畢業(yè)論文（設(shè)計(jì)）
外文翻譯
題 目：運(yùn)動學(xué)和軌跡規(guī)劃的黃瓜采摘機(jī)器人機(jī)械手
系部名稱： 專業(yè)班級：
學(xué)生姓名： 學(xué) 號：
指導(dǎo)教師： 教師職稱：
20**年03月10日
張利兵、王雁、楊慶華、寶冠君、高鋒、薰易
(教育部重點(diǎn)實(shí)驗(yàn)室的機(jī)械制造及自動化、浙江理工大學(xué)、中國杭州310012)
摘要：為了降低成本，提高黃瓜收獲經(jīng)濟(jì)效益，黃瓜收獲機(jī)器人得以發(fā)展。黃瓜果蔬采摘機(jī)器人由一輛汽車,一個(gè)四自由度關(guān)節(jié)機(jī)械手,一個(gè)手端,一個(gè)上一個(gè)視覺系統(tǒng)與監(jiān)控、四直流伺服驅(qū)動系統(tǒng)組成。把黃瓜的運(yùn)動學(xué)果蔬采摘機(jī)器人機(jī)械手使用D- H標(biāo)系建立了框架模型。而且它提供了一個(gè)逆運(yùn)動學(xué)軌跡規(guī)劃的基礎(chǔ)已經(jīng)解決了逆變換技術(shù)。擺線針輪運(yùn)動，它具有的性能的連續(xù)性和零速度和加速度的港口及有界區(qū)間，采用一種可行的
方法在關(guān)節(jié)空間軌跡規(guī)劃，研究了果蔬采摘機(jī)器人的機(jī)械臂的黃瓜。此外，硬件和摘要軟件基于上面的顯示器之間的交流及關(guān)節(jié)的控制器的設(shè)計(jì)。實(shí)驗(yàn)結(jié)果表明，上面的顯示器與四關(guān)節(jié)控制器的溝通，有效地摘要錯誤的思想和綜合四關(guān)節(jié)角不超過四度。誤差產(chǎn)生的可能因素分析及相應(yīng)的解決方案，為提高測量精度的措施提出了建議。
關(guān)鍵詞：黃瓜果蔬采摘機(jī)器人軌跡規(guī)劃、關(guān)節(jié)機(jī)械臂、運(yùn)動、摘要、擺線針輪
分類號：10.3965/j.issn.1934-6344.2009.01.001-007。
引文：張利兵，楊慶華，寶冠君，高鋒，薰易。運(yùn)動學(xué)和軌跡規(guī)劃黃瓜收獲機(jī)器人的機(jī)械手。農(nóng)業(yè)與生物學(xué)工程，2009；2（1）：1-7。
一．介紹
水果和蔬菜的收獲是一個(gè)勞力密集的工作，由人類勞動和收獲的成本大約是33％?總數(shù)的50％，生產(chǎn)成本[1]。因此，機(jī)械化和自動化，迫切需要水果和蔬菜收獲。目前，許多國家正在研究。
收稿日期：08-11-20 接受日期：009-03-28
傳記：張利兵，教授，博士，主要從事農(nóng)業(yè)機(jī)器人，機(jī)電一體化和控制。王雁，博士候選人浙江工業(yè)大學(xué)，主要從事，機(jī)器人，智能儀表。楊慶華，教授，博士，主要從事機(jī)器人技術(shù)，機(jī)電一體化和控制。寶冠君，講師，博士，主要從事機(jī)器人技術(shù)，控制人數(shù)及機(jī)器視覺。高峰，副教授，博士，主要從事機(jī)電工程等。薰易，博士，主要從事視覺系統(tǒng)和圖像處理。
通訊作者: 張利兵，教育部重點(diǎn)實(shí)驗(yàn)室機(jī)械制造、自動化、浙江工業(yè)大學(xué)310012技術(shù),中國,杭州，310012。電話及傳真：+86-571-88320007。電子郵箱：robot@zjut.edu.cn
研究了果蔬采摘機(jī)器人,尤其是荷蘭和日本。機(jī)器人的一些收獲,如黃瓜、西紅柿、葡萄收獲機(jī)器人已廣泛應(yīng)用在溫室里和其他人在農(nóng)場上[2、3]。在中國,雖然研究是遲于果蔬采摘機(jī)器人在發(fā)達(dá)國家,一些有利的方面取得通過努力在國內(nèi)許多高等院校和研究機(jī)構(gòu),就是這樣的采摘機(jī)器人的設(shè)計(jì)由中國茄子農(nóng)業(yè)大學(xué)和一個(gè)番茄收獲機(jī)器人浙江大學(xué)開發(fā)的。
國家高技術(shù)大力支持下,國家級高新技術(shù)研究和發(fā)展計(jì)劃(863)(2007AA04Z222),第一個(gè)系統(tǒng)化的黃瓜研究了果蔬采摘機(jī)器人在中國是聯(lián)合研制開發(fā)的中國農(nóng)業(yè)大學(xué)和浙江工業(yè)大學(xué)技術(shù)。它由一個(gè)車，一個(gè)4自由度（簡稱自由度）關(guān)節(jié)機(jī)械手，一最終效應(yīng)，一上位，視覺系統(tǒng)和四個(gè)直流伺服驅(qū)動系統(tǒng)。由浙江工業(yè)大學(xué)，利用一種工業(yè)機(jī)械手來代替四自由度關(guān)節(jié)機(jī)械手的關(guān)節(jié)，旨在減少成本和適應(yīng)環(huán)境的收獲。
