, with longer length chromosome and lower probability of crossover and mutation.Finally, testing with some critical functions shows that our solution can improve the convergence speed of genetic algorithm significantly , its comprehensive performance is better than that of the genetic algorithm which only reserves the best individual.Genetic algorithm is an adaptive searching technique based on a selection and reproduction mechanism found in the natural evolution process, and it was pioneered by Holland in the 1970s.It has become very famous with its global searching, parallel computing, better robustness, and not needing differential information during evolution.However, it also has some demerits, such as poor local searching, premature converging, as well as slow convergence speed.In recent years, these problems have been studied.In this paper, an improved genetic algorithm with variant chromosome length and variant probability is proposed.Testing with some critical functions shows that it can improve the convergence speed significantly, and its comprehensive performance is better than that of the genetic algorithm which only reserves the best individual.In section 1, our new approach is proposed.Through optimization examples, in section 2, the efficiency of our algorithm is compared with the genetic algorithm which only reserves the best individual.And section 3 gives out the conclusions.Finally, some proofs of relative theorems are collected and presented in appendix.Description of the algorithm 1.1 Some theorems Before proposing our approach, we give out some general theorems(see

appendix)as follows: Let us assume there is just one variable(multivariable can be divided into many sections, one section for one variable)x ∈ [ a, b ] , x ∈ R, and chromosome length with binary encoding is 1.Theorem 1

Minimal resolution of chromosome is s = ba 2l1Theorem 2

Weight value of the ith bit of chromosome is

wi = bai1(i = 1,2,…l)2l1Theorem 3

Mathematical expectation Ec(x)of chromosome searching step with one-point crossover is Ec(x)= baPc 2lwhere Pc is the probability of crossover.Theorem 4

Mathematical expectation Em(x)of chromosome searching step with bit mutation is Em(x)=(b-a)Pm

1.2 Mechanism of algorithm

During evolutionary process, we presume that value domains of variable are fixed, and the probability of crossover is a constant, so from Theorem 1 and 3, we know that the longer chromosome length is, the smaller searching step of chromosome, and the higher resolution;and vice versa.Meanwhile, crossover probability is in direct proportion to searching step.From Theorem 4, changing the length of chromosome does not affect searching step of mutation, while mutation probability is also in direct proportion to searching step.At the beginning of evolution, shorter length chromosome(can be too shorter, otherwise it is harmful to population diversity)and higher probability of crossover and mutation increases searching step, which can carry out greater domain searching, and avoid falling into local optimum.While at the vicinity of global optimum, longer length chromosome and lower probability of crossover and mutation will decrease searching step, and longer length chromosome also improves resolution of mutation, which avoid wandering near the global optimum, and speeds up algorithm

converging.Finally, it should be pointed out that chromosome length changing keeps individual fitness unchanged, hence it does not affect select ion(with roulette wheel selection).1.3 Description of the algorithm

Owing to basic genetic algorithm not converging on the global optimum, while the genetic algorithm which reserves the best individual at current generation can, our approach adopts this policy.During evolutionary process, we track cumulative average of individual average fitness up to current generation.It is written as 1X(t)= GGft1avg(t)where G is the current evolutionary generation, fitness.favg is individual average When the cumulative average fitness increases to k times(k> 1, k ∈ R)of initial individual average fitness, we change chromosome length to m times(m is a positive integer)of itself , and reduce probability of crossover and mutation, which can improve individual resolution and reduce searching step, and speed up algorithm converging.The procedure is as follows:

Step 1 Initialize population, and calculate individual average fitness and set change parameter flag.Flag equal to 1.favg0, Step 2 Based on reserving the best individual of current generation, carry out selection, regeneration, crossover and mutation, and calculate cumulative average of individual average fitness up to current generation

favg;

favgStep 3 If

favg0≥k and Flag equals 1, increase chromosome length to m times of itself, and reduce probability of crossover and mutation, and set Flag equal to 0;otherwise continue evolving.Step 4 If end condition is satisfied, stop;otherwise go to Step 2.2 Test and analysis

We adopt the following two critical functions to test our approach, and compare it with the genetic algorithm which only reserves the best individual: f1(x,y)0.5sin2x2y20.5[10.01xy222]

x,y∈ [5,5]

[1,1] f2(x,y)4(x22y20.3cos(3πx)0.4cos(4πy))

x,y∈2.1 Analysis of convergence During function testing, we carry out the following policies: roulette wheel select ion, one point crossover, bit mutation, and the size of population is 60, l is chromosome length, Pc and Pm are the probability of crossover and mutation respectively.And we randomly select four genetic algorithms reserving best individual with various fixed chromosome length and probability of crossover and mutation to compare with our approach.Tab.1 gives the average converging generation in 100 tests.In our approach, we adopt initial parameter l0= 10, Pc0= 0.3, Pm0= 0.1 and k= 1.2, when changing parameter condition is satisfied, we adjust parameters to l= 30, Pc= 0.1, Pm= 0.01.From Tab.1, we know that our approach improves convergence speed of genetic algorithm significantly and it accords with above analysis.2.2 Analysis of online and offline performance

Quantitative evaluation methods of genetic algorithm are proposed by Dejong, including online and offline performance.The former tests dynamic performance;and the latter evaluates convergence performance.To better analyze online and offline performance of testing function, w e multiply fitness of each individual by 10, and we give a curve of 4 000 and 1 000 generations for f1 and f2, respectively.(a)online

(b)online

Fig.1 Online and offline performance of f1

(a)online

(b)online

Fig.2 Online and offline performance of f2

From Fig.1 and Fig.2, we know that online performance of our approach is just little worse than that of the fourth case, but it is much better than that of the second, third and fifth case, whose online performances are nearly the same.At the same time, offline performance of our approach is better than that of other four cases.Conclusion In this paper, based on some general theorems, an improved genetic algorithm using variant chromosome length and probability of crossover and mutation is proposed.Testing with some critical functions shows that it can improve convergence speed of genetic algorithm significantly, and its comprehensive performance is better than that of the genetic algorithm which only reserves the best individual.Appendix With the supposed conditions of section 1, we know that the validation of Theorem 1 and Theorem 2 are obvious.Theorem 3 Mathematical expectation Ec(x)of chromosome searching step with one point crossover is baPc2lEc(x)=

where Pc is the probability of crossover.Proof

As shown in Fig.A1, we assume that crossover happens on the kth locus, i.e.parent’s locus from k to l do not change, and genes on the locus from 1 to k are exchanged.1During crossover, change probability of genes on the locus from 1 to k is 2

(“1” to “0” or “0” to “1”).So, after crossover, mathematical expectation of chromosome searching step on locus from 1 to k is

k11ba1baEck(x)wjl2j1l(2k1)

