通用液壓機(jī)械手設(shè)計(jì) -圓柱坐標(biāo)型
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畢業(yè)設(shè)計(jì)(論文)
任 務(wù) 書
課題名稱
通用液壓機(jī)械手設(shè)計(jì)
指導(dǎo)教師
學(xué)院
機(jī)械與電氣工程學(xué)院
專業(yè)
機(jī)械設(shè)計(jì)制造及其自動(dòng)化
班級(jí)
學(xué)生姓名
學(xué)號(hào)
開題日期
一、 主要任務(wù)與目標(biāo)：
1.1主要任務(wù)
認(rèn)真學(xué)習(xí)《機(jī)器人》和《液壓與氣壓傳動(dòng)》方面有關(guān)的書籍資料，尤其是有關(guān)機(jī)械人或機(jī)械手的結(jié)構(gòu)圖冊(cè)，進(jìn)一步熟悉機(jī)械人的基本理論和基本結(jié)構(gòu)。
機(jī)械手的運(yùn)動(dòng)速度快，要求質(zhì)量輕、轉(zhuǎn)動(dòng)慣量小，配置合理，運(yùn)動(dòng)平穩(wěn)，定位精度和重復(fù)定位精度高。通過調(diào)研和分析確定本設(shè)計(jì)要求的LR20通用液壓機(jī)械手設(shè)計(jì)的工作原理和傳動(dòng)方案。完成機(jī)械手的結(jié)構(gòu)設(shè)計(jì)，繪制裝配圖和全部零件圖。總圖量達(dá)到3張A0。
按照畢業(yè)設(shè)計(jì)要求完成，認(rèn)真閱讀15篇以上有關(guān)《機(jī)器人》、《液壓與氣壓傳動(dòng)》方面最新論文、經(jīng)典教材和專著，為機(jī)器人設(shè)計(jì)作好充分準(zhǔn)備，并結(jié)合設(shè)計(jì)實(shí)際完成開題報(bào)告、文獻(xiàn)綜述、外文翻譯、設(shè)計(jì)計(jì)算書的撰寫。
1.2目標(biāo)
機(jī)械手能夠代替工人長(zhǎng)期連續(xù)高效地完成設(shè)定動(dòng)作，在自動(dòng)化裝置中應(yīng)用廣泛，也是企業(yè)解決用工荒的重要方法，可見機(jī)械手的應(yīng)用維護(hù)將越普遍。
通過本課題的訓(xùn)練，初步掌握新產(chǎn)品設(shè)計(jì)的工作流程。本設(shè)計(jì)課題旨在提高機(jī)械產(chǎn)品的系統(tǒng)設(shè)計(jì)和結(jié)構(gòu)設(shè)計(jì)能力，有利于在生產(chǎn)企業(yè)從事新產(chǎn)品開發(fā)設(shè)計(jì)和裝備設(shè)計(jì)能力，同時(shí)為從事企業(yè)生產(chǎn)過程中的設(shè)備管理和技術(shù)管理工作奠定良好的基礎(chǔ)。
二、主要內(nèi)容與基本要求：
2.1技術(shù)參數(shù)：
工件：棒料，重量20公斤，最大長(zhǎng)度300mm, 直徑100－120mm
工作區(qū)域：取物高度不小于600-1500mm，作業(yè)半徑500-1500mm；回轉(zhuǎn)角度270?，
工作速度：移動(dòng)速度3m/s，定位精度±0.3mm；轉(zhuǎn)動(dòng)速度45?/s。
2.2主要內(nèi)容
設(shè)計(jì)計(jì)算書（論文）10000字以上，按學(xué)校格式要求打印、裝訂。內(nèi)容結(jié)合設(shè)計(jì)項(xiàng)目撰寫。包括：前言、系統(tǒng)方案的分析與確定、結(jié)構(gòu)參數(shù)的設(shè)計(jì)計(jì)算、運(yùn)動(dòng)分析與計(jì)算、結(jié)構(gòu)強(qiáng)度設(shè)計(jì)計(jì)算及校核、精度分析、結(jié)束語(yǔ)等。
根據(jù)設(shè)計(jì)參數(shù)確定結(jié)構(gòu)，選擇合適的執(zhí)行機(jī)構(gòu)、驅(qū)動(dòng)方式及機(jī)械傳動(dòng)部件。氣動(dòng)元器件可選擇合適的標(biāo)準(zhǔn)器件，必要時(shí)進(jìn)行自行設(shè)計(jì)，重點(diǎn)是整體結(jié)構(gòu)。
裝配圖用A0繪制，總圖為可畫3張A0。。
開題報(bào)告、文獻(xiàn)綜述、外文翻譯等，符合各項(xiàng)規(guī)定要求。
2.3基本要求
圖樣全部用計(jì)算機(jī)繪制，符合最新制圖標(biāo)準(zhǔn)；投影正確，表達(dá)完整，布局合理。
設(shè)計(jì)要滿足功能，注重性能、結(jié)構(gòu)和裝配工藝性，外觀造型力求簡(jiǎn)潔明快；實(shí)用可靠。
計(jì)算書理論分析完整清楚；設(shè)計(jì)推導(dǎo)簡(jiǎn)明扼要；計(jì)算正確可靠。避免冗長(zhǎng)，杜絕抄襲。
開題報(bào)告、文獻(xiàn)綜述、外文翻譯等要緊扣設(shè)計(jì)主題，認(rèn)真分析、歸納、加工、提煉，切不可照搬。
三、計(jì)劃進(jìn)度：
2013.09.16~2013.10.15 接受任務(wù)，熟悉設(shè)計(jì)內(nèi)容，搜集相關(guān)資料；
2013.10.15~2014.01.10 完成設(shè)計(jì)圖樣和說明書初稿；
2014.01.11~2014.04.20 修改圖樣、說明書，完成二稿；
2013.10.15~2014.04.20 完成開題報(bào)告，文獻(xiàn)綜述和翻譯；
2014.04.21~2014.05.10 修改、檢查全部資料，打印、上交資料；
2014.05.11~2011.05.20 準(zhǔn)備論文答辯。
四、主要參考文獻(xiàn)：
[1]張福學(xué)編．機(jī)器人技術(shù)及其應(yīng)用[M].．北京：電子工業(yè)出版社，2000
[2]朱世福，王宣銀.機(jī)器人技術(shù)及其應(yīng)用[M]..杭州：浙江大學(xué)出版社，2005
[3]《工業(yè)機(jī)械手圖冊(cè)》編寫組.工業(yè)機(jī)械手圖冊(cè)[M]..北京：機(jī)械工業(yè)出版社，1978
[4]路甬祥.液壓氣動(dòng)技術(shù)手冊(cè)[M].北京：機(jī)械工業(yè)出版社，2004.5
[5]徐灝.機(jī)械設(shè)計(jì)手冊(cè)[M]. 北京：機(jī)械工業(yè)出版社，2003.1
指導(dǎo)教師
2013年10月11日
系 主 任
2013年10月11日
機(jī)器人和電腦一體機(jī)制造
關(guān)于生成工業(yè)機(jī)器人機(jī)械手的運(yùn)動(dòng)
K. Kaltsoukalas, S. Makris, G. Chryssolouris
佩特雷大學(xué)實(shí)驗(yàn)室制造系統(tǒng)和自動(dòng)化,希臘
論文信息
文章歷史： 關(guān)鍵詞：
2013年10月17日收到初稿 路徑規(guī)劃
2014年9月19日收到修改稿 工業(yè)機(jī)器人運(yùn)動(dòng)
2014年10月8日通過審核 網(wǎng)格搜索
2014年10月29日網(wǎng)上資源共享
摘要
