SCARA机器人运动学仿真【说明书论文开题报告外文翻译】
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毕 业 设 计（论 文）任 务 书1本毕业设计（论文）课题应达到的目的：通过毕业设计，使学生受到电气工程师所必备的综合训练，在不同程度上提高各种设计及应用能力，具体包括以下几方面：1. 调查研究、中外文献检索与阅读的能力。2. 综合运用专业理论、知识分析解决实际问题的能力。3. 定性与定量相结合的独立研究与论证的能力。4. 实验方案的制定、仪器设备的选用、调试及实验数据的测试、采集与分析处理的能力。5. 设计、计算与绘图的能力，包括使用计算机的能力。6. 逻辑思维与形象思维相结合的文字及口头表达的能力。 2本毕业设计（论文）课题任务的内容和要求（包括原始数据、技术要求、工作要求等）：1.通过 MATLAB 软件完成毕业设计所需仿真内容。利用 DH 参数法对 SCARA 机器人进行了运动学建模。基于 MATLAB Robotic Toolbox 工具箱，编制了简单的程序语句，验证了 SCARA 机器人参数的合理性；利用关节驱动窗口，直观地展示了机器人关节角度驱动效果图；对机器人运动轨迹进行了仿真。利用 Robotic Toolbox 工具箱可以对机器人多个关节轨迹进行规划，快速且准确。2.按时完成开题报告书。3.按时完成毕业设计外文参考资料，定期开展毕业设计自查。4.在毕业设计过程中要有科学认真的工作态度，数据合理可靠。5.能够圆满完成指导老师布置的课题任务，技术设计方案合理，具有一定的可行性，能够体现一定的创新性。6.按时参加答辩，在答辩前各项规定的资料要齐全。 毕 业 设 计（论 文）任 务 书3对本毕业设计（论文）课题成果的要求包括图表、实物等硬件要求： 1.按期完成一篇符合金陵科技学院论文规范的毕业设计说明书（毕业论文） ，能详细说明设计步骤和思路；2.能有结构完整，合理可靠的技术方案；3.能有相应设计原理说明；4.有相应的图纸和技术参数说明；5.仿真成功，并在答辩时完成仿真展示。 4主要参考文献： 1 金以慧.过程控制 M. 北京：清华大学出版社.20022 楼顺天.基于 MATLAB 的系统分析与设计-控制系统 M. 西安：西安电子科技大学 出版社.20003 李宜达.控制系统设计与仿真 M. 北京：清华大学出版社.20044郭 洪 红 .工 业 机 器 人 技 术 .西 安 ： 西 安 电 子 科 技 大 学 出 版 社 ， 20055谢 存 喜 .机 器 人 技 术 及 其 应 用 .北 京 ： 机 械 工 业 出 版 社 ， 20126殷 际 英 .关 节 型 机 器 人 .北 京 ： 化 学 工 业 出 版 社 ， 20037高 国 富 .机 器 人 传 感 器 及 其 应 用 .北 京 ： 化 学 工 业 出 版 社 ， 20058方 建 军 .智 能 机 器 人 .北 京 ： 化 学 工 业 出 版 社 ， 20049刘 极 峰 .机 器 人 技 术 基 础 .北 京 ： 高 等 教 育 出 版 社 ， 200710林 以 敏 .机 器 人 制 作 .北 京 ： 机 械 工 业 出 版 社 ， 200711宗 光 华 .机 器 人 的 创 意 制 作 与 实 践 .北 京 ： 北 京 航 空 航 天 大 学 出 版 社 ，2007 12 Tan G Z， Wang Y C Theortical and experimental research on time optimal trajectory planning and control of industrial robots J Control Theory Applications， 2003 13 冯 飞 ， 张 洛 平 ， 张 波 四 自 由 度 机 器 人 Matlab 仿 真 实 例 J 河 南科 技 大 学 学 报 ( 自 然 科 学 版 ) ， 2008 14 罗 家 佳 ， 胡 国 清 基 于 Matlab 的 机 器 人 运 动 仿 真 研 究 J 厦 门大 学 学 报 ( 自 然 科 学 版 ) ， 2005 15 王 智 兴 ， 樊 文 欣 ， 张 保 成 ， 等 基 于 Matlab 的 工 业 机 器 人 运 动 学 分 析与 仿 真 J 机 电 工 程 ， 2012 16 Furuya N， Soma K， Chin E， Makino H Research and developmentof selective compliance assembly robot arm J Hardware andsoftware of SCARA controller， J Japan Society of PrecisionEngineering /Seimitsu Kogaku Kaishi， 1983 17 孙 涛 ， 张 征 ， 胡 俊 机 器 人 逆 运 动 学 算 法 及 Admas 仿 真 J 机 床 与液 压 ， 2008 18 王 永 龙 ， 张 兆 忠 ， 张 桂 红 Matlab 语 言 基 础 与 应 用 M 北 京 : 电 子工 业 出 版 社 ， 2010 19 Corke P A Robotics Toolbox for Matlab J IEEE Robotics andAutomation Magazine， 1996 20 谢 斌 ， 蔡 自 兴 基 于 Matlab Robotics Toolbox 的 机 器 人 学 仿 真 实 验教 学 J 计 算 机 教 育 ， 2010 21 阮 启 刚 ， 黄 磊 6R 机 器 人 轨 迹 规 划 与 仿 真 J 电 气 技 术 与 自 动 化 ，2010 毕 业 设 计（论 文）任 务 书5本毕业设计（论文）课题工作进度计划：2015.11.04-2015.11.282015.11.29-2015.12.162015.12.17-2016.01.102016.02.25-2016.03.092016.03.09-2016.04.282016.04.29-2016.05.092016.05.09-2016.05.132016.05.14-2016.05.21在毕业设计管理系统里选题与指导教师共同确定毕业设计课题查阅指导教师下发的任务书，准备开题报告提交开题报告、外文参考资料及译文、论文大纲进行毕业设计（论文） ，填写中期检查表，提交论文草稿等按照要求完成论文或设计说明书等材料,提交论文定稿教师评阅学生毕业设计；学生准备毕业设计答辩参加毕业设计答辩，整理各项毕业设计材料并归档所在专业审查意见：通过 负责人： 2016 年 1 月 12 日 毕 业 设 计（论文） 开 题 报 告 1结合毕业设计（论文）课题情况，根据所查阅的文献资料，每人撰写不少于1000 字左右的文献综述： 一、研究的背景和意义 随着科学技术不断进步，机器人作为二十世纪人类最伟大的发明之一对我们社会文明的进步起到重要推动作用。机器人技术是一个交叉学科，它融合了诸如机构学、控制工程、人工智能、微电子学、计算机科学、材料科学及仿生学等科学技术的综合性技术。由于机器人工作具有速度快，效率高，质量稳定，疲劳极限大，能够从事人类不能或难以胜任的工作，且能适应产品多样化等特点，因此被广泛地应用于了工业的各个领域。根据生产实践需要，加快机器人研发,提高开发效率,改善机器人的各项性能,已成为极需解决的问题。一直以来,在机器人的设计开发及优化设计中,机器人运动学建模与运动学仿真研究都是非常重要的工作。特别是针对复杂的空间机构,如何快速、准确地建立系统的运动学模型,并进行有关系统性能的各项仿真工作显得越来越重要。机器人运动学是机器人学的一个重要分支,是实现机器人运动控制的基础。论文以 D-H 坐标系理论为基础对 SCARA 机器人进行了参数设计,利用 MATLAB 机器人工具箱,对机器人的正运动学、逆运动学、轨迹规划进行了仿真。MATLAB 仿真结果说明了所设计的参数的正确性,能够达到预定的目标。机器人运动学的研究涉及大量的数学运算,计算工作相当繁锁。因此,采用一些工具软件对其分析可大大提高工作效率,增加研究的灵活性和可操作性。