22121j12j12Furthermore, probability of taking place crossover on each locus of k1chromosome is equal, namely l Pc.Therefore, after crossover, mathematical expectation of chromosome searching step is 1Ec(x)PcEck(x)

k1lSubstituting Eq.(A1)into Eq.(A2), we obtain l1PbaP(ba)11ba1Pcl(2k1)cl[(2i1)l]c(1l)2212l212l21k1llba0, so Ec(x)Pc where l is large, l2l21Ec(x)l1

Fig.A1 One point crossover

Theorem 4 Mathematical expectation Em(x)of chromosome searching step with bit mutation Em(x)(ba)Pm, where Pm is the probability of mutation.Proof Mutation probability of genes on each locus of chromosome is equal, say Pm, therefore, mathematical expectation of mutation searching step is Em(x)=åPm·wi=åPm·i=1i=1llb-ai-1b-a·2=P··(2i-1)=(b-a)·Pm mli2-12-1

一种新的改进遗传算法及其性能分析

摘要：虽然遗传算法以其全局搜索、并行计算、更好的健壮性以及在进化过程中不需要求导而著称，但是它仍然有一定的缺陷，比如收敛速度慢。本文根据几个基本定理，提出了一种使用变异染色体长度和交叉变异概率的改进遗传算法，它的主要思想是：在进化的开始阶段，我们使用短一些的变异染色体长度和高一些的交叉变异概率来解决，在全局最优解附近，使用长一些的变异染色体长度和低一些的交叉变异概率。最后，一些关键功能的测试表明，我们的解决方案可以显著提高遗传算法的收敛速度，其综合性能优于只保留最佳个体的遗传算法。

遗传算法是一种以自然界进化中的选择和繁殖机制为基础的自适应的搜索技术，它是由Holland 1975年首先提出的。它以其全局搜索、并行计算、更好的健壮性以及在进化过程中不需要求导而著称。然而它也有一些缺点，如本地搜索不佳，过早收敛，以及收敛速度慢。近些年，这个问题被广泛地进行了研究。

本文提出了一种使用变异染色体长度和交叉变异概率的改进遗传算法。一些关键功能的测试表明，我们的解决方案可以显著提高遗传算法的收敛速度，其综合性能优于只保留最佳个体的遗传算法。

在第一部分，提出了我们的新算法。第二部分，通过几个优化例子，将该算法和只保留最佳个体的遗传算法进行了效率的比较。第三部分，就是所得出的结论。最后，相关定理的证明过程可见附录。

1算法的描述

1.1 一些定理

在提出我们的算法之前，先给出一个一般性的定理（见附件），如下：我们假设有一个变量（多变量可以拆分成多个部分，每一部分是一个变量）x ∈ [ a, b ] , x ∈ R，二进制的染色体编码是1.定理1 染色体的最小分辨率是

s =

ba l21定理2 染色体的第i位的权重值是

bai1(i = 1,2,…l)2l1定理3 单点交叉的染色体搜索步骤的数学期望Ec(x)是

wi =

Ec(x)= baPc 2l其中Pc是交叉概率

定理4 位变异的染色体搜索步骤的数学期望Em(x)是

Em(x)=(b-a)Pm

其中Pm是变异概率 算法机制

在进化过程中，我们假设变量的值域是固定的，交叉的概率是一个常数，所以从定理1 和定理3我们知道，较长的染色体长度有着较少的染色体搜索步骤和较高的分辨率；反之亦然。同时，交叉概率与搜索步骤成正比。由定理4，改变染色体的长度不影响变异的搜索步骤，而变异概率与搜索步骤也是成正比的。

进化的开始阶段，较短染色体（可以是过短，否则它不利于种群多样性）和较高的交叉和变异概率会增加搜索步骤，这样可进行更大的域名搜索，避免陷入局部最优。而全局最优的附近，较长染色体和较低的交叉和变异概率会减少搜索的步骤，较长的染色体也提高了变异分辨率，避免在全局最优解附近徘徊，提高了算法收敛速度。

最后，应当指出，染色体长度的改变不会使个体适应性改变，因此它不影响选择（轮盘赌选择）。

算法描述

由于基本遗传算法没有在全局优化时收敛，而遗传算法保留了当前一代的最佳个体，我

们的方法采用这项策略。在进化过程中，我们跟踪到当代个体平均适应度的累计值。它被写成：

1GX(t)= favg(t)Gt1其中G是当前进化的一代，favg是个体的平均适应度。

当累计平均适用性增加到最初个体平均适应度的k(k> 1, k ∈ R)倍，我们将染色体长度变为其自身的m(m 是一个正整数)倍，然后减小交叉和变异的概率，可以提高个体分辨率、减少搜索步骤以及提高算法收敛速度。算法的执行步骤如下：

第一步：初始化群体，并计算个体平均适应度favg0，然后设置改变参数的标志flag。flag设为1.第二步：在所保留的当代的最佳个体，进行选择、再生、交叉和变异，并计算当代个体的累积平均适应度favg

favg0第三步：如果

favgk 且flag = 1，把染色体的长度增加至自身的m倍，减少交叉和变异概率，并设置flag等于0;否则继续进化。

第四步：如果满足结束条件，停止；否则转自第二步。

测试和分析

我们采用以下两种方法来测试我们的方法，和只保留最佳个体的遗传算法进行比较：

f1(x,y)0.5sin2x2y20.5[10.01xy222] [5,5]

x,y∈ [1,1] f2(x,y)4(x22y20.3cos(3πx)0.4cos(4πy))

x,y∈收敛的分析

在功能测试中，我们进行了以下政策：轮盘赌选择，单点交叉，位变异。种群的规

模是60。L是染色体长度，Pc和Pm分别是交叉概率和变异概率。我们随机选择4个遗传算法所保留的最佳个体来与我们的方法进行比较，它们具有不同的固定染色体长度和交叉和变异的概率。表1给出了在100次测试的平均收敛代。

在我们的方法中，我们采取的初始参数是l0 = 10，Pc0 = 0.3，Pm0 = 0.1和k = 1.2，当满足改变参数的条件时，我们调整参数l = 30，Pc = 0.1，Pm = 0.01。

1.1 在线和离线性能的分析

Dejong提出了遗传算法的定量评价方法，包括在线和离线性能评价。前者测试动态性能，而后者评估收敛性能。为了更好地分析测试功能的在线和离线性能，我们把个体的适应性乘以10，并f1和f2分别给出了4 000和1 000代的曲线：

(a)在线

(b)离线

图1 f1的在线与离线性能

(a)在线

(b)离线

从图1和图2可以看出，我们方法的在线性能只比第四种情况差一点点，但比第二种、第三种、第五种好很多，这几种情况下的在线性能几乎完全相同。同时，我们方法的离线性能也比其他四种好很多

结论

本文提出了一种使用变异染色体长度和交叉变异概率的改进遗传算法。一些关键功能的测试表明，我们的解决方案可以显著提高遗传算法的收敛速度，其综合性能优于只保留最佳个体的遗传算法。