在這個(gè)研究中，提出了一個(gè)智能搜索算法定義所需的位置和工業(yè)機(jī)器人機(jī)械手的定位效應(yīng)路徑的想法。這個(gè)算法通過選擇和評(píng)估機(jī)器人的配置逐步達(dá)到所需的配置。構(gòu)造網(wǎng)格的機(jī)器人替代配置使用一組參數(shù),減少了搜索空間并減少計(jì)算時(shí)間。對(duì)于可選擇性的評(píng)價(jià)，使用多個(gè)標(biāo)準(zhǔn)，用以滿足不同的要求。替代的配置重點(diǎn)是給機(jī)器人的關(guān)節(jié)，主要影響末端執(zhí)行器的位置。網(wǎng)格的分辨率和尺寸參數(shù)的設(shè)置在期望輸出的基礎(chǔ)上，高分辨率通過對(duì)目標(biāo)位置只提供一些中間點(diǎn)用于平滑的路徑和一個(gè)粗略的估計(jì)。規(guī)劃的路徑是一系列的機(jī)器人配置。這種方法為一個(gè)沒有經(jīng)驗(yàn)的程序員自動(dòng)生成機(jī)器人路徑提供了方便，這能達(dá)到預(yù)期的標(biāo)準(zhǔn)而不必記錄中間點(diǎn)到目標(biāo)位置。
2014?Elsevier有限公司保留所有權(quán)利
介紹
近年來(lái)，由于能適應(yīng)不同的市場(chǎng)需求和產(chǎn)品結(jié)構(gòu)的變化，對(duì)柔性制造系統(tǒng)的需求日益增加。動(dòng)態(tài)生產(chǎn)環(huán)境要求越來(lái)越多的裝配制造資源重新配置。自動(dòng)裝配系統(tǒng)，如機(jī)器人。它們的靈活性通常被制約因?yàn)楦叩木幊坦ぷ饕髾C(jī)器人軌跡調(diào)整去適應(yīng)不同的裝配單元布局。經(jīng)驗(yàn)豐富的機(jī)器人程序員不得不花大量時(shí)間采用常規(guī)的編程方法優(yōu)化每一個(gè)具體的應(yīng)用機(jī)器人的路徑。一種廣泛應(yīng)用的方法是演示編程，通過順序移動(dòng)機(jī)器人的每個(gè)位置并記錄中間點(diǎn)的位置來(lái)示教。通過機(jī)器人控制器的連接記錄點(diǎn)產(chǎn)生機(jī)器人的最后路徑，路徑考慮到機(jī)器人的動(dòng)力學(xué)約束并通過所有的約束點(diǎn)。機(jī)器人的最終軌跡高度依賴記錄點(diǎn)和程序員各自的編程經(jīng)驗(yàn)。機(jī)器人自動(dòng)路徑規(guī)劃提出了一個(gè)問題，在過去的幾十年里如何實(shí)現(xiàn)移動(dòng)機(jī)器人從初始到最終的位置進(jìn)行的研究，主要集中在路徑規(guī)劃避障。
一種運(yùn)動(dòng)規(guī)劃技術(shù)是通過采樣配置空間來(lái)構(gòu)建近似的模型。在過去的幾年里，已經(jīng)有很多為基于采樣的運(yùn)動(dòng)規(guī)劃算法進(jìn)行改善的工作在進(jìn)行了。在不同的類別中分類所有的規(guī)劃者很難定義一個(gè)單一的標(biāo)準(zhǔn)。經(jīng)典的分離是基于路線圖規(guī)劃者和邏輯樹規(guī)劃者之間。概率路線圖路徑規(guī)劃中引入一個(gè)計(jì)算機(jī)器人無(wú)碰撞路徑的新方法。這個(gè)方法分兩個(gè)階段進(jìn)行：學(xué)習(xí)和查詢。在學(xué)習(xí)階段，一個(gè)概率圖是通過生成機(jī)器人的隨機(jī)免費(fèi)配置和使用一個(gè)簡(jiǎn)單的運(yùn)動(dòng)規(guī)劃連接它們建設(shè)，也被稱為當(dāng)?shù)氐囊?guī)劃師。不同的方法已被用來(lái)解決各種各樣的問題，為了可變形物體的運(yùn)動(dòng)規(guī)劃而提出了構(gòu)建和查詢路線圖兩種不同的方法。還提出了另一個(gè)變形的技術(shù)可以應(yīng)用到生成的路徑中。介紹了障礙物的概率圖法，在生成節(jié)點(diǎn)的幾種策略進(jìn)行了闡述并且提出了復(fù)雜三維工作區(qū)多級(jí)連接策略。通過擴(kuò)展規(guī)劃無(wú)碰撞運(yùn)動(dòng)觸點(diǎn)配置的空間概率圖范例 ，隨機(jī)規(guī)劃被描述為在任意兩個(gè)多面體固體之間的CF兼容的運(yùn)動(dòng)規(guī)劃。這種方法的關(guān)鍵是隨機(jī)產(chǎn)生CF兼容的配置的新的采樣策略 。
引入了快速擴(kuò)展隨機(jī)樹的概念，基本的想法是，初始樣品（起始組態(tài)）是樹的根和新產(chǎn)生的樣本，然后連接到樹中已經(jīng)存在的樣品。兩個(gè)快速擴(kuò)展隨機(jī)樹（RRTS）扎根在開始和在目標(biāo)配置中。樹的每一個(gè)探索周圍的空間，也提出了對(duì)彼此通過一個(gè)簡(jiǎn)單的貪婪算法的使用。雖然它最初被計(jì)劃設(shè)計(jì)為人手臂的運(yùn)動(dòng)動(dòng)作（建模為一個(gè)自由度的運(yùn)動(dòng)鏈），在無(wú)碰撞把握和操作任務(wù)的自動(dòng)圖形動(dòng)畫中，該算法已被應(yīng)用于各種路徑規(guī)劃問題。邏輯樹規(guī)劃者們已證明是處理實(shí)時(shí)規(guī)劃和重新規(guī)劃問題的一個(gè)很好的框架。為了修復(fù)快速擴(kuò)展隨機(jī)樹進(jìn)行更改時(shí)配置空間，一個(gè)重新規(guī)劃算法被提了出來(lái)。不是放棄當(dāng)前RRT，該算法有效地只消除了新無(wú)效部分并保持休息。在工業(yè)環(huán)境中移動(dòng)機(jī)器人的動(dòng)態(tài)避障已經(jīng)開始研究調(diào)查。然而，工業(yè)機(jī)器人通常被編程以執(zhí)行預(yù)定義的路徑。機(jī)器人編程的方法主要有兩大類：在線編程和離線編程。
為了用戶的互動(dòng)轉(zhuǎn)化為簡(jiǎn)單任務(wù)提出了一個(gè)在線路徑規(guī)劃支持系統(tǒng)產(chǎn)生可接受的軌跡，適用于工業(yè)機(jī)器人的編程的問題。建議得出了一種新的方法，即機(jī)器人編程使用增強(qiáng)現(xiàn)實(shí)環(huán)境。為現(xiàn)場(chǎng)的機(jī)器人編程方法所需提供靈活性和適應(yīng)性以應(yīng)對(duì)不同環(huán)境。路徑規(guī)劃方法包括生成路徑的束搜索算法。有相似的研究表明，用戶能夠執(zhí)行的操作，即通過點(diǎn)的選擇和修改，為了實(shí)現(xiàn)一個(gè)光滑的無(wú)碰撞路徑。一個(gè)機(jī)器人運(yùn)動(dòng)規(guī)劃的方法，是根據(jù)預(yù)先計(jì)算的全局配置空間（C-）的連通性提出的。運(yùn)動(dòng)規(guī)劃，包括離線階段和在線階段和無(wú)碰撞的路徑將通過一個(gè)多分辨率策略下使用A*算法在C-空間中搜索。
在這個(gè)研究中，提出了一種智能搜索算法去定義工業(yè)機(jī)器人機(jī)械手端部執(zhí)行器所需的位置和方向的路徑?？晒┻x擇的配置的最大數(shù)量被一步步選擇和評(píng)價(jià)，直到所需的配置是接近預(yù)定的誤差范圍內(nèi)為止。替代的配置是一個(gè)聰明的方式產(chǎn)生，重視主要影響機(jī)器人的空間位置的關(guān)節(jié)角度。在配置空間上，有一個(gè)人工推導(dǎo)機(jī)器人的替代組態(tài)網(wǎng)格。一套巧妙的參數(shù)用于減少搜索空間，提高算法的性能。對(duì)于替代品的評(píng)價(jià)，使用多個(gè)標(biāo)準(zhǔn)，可以提高算法拓展的靈活性，這是為了滿足不同的要求，即滿足最短路徑的要求。