对机器人进行图形仿真,可以将机器人仿真的结果以图形的形式表示出来,从而直观地显示出机器人的运动情况,得到从数据曲线或数据本身难以分析出来的许多重要信息,还可以从图形上看到机器人在一定控制条件下的运动规律。论文首先设计了 SCARA 机器人的各连杆参数,然后讨论了正、逆运动学算法,轨迹规划问题,最后在 MATLAB 环境下,进行运动学仿真。机器人仿真利用计算机可视化和面向对象的手段，模拟机器人的动态特性，帮助研究人员了解机器人工作空间的形态及极限，揭示机构的合理的运动方案和控制算法，并在这台“机器人”上模拟能够实现的功能，使用户直接看到设计效果，及时找出缺点和不足，进行改进，从而解决在机器人设计、制造和运行过程中的问题，避免了直接操作实体可能造成的事故和不必要的损失，这将使机器人的研究和生产进入一个可预知的新时代。 二、研究内容 随着机器人技术的应用和发展,机器人技术逐渐应用到了工业的各个领域。根据项目需要,如何加快机器人开发进度,提高开发效率,改善机器人的各项性能,已成为极需解决的问题。一直以来,在机器人的设计开发及优化设计中,机器人运动学建模与运动学仿真研究都是非常重要的工作。本次毕业设计针对 SCARA机器人开发过程中的机构分析、运动学建模和仿真问题进行了研究，主要包括工业机器人机构模块划分，自由度计算，运动学建模，工作空间分析，机器人动画演示与运动仿真。对于工业机器人机构分析、运动学建模、工作空间与灵活性分析具有一定的理论和实际意义；同时对于指导工业机器人机械结构设计、开展运动学性能评价与优化设计、缩短工业机器人开发周期、降低机器人产品开发成本，具有积极的推动作用。论文采用齐次变换矩阵和 D-H 运动学分析方法对 SCARA 机器人进行了参数设计,利用 MATLAB 编程,对机器人的正运动学、逆运动学、轨迹规划进行了仿真。MATLAB 明了所设计的参数的正确性,能够达到预定的目标。本次毕业设计分为三部分:第一部分 SCARA 机器人参数设计 这部分对 6 自由度 SCARA 机器人参数设计进行了运动学分析，运用 D-H 表示法即 Denavit 和 Hartenberg 在 1955 年提出一种通用的方法，这种方法在机器人的每个连杆上都固定一个坐标系，然后用 44 的齐次变换矩阵来描述相邻两连杆的空间关系。通过依次变换可最终推导出末端执行器相对于基坐标系的位姿，从而建立机器人的运动学方程。及齐次变换矩阵建立了其运动学模型。对工业机器人设计及二次开发。 第二部分 SCARA 机器人运动学仿真算法 在这一部分中根据机器人结构选择合理的算法建立运动学方程，并利用坐标变换求出正向运动学及逆向运动学的解，机器人运动学逆问题就是已知工作时末端操作的空间位置和姿态，以及各连杆的结构参数，求满足预定要求时各关节变量的值。这是机器人学中的重要问题，也是对机械手进行控制的关键。从工程应用的角度出发，运动学逆解往往更具有实际意义。在运动学的基础上分析探讨动力学方程的建立以及求解，进行运动轨迹规划方法比较分析，这些为以后的运动系统和控制系统的建模仿真建立理论基础。 第三部分 SCARA 机器人建模仿真 机器人运动仿真主要是为了在产品开发阶段，了解所开发的机器人实现预定轨迹运动时各关节及连杆所反映出的运动学特性、产品在给定输入运动下的动作过程及机器人的综合性能，其仿真结果对机器人产品开发及结构优化设计等二次开发提供依据。在 CATIA 软件平台上，建立实体示意传动原理模型，为以后实际机器人的研制生产奠定了基础。以运动学、动力学以及轨迹规划的公式为依据，利用 MATLAB 机器人工具箱对运动系统进行建模仿真，同时对仿真出现的问题进行分析。分别得到了各关节的运动曲线，力矩曲线、轨迹曲线和控制方案的可行性。 参考文献：1黄献龙，梁斌.EMR 系统机器人工作空间与灵活性的分析.机械工程学报，2001， 37（2）：1216. 2张铁，谢存禧.机器人学M.广州:华南理工大学出版社.2001. 3吴振彪.工业机器人M.武汉:华中理工大学出版社.1997. 4王天然.机器人M.北京:化学工业出版社.2002. 5梅生伟.现代鲁棒控制理论与应用M.北京:清华大学出版社，2003.6谭民, 徐德, 侯增广, 等. 先进机器人控制M . 北京:高等教育出版社, 2007. 7申铁龙.机器人鲁棒控制基础M.北京:清华大学出版社，2001.8蔡自兴. 机器人学M . 北京: 清华大学出版社, 2003. 9阳明盛，熊西文，林建华.MATLAB 基础及数学软件M.大连:大连理工大学出版社,2003. 10曹毅，王树新，李群智，基于随机概率的机器人工作空间及其解析表达，设计与研 究，2005(2). 11陈善君，高元楼.蒙特卡洛方法在 Tricep 机器人工作空间分析中的应用.机床与液 压，2004，6(11)：1115. 12范波涛，张良.蒙特卡洛方法在喷浆机器人工作空间中的应用.山东工业大学学报， 1999，4：29(2). 13刑宏光.五自由度机器人灵活工作空间及仿真.北京航空航天大学硕士学位论文， 2004，3. 14李康.介入式手术机器人机械结构设计及运动学仿真.哈尔滨工业大学全国优秀硕 士论文，2006，6. 15殷际英，何广平编著.关节型机器人.北京：化学工业出版社工业装备与信息工程出版中心，2003. 16刘成良，张为公，翟羽健.RV12L 6R 焊接机器人运动学及计算机仿真系统研究.机器人，1998，9(25). 17曹毅，李秀娟，宁祎，杨冠英.三维机器人工作空间及几何误差分析.机械科学与 技术，2006，4(25). 18孙祥，徐流美，吴清编著.MatLab 7.0 基础教程.北京：清华大学出版社 2005，5. 19吴彦农，康志军编著.SolidWorks 2005 基础教程.北京：机械工业出版社，2005. 20江洪，陆利锋，魏峥等编著.SolidWorks 动画演示与运动分析实例解析.机械工业 出版社，2006，5. 21张晋西，郭学琴编著.SolidWorks 及 COSMOSMotion 机械仿真设计.高等学校教材计算机应用，清华大学出版社，2007，1. 22刘金馄.机器人控制系统的设计与 MATLAB 仿真M.北京:清华大学出版社，2008.毕 业 设 计（论文） 开 题 报 告 2本课题要研究或解决的问题和拟采用的研究手段（途径）： 本课题要研究或解决的问题是：1.SCARA 机器人参数设计 1.1 D-H 变换 1.2 SCARA 机器人的关节结构及其参数设计 2.SCARA 机器人运动学仿真与算法 2.1 机器人运动学正问题 2.2 机器人运动学逆问题 2.3 求解绘制机器人手爪的空间运动范围 3.机器人建模仿真 3.1 构建 SCARA 机器人仿真模型 3.2 机器人的 MATLAB 仿真 研究手段（途径）：1.去图书馆查阅相关资料，经过汇总，作为参考资料；2.充分利用网络资源，进行相关信息的搜索；3.运用 CATIA 建立实体模型； 4.利用 MATLAB 对 SCARA 机器人进行建模仿真分析得到了各关节运动学和轨迹规划的参数曲线结果，验证方程理论的正确性。毕 业 设 计（论文） 开 题 报 告 指导教师意见：1对“文献综述”的评语：综述内容较为丰富，参考文献合理，概括 SCARA 机器人在工业中的应用，机器人的运动学研究内容的相关背景、基础知识、历史发展等，同时还对本课题所研究的任务进行了一定的阐述，对本课题的研究有一定的指导意义。 2对本课题的深度、广度及工作量的意见和对设计（论文）结果的预测：本课题研究的任务是对 SCARA 机器人的运动学进行研究和仿真，是对电气控制领域应用较多的仿真技术的一个实例进行探讨，技术相对成熟，深度中等，但是涉及到的知识面较广，例如机器人学、控制系统、计算机仿真等技术，学生可以通过实例调研，查阅专业资料，进行系统调试，来实现最终的设计任务和结果，并对自己的专业应用能力是一个非常大的提高。3.