機(jī)械手機(jī)器人外文翻譯-平面串聯(lián)機(jī)械手的運(yùn)動(dòng)合成【中文3500字】【中英文WORD】,中文3500字,中英文WORD,機(jī)械手,機(jī)器人,外文,翻譯,平面,串聯(lián),運(yùn)動(dòng),合成,中文,3500,中英文,WORD 譯文標(biāo)題 平面串聯(lián)機(jī)械手的運(yùn)動(dòng)合成【中文3500字】 原文標(biāo)題 Planar Serial Manipulator Motion Synthesis 作 者 Yanhui Wei 譯 名 魏艷輝 國(guó) 籍 China 原文出處 Journal of Harbin Institute of Technology ( New Series) ，Vol．22，No．2，2015 譯文： 摘要：本文論述了平面串聯(lián)機(jī)器人手的運(yùn)動(dòng)合成問題，快速工作空間的解決方案和障礙物回避路徑規(guī)劃方法，它提出了一種一般形式的運(yùn)動(dòng)學(xué)反解，不依賴于機(jī)器人本身的自由度，通過確定目標(biāo)向量方向的最大和最小工作空間邊界和確定的工作空間極坐標(biāo)形式的表達(dá)方法，最后，根據(jù)平面軌跡規(guī)劃的障礙躲避問題，解決了安全避障的凹凸形式的運(yùn)動(dòng)學(xué)反解的方法，仿真結(jié)果驗(yàn)證了所提方法的可行性和通用性。 關(guān)鍵詞：平面串聯(lián)機(jī)器人 運(yùn)動(dòng)學(xué)反解 工作空間 軌跡規(guī)劃 矢量投影 1引言 串聯(lián)機(jī)械手的平面問題，這一特征點(diǎn)的機(jī)器人是可以在兩維平面運(yùn)動(dòng)的最后一個(gè)系列。運(yùn)動(dòng)控制是很容易實(shí)現(xiàn)的，其中A型機(jī)械手每個(gè)接頭大范圍的運(yùn)動(dòng)。相當(dāng)經(jīng)典的串聯(lián)機(jī)械手由安切洛蒂來配置。例如，PUMA機(jī)器人增加了第一個(gè)旋轉(zhuǎn)接頭和第三個(gè)關(guān)節(jié)的基礎(chǔ)上的平面結(jié)構(gòu)，滿足要求的三維空間機(jī)器人的位置，通過正交布局，達(dá)到要求空間工作點(diǎn)的位置。先進(jìn)的平面串聯(lián)機(jī)械手已經(jīng)應(yīng)用在一些特殊情況下，如水型機(jī)器人臂。 對(duì)于空間機(jī)器人的運(yùn)動(dòng)學(xué)分析，將機(jī)器人的配置分為多個(gè)平面的配置形式?？芍貥?gòu)機(jī)器人通過一個(gè)模塊可以自由組合的復(fù)雜機(jī)器人的配置和地址的運(yùn)動(dòng)學(xué)分析，動(dòng)力學(xué)分析和軌跡規(guī)劃問題。為了解決自動(dòng)重構(gòu)機(jī)器人運(yùn)動(dòng)學(xué)逆解、魏等人。［1］提出配置平面的概念。在這個(gè)概念中，一個(gè)三維的機(jī)器人配置被分解成一個(gè)二維平面結(jié)構(gòu)，以簡(jiǎn)化運(yùn)動(dòng)學(xué)反解問題，實(shí)現(xiàn)自動(dòng)和快速的解決方案的目標(biāo)。一般情況下，分析的解決方法是很難獲得多參數(shù)、非線性、強(qiáng)耦合的解決方案，并參與到6R機(jī)器人運(yùn)動(dòng)學(xué)反解的代數(shù)方程中［2］。人們用半解析方法和解決空間NR機(jī)器人運(yùn)動(dòng)學(xué)反解問題的一般方法。已經(jīng)進(jìn)行了一個(gè)運(yùn)動(dòng)分析與任何形式的平面結(jié)構(gòu)，從而成為一個(gè)可重構(gòu)機(jī)器人系列，是機(jī)器人運(yùn)動(dòng)分析的關(guān)鍵問題之一。 本文以矢量投影法為研究重點(diǎn)，對(duì)平面串聯(lián)機(jī)器人的運(yùn)動(dòng)學(xué)反解和工作空間的軌跡規(guī)劃進(jìn)行了研究。本研究的目的是獲得一個(gè)簡(jiǎn)單的和快速的方法和一般的運(yùn)動(dòng)學(xué)反解求解的可重構(gòu)機(jī)器人軌跡規(guī)劃，并提供一個(gè)參考的空間形式的串聯(lián)機(jī)械手。 2自動(dòng)運(yùn)動(dòng)學(xué)解 2.1平面串聯(lián)機(jī)器人 平面串聯(lián)機(jī)器人主要由旋轉(zhuǎn)接頭、平移關(guān)節(jié)和連桿?？紤]到連桿不是一個(gè)單一的連接形式，當(dāng)機(jī)器人運(yùn)動(dòng)模型建立與基本運(yùn)動(dòng)單元的旋轉(zhuǎn)關(guān)節(jié)，運(yùn)動(dòng)的變換 矩陣是θ是轉(zhuǎn)動(dòng)關(guān)節(jié)運(yùn)動(dòng)；H是相鄰的旋轉(zhuǎn)接頭中心連接桿的長(zhǎng)度，其值的變化時(shí)，它包括移動(dòng)節(jié)點(diǎn) 一般的平面機(jī)械手是串聯(lián)的形式顯示在圖1結(jié)束點(diǎn)的姿態(tài)矩陣是： 當(dāng) 圖1總平面形狀的串聯(lián)機(jī)械手運(yùn)動(dòng)模型 2.2平面串聯(lián)機(jī)械臂的自動(dòng)求解方法 這種方法不包含相當(dāng)大的平移關(guān)節(jié)在一個(gè)共同的平面串聯(lián)機(jī)械手的構(gòu)象，但符合空間位置要求或空間冗余任務(wù)，機(jī)器人關(guān)節(jié)的過度運(yùn)動(dòng)會(huì)降低整體控制過程中的性能和剛度特性。 如圖1所示，平面串聯(lián)機(jī)械手的運(yùn)動(dòng)學(xué)反解可以分為兩個(gè)部分，即姿勢(shì)和位置的要求。具有冗余形式平面串聯(lián)機(jī)器人（三自由度以上），他們的姿勢(shì)的要求是第N－1接頭部分必須保證N接頭運(yùn)動(dòng)范圍的條件下。結(jié)束姿勢(shì)要求可以通過最后一個(gè)旋轉(zhuǎn)接頭來實(shí)現(xiàn)的，其位置的要求可以通過組合第一N－1接頭實(shí)現(xiàn)。對(duì)于平面串聯(lián)機(jī)器人的自由度小于或等于3，它的三個(gè)關(guān)節(jié)都需要滿足的姿勢(shì)崗位要求，它可以解析求解應(yīng)用式（2）。我們利用向量投影法求解平面機(jī)器人的各種表單自動(dòng)滿足以下約束： 在‖P‖是結(jié)束向量的范數(shù)；AI是矢量P→用聯(lián)合杠桿臂的投影之間的比例和關(guān)節(jié)臂。考慮向量投影的方向，AI表示如下： θ是關(guān)節(jié)臂和目標(biāo)點(diǎn)矢量之間的夾角 圖2，P點(diǎn)目標(biāo)點(diǎn)。