助行機(jī)器人定位關(guān)鍵技術(shù)研究
《助行機(jī)器人定位關(guān)鍵技術(shù)研究》由會(huì)員分享,可在線(xiàn)閱讀,更多相關(guān)《助行機(jī)器人定位關(guān)鍵技術(shù)研究(152頁(yè)珍藏版)》請(qǐng)?jiān)谘b配圖網(wǎng)上搜索。
1、 申請(qǐng)上海交通大學(xué)博士學(xué)位論文 助行機(jī)器人定位關(guān)鍵技術(shù)研究 專(zhuān) 業(yè):機(jī)械電子工程 博士生:朱笑笑 導(dǎo) 師:曹其新教授 上海交通大學(xué)機(jī)械與動(dòng)力工程學(xué)院 2014年 2月 Ph.D. Dissertation Submitted to Shanghai Jiao Tong University Research on Key Technologies of Localization Method for Walking Assistant Robot Specialty: Mechatronics Engineering Aut
2、hor: Zhu Xiaoxiao Advisor: Prof. Cao Qixin School of Mechanical and Power Engineering Shanghai Jiao Tong University February,2014 學(xué)位論文版權(quán)使用授權(quán)書(shū) 本學(xué)位論文作者完全了解學(xué)校有關(guān)保留、使用學(xué)位論文的規(guī)定,同意 學(xué)校保留并向國(guó)家有關(guān)部門(mén)或機(jī)構(gòu)送交論文的復(fù)印件和電子版,允許論文 被查閱和借閱。本人授權(quán)上海交通大學(xué)可以將本學(xué)位論文的全部或部分內(nèi) 容編入有關(guān)數(shù)據(jù)庫(kù)進(jìn)行檢索,可以采用影印、縮印或掃描等復(fù)制手段保存 和匯編本
3、學(xué)位論文。 (請(qǐng)?jiān)谝陨戏娇騼?nèi)打“√”) 本人鄭重聲明:所呈交的學(xué)位論文,是本人在導(dǎo)師的指導(dǎo)下,獨(dú)立進(jìn) 行研究工作所取得的成果。除文中已經(jīng)注明引用的內(nèi)容外,本論文不包含 任何其他個(gè)人或集體已經(jīng)發(fā)表或撰寫(xiě)過(guò)的作品成果。對(duì)本文的研究做出重 要貢獻(xiàn)的個(gè)人和集體,均已在文中以明確方式標(biāo)明。本人完全意識(shí)到本聲 明的法律結(jié)果由本人承擔(dān)。 摘要 助行機(jī)器人定位關(guān)鍵技術(shù)研究 摘要 助行機(jī)器人是一種可以輔助老人行走的特殊服務(wù)機(jī)器人,它的目標(biāo)是代替?zhèn)? 統(tǒng)的助行器(如拐杖、助步架等)在保證老人行走安全的基礎(chǔ)上,大大提高其獨(dú)
4、 立生活能力及生活質(zhì)量。除了能夠提供基本的輔助行走功能,它還需具備多種智 能化功能,如用戶(hù)健康狀態(tài)監(jiān)控,語(yǔ)音交互,定位導(dǎo)航,用戶(hù)識(shí)別,用戶(hù)計(jì)劃提 醒,信息播報(bào)服務(wù)等等。定位系統(tǒng)作為助行機(jī)器人一個(gè)重要組件,是實(shí)現(xiàn)多項(xiàng)智 能化功能的一個(gè)基礎(chǔ)。本文針對(duì)助行機(jī)器人定位系統(tǒng)的幾項(xiàng)關(guān)鍵技術(shù)開(kāi)展研究, 具體研究?jī)?nèi)容如下。 (1)環(huán)境地圖是助行機(jī)器人自主定位導(dǎo)航的重要先驗(yàn)知識(shí),常用的 2D地圖 能夠滿(mǎn)足機(jī)器人自定位的需求,但由于存在高度方向的不確定性,在家居狹小空 間內(nèi)的自主導(dǎo)航應(yīng)用中存在明顯不足。而傳統(tǒng)的 3D地圖創(chuàng)建方法一般需要使用 價(jià)格昂貴的激光傳感器,操作也較為復(fù)雜,不適合家
5、庭使用。本文對(duì)利用 RGB-D (顏色-深度)傳感器的 3D地圖創(chuàng)建方法進(jìn)行研究,提出基于改進(jìn) KinectFusion 算法的地圖創(chuàng)建方法,使其可以較為方便對(duì)家庭環(huán)境進(jìn)行創(chuàng)建。對(duì) KinectFusion 算法進(jìn)行兩個(gè)方面的改進(jìn),一方面提出使用環(huán)境中的邊線(xiàn)特征點(diǎn)匹配來(lái)提高其定 位魯棒性,另一方面在點(diǎn)云模型中預(yù)設(shè)一個(gè)地面點(diǎn)云來(lái)減少累積誤差提高精度。 并且提出了基于標(biāo)志物的子地圖拼接方法,解決 KinectFusion算法只能創(chuàng)建小規(guī) 模地圖的問(wèn)題。 (2 )助行機(jī)器人工作形式靈活,經(jīng)常需要在自主運(yùn)行和被動(dòng)控制之間切換, 同時(shí)其運(yùn)行環(huán)境也會(huì)在室內(nèi)和室外變化。因此連續(xù)定位會(huì)
6、頻繁的中斷,這就要求 助行機(jī)器人具有較強(qiáng)的全局定位功能,可以快速地重新定位。本文對(duì)全局搜索定 位算法進(jìn)行研究,提出利用旋轉(zhuǎn)不變量首先進(jìn)行位置空間搜索得到可行的機(jī)器人 位置,然后在方向空間進(jìn)行搜索得到機(jī)器人的朝向,對(duì)全局搜索定位方法進(jìn)行降 維,這樣大大提升了全局定位的效率。 (3)傳統(tǒng)的 2D連續(xù)位置跟蹤方法較為成熟但是需要使用激光傳感器,對(duì)助 行機(jī)器人的成本控制不利。本文嘗試以 RGB-D傳感器來(lái)代替 2D激光傳感器進(jìn) I 上海交通大學(xué)博士學(xué)位論文 行連續(xù)定位,通過(guò)充分利用 RGB-D的 3D點(diǎn)云信息彌補(bǔ)其水平方向視野較小的 缺點(diǎn)。而傳統(tǒng)
7、的 3D點(diǎn)云配準(zhǔn)定位算法,無(wú)法達(dá)到實(shí)時(shí)定位的需求,本文提出了 基于 3DLUT(Lookup Table)的 3D點(diǎn)云快速配準(zhǔn)方法,該方法可以達(dá)到實(shí)時(shí)的 處理速度,同時(shí)具有較高的定位精度。 (4 )助行機(jī)器人的用戶(hù)定位功能是一項(xiàng)非常重要的功能,對(duì)提高助行機(jī)器人 的易用性起很大的作用。傳統(tǒng)的基于激光傳感器的用戶(hù)定位方法由于沒(méi)有用戶(hù)區(qū) 分的能力,所以在行人干擾較多的情況下無(wú)法正常工作;基于視覺(jué)的方法則因?yàn)? 對(duì)光線(xiàn)變化,觀察角度等非常敏感,所以魯棒性不高。本文提出基于全向視覺(jué)及 紅外標(biāo)志物識(shí)別的方法來(lái)定位用戶(hù)。通過(guò)調(diào)節(jié)相機(jī)曝光值,使得系統(tǒng)在室內(nèi)室外 均能穩(wěn)定的識(shí)別用戶(hù)。在對(duì)全向視覺(jué)系