是否同意开题： 同意 不同意指导教师： 2016 年 03 月 05 日所在专业审查意见：同意 负责人： 2016 年 03 月 08 日0译文题目：Combination of robot control and assembly planning for a precision manipulator机器人控制和装配计划相结合的精密机械手 COMBINATION OF ROBOT CONTROL AND ASSEMBLY PLANNING FOR A PRECISION MANIPULATORAbstract This paper researches how to realize the automatic assembly operation on a two-finger precision manipulator. A multi-layer assembly support system is proposed. At the task-planning layer, based on the computer-aided design (CAD) model, the assembly sequence is first generated, and the information necessary for skill decomposition is also derived. Then, the assembly sequence is decomposed into robot skills at the skill-decomposition layer. These generated skills are managed and executed at the robot control layer. Experimental results show the feasibility and efficiency of the proposed system. Keywords Manipulator Assembly planning Skill decomposition Automated assembly1 IntroductionOwing to the micro-electro-mechanical systems (MEMS) techniques, many products are becoming very small and complex, such as microphones, micro-optical components, and microfluidic biomedical devices, which creates increasing needs for technologies and systems for the automated precision assembly of miniature parts. Many efforts aiming at semi-automated or automated assembly have been focused on microassembly technologies. However, microassembly techniques of high flexibility, efficiency, and reliability still open to further research. Thispaper researches how to realize the automatic assembly operation on a two-finger micromanipulator. A multi-layer assembly support system is proposed. Automatic assembly is a complex problem which may involve many different 1issues, such as task planning, assembly sequences generation, execution, and control, etc. It can be simply divided into two phases; the assembly planning and the robot control. At the assembly-planning phase, the information necessary for assembly operations, such as the assembly sequence, is generated. At the robot control phase, the robot is driven based on the information generated at the assembly-planning phase, and the assembly operations are conducted. Skill primitives can work as the interface of assembly planning to robot control. Several robot systems based on skill primitives have been reported. The basic idea behind these systems is the robot programming. Robot movements are specified as skill primitives, based on which the assembly task is manually coded into programs. With the programs, the robot is controlled to fulfill assembly tasks automatically.A skill-based micromanipulation system has been developed in the authors lab, and it can realize many micromanipulation operations. In the system, the assembly task is manually discomposed into skill sequences and compiled into a file. After importing the file into the system, the system can automatically execute the assembly task. This paper attempts to explore a user-friendly, and at the same time easy, sequence-generation method, to relieve the burden of manually programming the skillsequence.It is an effective method to determine the assembly sequence from geometric computer-aided design (CAD) models. Many approaches have been proposed. This paper applies a simple approach to generate the assembly sequence. It is not involved with the low-level data structure of the CAD model, and can be realized with the application programming interface (API) functions that many commercial CAD software packages provide. In the proposed approach, a relations graph