本文主要考察了四自由度鉸接式機(jī)器人運(yùn)動學(xué)和軌跡規(guī)劃，這是概述如下。在第一節(jié)中，結(jié)構(gòu)黃瓜收獲機(jī)器人機(jī)械臂描述。機(jī)械手的運(yùn)動學(xué)建造的第2節(jié)逆運(yùn)動學(xué)和第3節(jié)中得到解決。第4節(jié)的軌跡規(guī)劃算法擺線運(yùn)動。硬件和軟件設(shè)計(jì)軌跡規(guī)劃基于CAN總線技術(shù)的引入第5節(jié)。實(shí)驗(yàn)測量的實(shí)際位置4節(jié)進(jìn)行搶修，對錯誤的可能原因在第6節(jié)進(jìn)行了分析。最后，結(jié)論是畫在第7節(jié)。
二．黃瓜采摘機(jī)器人機(jī)械手結(jié)構(gòu)
本文詳細(xì)介紹了運(yùn)動學(xué)機(jī)械手和軌跡規(guī)劃的實(shí)現(xiàn)基于CAN控制總線。線圖和關(guān)節(jié)機(jī)械手的照片顯示在圖1。它是由四個(gè)旋轉(zhuǎn)接頭：腰圍關(guān)節(jié)（J1），肩關(guān)節(jié)（J2），肘關(guān)節(jié)（J3）和手腕聯(lián)合（J4）。一端固定在底座上，另一端連接到終端效應(yīng)其中包含兩個(gè)部分：一爪抓水果和切割設(shè)備另外從植物的果
圖1線框圖和相片的黃瓜果蔬采摘機(jī)器人機(jī)械臂
該系統(tǒng)采用黃瓜采摘機(jī)器人多CPU，分布式控制，上位機(jī)和聯(lián)合伺服控制器的結(jié)構(gòu)。
此外，四個(gè)關(guān)節(jié)驅(qū)動的完美和諧的工作通過CAN總線通訊，有效支持分布式實(shí)時(shí)控制系統(tǒng)。該通信系統(tǒng)黃瓜收獲機(jī)器人如圖2所示。在上位監(jiān)控用于監(jiān)控和管理整個(gè)機(jī)器人系統(tǒng)，找到黃瓜目標(biāo)，并規(guī)劃軌跡。 CAN總線是傳輸?shù)臉蛄荷衔槐O(jiān)控和聯(lián)合控制器。伺服控制器，分布在各個(gè)關(guān)節(jié)驅(qū)動力矩馬達(dá)和他們能夠?qū)崿F(xiàn)閉環(huán)控制從接受角度編碼器反饋信號。
圖2通信系統(tǒng)中的黃瓜收獲機(jī)器人
三．學(xué)模型坐標(biāo)框架
運(yùn)動學(xué)模型坐標(biāo)框架Denavit-Hartenberg模型,構(gòu)造了(D- H型),這已被廣泛使用在機(jī)器人由于它嗎明確的機(jī)制和物理解釋在相對容易實(shí)施的程序機(jī)器人操作臂控制的。D- H標(biāo)系框架模型基于任務(wù)的笛卡爾坐標(biāo)框架固定相對于機(jī)器人機(jī)械臂的每一環(huán)節(jié)。而且它描述了空間變換關(guān)系兩個(gè)連續(xù)的4×4連結(jié)變換矩陣我i-1Ai，以鏈接的氮轉(zhuǎn)化成相應(yīng)的坐標(biāo)框架坐標(biāo)系可以被寫為[4,5]：
其中a是一個(gè)是接近的方向向量；0定向的矢量，n = 0 × a 是一個(gè)正常的向量；P為最終效應(yīng)相對位置向量基礎(chǔ)坐標(biāo)系。
在D- H的變換矩陣i-1Ai關(guān)一數(shù)的旋轉(zhuǎn)和平移兩連續(xù)幀坐標(biāo)表示為[6，7]：
其中θ是聯(lián)合角；αi是扭轉(zhuǎn)角；di是一個(gè)聯(lián)合抵消；ai是一個(gè)鏈路長度。
圖3所示的D – H坐標(biāo)系的幀機(jī)器人機(jī)械臂和表1總結(jié)它的D – H參數(shù)。
圖3 D– H坐標(biāo)系黃瓜收割機(jī)器人操作臂控制
表1機(jī)器人的機(jī)械臂D – H參數(shù)
四．黃瓜收獲機(jī)器人的機(jī)械手逆運(yùn)動學(xué)
逆運(yùn)動學(xué)問題的機(jī)器人機(jī)械手是要找到一個(gè)載體，聯(lián)合變量產(chǎn)生一個(gè)理想的最終效應(yīng)位置和方向。逆變換技術(shù)來解決問題[8,9]。為了挑選黃瓜方便，腕關(guān)節(jié)，必須平行于X軸的坐標(biāo)系的基礎(chǔ)，所以可以得到：
θ2 + θ3 +θ4 = 0°
對于方程（1），它可以改寫為：
而
首先，讓等式（3,4）矩陣（4）及（5）是等價(jià)的，θ1可表示為：
那就讓等式（1，4）和（2,4）矩陣（4）及（5）是等價(jià)的，下面的公式可以得到：
通過簡化方程（7）：