8、統(tǒng)進(jìn)行標(biāo)定時(shí),利用鏡面基底圓輪廓的成 像來(lái)計(jì)算鏡面位姿確定內(nèi)部參數(shù)的方法,并提出了使用鏡面中心點(diǎn)來(lái)確定鏡面位 姿兩組可能解中的真實(shí)解,同時(shí)提出了利用一種具有單一解的 Non-SVP(非單 一中心)P3P解法來(lái)確定全向視覺(jué)系統(tǒng)的外部參數(shù)的方法。該標(biāo)定方法簡(jiǎn)單快速, 對(duì)標(biāo)定物要求低,并具有較高的精度。 (5)根據(jù)本文提出的幾項(xiàng)關(guān)鍵技術(shù)解決方案,開(kāi)發(fā)搭建了 WalkMateIII型助 行機(jī)器人軟硬件系統(tǒng)。為了方便系統(tǒng)軟件的開(kāi)發(fā)集成,提高系統(tǒng)的結(jié)構(gòu)清晰度, 本文利用基于模塊化的方法來(lái)搭建助行機(jī)器人的軟件系統(tǒng)。最后通過(guò)實(shí)現(xiàn)兩個(gè)典 型任務(wù):開(kāi)機(jī)用戶(hù)查找,用戶(hù)跟蹤的,對(duì)整套系統(tǒng)
9、的可行性進(jìn)行驗(yàn)證。 國(guó)內(nèi)助行機(jī)器人的研究剛剛起步,而助行機(jī)器人由于其特殊的工作方法和一 般的移動(dòng)服務(wù)機(jī)器人有多方面的差別,還有很多問(wèn)題有待解決。本文的研究目的 是:通過(guò)對(duì)助行機(jī)器人的定位系統(tǒng)的研究,解決幾項(xiàng)關(guān)鍵問(wèn)題。論文的研究有助 于助行機(jī)器人早日進(jìn)入實(shí)用階段,為解決人口老齡化帶來(lái)的老人護(hù)理問(wèn)題打下基 礎(chǔ),具有重要的社會(huì)意義和經(jīng)濟(jì)價(jià)值。 關(guān)鍵詞:助行機(jī)器人,全向視覺(jué)標(biāo)定,3D點(diǎn)云地圖創(chuàng)建,全局定位,快速點(diǎn)云 配準(zhǔn)算法,機(jī)器人模塊化,用戶(hù)定位 II 摘要 Research on Key Technologies of Localization Method
10、for Walking Assistant Robot ABSTRACT The walking assistant robot (WAR) is a special kind of service robot which can assist the elderly to walk. The reason behind the development of the WAR is to replace traditional walking aids such as crutches and the walking frame.
11、 Moreover, besides the walking assistant function, it also offers more intelligent functions, such as health condition monitoring, voice interaction, navigation, user identification, user program reminders, information services, etc. The localization system which is an important c
12、omponent of WAR acts as a base for many intelligent functions. This dissertation covers a study of the localization system and the research contents herein are as follows. 1,The map of the environment is key for a-priori knowledge for the autonomous localization and navigation
13、 function of the WAR. Although 2D maps can meet the needs of the robot for self-localization, its drawback of uncertainty in the vertical direction made it unable to meet the demand for autonomous navigation in narrow environment such as would be encountered in a typical ho
14、me setting. Traditional 3D mapping methods need expensive equipment and the operation is complex. In this dissertation, we studied the 3D mapping method based on RGB-D (color- depth) sensor and proposed a map creation method based on improved “KinectFusion”, enabling
15、users to more easily re-create the family environment. This dissertation advances the KinectFusion algorithm with two improvements. On the one hand use is made of the environment feature to point out matching edges and consequently improve its positioning robustness, on the
16、 other hand ground point cloud is preset in the point cloud model to reduce the accumulated error and hence improve accuracy. III 上海交通大學(xué)博士學(xué)位論文 Additionally, a sub-map stitching method is proposed to solve the limitation of the size of the map built by “KinectFusion”,
17、based on the ground consistency and the calibration marker. 2,The working style of WAR is flexible and there is often the need to switch between passive control and autonomous operation, especially when its operating environment switches between indoor and outdoor. In this manner the c
18、ontinuous positioning is frequently interrupted. This requires the robot to have a strong global positioning feature and the ability to quickly re-orient itself. In this dissertation, the global search positioning dimensionality reduction method is proposed using the r