附件

有了第一部分中假定的条件，定理1和定理2的验证是显而易见的。下面给出定理3和定理4的证明过程：

定理3 单点交叉的染色体搜索步骤的数学期望Ec(x)是

Ec(x)= 其中Pc是交叉概率

baPc 2l证明：

如图A1所示，我们假设交叉发生在第k个基因位点，从k到l的父基因位点没有变化，基因位点1到k上的基因改变了。

在交叉过程中，1到k基因位点上的基因改变的概率为0.5(“1”变化”0”或者”0”变为”1”)，因此，交叉之后，基因位点上的染色体搜索步骤从1到k的数学期望是

k11ba1baEck(x)wjl2j1l(2k1)

22121j12j121此外，每个位点的染色体发生交叉的概率是相等的，即lPc。交叉后，染色

k体搜索步骤的数学期望是

1Ec(x)PcEck(x)k1l

把Eq.(A1)替换为Eq.(A2)，我们得到 l1PbaP(ba)11ba1Pcl(2k1)cl[(2i1)l]c(1l)l22l2l212121k1lba0，所以Ec(x)Pc 其中l是非常大的，l2l21Ec(x)l1图1 单点交叉

定理4 位变异的染色体搜索步骤的数学期望是

Em(x)(ba)Pm

其中Pm是变异概率。证明：

每个基因位点上的基因的变异概率是相等的，比如Pm，因此变异搜索步骤的数学期望是：

Em(x)=åPm·wi=åPm·i=1i=1ll

b-ai-1b-a·2=P··(2i-1)=(b-a)·Pmmli2-12-1

第四篇：爬墙机器人外文翻译

The development trend of the robot 1.Preface: Climbing robot is an important branch in the field of mobile robot, flexible mobile on vertical wall, replace artificial under the condition of the limit to complete various tasks, is one of the hotspot in research of the robot.It is mainly used in the nuclear industry, petrochemical industry, shipbuilding, fire departments and investigation activities, such as the building external wall cleaning, material storage tank in petrochemical enterprise testing and maintenance, the outer wall of large steel plate spray paint, and in building accident rescue and relief, etc., and achieved good social benefits and economic benefits, has wide development prospects.After 30 years of development, the field of robot which has emerged a large number of fruitful results, especially since the 1990 s, especially rapid development in the field of climbing robot at home and abroad.In recent years, due to the development of a variety of new technology, the robot which solved many technical challenges, greatly promote the development of the climbing robot.The robot design activities of universities in our country also has a wide development, this kind of atmosphere for our robot research and development of special and professional talents' cultivation is of positive significance.2.Climbing robot research status abroad 1966 Japanese professor west light wall mobile robot prototype is developed for the first time, and performance success in Osaka prefecture university.This is a kind of rely on negative pressure adsorption climbing robot.Then appeared various types of climbing robot, has already begun to the late 80 s application in the production.Japan's most rapid development in the development of climbing robot, mainly used in the construction industry and nuclear industry.Such as: Japan shimizu construction company has developed with the outer wall of the building industry coating with ceramic tile of the robot, they developed by negative pressure adsorption cleaning climbing robot, on the surface of the glass for the Canadian embassy to clean.Tokyo university of technology development of the wireless remote control magnetic adsorption climbing robot.In Japan's miti “limit homework robot” national research projects, supported by day CDH, developed a large pot of negative pressure adsorption surface inspection robots used in nuclear power plants, etc.Other countries are also added to the climbing robot research upsurge, such as: Seattle Henry R Seemann under the funding of the Boeing company developed a vacuum adsorption crawler “AutoCrawler” robot.On the two tracks each containing a number of small adsorption chamber, with the moving of the crawler, adsorption chamber form continuous vacuum cavity and makes the crawler walking against the wall.American CaseWestern Reserve University developed by using four climbing robot prototype “legs”.Similar to the first two robots, the robot depends on four “legs” on biomimetic viscous materials to adsorption, the prototype is the four legs wheel on the sole of the foot even special distribution is more advantageous to the robot stable crawling on the wall.The quality of the robot is only 87 g.Polytechnic school in the early 1990 s, British Portsmouth has developed a climbing robot multilegged walking type.Adopting modular design, the robot is composed of two similar modules, each module includes two mechanical legs and leg controller.According to the task need to install a different number of legs, reconfigurable ability.Mechanical legs using bionics mechanism, simulation of the large animals arm muscle function, is two type, including upper and lower two and three double-acting cylinder, with three degrees of freedom.Good stability and bearing capacity is big, the robot's lightweight, and can span bigger obstacles.In addition to the leg on one end of vacuum cups, robot equipped with suction cups, abdomen mass ratio of powder and make the robot has a larger load of 2:1.3.Climbing robot research status in China China is also in a similar study since the 1990 s.In 1988 at the national “863” high technology program, under the support of the robotics institute of Harbin institute of technology has successfully developed the use of magnetic adsorption and vacuum adsorption two series of five types of wall climbing robot.Successful development of the our country the first wall climbing robot remote detection, using negative pressure adsorption, omni-directional mobile wheel, used for nuclear waste storage jars of wall weld defect detection.Developed in 1994 for tall buildings wall climbing robot cleaning CLRⅡ, driven by two independent ways--coaxial two-wheeled differential mechanism, through the coordination of two rounds of speed control to realize the omni-directional mobile robot, the robot ontology and using power line carrier communication methods between the ground control station.Above-mentioned three climbing machine adopts single suction cup structure, spring air sealed, ensure the crawl robot with high speed and reliable adhesion ability.In 1995 successfully developed the metal corrosion by magnetic adsorption climbing robot, structure of permanent magnetic adsorption, accomplished by two tracks positive &negative mobile turn.The robot can do for petrochemical enterprises to the outer wall of the metal material storage tank to spray paint, sandblasting, as well as with automatic detection system to test the tank wall thickness.Developed in 1997's detection of water wall climbing robot, a circular permanent magnet adsorption block in conformity with the tank wall arc, improve the adsorption capacity, and improve the efficiency of the operation.Shanghai university also conducted early tall wall cleaning robot research, successively developed a vertical wall climbing robot and spherical wall climbing robot.The spherical wall climbing robot adopts many suckers, negative pressure adsorption, 6 foot independent driving leg feet walking style, can be used for different radius of curvature of the spherical outer wall since 1996, the Beijing university of aeronautics and astronautics has successfully developed WASH2 MAN, CLEANBOT 1, SKYCLEAN, “hanging basket type window robot” and “LanTianJie treasure” curtain wall cleaning robot prototype.For all the window is brushed pneumatic robot;Hanging basket type cleaning robot, the robot depends on the roof of the safety line traction, attached with the negative pressure made by fan robot on the wall in the application background of national grand theatre ellipsoid ceiling cleaning developed suitable for complex curved surface from climbing robot prototype, the climbing mechanism, mobile mechanism, cleaning robot has many similarities, but due to its special working environment and mission requirements, in terms of theory and technology has some particularity.4.The key technology of robot: 4.1 adsorption mechanism, adsorption mechanism of action is to produce an upward force to balance the gravity of the robot, keep it on the wall.Currently, magnetic adsorption methods mainly include vacuum negative pressure adsorption, adsorption, propeller thrust and binder etc.Several ways.Due to the adsorption methods each have limitations, climbing robot developed by often targeted strong, applies only to a specific task, difficult to generalize.Robot design need to work on task, environment, choose the right means of adsorption.In recent years, people through the study of the adsorption mechanism of gecko reptiles such as the soles of your feet, making the polymer synthesis of viscous material, the use of van der Waals force between the molecules and molecular materials, can be obtained on the contact area of small huge adsorption capacity, and has the advantages of adsorption has nothing to do with the surface material properties.Short life but at the moment, the use of these materials, the use of a certain number of times after lose viscosity, practical, need further study.4.2 mobile mechanism and motion control system: mobile mechanism and the movement control system of robot which major wheeled mobile mechanism, more foot type, such as caterpillar, among them, the wheel and foot type which has been widely used, caterpillar much for magnetic adsorption method.Obstacle ability is wall robot which used to an important indicator of performance.When work surface is convex, groove, the robot to go through these obstacles, we must have enough obstacle ability.All kinds of mobile mechanism, more foot type robot obstacle-navigation ability is stronger, its each leg small suction cup is placed, when faced with obstacles, can control the “leg”, make the small suction cup across the obstacles one by one.Wall mobile mechanism of the robot can make the robot on the premise of reliable adsorption can move on the wall.Due to the particularity of climbing robot working in wall, mobile mechanism and adsorption mechanism exists coupling, which brought some difficulties to the robot's motion control.Than climbing robot sucker foot type and legs with a suction cup at the end, every move a leg needs to be done “to eliminate suctionWallace leg, left leg-gasoline, hydrogen fuel can have higher weight ratio, such as advanced micro internal combustion engine can also be applied to the climbing robot.Safety problems: 4.4 the robot by interference, environmental change circumstances, how to ensure the safety of the robot is attached to the wall without falling, falling or after how to minimize the damage of the robot.The past buildings cleaning climbing robot, developed by most used by in carrying the car at the top of the tower, hoisting and wire rope of insurance system on the robot.Robot for some other purposes, such as detection with small climbing robot, the goal is not sure, cannot use the rope way of insurance, so need to study new way to prevent falling.Could consider using a parachute, small power into a pulp, fast supporting resistance drop plate, etc., these may be a future development direction of climbing robot safety measures.5.Development trend of the robot Hard drive, sensor and control the development of software technology has greatly promoted the development of climbing robot technology, the demand of the practical application is also put forward the challenge, the development of robot climbing robot development trend in the aggregate, basically has the following several aspects.(1)the development of new adsorption technology.Adsorption technology has been a bottleneck of the development of the robot, it determines the application range of the robot.(2)the task of robot from simplification to muti_function change direction.The past most climbing robot which is used for washing, spraying, detection and so on homework, homework tasks are often confined to a single task.Now people want climbing robot can equipped with a variety of tools, are working on different occasions.(3)the miniaturization, micromation is currently the trend of the development of the robot.On the premise of meet the functional requirements, small volume, light quality of robot can be less energy consumption, high flexibility, and in some special occasions are also need robot with small volume.(4)by the mooring operation development to the direction of untethered.Because the robot working space is generally larger, mooring operation greatly limits the robot working space, so, in order to improve the flexibility of robot and expand the working space, no cable is changed and is now and the future development trend of the robot.(5)by simple remote monitoring to intelligent direction.Combined with artificial intelligence, the robot can in a closed environment has a certain capacity for independent decision and complete the task, and have ego to protect ability, is the important direction of mobile robot, is also a important development direction of mobile robot climbing wall.(6)the adaptability of the reconfigurable robot is an important indicator.In order to make the robots could be used in different occasions, according to the mission requirements, under the condition of the system does not need to design, make full use of existing robot system, should make with reconfigurable robot, which has a modular structure.According to the mission requirements, the need of module is directly connected to form a new robot.译文：