On generating the motion of industrial robot manipulatorsK. Kaltsoukalas, S. Makris, G. Chryssolourisn,1Laboratory for Manufacturing Systems and Automation, University of Patras, Greecea r t i c l e i n f oArticle history:Received 17 October 2013Received in revised form19 September 2014Accepted 8 October 2014Available online 29 October 2014Keywords:Path planningIndustrial robot motionGrid searcha b s t r a c tIn this study, an intelligent search algorithm is proposed to define the path that leads to the desiredposition and orientation of an industrial robots manipulator end effector. The search algorithm graduallyapproaches the desired configuration by selecting and evaluating a number of alternative robotsconfigurations. A grid of the robots alternative configurations is constructed using a set of parameterswhich are reducing the search space to minimize the computational time. In the evaluation of thealternatives, multiple criteria are used in order for the different requirements to be fulfilled. Thealternative configurations are generated with emphasis being given to the robots joints that mainlyaffect the position of the end effector. Grid resolution and size parameters are set on the basis of thedesired output. High resolution is used for a smooth path and lower for a rough estimation, by providingonly a number of the intermediate points to the goal position. The path derived is a series of robotconfigurations. This method provides an inexperienced robot programmer with flexibility to generateautomatically a robotic path that would fulfill the desired criteria without having to record intermediatepoints to the goal position.& 2014 Elsevier Ltd. All rights reserved.1. IntroductionIn the recent years, there is an increasing need for flexiblemanufacturing systems, capable of adapting to different marketdemands and product-mix changes 1. The dynamic environmentin production requires an increasing number of reconfigurationson assembly manufacturing resources 3. In automated assemblysystems such as robots, the flexibility is normally restricted due tothe high programming effort required in order for robot trajec-tories to adjust to different assembly cell layouts. Experiencedrobot programmers have to spend considerable time in order tooptimize the robotic paths for each specific application by usingconventional programming methods. A method that is widelyused is programming by demonstration, where the intermediatepoints to the goal position are recorded by sequentially movingthe robot to each position using the teach pendant. The robotsfinal path is generated by connecting the recorded points via arobot controller, which tries to pass through all the points bytaking into consideration the dynamic constraints of the robot. Therobots final trajectory is highly dependent on the points recordedand the experience of the respective programmer, who has carriedthis out. Automatic path planning for robotics poses the questionas to how a robot can move from its initial to the final position andhas been investigated during the last decades mainly focusing onpath planning for collision avoidance.One of the techniques for motion planning is the construction ofapproximate models by sampling their configuration space. Over thelast few years, there has been a