如果聯(lián)合N固定長(zhǎng)度的HN，聯(lián)合體育中心的空間位置是可以計(jì)算出來的。因此，整個(gè)計(jì)算是一個(gè)組合的前n－1接頭后，接頭的N－1配合中心聯(lián)合N圖中的結(jié)束，沒有一個(gè)固定的長(zhǎng)度，移動(dòng)節(jié)點(diǎn)的存在，利用最短的長(zhǎng)度。聯(lián)合我的關(guān)節(jié)n + 1的杠桿臂之間是一個(gè)最大長(zhǎng)度的狀態(tài)，確保吉+ 1約長(zhǎng)度最大，中心節(jié)點(diǎn)圖n計(jì)算，這是初步j(luò)'n。 圖2運(yùn)動(dòng)學(xué)求解過程 自動(dòng)計(jì)算被闡明如下： （1）在關(guān)節(jié)運(yùn)動(dòng)的情況下，最大限度的投影量。 找到點(diǎn)（j'i + 1）與+ 1與j'n，如圖所示，j'i + 1與，j'i + 1 j'n相比；如果j'i + 1 j'n＞j'i + 1，自動(dòng)計(jì)算；如果j'i + 1 j'n≤j'i + 1，進(jìn)行下一步。 （2）在關(guān)節(jié)運(yùn)動(dòng)的情況下，逆投影量的范圍。 找到最大點(diǎn)（J″i + 1）與+ 1與j'n，如圖所示。J″+ 1與J″+ 1 j'n相比；如果J″+ 1 j'n≥J″，+ 1，自動(dòng)計(jì)算，關(guān)節(jié)運(yùn)動(dòng)在允許范圍的情況下，J″+ 1 j'n符合要求；否則，進(jìn)行下一步。 （3）+ 1關(guān)節(jié)調(diào)整到N－1關(guān)節(jié)運(yùn)動(dòng)使J″+ 1的長(zhǎng)度是最短的。J″+ 1與J″+ 1 j'n相比；如果j″+ 1 j'n≥J″+ 1，J″+ 1的長(zhǎng)度是根據(jù)位置的要求；如果J″+ 1 j'n＜J″+ 1，逆投影量最大值點(diǎn)J″+ 1j'n， + 1節(jié)自動(dòng)計(jì)算。 從第一關(guān)節(jié)開始，一個(gè)固定的周期可以滿足要求，在機(jī)器人運(yùn)動(dòng)學(xué)逆解。 3自動(dòng)解算的工作區(qū) 機(jī)器人的工作空間，可以顯示機(jī)器人的工作范圍，是評(píng)價(jià)機(jī)器人的重要指標(biāo)，然而，平面機(jī)器人的工作空間與機(jī)器人的工作空間是不同的。組成關(guān)節(jié)的運(yùn)動(dòng)范圍也不同。因此，我們獲得的工作是復(fù)雜的，會(huì)形成一個(gè)復(fù)雜的區(qū)域，這是由三，如圖3所示。這一特征使工作空間的解決方案很難獲得。 圖3工作區(qū)采用多域 為解決機(jī)器人工作空間主要包括分析、圖形的方法和數(shù)值方法［4］。在分析方法中，工作空間的邊界是由多個(gè)信封決定。然而，這種方法是復(fù)雜的，普遍應(yīng)用于機(jī)器人的關(guān)節(jié)。圖解法求解邊界工作空間，我們可以得到各種相交的線或相交的表面。這種方法是有效的但也是由自由度的數(shù)目有限，當(dāng)節(jié)點(diǎn)的數(shù)量是很大的，我們應(yīng)該通過組［6］處理。數(shù)值計(jì)算方法是基于極值理論和優(yōu)化方法來計(jì)算機(jī)器人工作空間的邊界曲面的特征點(diǎn)，這是用來構(gòu)成邊界曲線和形狀的邊界表面。代表結(jié)果的搜索方法，迭代法和蒙特卡羅［7－9］。為了計(jì)算串聯(lián)機(jī)器人定姿態(tài)工作空間，提出了一種基于二進(jìn)制逼近原理的快速搜索方法 基于上述方法，每一種方法的目的是利用該區(qū)域的自動(dòng)求解工作區(qū)的邊界的確定，如圖3所示，以方便快速評(píng)價(jià)工作區(qū)的平面串聯(lián)機(jī)械手和快速匹配的配置平面的可重構(gòu)機(jī)器人，我們通常會(huì)給平面矢量來解決這個(gè)位置，機(jī)器人可以實(shí)現(xiàn)對(duì)矢量。在本文中，我們使用了一種方法的基礎(chǔ)上的工作空間矢量的空間矢量的情況下，在這個(gè)向量的工作空間邊界迅速確定。 4軌跡規(guī)劃方法 軌跡規(guī)劃的目標(biāo)是規(guī)劃理想的任務(wù)和關(guān)節(jié)空間的運(yùn)動(dòng)軌跡，使機(jī)器人運(yùn)動(dòng)速度快，精度高，運(yùn)動(dòng)點(diǎn)效率高，軌跡跟蹤精度高，滿足路徑、障礙和運(yùn)動(dòng)學(xué)約束。 避障是軌跡規(guī)劃的一個(gè)關(guān)鍵問題。通常采用的方法是規(guī)劃?rùn)C(jī)器人空間軌跡的終點(diǎn)會(huì)議空間避障要求，使用機(jī)器人的運(yùn)動(dòng)學(xué)反解求解各空間點(diǎn)的每個(gè)關(guān)節(jié)的價(jià)值。調(diào)整速度和平移關(guān)節(jié)加速度使機(jī)器人能達(dá)到更好的運(yùn)動(dòng)效果。實(shí)現(xiàn)避障任務(wù)更好，許多研究已經(jīng)簡(jiǎn)化了壁壘概述由包絡(luò)圓。參考文獻(xiàn)［12］，阻擋接近一點(diǎn)，以最小的點(diǎn)與杠桿臂之間的距離作為避障的基礎(chǔ)，該方法擴(kuò)展了障礙物的空間，減少了實(shí)際工作環(huán)境中的實(shí)際機(jī)器人的工作空間機(jī)器人的可操作性。使用新的雙向快速探索隨機(jī)樹算法對(duì)復(fù)雜空間躲避障礙物的軌跡規(guī)劃。這些算法不需要運(yùn)動(dòng)學(xué)反解計(jì)算方法，但我們可以通過擴(kuò)展樹方法實(shí)現(xiàn)空間避障任務(wù)。 perumaal等人提出一種自動(dòng)軌跡規(guī)劃確定平滑，為中存在的障礙，一個(gè)五自由度機(jī)械手抓放操作的最小時(shí)間和無碰撞軌跡。該計(jì)劃是能夠處理的軌跡與不通過點(diǎn)和痕跡的光滑，無碰撞，近段時(shí)間最優(yōu)軌跡，不僅為機(jī)器人的端部執(zhí)行器，但也為它的鏈接確保無碰撞軌跡。 capisani等人。提出一個(gè)簡(jiǎn)單而有效的路徑規(guī)劃策略，目標(biāo)是代表機(jī)器人的配置空間的障礙，表示允許獲得一個(gè)有效的和準(zhǔn)確的軌跡規(guī)劃和跟蹤，以及一個(gè)專用的碰撞檢測(cè)規(guī)則的機(jī)器人與障礙物之間。 第2節(jié)描述機(jī)器人運(yùn)動(dòng)學(xué)求解方法。當(dāng)空間障礙存在，其空間軌跡規(guī)劃。干擾與障礙的發(fā)生，如圖4所示。 