19、otational invariants for the initial search for a viable space robot position, and subsequently in the direction of the search space to get the orientation of the robot thus greatly enhancing the efficiency of its global positioning. 3,The traditional 2D continuous location trac
20、king method is mature, but it requires the use of laser sensors on the WAR which is unfavorable for purposes of minimizing cost. This article attempts to employ an RGB-D sensor instead of a 2D laser sensor for continuous positioning. The main idea is to exclusively use RGB-D information as
21、 a 3D point cloud for position tracking, making up for its disadvantage by selecting a small field of view in the horizontal direction. Traditional 3D point cloud registration algorithm, cannot fulfill the demands of real-time location. This dissertation presents a study of three-d
22、imensional point cloud registration using RGB-D sensors, and proposes a fast 3D point cloud registration method based on 3DLUT (Lookup Table) algorithm. This method can not only achieve real-time processing speeds, but also has a high degree of accuracy. 4,The human positioning funct
23、ion is a very important function and plays a great role towards improving user-friendliness of the WAR. The traditional laser-based localization method lacks the capacity to identify the user hence cannot work well in an environment full of people. Vision-based methods on
24、 the other hand are very sensitive to changes in light characteristics hence have low robustness. In this dissertation, we propose a people positioning based on omni-dimensional visual and IV 摘要 infrared markers for identification. The test results proved it to
25、be stable both indoors and outdoors. For the omni-directional vision system (odvs) calibration, we propose to use the image of the base circle contour to compute the posture of the mirror and determine the internal parameters, and then use the center of the mirror to determine the
26、true solution from two possibilities. Next, we propose using a special unique solution -Non-SVP P3P method– to determine the external parameters. The calibration method is simple and fast, and not only places low demand on the calibration object, but also
27、 has high accuracy. 5,Using the solutions for these key technologies, the hardware and software system for the WalkMate III WAR was designed and built. We proposed to use the module based system model to make the development of the software system easier, and make the structure of the
28、system clearer. Finally two intelligence functions were tested in order to evaluate the Feasibility of the whole system. These are the users finding function (when the robot power is switched on) and user tracking. The domestic research of WAR has just started. Because of its’ s
29、pecial working methods and have many differences with general mobile service robots, there are many issues to be resolved. The purpose of this study is: research on the localization system of WAR, and solve several key issues. The research contained in this dissertati
30、on should be useful towards helping the WAR enter the practical stage as soon as possible, laying the foundation for solving the problem of caring for the elderly caused by aging population problem. Eventually this and has important social significance and results in economic