從方程（7），可得出θ2 ，θ3 可表示為：
五．在關(guān)節(jié)空間軌跡規(guī)劃的基礎(chǔ)上擺線運(yùn)動
該機(jī)器人的機(jī)械手軌跡規(guī)劃以這種方式定義：找到共同的時(shí)空運(yùn)動規(guī)律位置，速度和加速度，根據(jù)給定操作的最終效應(yīng)。運(yùn)動規(guī)律由軌跡規(guī)劃師產(chǎn)生的必須使用一些特別是戰(zhàn)略來消除額外的運(yùn)動，如抖振和共鳴。他們必須是足夠光滑，連續(xù)的第一及第二衍生物[10,11]。在規(guī)劃數(shù)算法，擺線運(yùn)動，尤其適合適用于點(diǎn)對一點(diǎn)，因?yàn)樗能壽E規(guī)劃金額較小的計(jì)算，平滑度和連續(xù)性，零速度和加速度，并在最初的功能和有界區(qū)間[12]終點(diǎn)。它的運(yùn)動曲線可以描述為[13]：
那么它的第一和第二導(dǎo)數(shù)可以表示為：
而
是常規(guī)時(shí)間，T為一個(gè)收獲的工作時(shí)間。
圖4顯示了彎的擺線針輪運(yùn)動和它的第一和第二衍生物在規(guī)范區(qū)間(- 1,1)。從圖4,它可以清楚地看出擺線針輪運(yùn)動是平的;同時(shí),充分的速度和加速度運(yùn)動和價(jià)值觀都是連續(xù)的。
圖 4 擺線運(yùn)動和第一及第二衍生物
開始和結(jié)束點(diǎn)的區(qū)間0≤τ≤1足輕重。這證明了機(jī)器人末端執(zhí)行器的的運(yùn)動機(jī)器人操作臂控制不會抖振，所以它可以確保運(yùn)動穩(wěn)定性的機(jī)器人系統(tǒng)。
如屬聯(lián)名我，軌跡規(guī)劃和位置依賴定位最終效應(yīng)。所以,第一步的獲取軌跡規(guī)劃是三維的描述目標(biāo)的空間小黃瓜。這描述是基于感官信息等機(jī)器視覺以及先驗(yàn)信息機(jī)器人的機(jī)械臂運(yùn)動學(xué)結(jié)構(gòu)。從目標(biāo)位置的機(jī)器人末端執(zhí)行器與逆6日運(yùn)動學(xué)(Eqs 10、12、13)。開始后關(guān)節(jié)角qi(f)我問被紅牌罰下,通過從關(guān)節(jié)控制器的摘要,這個(gè)位置,速度,加速度方程的基礎(chǔ)上擺線針輪運(yùn)動可以表達(dá)為:開機(jī)后關(guān)節(jié)角度qi(0)智商已經(jīng)從通過CAN總線控制器的聯(lián)合，位置，速度，加速度方程的基礎(chǔ)上擺線運(yùn)動可以表示為：
六．硬件和軟件設(shè)計(jì)的軌跡規(guī)劃基于CAN總線
6 – 1. 接口電路的CAN總線
控制器區(qū)域網(wǎng)絡(luò)（CAN）是一種先進(jìn)的串行通訊協(xié)議的分布式實(shí)時(shí)控制系統(tǒng)。不同的設(shè)備，如處理器，傳感器和執(zhí)行器可以連接到CAN總線通過雙絞線，可以互相溝通通過交換信息。最大傳輸速率可達(dá)1Mbps的在嘈雜的環(huán)境。和它利用載波感測多重存取及碰撞檢測（CSMA/ CD）為仲裁機(jī)制使其附著節(jié)點(diǎn)有訪問總線[14-16]。黃瓜收獲機(jī)器人系統(tǒng)采用點(diǎn)多點(diǎn)的CAN總線通信。該上位機(jī)和四個(gè)控制器是由聯(lián)合dsPIC30F4012為數(shù)字信號處理器包含標(biāo)準(zhǔn)CAN控制器和MCP2551收發(fā)器。和一個(gè)4線接口的設(shè)計(jì)基于CAN總線協(xié)議（CAN2.0A），它提供電源，接地和基礎(chǔ)兩個(gè)數(shù)據(jù)線（CAN高和CAN低）。該接口的CAN總線電路示于圖5。和上監(jiān)視電路板如圖6所示。該的CAN總線通信，采用1Mbps的傳輸率，和消息傳遞由2個(gè)字節(jié)的標(biāo)識符，1個(gè)字節(jié)的數(shù)據(jù)長度和8字節(jié)的數(shù)據(jù)。消息以時(shí)間為10毫秒內(nèi)透光根據(jù)收獲的要求。 CAN總線通信具有良好的實(shí)時(shí)性能，在實(shí)際申請專利。
圖5接口電路的CAN總線
圖6上監(jiān)視電路板
6 – 1. 軟件設(shè)計(jì)的軌跡規(guī)劃黃瓜采摘機(jī)器人
上部顯示器具有管理職能和監(jiān)理的機(jī)器人系統(tǒng)，黃瓜目標(biāo)位置和軌跡規(guī)劃。該方案設(shè)計(jì)采用了模塊化的構(gòu)想，是由幾個(gè)子程序。圖7說明過程為黃瓜收獲機(jī)器人軌跡規(guī)劃。它包括如CAN總線發(fā)送和子程序接收，黃瓜目標(biāo)捕獲，逆運(yùn)動學(xué)和軌跡規(guī)劃。