圖4平面障礙配置運(yùn)動(dòng)反解回避問題 我們繼續(xù)使用2節(jié)的仿真實(shí)例，其中機(jī)器人從初始點(diǎn)移動(dòng)到目標(biāo)點(diǎn)，圖8中的區(qū)域1由實(shí)際障礙形成的，考慮機(jī)器人的尺寸和安全距離，我們展開1區(qū)的距離，形成安全的避障區(qū)2，根據(jù)運(yùn)動(dòng)學(xué)反解在軌跡規(guī)劃過程中，機(jī)器人的結(jié)構(gòu)形式表現(xiàn)出明顯的干擾，從而平衡運(yùn)動(dòng)學(xué)反解的自動(dòng)解和避障問題。 5結(jié)論 1）利用矢量投影法和關(guān)節(jié)約束，求解平面串聯(lián)機(jī)械臂的運(yùn)動(dòng)學(xué)問題。仿真結(jié)果表明，該方法避免了傳統(tǒng)的分析方法，它依賴于機(jī)器人的配置和自由度的形式，以及解決速度和精度的問題時(shí)，使用數(shù)值方法，這種方法也實(shí)用和通用。 2）在矢量方向上提出一個(gè)工作范圍，作為平面機(jī)器人的工作空間表達(dá)式。 此方法使用一個(gè)搜索的方法來解決工作區(qū)范圍迅速的方向上的設(shè)置矢量角。這種方法也自動(dòng)和快速。此外，該方法是將三維空間機(jī)器人分解為二維平面機(jī)器人的基礎(chǔ)。 3）通過對(duì)平面串聯(lián)機(jī)械手的運(yùn)動(dòng)學(xué)反解求解方法的改進(jìn)，實(shí)現(xiàn)了軌跡規(guī)劃 平面機(jī)器人工作空間的障礙。仿真結(jié)果表明，該方法是通用的和實(shí)際的障礙與凸形式。 原文： Planar Serial Manipulator Motion Synthesis Yanhui Wei* ，Han Han，Zepeng Wang，Xin Liu and Guangchun Li ( College of Automation，Harbin Engineering University，Harbin 150001，China) Abstract: This paper deals with the universal serial manipulator on the inverse kinematics problem of planetype，the fast working space solution method，and the obstacle avoidance path planning method．With the vectorprojection as the main constraint condition of the target，it proposes a general form of the inverse kinematics solution which does not depend on the robot configuration of freedom degree．By identifying the target vector direction maximum and minimum workspace boundary and determining the destination vector by thick search on the workspace boundary method，an expressing method of the polar coordinate form of work space is then introduced． Finally，according to the form of plane trajectory planning for obstacle avoidance problem，the method of solving the inverse kinematics solution of the concave and convex forms of the safe obstacle avoidance area is improved．The simulation results verify that the proposed method has feasibility and generality． Keywords: planar serial manipulators; inverse kinematics; workspace; trajectory planning; vector projection 1 Introduction Planar serial manipulators refer to the feature in which a robot can point in a two-dimensional plane movement at the end of a series． Planar serial robot motion control is easy to implement，in which a robot forms a single，large range of movement of each joint． Considerable classic serial robot configuration has evolved． For example，PUMA robot increases the first rotary joints to the second and third joints based on planar configuration and satisfies the requirement of a three-dimensional space robot position by orthogonal layout to request the position of space operating point． Planar serial manipulators have been advanced in some special circumstances，such as under water-type robot arm． For the space robot kinematics analysis，the robot configuration can be divided into multiple planar configuration forms． Ｒeconfigurable robot through a module can free the combination of complex robot configuration and address the kinematics analysis， dynamics analysis，and trajectory planning problems．To solve the inverse kinematics solution of an automatically reconfigurable robot， Wei et al．