31、value. Keywords: walking assistant robot, calibration of omnidirectional camera, 3D point cloud creating, global localization, fast point registration algorithm, modular robots, people localization V 上海交通大學(xué)博士學(xué)位論文 目錄 摘要 ................................................................
32、................................................................I ABSTRACT.................................................................................................................III 目錄 .......................................................................................................
33、......................VI 第一章緒論 .................................................................................................................1 1.1課題來(lái)源、研究背景及意義.........................................................................1 1.1.1課題來(lái)源.................................................
34、.............................................1 1.1.2課題研究背景及意義..........................................................................1 1.2助行機(jī)器人國(guó)內(nèi)外研究現(xiàn)狀.........................................................................3 1.2.1國(guó)外研究現(xiàn)狀...........................................................
35、...........................3 1.2.2國(guó)內(nèi)研究現(xiàn)狀......................................................................................9 1.3助行機(jī)器人定位關(guān)鍵技術(shù)...........................................................................12 1.3.1助行機(jī)器人功能需求...............................................................
36、.........12 1.3.2助行機(jī)器人定位系統(tǒng)關(guān)鍵技術(shù)........................................................14 1.4研究?jī)?nèi)容與論文組織...................................................................................24 1.4.1研究?jī)?nèi)容............................................................................................24 1.4.2
37、論文組織............................................................................................25 第二章基于改進(jìn) KinectFusion算法的 3D點(diǎn)云地圖創(chuàng)建.....................................26 2.1引言...............................................................................................................26 2.2
38、RGB-D傳感器介紹......................................................................................27 2.3 KinectFusion算法.........................................................................................28 2.3.1 KinectFusion算法的 ICP定位方法.................................................29 2.3.2
39、 KinectFusion算法的 TSDF點(diǎn)云融合算法 .....................................32 2.4改進(jìn)的 KinectFusion算法..........................................................................33 2.4.1 KinectFusion算法的兩個(gè)問(wèn)題分析..................................................33 2.4.2邊線(xiàn)點(diǎn)對(duì)應(yīng)關(guān)系改進(jìn)...............................
40、.........................................35 2.4.3預(yù)設(shè)地面模型改進(jìn)............................................................................41 VI 目錄 2.5基于標(biāo)志物的點(diǎn)云地圖拼接.......................................................................44 2.5.1標(biāo)志物及其在子圖中的布置......................................