lot of work carried out for theimprovement of sampling based motion planning algorithms. It ishard to define a single criterion that can classify all planners indistinct categories. The classical separation is between roadmap-based planners and tree-based planners 4.The probabilistic road-map path planning was introduced in 5 as a new method ofcomputing collision-free paths for robots. The method proceeds intwo phases: those of learning and query. In the learning phase, aprobabilistic roadmap is constructed by generating the robotsrandom free configurations and connecting them using a simplemotion planner, also known as a local planner. Different approacheshave been used to address a variety of problems. In 6, two differentmethods for constructing and querying roadmaps are suggested forthe motion planning of deformable objects. Another two deforma-tion techniques that can be applied to the resulting path are alsopresented. The obstacle probabilistic roadmap method is introducedinto 7, where several strategies for node generation are describedand multi-stage connection strategies are proposed for cluttered3-dimensional workspaces. In 8, a randomized planner is describedfor planning CF-compliant motion between two arbitrary polyhedralsolids, by extending the probabilistic roadmap paradigm for plan-ning collision-free motion to the space of contact configurations. Thekey to this approach is a novel sampling strategy of generatingrandom CF-compliant configurations.Contents lists available at ScienceDirectjournal homepage: and Computer-Integrated Manufacturinghttp:/dx.doi.org/10.1016/j.rcim.2014.10.0020736-5845/& 2014 Elsevier Ltd. All rights reserved.nCorresponding author.E-mail address: xrisollms.mech.upatras.gr (G. Chryssolouris).1Tel.: 30 2610 997262.Robotics and Computer-Integrated Manufacturing 32 (2015) 6571The concept of Rapidly-exploring the Random Tree is introducedin 9. The basic idea is that an initial sample (the starting config-uration) is the root of the tree and newly produced samples are thenconnected to the samples already existing in the tree. In 10, twoRapidly-exploring Random trees (RRTs) were rooted at the start andduring the goal configurations. Each one of the trees explores thespace around it and also advances towards each other through theuse of a simple greedy heuristics. Although it was originallydesigned that motions be planned for a human arm (modeled as a7-DOF kinematic chain), in the automatic graphic animation ofcollision-free grasping and manipulation tasks, the algorithm hasbeen applied to a variety of path planning problems. Tree-basedplanners have proven to be a good framework for dealing with real-time planning and re-planning problems. In 11, a re-planningalgorithm is presented for repairing Rapidly-exploring RandomTrees when changes are made to the configuration space. Insteadof abandoning the current RRT, the algorithm efficiently removesonly the newly-invalid parts and maintains the rest. Dynamicobstacle avoidance has been investigated for the mobile robotsfound in industrial environments in 12. However, industrialmanipulators are typically programmed to execute predefined paths.The two main categories of robotic programming methods are thoseof online programming and offline programming.In 13, an online path planning and programming