圖 7 流程圖的軌跡規(guī)劃
七．實(shí)驗(yàn)和分析
為了驗(yàn)證彈道精度規(guī)劃算法和CAN總線通信，實(shí)驗(yàn)測量的實(shí)際位置的四個(gè)黃瓜收獲機(jī)器人的機(jī)械手的執(zhí)行關(guān)節(jié)與坐標(biāo)測量機(jī)（CMM）的法魯技術(shù)白金FaroArm測量臂法團(tuán)。作為世界上最暢銷的便攜式測量臂，鉑FaroArm測量臂是在尺寸規(guī)格從1.2米到3.7米，有精度高達(dá)0.013毫米。
實(shí)驗(yàn)進(jìn)行如下：
1）設(shè)置最終effecor位置：
Px = 700mm, Py = 200mm, Pz = 668mm 。通過利用逆運(yùn)動學(xué)，四個(gè)關(guān)節(jié)角度可以計(jì)算出來方程（6）?（13）：θ1 =15.95°， θ2 =55.82 °，θ3 =-33.48°，θ4 =-22.34
°。
2）對每一節(jié)理面與擺線軌跡運(yùn)動算法和發(fā)送郵件的計(jì)劃角通過CAN總線控制器的聯(lián)合。
3）使用鉑FaroArm測量臂的角度來衡量實(shí)際扭矩馬達(dá)的旋轉(zhuǎn)。
4）其他9月底效應(yīng)，重復(fù)（1）?（3）步的位置。實(shí)驗(yàn)結(jié)果列于表2。
實(shí)驗(yàn)結(jié)果表明，四個(gè)關(guān)節(jié)角度的綜合誤差不超過四度。對實(shí)驗(yàn)誤差的可能原因是：
（1）單關(guān)節(jié)控制精度為0°?1 °，（2）機(jī)械結(jié)構(gòu)錯誤，包括安裝和變形誤差;（3）最終沒有意識到效應(yīng)閉環(huán)位置控制。相應(yīng)的解決方案是：（1）添加一些補(bǔ)償算法，以提高單關(guān)節(jié)控制精度，（2）代替鋁用于PVC合金制造的機(jī)械手，以減少機(jī)械誤差;（3）安裝在一個(gè)小型攝像機(jī)最終效應(yīng)，實(shí)現(xiàn)了閉環(huán)控制機(jī)械手。
表2實(shí)驗(yàn)結(jié)果對實(shí)際測量的位置機(jī)器人機(jī)械手的四個(gè)關(guān)節(jié)
理論值（度） 測量值（度）
八．結(jié)論
1)研究了果蔬采摘機(jī)器人運(yùn)動學(xué)的黃瓜機(jī)械手使用D – H坐標(biāo)系建立了框架模型。逆向運(yùn)動學(xué),它提供了一個(gè)軌跡規(guī)劃的基礎(chǔ),已經(jīng)解決了反變換技術(shù)。
2）擺線運(yùn)動，它的性質(zhì)連續(xù)性，計(jì)算量小，速度為零并在有界區(qū)間的港口加速，是建議，作為可行的方法進(jìn)行規(guī)劃，關(guān)節(jié)軌跡空間機(jī)器人的機(jī)械手。
3）軟件和CAN總線的硬件上位機(jī)之間的溝通和聯(lián)合控制器的設(shè)計(jì)。
4）實(shí)驗(yàn)結(jié)果表明,上面的顯示器有四個(gè)共同控制器有效地溝通摘要的,綜合誤差四關(guān)節(jié)角均小于四度。
承認(rèn)：這項(xiàng)工作是支持國家自然科學(xué)中國基金（50575206）和國家高技術(shù)研究與發(fā)展（863）中國項(xiàng)目方案（2007AA04Z222）。
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Kinematics and trajectory planning of a cucumber harvesting robot manipulator
Zhang Libin, Wang Yan, Yang Qinghua, Bao Guanjun, Gao Feng, Xun Yi
(The MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310012, China)