among different components is first constructed by analyzing the assembly model, and then, possible sequences are searched, based on the graph. According to certain criterion, the optimal sequence is finally obtained. To decompose the assembly sequence into robot skill sequences, some works have been reported. In Nnaji et al.s work, the assembly task commands are expanded to more detailed commands, which can be seen as robot skills, according to a predefined format. The decomposition approach of Mosemann and Wahl is based on the analysis of hyperarcs of AND/OR graphs representing the automatically generated assembly plans. This paper proposes a method to guide the skill decomposition. The assembly processes of parts are grouped into different phases, and parts are at 2different states. Specific workflows push forward parts from one state to another state. Each workflow is associated with a skill generator. According to the different start state and target state of the workflow, the skill generator creates a series of skills that can promote the part to its target state.The hierarchy of the system proposed here ,the assembly information on how to assemble a product is transferred to the robot through multiple layers. The top layer is for the assembly-task planning. The information needed for the task planning and skill generation are extracted from the CAD model and are saved in the database. Based on the CAD model, the assembly task sequences are generated. At the skill-decomposition layer, tasks are decomposed into skill sequences. The generated skills are managed and executed at the robot control layer.2 Task planningSkills are not used directly at the assembly-planning phase. Instead, the concept of a task is used. A task can fulfill a series of assembly operations, for example, from locating a part, through moving the part, to fixing it with another part. In other words, one task includes many functions that may be fulfilled by several different skills. A task is defined as: T =（Base Part; Assembly Part; Operation） Base_Part and Assembly_Part are two parts that are assembled together. Base_Part is fixed on the worktable, while Assembly_Part is handled by robots end-effector and assembled onto the Base_Part. Operation describes how the Assembly_Part is assembled with the Base_Part; Operation Insertion_T, screw_T, align_T,.The structure of microparts is usually uncomplicated, and they can be modeled by the constructive solid geometry (CSG) method. Currently, many commercial CAD software packages can support 3D CSG modeling. The assembly model is represented as an object that consists of two parts with certain assembly relations that define how the parts are to be assembled. In the CAD model, the relations are defined by geometric constraints. The geometric information cannot be used directly to guide the assembly operationwe have to derive the information necessary for assembly operations from the CAD model. Through searching the assembly tree and geometric relations (mates relations) defined in the assemblys CAD model, we can generate a relation graph among parts, 3for example, In the graph, the nodes represent the parts. If nodes are connected, it means that there are assembly relations among these connected nodes (parts).2.1 Mating directionIn CSG, the relations of two parts, geometric constraints, are finally represented as relations between planes and lines, such as