supportsystem is proposed for the transformation of the users interactioninto a simplified task that generates acceptable trajectories,applicable to industrial robot programming. In 14, a novelapproach to robot programming using an Augmented Realityenvironment was proposed, offering flexibility and adaptabilityto different environments when an on-site robot programmingapproach was desired. The path planning methodology included abeam search algorithm to generate paths. In 15, there is a similarstudy, where the user is able to perform operations, namely via-points selection and modification, in order for a smooth andcollision-free path to be achieved. An on-line robot motionplanning approach that is based upon pre-computing the globalconfiguration space (C-space) connectivity is proposed. In 16, themotion planner consists of an off-line stage and an on-line stageand the collision-free path is searched in this C-space by using theA*algorithm under a multi-resolution strategy.In this study, an intelligent search algorithm is proposed todefine an industrial robot manipulators path that leads to thedesired position and orientation of the end effector. A maximumnumber of alternative configurations are selected and evaluated ineach step until the desired configuration is approached within apredefined error. The alternative configurations are generated in aclever way giving emphasis to the joint angles that mainly affectthe robots position in the workspace. In the configuration space,there is a grid constructed to derive the robots alternative config-urations. A set of clever parameters are used to reduce the searchspace and increase the performance of the algorithm. In theevaluation of the alternatives, multiple criteria that would enhancethe algorithms flexibility to extend are used, in order for thedifferent requirements, namely the shortest path, to be fulfilled.2. ApproachFor an industrial robot manipulator (usually six degrees offreedom), the path planning problem is described via threehierarchical levels as shown in Fig. 1. For a given starting and goalposition, the requested paths include the robots intermediateconfigurations, where each configuration is a set of six jointparameters.2.1. Grid search of the alternative configurationFor an industrial robot manipulator with n degrees of freedom(n-DoF), the alternative configurations are defined from a set of njoint angles. If the possible values of each joint angle are equal to2k1, with resolution d(Fig. 2), the number of alternativeconfigurations is given by the following equation:Number of alternative configurations N 2k1n1For each joint angle that can be incremented, a dnresolutionhas to be selected.The number of alternative configurations increases for a robotwith higher degrees of freedom and a larger grid (k) size. For thisreason, the following parameters are used for the reduction of thealternative configurations, where a multi-criteria evaluation willbe carried out as follows:?Decision Horizon (DH): This parameter is taking values from oneto n (DoF of the robot). Starting from the base of the robot, DHFig. 1. Hierarchical levels for path planning problem (6 DOFs robot).K. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 657166parameter defines the degrees of freedom which are taken inconsideration while constructing the grid of the alternativeconfigurations. For joint angles, in the decision horizon, a grid iscreated as shown in Fig. 2. For the remaining joints, outside thedecision horizon, only a number of samples are randomly takenin order to have complete alternative robot configurations. Therobots joints are separated into those that mainly affect therobots movement in the workspace (position of the end effector)and those that mainly affect the orientation of the end effector.When only the target position has to be reached and theorientation of the end effector is ignored this parameter couldbe reduced for better performance and less computational time.?Maximum number of alternatives (MNA): A maximum number ofalternatives from the grid in the decision horizon are randomlyselected for evaluation. If MNA4N then automatically theparameter MNAN.?Sample Rate (SR): A sample rate is defined as the number ofsamples taken from the joints, outside the decision horizon, inorder to form the robots complete alternative configurations.When the orientation of the end effector is considered, SRparameter should be increased in order to generate morealternative configurations which affect the orientation of theend effector.For an industrial manipulator with 6 DOF (n6, Fig. 3), even fork1 and d101 for each degree of freedom, the number ofalternative configurations is given by Eq. (1): (Figs. 46)N 36 729 Alternative neighbor configurations of robotBy setting DH3, only the first three degrees of freedom aretaken into consideration whilst the number of the alternativeconfiguration on the grid drops down toNDH 3 33 27 Alternative configurations for DH 3The maximum number of alternatives in the decision horizon isdefined as follows:MNArNThe probability of getting the alternative configuration closer tothe desired position is given by the following equation:pDH;MNA MNAN2From 1 and 2pDH; MNA MNA2k1DH3Therefore, in the example with the 6 DOFs robot where, thenumber of the alternative configurations was found to be N27(for DH3)If MNA20, the probability of getting the alternative config-uration that is closer to the desired position is given by Eq.(2)Fig. 2. Available joint angles for each degree of freedom in the DH.Fig. 3. COMAU Smart5 Six, 6 DOF, Industrial Manipulator.Fig. 4. Alternative configurations using MNA3, DH3 and SR2 parameters for 6 DOFs.K. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 657167Probability to get the best alternative configuration in DH,P(DH3, MNA20) 20=27 74%Consequently, for exhaustive search in DH (P1), MNAN27Giving sample rate (SR)2 for each alternative in the decisionhorizon, two samples are taken from the rest of the joints; thus,the number of complete alternative configurations becomesN completeMNA 27; SR 2 MNAnSR 27 ? 2 54 complete alternativesIn general, the number of complete alternative configurationsfor the predefined MNA and SR parameters is given by thefollowing equation:Number of complete alternative configurationsMNA;SR;Ncomplete MNAnSR4The proposed algorithm does not have to search the entire work-space of the robot. During each iteration, only a maximum numberof neighbor configurations are evaluated. Calculation time for acomplete target path depends on the distance of the starting pointto the target. Calculation time also increases