［1］ proposed the concept of configuration plane． In this concept， a three-dimensional robot configuration is decomposed into a two-dimensional plane configuration to simplify the inverse kinematics problem and achieve the goal of an automatic and fast solution． Generally， the analytic solutions are difficult to obtain due to the multi-parameters， nonlinearity and coupling of the solutions，and the algebra equations involved in the inverse kinematics of 6Ｒ serial manipulators［2］． Wei et al．［3］ used a semi-analytic method and a general method to solve the spatial nＲ robot inverse kinematics problem． A motion analysis has been conducted with any form of planar configuration，which becomes a reconfigurable robot series and is one of the key problems of the robot motion analysis． In this paper，the inverse kinematics of planar serial manipulators and the workspace and trajectory planning are studied，with the vector projection method as the focus． This study aims to obtain a simple and fast method and a general inverse kinematics solution for the reconfigurable robot trajectory planning and to provide a reference for space in the form of serial manipulators． 2 Automatic Kinematics Solution 2. 1 General Form of Planar Serial Manipulators Planar serial manipulators are mainly composed of rotational joints，translational joint，and a connecting rod．Considering that the connecting rod is not in the form of a single connection，when a robot motion model is established，with the rotational joint of the basic movement unit，the motion transformation matrix is where θ is the rotational joint exercise; h is the length of the connecting rod of two adjacent rotational joint centers，whose value varies when it includes mobilejoints．The general form of planar serial manipulators is shown in Fig．1． The end point of the pose matrix is: Where Fig． 1 General form of the planar serial manipulator motion model 2．2 Automatic Solving Method of Planar Serial Manipulator This method does not contain considerable ranslational joint in a common conformation of planar serial manipulator but meets the space position requirements or space redundant tasks． The excessive movement of the robot joints will reduce the performance and stiffness characteristics in the overall controlling process． As shown in Fig． 1，the inverse kinematics of planar serial manipulator can be divided into two parts， i． e．，the posture and position requirements． For the planar serial robot with a redundant form ( more than three degrees of freedom) ，their posture requirements are under the conditions that the first n － 1 joint part must guarantee the range of n joints’motion． The end posture requirements can be achieved through the last one rotating joints，and its location requirements can be implemented by combining the first n － 1 joints． For the planar serial robot whose degree of freedom is less than or equal to 3，its three joints all need to meet the posture and position requirements and it can be analytically solved using Eq． ( 2) ． We use the vector projection method to solve the various forms of planar serial robot automatically，which satisfies the following constraints: where ‖p‖ is the norm of the end vector; ai is the ratio between the projection of ith joint lever arm on the vector p→ and the joint lever arm． Considering the direction of vector projection， ai is expressed as follows: where θ'i is the angle between ith joint lever arm and the target point vector． In Fig．