collinear, coplanar, tangential, perpendicular, etc. For example, a shaft is assembled in a hole. The assembly relations between the two parts may consist of such two constraints as collinear between the centerline of shaft Lc_shaft and the centerline of hole Lc_hole and coplanar between the plane P_Shaft and the plane P_Hole. The mating direction is a key issue for an assembly operation. This paper applies the following approach to compute the possible mating direction based on the geometric constraints (the shaft-in-hole operation of Fig. 3 is taken as an example): 1. For a part in the relation graph, calculate its remaining degrees of freedom,also called degrees of separation, of each geometric constraint. For the coplanar constraint, the remaining degrees of freedom are . For the collinear constraint, the remaining degrees of freedom are zRotyx,1. and can also be represented as and 212R1,0,1R. Here, 1 means that there is a degree of separation between the two ,0,parts. , and so, the degree of freedom around the z axis will be 21，ignored in the following steps. In the case that there is a loop in the relation graph, such as parts Part 5, Part 6, and Part 7 in Fig. 2, the loop has to be broken before the mating direction is calculated. Under the assumption that all parts in the CAD model are fully constrained and not over-constrained, the following simple approach is adopted. For the part t in the loop, calculate the number of 1s in ; where is the remaining iniiti RN.21ikdegrees of freedom of constraint k by part i. For example, in Fig. 2, given that the number of 1s in and is larger than and , 7,5partU7,6part 6,5partU5,6partrespectively, then it can be regarded that the position of Part 7 is determined by constraints with both Part 5 and Part 6, while Part 5 and Part 6 can be fully constrained by constraints between Part 5 and Part 6.We can unite Part 5 and Part 6 as one node in the relation graph, also called a composite node, as shown in Fig. 2b. The composite node will be regarded as a single part, but it is obvious that the composite node implies an assembly sequence.2. Calculate mating directions for all nodes in the relation graph. Again, 4beginning at the state that the shaft and the hole are assembled, separate the part in one degree of separation by a certain distance (larger than the maximum tolerance), and then check if interference occurs. Separation in both x axis and y axis of R1 causes the interference between the shaft and the hole. Separation in the +z direction raises no interference. Then, select the +z direction as the mating direction, which is represented as a vector M measured in the coordinate system of theassembly. It should be noted that, in some cases, there may be several possible mating directions for a part. The condition for assembly operation in the mating direction to be ended should be given. When contact occurs between parts in the mating direction at the assembled state, which can be checked simply with geometric constraints, the end condition is measured by force sensory information, whereas position information is used as an end condition.3. Calculate the grasping position. In this paper, parts are handled and manipulated with two separate probes, which will be discussed in the Sect. 4, and planes or edges are considered for grasping. In the case that there are several mating directions, the grasping planes are selected as G1G2.Gi, where Gi is possible grasping