when more inter-mediate points are requested for a smoother path that betterfulfills the desired criteria.2.2. Evaluation of the alternative configurationsMultiple criteria are used for the evaluation of the alternativeconfigurations. A decision matrix is built as shown in the followingtable. In the context of this study, two criteria have been taken intoconsideration, those of the distance due to translation and the distancedue to rotation from the target position and the robots orientation.Despite the fact that the proposed algorithm could also be used justfor the definition of the joint parameters for a given position andorientation of the robots end effector (inverse kinematics), the mainpurpose of this study is to plan the robots path, which better fulfillsthe multiple criteria defined by the user. The search algorithm is easilyextensible for more criteria. (Tables 1 and 2)The utility for each of the alternatives is calculated as theweighted sum of the distance due to translation and to orientation.Ui WtjjXi?XjjWrfqi;q5where Xi?X, is the Euclidean distance of the end effector from thetarget position and fqi;qtarget is the distance due to rotation(orientation of the target configuration).The weight factors Wtand Wrare selected from the user inorder to give emphasis to the desired criterion. If the user is onlyinterested in the position of the end effector, the factors Wt1 andWr0 should be used.The metric of the distance between rotations is the Norm of theDifference of Quaternions, described in detail in 17.fqi;qtarget min fjjqi?qtargetjj;jjqiqtargetjjg6where, J J denotes the Euclidean norm (or 2-norm) and q theorientation of the end effector, expressed in quaternions. Themetric gives values in the range 0;ffiffiffi2p?.The alternative configuration with the smaller utility function isselected at each decision point.Path search algorithmInput: Target position (X Y Z), target orientation (Euler anglesZYZ”), DH, MNA, SR, (k, d: grid size & resolution)Output: Target configuration (123 n) & the sequenceof the intermediate configurations (path)1. The Grid parameters k & dare defined.2. The DH is defined. DH1/number of the robots DOF.3. The Grid is constructed for DH. Alternatives are generated.4. The MNA is selected in order to enable a configuration near thetarget.5. The SR is defined. Random samples are taken from the jointsafter the DH.6. A decision matrix is built; MNAnSR complete alternatives areevaluated. The alternative configuration that provides thesmaller value of the utility function is selected.7. The resolution and the size of the grid are redefined.8. Steps 17 are repeated until there is an alternative configura-tion that provides the target position and target orientationwithin the pre-defined distance error.2.3. Industrial manipulator motion generationThe proposed algorithm calculates the robots sequential,intermediate configurations in order to approach the target posi-tion while fulfilling the predefined criteria for the path. Everyconfiguration of the robot is within its joint limits. The robotcontroller uses the derived path in order to generate the motion ofthe industrial manipulator, taking into consideration the dynamicconstraints of the robot.3. ImplementationThe proposed algorithm has been implemented in Matlab withthe use of the Robotics Toolbox 18. The flowchart of thealgorithm is presented in the following figure.Fig. 5. Industrial robot motion generation.Table 1Evaluation of the alternatives according to the distance criteria.AlternativeConfigurationsNormalized criteriaUtility valueDistance dueto translationDistance dueto rotationUi W1Ci1 W2Ci2(where W1and W2the criteria weights)Alternative 1C11C12U1Alternative 2C21C22U2Alternative 3C31C32U3AlternativemMNAnSRCm1Cm2UmK. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 6571684. ResultsIn Figs. 7 and 8, it is observed that the grid size and resolutionparameters (k, d) have a great influence on the smoothness ofthe path towards the desired position. Lower values of theseparameters lead to better paths, however, the computational timeis increased.4.1. Search algorithm parameters correlationIn order for the correlation among the search parameters MNA,DH and SR to be examined, a set of experiments was designedusing the Taguchi method with the objective of process timeminimization. The initial values of the grid parameters wereselected to be k5 and d0.1 rad (E61).4.1.1. Taguchi design of experimentsThe effect of the search parameters DH, MNA, and SR will beexamined so as for the process time required for finding the pathto be minimized to the target position. Four levels are selected foreach parameter. The proposed set of experiments, according to theTaguchi method, is given in L16 table.L16 table:Fig. 7. Grid resolution effect on the on the path (a) d0.01 rad and (b) d0.1 rad.Fig. 6. Flowchart of the proposed algorithm.Table 2Set of experiments for 4 levels of the parameters DH, MNA, and SR.Exp. no.DHMNASRTime (Sec)122510.60225020.57327531.124210041.82532540.72635030.91737520.918310011.17942520.551045010.911147542.1612410031.601352531.291455042.841557510.4816510022.01K. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 6571694.1.1.1. Analysis of means (ANOM)?From Figs. 9 and 10, it is observed that the target position of theend effector is better approached for DH3 (first three degreesof freedom of the robot). The higher values of MNA and SR aresufficient only when the orientation is taken into consideration.In order for both the target position and orientation of the endeffector to be approached, the best results (lowest computingtime) are given for DH3, MNA25 and SR2.?The interaction among the parameters DH, MNA and SR andtheir effect on the computing time is presented in Fig. 11. It isconfirmed that for lower DH values sufficient SR has to beconsider whilst for higher DH values the SR value should beminimum for less computing time.Fig. 8. Grid size effect on the path (a) path generated for k1 and (b) path generated for k5.Fig. 9. DH, MNA and SR vs. processing time (target position).Fig. 10. DH, MNA and SR vs. processing time (target position and orientation).Fig. 11. Interaction of DH with SR (target position).K. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 6571705. ConclusionsIn this study, an intelligent search algorithm is proposed todefine the path that leads to the desired position and orientation ofthe end effector of an industrial robot manipulator. The gridparameters as well as the search algorithm parameters DH, MNA,SR are proven to be drastically reducing the processing
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