Abstract:In order to reduce cucumber harvesting cost and improve economic benefits, a cucumber harvesting robot was developed. The cucumber harvesting robot consists of a vehicle, a 4-DOF articulated manipulator, an end-effector, an upper monitor, a vision system and four DC servo drive systems. The Kinematics of the cucumber harvesting robot manipulator was constructed using D-H coordinate frame model. And the inverse kinematics which provides a foundation for trajectory planning has been solved with inverse transform technique. The cycloidal motion, which has properties of continuity and zero velocity and acceleration at the ports of the bounded interval, was adopted as a feasible approach to plan trajectory in joint space of the cucumber harvesting robot manipulator. Moreover, hardware and software based on CAN-bus communication between the upper monitor and the joint controllers have been designed. Experimental results show that the upper monitor communicates with the four joint controllers efficiently by CAN-bus,
and the integrated errors of four joint angles do not exceed four degrees. Probable factors resulting in the errors were analyse and the corresponding solutions for improving precision are proposed.
Keyword:cucumber harvesting robot, articulated manipulator, trajectory planning, cycloidal motion, CAN-bus
DOI:10.3965/j.issn.1934-6344.2009.01.001-007
Citation:Zhang Libin, Wang Yan, Yang Qinghua, Bao Guanjun, Gao Feng, Xun Yi. Kinematics and trajectory planning of a cucumber harvesting robot manipulator. Int J Agric & Biol Eng, 2009; 2(1): 1－7.
1 Introduction
Fruit and vegetable harvesting is a labor-intensive job,and the harvesting cost by human labor is about 33%～50% of the total production cost[1]. Therefore, it isurgent to mechanize and automate fruit and vegetable harvesting. Currently, many countries are studying.
Received date: 2008-11-20 Accepted date: 2009-03-28
Biographies:Zhang Libin, professor, Ph.D, mainly engaged in agricultural robot, mechatronics and control. Wang Yan, Ph.D candidate of Zhejiang University of Technology, mainly engaged in robotics, intelligent instruments. Yang Qinghua, professor, Ph.D, mainly engaged in robotics, mechatronics and control. Baoguanjun, lecturer, Ph.D, mainly engaged in robotics, control and machine vision. Gao Feng, associate professor, Ph.D, mainly engaged in electromechanical engineering. Xun Yi, Ph.D, mainly engaged in vision system and image processing.