plane/edge set for the ith mating direction when the part is at its free state. For example, in Fig. 4, the pair planes P1/P1, P2/P2, and P3/P3 can serve as possible grasping planes, and then the grasping planes are 1P/2/,1P/3/,1P/3/,2P/,1/ _2_ dirmatngdirmatngdirmatngGGThe approaching direction of the end-effector is selected as the normal vector of the grasping planes. It is obvious that not all points on the grasping plane can be grasped. The following method is used to determine the grasping area. The end-effector, which is modeled as a cuboid, is first added in the CAD model, with the constraint of coplanar or tangential with the grasping plane. Beginning at the edge that is far away from the Base_Part in the mating direction, move the end-effector in the mating direction along the grasping plane until the end-effector is fully in contact with the part, the grasping plane is fully in contact with the end-effector, or a collision occurs. Record the edge and the distance, both of which are measured in the parts coordinate system.4. Separate gradually the two parts along the mating direction, while checking interference in the other degrees of separation, until no interference occurs in all of the other degrees of separation. There is obviously a separation distance that assures 5interference not to occur in every degree of separation. It is called the safe length in that direction. This length is used for the collision-free path calculation, which will be discussed in the following section.2.2 Assembly sequenceSome criteria can be used to search the optimal assembly sequence, such as the mechanical stability of subassemblies, the degree of parallel execution, types of fixtures, etc. But for microassembly, we should pay more attention to one of its most important features, the limited workspace, when selecting the assembly sequence. Microassembly operations are usually conducted and monitored under microscopy, and the workspace for microassembly is very small. The assembly sequence brings much influence on the assembly efficiency. For example, a simple assembly with three parts. In sequence a, part A is first fixed onto part B. In the case that part C cannot be mounted in the workspace at the same time with component AB because of the small workspace, in order to assemble part C with AB, component AB has to be unmounted from the workspace. Then, component C is transported and fixed into the workspace. After that, component AB is transported back into the workspace again. In sequence b, there is no need to unmount any part. Sequence a is obviously inefficient and may cause much uncertainty. In other words, the greater the number of times of unmounting components required by an assembly sequence, the more inefficient the assembly sequence. In this paper, due to the small -workspace feature of microassembly, the number of times necessary for the mounting of parts is selected as the search criteria to find the assembly sequence that has a few a number of times for the mounting of parts as possible.This paper proposes the following approach to search the assembly sequence. The relation graph of the assembly is used to search the optimal assembly sequence. Heuristic approaches are adopted in order to reduce the search times:1. Check nodes connected with more than two nodes. If the mating directions of its connected nodes are different, mark them as inactive nodes, whereas mark the same mating