41、......................44 2.5.2子地圖中標(biāo)志物坐標(biāo)提取................................................................45 2.5.3相鄰子地圖位置計(jì)算........................................................................47 2.5.4基于 BA算法的閉環(huán)優(yōu)化................................................................48 2.6實(shí)驗(yàn)與分析.....
42、..............................................................................................50 2.6.1邊線(xiàn)點(diǎn)對(duì)應(yīng)關(guān)系改進(jìn)方法測(cè)試........................................................50 2.6.2預(yù)設(shè)地面模型改進(jìn)方法測(cè)試............................................................53 2.6.3子地圖拼接精度測(cè)試.............................
43、...........................................53 2.7小結(jié)...............................................................................................................55 第三章基于旋轉(zhuǎn)不變量的全局自定位方法 ...........................................................56 3.1引言...........................................
44、....................................................................56 3.2 2D距離傳感器數(shù)據(jù)的旋轉(zhuǎn)不變量..............................................................57 3.2.1 2D距離傳感器數(shù)據(jù)的數(shù)學(xué)定義.......................................................57 3.2.2旋轉(zhuǎn)不變量的定義...................................................
45、.........................58 3.2.3基于旋轉(zhuǎn)不變量的位置濾波及其閾值確定....................................58 3.2.4旋轉(zhuǎn)不變量濾除率分析....................................................................60 3.3基于旋轉(zhuǎn)不變量的二步定位法...................................................................62 3.3.1地圖遍歷.........................
46、...................................................................63 3.3.2 Omni_Scan采集.................................................................................65 3.3.3歐幾里得聚類(lèi)....................................................................................65 3.3.4基于相關(guān)度匹配的朝向確定...........
47、.................................................66 3.3.5重定位策略........................................................................................67 3.3.6處理過(guò)程的中間結(jié)果示例................................................................68 3.4實(shí)驗(yàn)與分析.....................................................
48、..............................................68 3.4.1直方圖數(shù)目和距離掃描采樣數(shù)的實(shí)驗(yàn)確定....................................69 3.4.2環(huán)境中有動(dòng)態(tài)物體時(shí)的定位精度測(cè)試............................................73 3.4.3地圖尺寸對(duì)定位的影響測(cè)試............................................................73 3.4.4與基于線(xiàn)段特征的全局定位方法對(duì)比實(shí)驗(yàn)..............
49、......................74 VII 上海交通大學(xué)博士學(xué)位論文 3.4.5機(jī)器人定位精度試驗(yàn)........................................................................76 3.5小結(jié)...............................................................................................................77 第四章基于 3DLUT點(diǎn)云快速配準(zhǔn)算法的實(shí)時(shí)位置跟蹤方法......
50、.......................78 4.1引言...............................................................................................................78 4.2加速 ICP算法研究現(xiàn)狀 ..............................................................................78 4.3 2DLUT(Look Up Table,查找表)算法.....................
51、...............................79 4.3.1配準(zhǔn)問(wèn)題定義與分析........................................................................80 4.3.2誤差方程定義及基于 RPROP算法的誤差優(yōu)化.............................81 4.3.3 2D查找表的建立...............................................................................82 4.3.4基于 2DLUT的
52、連續(xù)位置跟蹤算法.................................................84 4.4 3DLUT算法..................................................................................................84 4.4.1 3D查找表的建立...............................................................................85 4.4.2內(nèi)存的優(yōu)化...................
53、.....................................................................86 4.4.3 RGB-D傳感器標(biāo)定...........................................................................87 4.5實(shí)驗(yàn)與分析...................................................................................................89 4.5.1與 ICP算法對(duì)比實(shí)驗(yàn)
54、.......................................................................89 4.5.2實(shí)際環(huán)境定位精度測(cè)試....................................................................91 4.6小結(jié)...............................................................................................................93 第五章基于全向視覺(jué)及紅外標(biāo)志的用戶(hù)定
55、位方法 ...............................................94 5.1引言...............................................................................................................94 5.2基于全向視覺(jué)及紅外標(biāo)志物的用戶(hù)定位...................................................94 5.2.1全向視覺(jué)系統(tǒng).....................................
56、...............................................94 5.2.2紅外標(biāo)志物目標(biāo)識(shí)別........................................................................95 5.2.3目標(biāo)的位置確定................................................................................99 5.3全向視覺(jué)傳感器標(biāo)定...................................................