2，P point is the target point． If the length hn of the joint n is fixed，the spatial location of the joint’s sports center can be calculated． Therefore，the entire calculation is after a combination of the former N － 1 joint，and the ends of the joint n － 1 coincide with the center joint n in the figure． Without a fixed length，mobile joints exist，which utilize the shortest length． The joint I to the joint n + 1 between the lever arm is in a state of maximum length，ensuring that the length of ji+1 jn is maximum． The center of the joints with the picture n is calculated，which is the tentative for j'n ． Fig．2 Kinematics solving process The automatic calculation is elucidated as follows: 1) In the case of joint movement i range，the projection quantity maximum． Point ( j'i+1) of ji ji+1 is found in ji j'n，as shown in Fig．2． The length of j'i+1 jn is compared with that of j'i+1 j'n; if j'i+1 j'n ＞ j'i+1 jn，i + 1 joint automatic calculation is conducted; if j'i+1 j'n ≤ j'i+1 jn，the next step is performed; 2) In the case of joint movement i range，the inverse projection quantity． Maximum point ( j″i+1) of ji ji+1 is found in ji j'n，as shown in Fig．2． The length of j″i+1 jn is compared with that of j″i+1 j'n ; if j″i+1 j'n ≥ j″i+1 jn，the automatic calculation is conducted at the end of I joint． In the case of joint movement I range，ji+1 j'n is found to meet the requirements; otherwise， the next step is performed; 3) I + 1 joint is adjusted to n － 1 joint exercise to make the length of j″i+1 jn be the shortest． The length of j″i+1 jn is compared with that of j″i+1 j'n ; if j″i+1 j'n ≥ j″i+1 jn，the length of j″i+1 jn is adjusted to meet the position requirements; if j″i+1 j'n ＜ j″i+1 jn，the inverse projection quantity maximum point of ji ji+1 is found in ji j'n and I + 1 joint automatic calculation is conducted． Starting from the first joint，a constant cycle can meet the requirements at the end of the robot kinematics inverse solutions． 3 Automatic Solution of the Workspace The workspace of the robot，which can show the operating range that the robot can achieve， is an important indicator for evaluating robots． However，the workspace of planar robot differs because the number of composition joint and the range of motion also differ．Thus，the workspace we obtain is complex and will form a complex region， which is made of multidomains，as shown in Fig．3． This feature makes the solution of the workspace difficult to obtain． Fig．3 Workspace made of multi-domains The method for solving the robot workspace mainly includes analytical， graphical， and numerical methods［4］． In the analytical method，the boundary of workspace is determined by multiple envelopes．