1.引言：

爬壁机器人是移动机器人领域的一个重要分支,可在垂直壁面上灵活移动,代替人工在极限条件下完成多种作业任务,是当前机器人领域研究的热点之一。它主要应用于核工业、石化工业、造船业、消防部门及侦查活动等,如对高楼外壁面进行清洗,对石化企业中的储料罐外壁进行检测和维护,对大面积钢板进行喷漆,以及在高楼事故中进行抢险救灾等，并且取得了良好的社会效益和经济效益，具有广阔的发展前景。

经过30多年的发展,爬壁机器人领域已经涌现出一大批丰硕的成果,特别是20世纪90年代以来,国内外在爬壁机器人领域中的发展尤为迅速。近年来,由于多种新技术的发展,爬壁机器人的许多技术难题得到解决,极大地推动了爬壁机器人的发展。在我国各高校机器人设计活动也已经很广的开展起来，这种氛围对我国机器人的研制开发特别以及专业方面人才的培养是具有积极意义的。

2.国外爬壁机器人研究现状

1966年日本的西亮教授首次研制成功壁面移动机器人样机,并在大阪府立大学表演成功。这是一种依靠负压吸附的爬壁机器人。随后出现了各种类型的爬壁机器人,到80年代末期已经开始在生产中应用。日本在开发爬壁机器人方面发展最为迅速,主要应用在建筑行业与核工业。如：日本清水建设公司开发了建筑行业用的外壁涂装与贴瓷砖的机器人,他们研制的负压吸附清洗玻璃面的爬壁机器人,曾为加拿大使馆清洗。东京工业大学开发了无线遥控磁吸附爬壁机器人。在日本通产省”极限作业机器人"国家研究计划支持下,日晖株式会社开发了用于核电站大罐的负压吸附壁面检查机器人等。

其他各国也加入到爬壁机器人研究的热潮中如：美国西雅图的Henry R Seemann在波音公司的资助下研制出一种真空吸附履带式爬壁机器人“AutoCrawler”。其两条履带上各装有数个小吸附室,随着履带的移动,吸附室连续地形成真空腔而使得履带贴紧壁面行走。美国CaseWestern Reserve University研制的采用4个“腿轮”的爬壁机器人样机。与前两种机器人相似,该机器人依靠4个“腿轮”上的仿生粘性材料来吸附,样机不同的是这4个腿轮上脚掌的特殊分布更有利于机器人在壁面上稳定爬行。该机器人质量仅有87 g。20世纪90年代初,英国朴次茅斯工艺学校研制了一种多足行走式的爬壁机器人。采用模块化设计,机器人由两个相似的模块组成,每个模块包括两个机械腿和腿部控制器。可根据任务需要来安装不同数量的腿,可重构能力强。机械腿采用仿生学机构,模拟大型动物臂部肌肉的功能,为两节式,包括上、下两个杆和3个双作用气缸,具有3个自由度。稳定性好,承载能力大,利于机器人的轻量化,并能跨越较大的障碍物。除腿端部各有一真空吸盘外,机器人腹部设有吸盘, 使机器人具有较大的负载质量比,可达2∶1。