Corresponding author:Zhang Libin, MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310012, China. Tel & fax: +86-571-88320007. Email: robot@zjut.edu.cn
harvesting robot, especially Netherlands and Japan. Some of the harvesting robots, such as cucumber, tomato, grape harvesting robots have been applied in greenhouses
and others on farms[2,3]. In China, though research on harvesting robot is later than that in developed countries,some favorable achievements have been made through efforts in many universities and research institutes, such as the eggplant picking robot designed by China Agricultural University and the tomato harvesting robot developed by Zhejiang University.
Under the support of the National High-Tech Research and Development (863) Program of China(2007AA04Z222), the first systematical cucumber harvesting robot in China was jointly developed by China Agricultural University and Zhejiang University of Technology. It consists of a vehicle, a 4-degree of freedom (DOF for short) articulated manipulator, an end-effector, an upper monitor, a vision system and four DC servo drive systems. Instead of utilizing an industrial manipulator, the 4-DOF articulated manipulator was designed by Zhejiang University of Technology to reduce the cost and adapt to the harvesting environment.
This paper mainly investigates the 4-DOF articulated manipulator kinematics and trajectory planning, and it is outlined as follows. In Section 1, the structure of cucumber harvesting robot manipulator is described. The kinematics of manipulator is constructed in Section 2 and the inverse kinematics is solved in Section 3. Section 4 presents the trajectory planning algorithm of cycloidal motion. The hardware and software design of trajectory planning based on CAN-bus is introduced in Section 5. Experiments measuring actual position of four joints are carried out and possible causes for errors are analyzed in Section 6. Finally, conclusions are drawn in Section 7.