However，this method is complicated and is generally applied to the robots with less than three joints［5］． The graphical method is used to solve the boundary of workspace． We can obtain various intersecting lines or intersecting surfaces． This method is effective but is also limited by the number of degrees of freedom．When the number of joints is large，we should handle it by group［6］． The numerical method is based on extreme value theory and optimization methods to calculate the feature points on the boundary surfaces of robots’workspace，which are used to constitute the boundary curves and form the boundary surface． The representative results are the search method，iterative method，and Monte Carlo［7－9］． In order to compute the constant-orientation workspace of serial robots，a fast search method based on the binary approximating principle is proposed［10］． Based on the above methods，each method aims to utilize the area formed by the workspace． The problem of automatically solving the workspace is the determination of the boundary of the workspace． As shown in Fig．3， to facilitate the rapid evaluation workspace of planar serial manipulator and the fast matching configuration plane of reconfigurable robots，we usually give plane vector to solve the position that the robot can achieve on the vector． In this paper，we use a method based on the workspace expression of planar serial manipulator in the polar form，i．e．，in the condition in which the space vector is known，the workspace boundaries on this vector angle is rapidly determined． 4 Trajectory Planning Method The objective of trajectory planning is to plan ideal task and joint space trajectories，make the robot motion fast，accurate and stable with high movement point efficiency and high trajectory tracking accuracy，and satisfy the path， obstacle， and kinematics constraints． The obstacle avoidance is a key problem in the trajectory planning． The usual approach used is planning the robot end-point space trajectory，meeting the space avoiding obstacle requirements，and using robot inverse kinematics to solve each joint value at each space point． Adjusting the speed and acceleration of the translational joint allows the robot to achieve better motion effects． To achieve the obstacle avoidance task better，many studies have simplified the barriers’ outline by enveloping circle［11］． In Ｒef． ［12 ］，the barrier approximates a point and takes the minimum distance between the point and the lever arm as the basis of obstacle avoidance． This method expands the obstacle space，reduces the actual robot working space in the actual working environment， and limits the robot’s workability． Xie et al．［13］ used new bidirectional rapidly exploring random tree algorithms for complex spatial obstacle avoidance trajectory planning． These algorithms do not require the inverse kinematics calculation method，but we can achieve the spatial obstacle avoidance task by expanding the tree method Duguleana［14］ proposes a new approach for solving the problem of obstacle avoidance during manipulation tasks performed by redundant manipulators． In which q-learning is used together with neural networks in order to plan and execute arm movements at each time instant． Perumaal et al．