3.国内爬壁机器人研究现状

中国也于20世纪90年代以来进行类似的研究。1988年在国家“863”高技术计划的支持下,哈尔滨工业大学机器人研究所先后研制成功了采用磁吸附和真空吸附两个系列的5种型号壁面爬行机器人。研制成功的我国第一台壁面爬行遥控检测机器人,采用负压吸附,全方位移动轮,用于核废液储存罐罐壁焊缝缺陷检测。1994年开发的用于高楼壁面清洗作业的爬壁机器人CLR-Ⅰ,采用全方位移动机构,机器人在原地就可以任意改变运动方向。之后开发的CLR-Ⅱ,采用两轮独立驱动方式———同轴双轮差速机构, 通过对两轮速度的协调控制实现机器人的全方位移动,机器人本体和地面控制站之间采用电力线载波通讯方式。上述3款爬壁机器人均采用单吸盘结构,弹簧气囊密封,保证了机器人具有较高爬行速度和可靠的附着能力。1995年研制成功的金属管防腐用磁吸附爬壁机器人,采用永磁吸附结构,靠两条履带的正反转移动来实现转弯。该机器人可以为石化企业金属储料罐的外壁进行喷漆、喷砂,以及携带自动检测系统对罐壁涂层厚度进行检测。1997年研制的水冷壁清检测爬壁机器人,呈圆弧形永磁吸附块与罐壁圆弧相吻合,提高了吸附力,也提高了作业的效率。上海大学也较早开展高楼壁面清洗作业机器人的研究,先后研制出垂直壁面爬壁机器人和球形壁面爬壁机器人。该球形壁面爬壁机器人采用多吸盘、负压吸附、6足独立驱动腿足行走方式,可用于不同曲率半径的球形外壁1996年以来,北京航空航天大学先后研制成功WASH2 MAN,CLEANBOT 1,SKYCLEAN,“吊篮式擦窗机器人”和“蓝天洁宝”等幕墙清洗机器人样机。为全气动擦窗机器人;吊篮式清洗机器人,机器人依靠楼顶上的安全吊索牵引移动,利用风机产生的负压使机器人贴附在壁面上以国家大剧院椭球形顶棚清洗为应用背景研制的适用于复杂曲面的自攀爬式机器人样机,由攀爬机构、移动机构、清机器人有许多相似之处,但由于其特殊的工作环境和任务要求,在理论和技术等方面又有一些特殊性。

4.爬壁机器人的关键技术：

4.1吸附机构：吸附机构的作用是产生一个向上的力来平衡机器人的重力,使其保持在壁面上。目前,吸附方式主要有真空负压吸附、磁吸附、螺旋桨推力及粘结剂等几种方式。由于这些吸附方式各自都有局限性,所研制的爬壁机器人往往针对性较强,只适用于某种特定任务,较难通用化。机器人的设计需要针对工作任务、环境,选取合适的吸附方式。近年来,人们通过研究壁虎等爬行动物脚掌的吸附机理,制作出高分子合成的粘性材料,这些材料利用分子与分子之间的范德华力,在很小的接触面积上就可获得巨大的吸附力,而且具有吸附力与表面材料特性无关的优点。但目前这些材料的使用寿命较短, 使用一定次数之后就失去粘性,难以实用化,需要进一步进行研究。

4.2移动机构及运动控制系统：移动机构及运动控制系统爬壁机器人的移动机构主要有轮式、多足式、履带式等,其中,轮式和足式使用较为广泛,履带式多用于磁吸附方式。越障能力是爬壁机器人壁面适应性能的一个重要指标。当工作面上有凸起、沟槽时,机器人要通过这些障碍物,就必须有足够的越障能力。各种移动机构中,多足式机器人的越障能力较强,其每个腿部都置有小吸盘,当遇到障碍物时,可控制各个“腿”,使小吸盘逐个跨过障碍物。壁面机器人的移动机构可以使机器人在可靠吸附的前提下能够在壁面上灵活移动。由于爬壁机器人工作于壁面的特殊性,移动机构常和吸附机构存在耦合,这给机器人的运动控制带来了一些困难。如多吸盘足式爬壁机器人,腿末端各有一个吸盘,每移动一个腿需要完成“消除吸力—抬腿—迈腿—落腿—产生吸附力”一系列动作。在此过程中,机器人移动机构的动作要和吸附机构相互协调,才能保证机器人在壁面上的灵活移动。此外,也有移动机构与吸附机构分离的,如单吸盘爬壁机器人,吸盘可持续吸附,驱动轮连续运动实现机器人的移动,运动控制较为简单。

4.3能源供应及驱动方式：能源供应及驱动方式能源供应方式有通过电线管路为机 器人提供电、气等能源的方式,也有自带电池、气瓶等方式。驱动方式主要有电机气动等几种方式。爬壁机器人的设计尽量采用具有高功效质量比的驱动器和动力源,特别是采用无线控制情况下。采用电机驱动时,能源供应主要有聚合物锂电池、镍氢电池、电化学电池和燃料电池。此外,由于内燃机的能源———汽油、氢等燃料具有较高的能重比,先进的微型内燃机也可应用于爬壁机器人。

4.4安全问题：机器人在受到外界干扰、环境变化情况下,如何保证机器人安全附着于壁面而不至于坠落,或坠落后如何尽量减小机器人的损伤。过去所研制的高楼清洗爬壁机器人, 大都采用由置于高楼顶上的运载小车、卷扬机构和系在机器人上的钢丝绳组成保险系统。而对于一些其他用途的机器人,比如侦查用的小型爬壁机器人,其目标并不确定,不能采用保险绳的方式,因而需要研究新的防坠落方式。可以考虑采用降落伞、小功率螺旋降落浆、快速撑起阻降板等,这些可能会成为未来爬壁机器人安全措施的发展方向。

5.爬壁机器人的发展趋势

驱动、传感、控制等硬软件技术的发展极大地推动了爬壁机器人技术的发展,实际应用的需求也对爬壁机器人的发展提出了挑战,爬壁机器人的发展趋势归结起来主要有以下几方面。(1)新型吸附技术的发展。吸附技术一直是爬壁机器人发展的一个瓶颈,它决定了机器人的应用范围。(2)爬壁机器人的任务由单一化向多功能化方向发展。过去所研制的爬壁机器人大多用于清洗、喷涂、检测等作业,作业任务往往只局限于单一的任务。而目前人们则希望爬壁机器人能够装备多种工具,在不同的场合进行工作。(3)小型化、微型化是当前爬壁机器人发展的趋势。在满足功能要求的前提下,体积小、质量轻的机器人可较小能耗,具有较高灵活性,并且在某些特殊场合也需要机器人具有小的体积。(4)由带缆作业向无缆化方向发展。由于爬壁机器人的作业空间一般都较大,带缆作业极大地限制了机器人的作业空间,所以,为了提高机器人的灵活性和扩大工作空间,无缆化成为现在和未来爬壁机器人的发展趋势。(5)由简单远距离遥控向智能化方向发展。与人工智能相结合,使机器人在封闭环境中能够具有一定的自主决策能力, 完成任务,并具有自我保护能力,是移动机器人发展的重要方向,也是爬壁移动机器人的重要发展方向。(6)可重构是机器人适应能力的一项重要指标。为了使机器人能够应用于不同场合,根据任务需求,在不需要重新设计系统条件下,充分利用已有的机器人系统,应使机器人具有可重构性,即具有模块化结构。根据任务需求,把需要的模块直接连接起来组成新的机器人。