2 Cucumber harvesting robot manipulator structure
This paper describes in detail the kinematics of the robot manipulator and realization of trajectory planning control based on CAN-bus. The line diagram and photograph of the articulated manipulator is shown in Figure 1. It is composed of four rotation joints: waist joint (J1), shoulder joint (J2), elbow joint (J3) and wrist joint (J4). One end is fixed on the base, and the other end is connected to an end-effector which contains two parts: a gripper to grasp the fruit and a cutting device to separate the fruit from the plant.
Figure 1 Line diagram and photograph of the cucumber harvesting robot manipulator
The cucumber harvesting robot system employs multi-CPU, distributed control structure of upper monitor and joint servo controllers. Moreover, the four joints are driven to work in perfect harmony by CAN-bus communication which efficiently supports the distributed real-time control system. The communication system of
the cucumber harvesting robot is shown in Figure 2. The Upper monitor is used to monitor and manage the whole robot system, locate cucumber target, and plan
trajectory. The CAN-bus is the transmission bridge between upper monitor and joint controllers. The servo controllers are distributed in each joint to drive torque
motors and they can realize close-loop control by receiving feed back signals from angle encoders.
Figure 2 Communication system of the cucumber harvesting robot
3 Coordinate frames of kinematics models
Coordinate frames of kinematics models are constructed by Denavit-Hartenberg model (D-H for short), which has been widely adopted in robotics due to its explicit physical interpretation of mechanisms and relatively easy implementation in the programming of the robot manipulator. D-H coordinate frame model is based on assignment of Cartesian coordinate frames fixed relative to each link of robot manipulator. And it describes spatial transformation between two consecutive links by 4×4 transformation matrix i-1Ai, so the transformation of link n coordinate frame into the basecoordinate frame can be written as[4,5]:
where a is the vector of approaching direction; 0 is orientation vector, n = a×0 is the normal vector;P is the position vector of end-effector relative to thebase coordinate frame.
The D-H transformation matrix i-1Ai-relating to a number of rotations and translations between two consecutive coordinate frames is expressed as[6,7]:
Where θi is joint angle;αi is twist angle;di is joint offset;ai is the length of link.
Figure 3 illustrates the D-H coordinate frames of the robot manipulator and Table 1 summarizes its D-H parameters.
Figure 3 D-H coordinate frames of the cucumber harvesting robot manipulator
Table 1 D-H parameters of the robot manipulator
4 Inverse kinematics of the cucumber harvesting robot manipulator
The inverse kinematics problem for a robot manipulator is to find a vector of joint variables that produces a desired end-effector position and orientation.
The inverse transform technique is used to solve the problem[8,9]. In order to pick cucumbers conveniently, the wrist joint has to be parallel to X axis of the base coordinate frame, so it can be obtained:
θ2 + θ3 +θ4 = 0°
For equation (1), it can be rewritten as:
Where
First, let element (3,4) of matrix (4) and (5) be equal,θ1 can be given by:
Then let element (1, 4) and (2, 4) of matrix (4) and (5) be equal, the following equations can be obtained:
By simplifying equation (7):
From equation (7), θ2, θ3 can be expressed as:
5 Trajectory planning in joint space based oncycloidal motion
Trajectory planning of the robot manipulator is defined in this way: find temporal motion laws for joint position, velocity and acceleration according to a given operation of the end-effector. The motion laws generated by trajectory planner have to use some particular strategies to eliminate extra movements such as chattering and resonance. They have to be smooth enough, and continuous for their first and second derivatives[10,11]. Within a number of planning algorithms, cycloidal motion is especially suitable to apply in point-to-point trajectory planning because of its smaller amount of calculation, smoothness and continuity,
and features of zero velocity and acceleration at the initial and end points of the bounded interval[12]. Its motion curve can be described as[13]:
Then its first and second derivatives can be expressed as:
Where
is normalized time； T is a single harvest operation time.