［15］ proposed an automated trajectory planner to determine a smooth，minimumtime and collision-free trajectory for the pick-and-place operations of a 5-DOF robotic manipulator in the presence of an obstacle． The proposed planner is able to handle the trajectory with and without via-point and traces the smooth， collision-free， near-time-optimal trajectory． The collision-free trajectory is ensured not only for the robot’s end-effector but also for its links． Capisani et al．［16］ proposed a simple but effective path planning strategy． The goal is to represent the obstacles in the robot configuration space． The representation allows obtaining an efficient and accurate trajectory planning and tracking． And a dedicated collision checking rule between the manipulator and obstacles is also proposed． Section 2 describes the method for solving the robot kinematics． When space obstacles exist，their spatial trajectory is planned． Interference will occur with the obstacle，as shown in Fig．4． Fig.4 Planar obstacle configuration inverse movement solving the avoidance problem We continue to use the simulation example of Section 2，in which the robot moves from the initial point D to the target point P． The area 1 in Fig．4 is formed by the actual obstacle． Considering the robot link’s dimension and safe distance，we expand zone 1 in k distance，which forms the secure avoiding obstacle zone 2． According to the inverse kinematics solution during the trajectory planning，the final form of the robot configuration shows noticeable interference． How to balance the inverse kinematics automatic solution and the obstacle avoidance is to be solved． 5 Conclusions 1) Using the constraints of the vector projection method and joints，the kinematics problem of the planar serial manipulator is solved． The simulation results show that this method avoids the traditional analytical method which relies on the forms of robot configurations and the degrees of freedom，as well as the problem of solving speed and precision when using numerical methods． This method is also practical and versatile． 2) A working range is proposed in the direction of the vector as the workspace expression of planar robot．This method uses a searching way to solve the workspace range rapidly in the direction of the setting vector angle． This method is also automatic and fast． Furthermore，this method is the foundation of the research in decomposing a three-dimensional space robot into a two-dimensional planar robot． 3 ) Through the inverse kinematics solution method of planar serial manipulator with improved forms， the trajectory plan is achieved when the workspace of a planar robot presents obstacles． The simulation results show that the method is versatile and practical to the barrier with a convex form． 指 導(dǎo) 教 師 評(píng) 語 外文翻譯成績(jī)： 指導(dǎo)教師簽字： 年 月 日 注：1. 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