第五篇：外文翻译--六自由度机器人

六自由度并联机器人基于Grassmann-Cayley代数的奇异性条件

Patricia Ben-Horin和Moshe Shoham，会员，IEEE

摘要

本文研究了奇异性条件大多数的六自由度并联机器人在每一个腿上都有一个球形接头。首先,确定致动器螺丝在腿链中心。然后用凯莱代数和相关的分解方法用于确定哪些条件的导数(或刚度矩阵)包含这些螺丝是等级不足。这些工具是有利的,因为他们方便操纵坐标-简单的表达式表示的几何实体,从而使几何解释的奇异性条件是更容易获得。使用这些工具,奇异性条件(至少)144种这类的组合被划定在四个平面所相交的一个点上。这四个平面定义为这个零距螺丝球形关节的位置和方向。指数Terms-Grassmann-Cayley代数，奇点，三条腿的机器。

一、介绍

在过去的二十年里,许多研究人员广泛研究并联机器人的奇异性。不像串联机器人,失去在奇异配置中的自由度,尽管并联机器人的执行器都是锁着但是他们的的自由度还是可以获得的。因此,这些不稳定姿势的全面知识为提高机器人的设计和确定机器人的路径规划是至关重要的。

主要的方法之一,用于寻找奇异性并行机器人是基于计算雅可比行列式进行的。Gosselin和安杰利斯[1]分类奇异性的闭环机制通过考虑两个雅克比定义输入速度和输出速度之间的关系。当圣鲁克和Gosselin[2]减少了算术操作要求定义的雅可比行列式高夫·斯图尔特平台(GSP),从而使数值计算得到多项式。

另一个重要的工具,为分析螺旋理论中的奇异性,首先阐述了1900的论文[6]和开发机器人应用程序。几项研究已经应用这个理论找到并联机器人的奇异性,例如,[11]-[14]。特别注意到情况,执行机构是线性和代表螺丝是零投的。在这些情况下,奇异的配置是解决通过使用几何,寻找可能的致动器线依赖[15]-[17]。其他分类方法闭环机制可以被发现在[18]-[22]。

在本文中,我们分析了奇异点的一大类三条腿的机器人,在每个腿链有一个球形接头上的任何点。我们只关注了正运动学奇异性。首先,我们发现螺丝相关执行机构的每个链。因为每一个链包含一个球形接头,自致动器螺丝是相互联合的,他们是通过球形关节的零螺距螺杆螺丝。然后我们使用Grassmann-Cayley代数和相关的发展获得一个代数方程,它源于管理行机器人包含的刚度矩阵。直接和高效检索的几何意义的奇异配置是最主要的一个优点,在这里将介绍其方法。

虽然之前的研究[53]分析7架构普惠制,各有至少三条并发关节,本文扩展了奇点分析程度更广泛的一类机器人有三条腿和一个球形关节。使用降低行列式和Grassmann-Cayley运营商我们获得一个通用的条件,这些机器人的奇异性提供在一个简单的几何意义方式计算中。

本文的结构如下。第二节详细描述了运动学结构的并联机器人。第三节包含一个简短的在螺丝和大纲性质的背景下驱动器螺丝,零距螺丝作用于中心的球形关节。第四部分包含一个介绍Grassmann-Cayley代数的基本工具用于寻找奇异性条件。这部分还包括刚度矩阵(或导数)分解成坐标自由表达。第五节中一个常见的例子给出了这种方法。最后,第六章比较了使用本方法结果与结果的其他技术。

二、运动构架

本文阐述了6自由度并联机器人有六间连通性基础和移动平台。肖海姆和罗斯[54]提供了调查可能的结构,产生基于流动公式6自由度的Grubler和Kutzbach。他们寻找了所有的可能性,满足这个公式对关节的数目和任何链接。GSP和三条腿的机器人结构的一个子集所列出的6自由度Shoham和罗斯。一个类似的例子也证实了了Podhorodeski和Pittens[55],他发现了一个类的三条腿的对称并联机器人,球形关节、转动关节的平台在每个腿比其他结构潜在有利。正如上面所讨论的,大多数的报告文献限制他们的分析结构和球形关节位于移动平台和棱柱关节作为驱动的关节。在这个分类,我们包括五种类型的关节和更多的可选职位的球形关节。

我们处理机器人有三个链连接到移动平台,每个驱动有两个1自由度关节或一个二自由度关节。这些链不一定是平等的,但都有移动和连接六个基地和之间的平台。除了球形接头(S),关节考虑是棱镜(P),转动(R)、螺旋(H)、圆柱(C)和通用(U),前三个是1自由度关节和最后两个二自由度的关节。所有的可能性都显示在表I和II。该列表只包含机器人,有平等的连锁,总计144种不同的结构,但是机器人与任何可能的组合链也可以被认为是membersof这类方法。组合的总数,大于500 000,计算方式如下:

三、管理方法

本节涉及螺丝和平台运动的确定。因为考虑机器人有三个串行链,每个驱动器螺丝的方向可以由其互惠到其他关节螺钉固定在链条。被动球形接头在每个链部队驱动器螺丝为零距(行)并且通过它的中心。因此,三个平面是创建中心位于自己的球形关节。

以下简要介绍了螺旋理论,广泛的解决[7],[73],[75];我们解决在第二节中列出相互的所有关节螺钉系统。

上述类的机器人的几何结果奇点现在相比其他方法获得的结果要准确。首先,我们比较奇异条件在上述3 GSP平台与结果报告线几何方法。

根据相对几何条件的他行方法区分不同的几种类型沿着棱镜致动器[81]的奇异性。我们表明,所有这些奇异点是特定情况下的条件通过(17 c)提供,这是有效的三条腿以及6:3 GSP平台的机器人的考虑。这种结构的奇异的配置根据线几何分析包括五种类型:3 c、4 b、4 d,5 a和5 b[17],[36]。