Figure 4 shows the curves of the cycloidal motion andits first and second derivatives in canonical interval (-1,1). From Figure 4, it can be clearly seen that the cycloidal motion is adequately smooth; also, the velocity and acceleration motions are continuous and the values at
Figure 4 Cycloidal motion and its first and second derivatives the initial and end points of interval 0≤τ ≤1 are zeros.This demonstrates that the motion of the end-effector of robot manipulator won’t result chattering, so it can ensure motion stability of the robot system.
For joint i , trajectory planning relies on position and orientation of end-effector. So, the first step of trajectory planning is acquiring the three dimensional space description of the target cucumber. This description is based on sensory information such as machine vision as well as priori knowledge about
kinematics structure of robot manipulator. Then the goal angles qi(f) of the four joints can be obtained from the target position of the end-effector with inverse kinematics (Eqs 6, 10, 12, 13). After the start joint angles qi(0) i q being sent from joint controllers through CAN-bus, the position, velocity, acceleration equations based on cycloidal motion can be expressed as:
6 Hardware and software design of trajectory planning based on CAN-bus
6.1 Interface circuit of CAN-bus
Controller Area Network (CAN) is an advanced serial communication protocol for distributed real-time control system. Different devices such as processors, sensors and actuators can be connected to CAN-bus via twisted-pair wires and can communicate with each other by exchanging messages. The maximum transmission
rate can reach up to 1Mbps in a noisy environment. And it utilizes Carrier Sense Multiple Access with Collision Detection (CSMA/CD) as the arbitration mechanism to enable its attached nodes to have access to the bus[14-16].
The cucumber harvesting robot system employs the point to multi-points communication of CAN-bus. The upper monitor and four joint controllers are composed of dsPIC30f4012 digital signal processor which contains standard CAN controller and MCP2551 transceiver. And a 4-wire interface is designed based on CAN-bus protocol(CAN2.0A), which provides power, ground and two data lines(CAN High and CAN Low). The interface circuit of CAN-bus is shown in Figure 5. And the upper monitor circuit board is shown in Figure 6. The Baudrate of CAN-bus communication is adopted 1Mbps, and the messages transmitted consist of 2-byte identifier, 1-byte data length and 8-byte data. Messages are transmitted with a time internal of 10 ms according to the harvesting requirements. CAN-bus communication exhibits good real-time performance in practical application.
Figure 5 Interface circuit of CAN-bus
Figure 6 Upper monitor circuit board
6.2 Software design for trajectory planning of the cucumber harvesting robot
The upper monitor has functions of management and supervision for the robot system, location of cucumber target and trajectory planning. The program design
employs the modularization idea which is composed of several subprograms. Figure 7 illustrates the process of the trajectory planning for the cucumber harvesting robot. It consists of subprograms such as CAN-bus sending and receiving, acquisition of cucumber target, inverse kinematics and trajectory planning.
Figure 7 Flow chart for the trajectory planning
7 Experiments and analysis
In order to verify the accuracy of the trajectory planning algorithm and CAN-bus communication, experiments to measure the actual position of the four
joints of the cucumber harvesting robot manipulator were performed with the coordinate measurement machine(CMM) Platinum FaroArm of FARO Technologies Incorporation. As the world’ s best-selling portable measurement arm, Platinum FaroArm is available in sizes ranging from 1.2 m to 3.7 m and has precision of up to 0.013 mm.
Experiments were carried out as follows:
1) Set the position of the end-effecor:Px = 700mm, Py = 200mm, Pz = 668mm . By utilizing the inverse kinematics, the four joint angles can be computed from
equation (6) ～ (13):
θ1 =15.95°， θ2 =55.82 °，θ3 =-33.48°，θ4 =-22.34°.
2) Plan trajectories for each joint with cycloidal motion algorithm and send the planned angle messages to joint controllers by CAN-bus.
3) Use Platinum FaroArm to