directions as active mating direction.2. Select a node that is not an inactive node. Mark the current node as the base node (part). The first base part is fixed on the workspace with the mating direction upside (this is done in the CAD model). Compare the size (e.g., weight or volume) of the base part with its connected parts, which can be done easily by reading the bill of materials (BOM) of the assembly. If the base part is much smaller, then mark it as an 6inactive node.3. Select a node connected with the base node as an assembly node (part). Check the mating direction if the base node needs to be unmounted from the workspace. If needed, update a variable, say mount+. Reposition the component (note that there may be not only the base part in the workspace; some other parts may have been assembled with the base part) in the workspace so that the mating direction is kept upside.4. In the CAD model, move the assembly part to the base part in the possible mating direction, while checking if interference (collision) occurs. If interference occurs, mark the base node as an inactive node and go to step 2, whereas select the Operation type according to parts geometric features. In this step, an Obstacle Box is also computed. The box, which is modeled as a cuboid, includes all parts in the workspace. It is used to calculate the collision-free path to move the assembly part, which will be introduced in the following section. The Obstacle Box is described by a position vector and its width, height, and length.5. Record the assembly sequence with the Operation type, the mating direction, and the grasping position.6. If all nodes have been searched, then mark the first base node as an inactive node and go to step 2. If not, select a node connected with the assembly node. Mark it as an assembly node, and the assembly node is updated as a base node. Check if there is one of the mating directions of the assembly node that is same as the mating direction of the former assembly node. If there is, use the former mating direction in the following steps. Go to step 3. After searching the entire graph, we may have several assembly sequences. Comparing the values of mount, the more efficient one can be selected. If not even one sequence is returned, then users may have to select one manually. If there are N nodes in the relation graph of Fig. 2b, all of which are not classed as inactive node, and each node may have M mating directions, then it needs MN computations to find all assembly sequences. But because, usually, one part only has one mating direction, and there are some inactive nodes, the computation should be less than MN. It should be noted that, in the above computation, several coordinate systems are involved, such as the coordinates of the assembly sequence, the coordinates of the base part, and the coordinates of the assembly. The relations among the coordinates are represented by a 44 transformation matrix, which is calculated based on the 7assembly CAD model when creating the relations graph. These matrixes are stored with all of the related parts in the database. They are also used in skill decomposition.3 Skill decomposition and execution3.1 Definition of skill primitiveSkill primitives are the interface between the assembly planning and robot control. There have been some definitions on skill primitives. The basic difference among these d
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