四、奇异性分析

本节确定奇异性条件定义在第二节的机器人。第一部分包括寻找方向的执行机构的行动路线,基于解释第三节中介绍。他行通过球形接头中心,而他们的方向取决于关节的分布和位置。第二部分包括应用程序的方法使用了Grassmann-Cayley代数在第四节定义奇点。因为每对线满足在一个点(球形接头),所有例子的解决方案是象征性地平等,无论点位置的腿或腿的对称性。我们从文献中举例说明使用三个机器人的解决方案。

1.方向的致动器螺丝

第一个例子是3-PRPS机器人提出Behi[61][见图3(a)]。对于每个腿驱动螺丝躺在这家由球形接头中心和转动关节轴。特别是,致动器螺杆是垂直于轴的,和致动器螺杆是垂直于轴的,这些方向被描绘在图3(b)。第二个例子是the3-USR机器人提出Simaan et al。[66][见图4(a)]。每条腿有驱动器螺丝躺在通过球形接头中心和包含转动关节轴中。驱动器螺丝穿过球形接头中心并与转动关节轴相连。这些方向被描绘在图4(b)。

第三个例子是3-PPSP Byun建造的机器人和[65][见图5(一个)]。每条腿,驱动螺丝躺在飞机通过球形接头中心和正常的棱镜接头轴。驱动器螺丝垂直于轴的,和致动器螺杆是垂直于轴的,这些方向被描绘在图5(b)。

图3(a)3-PRPS机器人提出Behi[61]

(b)飞机和致动器螺丝

图4(a)3自由度机器人提出Simaan和Shoham[66]

(b)飞机和致动器螺丝的3自由度机器人

图5(a)3-PPSP机器人提出Byun[65]

(b)飞机和致动器螺丝

2、.奇异性条件

雅克(或superbracket)的机器人是分解成普通支架monomials使用麦克米兰的分解,即(16)。解释部分3—b机器人，本文认为每个链有两个零距驱动器螺丝通过球形接头。拓扑,这个描述等于行6:3 GSP(或在[53]),这三条线,每经过一个双球面上的接头平台(见图6)。这意味着每对线共享一个公共点(这些点在图6中)。因此类的机器人被认为是在本文中,我们可以使用相同的标记点的至于6:3 GSP。六线与相关各机器人通过双点,并且,用同样的方式在图6。

图6 6-3 GSP

五、结果

本文提出一个广义奇异性分析并联机器人组成元素。这些是有一个球形接头在每个腿链的三条腿的6自由度机器人。因为球形关节需要驱动器，螺丝是纯粹的力量作用于他们的中心,他们的位置沿链是不重要的。组成元素包括144机制不同类型的关节,每个都有不同的联合装置沿链。提出并建立描述几个机器人出现在列表中。大量的机器人相关的分析组合不同被认为是。奇点的分析是由第一个找到的执行机构使用互惠的螺丝。然后,借助组合方法和Grassmann-Cayley方法,得到刚度矩阵行列式在一个可以操作的协调自由形式,可以翻译成一个简单的几何条件之后。其定义是几何条件由执行机构位置的线条和球形接头,至少有一个相交点。这个有效的奇异点条件考虑所有组成元素中的机器人。一个比较的结果与结果的奇点证明了其他技术所有先前描述奇异条件实际上是特殊情况下的几何条件的四架飞机交叉在一个点,一个条件获取的方法直接在这里提出。

Singularity Condition of Six-Degree-of-Freedom Three-Legged Parallel Robots Based on Grassmann–Cayley Algebra Patricia Ben-Horin and Moshe Shoham, Associate Member, IEEE

ABSTRACT This paper addresses the singularity condition of a broad class of six-degree-of-freedom three-legged parallel robots that have one spherical joint somewhere along each leg.First, the actuator screws for each leg-chain are determined.Then Grassmann–Cayley algebra and the associated superbracket decomposition are used to find the condition for which the Jacobian(or rigidity matrix)containing these screws is rank-deficient.These tools are advantageous since they facilitate manipulation of coordinate-free expressions representing geometric entities, thus enabling the geometrical interpretation of the singularity condition to be obtained more easily.Using these tools, the singularity condition of(at least)144 combinations of this class is delineated to be the intersection of four planes at one point.These four planes are defined by the locations of the spherical joints and the directions of the zero-pitch screws.Index Terms—Grassmann–Cayley algebra, singularity, three-legged robots.I.INTRODUCTION During the last two decades, many researchers have extensively investigated singularities of parallel robots.Unlike serial robots that lose degrees of freedom(DOFs)in singular configurations, parallel robots might also gain DOFs even though their actuators are locked.Therefore, thorough knowledge of these unstable poses is essential for improving robot design and determining robot path planning.One of the principal methods used for finding the singularities of parallel robots is based on calculation of the Jacobian determinant degeneracy.Gosselin and Angeles [1] classified the singularities of closed-loop mechanisms by considering two Jacobians that define the relationship between input and output velocities.St-Onge and Gosselin [2] reduced the arithmetical operations required to define the Jacobian determinant for the Gough–Stewart platform(GSP), and thus enabled numerical calculation of the obtained polynomial in real-time.Zlatanov et al.[3]–[5] expanded the classification proposed by Gosselin and Angeles to define six types of singularity that are derived using equations containing not only the input and output velocities but also explicit passive joint velocities.Another important tool that has served in the analysis of singularities is the screw theory, first expounded in Ball’s 1900 treatise [6] and developed for robotic applications by Hunt [7]–[9] and Sugimoto et al.[10].Several studies have applied this theory to find singularities of parallel robots, for example, [11]–[14].Special attention was paid to cases in which the actuators are linear and the representing screws are zero-pitched.In these cases, the singular configurations were solved by using line geometry, looking for possible actuator-line dependencies [15]–[17].Other approaches taken to classify singularities of closed-loop mechanisms can be found in [18]–[22].In this paper, we analyze the singularities of a broad class of three-legged robots, having a spherical joint at any point in each individual leg-chain.We focus only on forward kinematics singularities.First, we find the screws associated with the actuators of each chain.Since every chain contains a spherical joint, and since the actuator screws are reciprocal to the joint screws, they are zero-pitch screws passing through the spherical joints.Then we use Grassmann–Cayley algebra and related developments to get an algebraic equation which originates from the rigidity matrix containing the governing lines of the robot.The direct and efficient retrieval of the geometric meaning of the singular configurations is one of the main advantages of the method presented here.While the previous study [53] analyzed only seven architectures of GSP, each having at least three pairs of concurrent joints, this paper expands the singularity analysis to a considerably broader class of robots that have three legs with a spherical joints somewhere along the legs.Using the reduced determinant and Grassmann–Cayley operators we obtain one single generic condition for which these robots are singular and provide in a simple manner the geometric meaning of this condition.The structure of this paper is as follows.Section II describes in detail the kinematic architecture of the class of parallel robots under consideration.Section III contains a brief background on screws and outlines the nature of the actuator screws, which are zero-pitch screws acting on the centers of the spherical joints.Section IV contains an introduction to Grassmann–Cayley algebra which is the basic tool used for finding the singularity condition.This section also includes the rigidity matrix(or Jacobian)decomposition into coordinate-free expressions.In Section V a general example of this approach is given.Finally, Section VI compares the results obtained using the present method with results obtained by other techniques.II.KINEMATIC ARCHITECTURE This paper deals with 6-DOF parallel robots that have connectivity six between the base and the moving platform.Shoham and Roth [54] provided a survey of the possible structures that yield 6-DOF based on the mobility formula of Grübler and Kutzbach.They searched for all the possibilities that satisfy this formula with respect to the number of joints connected to any of the links.The GSP and three-legged robots are a subset of the structures with 6-DOF listed by Shoham and Roth.A similar enumeration was provided also by Podhorodeski and Pittens [55], who found a class of three-legged symmetric parallel robots that have spherical joints at the platform and revolute joints in each leg to be potentially advantageous over other structures.As discussed above, most of the reports in the literature limit their analysis to structures with spherical joints located on the moving platform and revolute or prismatic joints as actuated or passive additional joints.Exceptions are the family of 14 robots proposed by Simaan and Shoham [28] which contain spherical-revolute dyads connected to the platform, and some structures mentioned below which have revolute or prismatic joints on the platform.In this classification, we include five types of joints and more optional positions for the spherical joints.We deal with robots that have three chains connected to the moving platform, each actuated by two 1-DOF joints or one 2-DOF joint.These chains are not necessarily equal, but all have mobility and connectivity six between the base and the platform.Besides the spherical joint(S), the joints taken into consideration are prismatic(P), revolute(R), helical(H), cylindrical(C), and universal(U), the first three being 1-DOF joints and the last two being 2-DOF joints.All the possibilities are shown in Tables I and II.The list contains only the robots that have equal chains, totaling 144 different structures, but robots with any possible combination of chains can also be considered as membersof this class.The total number of combinations, , is larger than 500 000, calculated as follows:

III.GOVERNING LINES This section deals with the screws that determine the platform motion.Since the robots under consideration have three serial chains, the direction of each actuator screw can be determined by its reciprocity to the other joint screws in the chain.The passive spherical joint in each chain forces the actuator screws to have zero-pitch(lines)and to pass through its center.Therefore, three flat pencils are created having their centers located at the spherical joints.Following a brief introduction to the screw theory that is extensively treated in [7], [73]–[75];we address the reciprocal screw systems of all the joints listed in Section II.The geometric result for the singularity of the aforementioned class of robots is now compared with the results obtained by other approaches in the literature.First, we compare the singularity condition described above for the 6-3 GSP platform with the results reported for the line geometry method.The line geometry method distinguishes among several types of singularities, according to the relative geometric condition of he lines along the prismatic actuators [81].We show that all these singularities are particular cases of the condition provided by(17c), which is valid for the three-legged robots under consideration as well as for the 6-3 GSP platform.The singular configurations of this structure according to line geometry analysis include five types: 3C, 4B, 4D, 5A, and 5B [17], [36].IV.SINGULARITY ANALYSIS This section determines the singularity condition for the class of robots defined in Section II.The first part consists of finding the direction of the actuator lines of action, based on the explanation introduced in Section III.The lines pass through the spherical joint center while their directions depend on the distribution and position of the joints.The second part includes application of the approach using Grassmann–Cayley algebra presented in Section IV for defining singularity when considering six lines attaching two platforms.Since every pair of lines meet at one point(the spherical joint), the solution for all the cases is symbolically equal, regardless of the points’ location in the leg or the symmetry of the legs.We exemplify the solution using three robots from the literature.A.Direction of the Actuator Screws The first example is the 3-PRPS robot as proposed by Behi [61] [see Fig.3(a)].For each leg the actuated screws lie on theplane defined by the spherical joint center and the revolute joint axis.In particular,the actuator screw is perpendicular to the axis of , and the actuator screw is perpendicular to the axis of , these directions being depicted in Fig.3(b).The second example is the3-USR robot as proposed by Simaan et al.[66][see Fig.4(a)].Every leg has the actuator screws lying on the plane passing through the spherical joint center and containing the revolute joint axis.The actuator screw passes through the spherical joint center and intersects the revolute joint axis and.Similarly, the actuator screw passes through the spherical joint center and intersects the revolute joint axis and , these directions being depicted in Fig.4(b).The third example is the 3-PPSP robot built by Byun and Cho [65] [see Fig.5(a)].For every leg the actuated screws lie on the plane passing through the spherical joint center and being normal to the prismatic joint axis.The actuator screw is perpendicular to the axis of , and the actuator screw is perpendicular to the axis of , these directions being depicted in Fig.5(b).Fig.3.(a)The 3-PRPS robot as proposed by Behi [61].(b)Planes and actuator screws.Fig.4.(a)The 3-USR robot as proposed by Simaan and Shoham [66].(b)Planes and actuator

screws of the 3-USR robot.Fig.5.(a)3-PPSP robot as proposed by Byun and Cho [65].(b)Planes and actuator screws.B.Singularity Condition

The Jacobian(or superbracket)of a robot is decomposed into ordinary bracket monomials using McMillan’s decomposition, namely(16).As explained in Section III-B, all the robots of the class considered in this paper have two zero-pitch actuator screws passing through the spherical joint of each chain.Topologically, this description is equivalent to the lines of the 6-3 GSP(or in [53]), which has three pairs of lines, each passing through a double spherical joint on the platform(see Fig.6).This means that each pair of lines share one common point(in Fig.6 these points are , , and).Therefore for the class of robots considered in this paper, we can use the same notation of points as for the 6-3 GSP.The six lines associated with each robot pass through the pairs of points,and , in the same way as in Fig.6.Due to the common points of the pairs of lines ,and ,denoted , and respectively, many of the monomials of(16)vanish due to(4).Fig.6.6-3 GSP.V.CONCLUSION

This paper presents singularity analysis for a broad family of parallel robots.These are 6-DOF three-legged robots which have one spherical joint in each leg-chain.Since the spherical joints entail the actuator screws to be pure forces acting on their centers, their location along the chain is not important.The family includes 144 mechanisms incorporating diverse types of joints that each has a different joint arrangement along the chains.Several proposed and built robots described in the literature appear in this list.A larger number of robots are relevant to this analysis if combinations of different legs are considered.The singularity analysis was performed by first finding the lines of action of the actuators using the reciprocity of screws.Then, with the aid of combinatorial methods and Grassmann–Cayley operators, the rigidity matrix determinant was obtained in a manipulable coordinate-free form that could be translated later into a simple geometric condition.The geometric condition consists of four planes, defined by the actuator lines and the position of the spherical joints, which intersect at least one point.This singularity condition is valid for all the robots in the family under consideration.A comparison of this singularity result with results obtained by other techniques demonstrated that all the previously described singularity conditions are actually special cases of the geometrical condition of four planes intersecting at a point, a condition that was obtained straightforwardly by the method suggested here