57、..............................100 5.3.1研究現(xiàn)狀..........................................................................................100 5.3.2參數(shù)定義..........................................................................................101 5.3.3全向視覺(jué)成像模型建立..........................................
58、........................102 5.3.4基于鏡面輪廓的內(nèi)部參數(shù)標(biāo)定......................................................103 VIII 目錄 5.3.5基于單一解 Non-SVP問(wèn)題的外部參數(shù)標(biāo)定................................105 5.3.6多點(diǎn)優(yōu)化..........................................................................................107 5.4實(shí)驗(yàn)
59、與分析.................................................................................................108 5.4.1全向視覺(jué)標(biāo)定實(shí)驗(yàn)..........................................................................108 5.4.2已知高度單點(diǎn)位置測(cè)量精度實(shí)驗(yàn)..................................................112 5.4.3未知高度的兩點(diǎn)測(cè)量精度實(shí)驗(yàn)...........
60、...........................................113 5.5小結(jié).............................................................................................................114 第六章 WalkMateIII實(shí)驗(yàn)平臺(tái)及功能測(cè)試............................................................115 6.1引言......................................
61、.......................................................................115 6.2 WalkmateIII硬件系統(tǒng) ................................................................................115 6.3 WalkmateIII軟件系統(tǒng) ................................................................................116 6.4集成功能測(cè)試...
62、..........................................................................................119 6.4.1開(kāi)機(jī)用戶(hù)查找功能..........................................................................119 6.4.2用戶(hù)跟隨功能..................................................................................121 6.5小結(jié)..........
63、...................................................................................................122 zhi ku quan 20150721 第七章總結(jié)與展望 .................................................................................................123 7.1全文總結(jié)......................................................
64、...............................................123 7.2主要?jiǎng)?chuàng)新點(diǎn).................................................................................................124 7.3研究展望.....................................................................................................124 參考文獻(xiàn) ....................
65、...............................................................................................126 攻讀博士學(xué)位期間已發(fā)表或錄用的論文及專(zhuān)利 ...................................................134 攻讀博士學(xué)位期間參與的科研項(xiàng)目 .......................................................................135 致謝 ............................
66、...............................................................................................136 IX zhi ku quan 20150721 第一章緒論 第一章緒論 1.1課題來(lái)源、研究背景及意義 1.1.1課題來(lái)源 本論文受?chē)?guó)家 863計(jì)劃先進(jìn)制造技術(shù)領(lǐng)域重點(diǎn)項(xiàng)目“助老/助殘機(jī)器人概念 樣機(jī)研究與開(kāi)發(fā)”(2006AA040203)資助。 1.1.2課題研究背景及意義 全球經(jīng)濟(jì)日益繁榮、科技不斷進(jìn)步的同時(shí),世界各國(guó)也正在步入一個(gè)老齡化 的階段。據(jù)統(tǒng)計(jì)1950年至2010年期間,發(fā)達(dá)國(guó)家60歲以上老年人口升至8%~17%, 發(fā)展中國(guó)家也升至4%~6%。到本世紀(jì)中葉,這兩個(gè)數(shù)字將分別達(dá)到 26%和 14%[1]。 而中國(guó)則面臨著更加嚴(yán)峻的人口老齡化問(wèn)題,據(jù)中國(guó)社科院發(fā)布的《中國(guó)老齡事 zhi ku quan 20150721 業(yè)發(fā)展報(bào)告(2013)》[2]中指出截至 2012年底,我國(guó) 60歲以上老年人口數(shù)量達(dá)到 1
- 溫馨提示:
1: 本站所有資源如無(wú)特殊說(shuō)明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請(qǐng)下載最新的WinRAR軟件解壓。
2: 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請(qǐng)聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶(hù)所有。
3.本站RAR壓縮包中若帶圖紙,網(wǎng)頁(yè)內(nèi)容里面會(huì)有圖紙預(yù)覽,若沒(méi)有圖紙預(yù)覽就沒(méi)有圖紙。
4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
5. 裝配圖網(wǎng)僅提供信息存儲(chǔ)空間,僅對(duì)用戶(hù)上傳內(nèi)容的表現(xiàn)方式做保護(hù)處理,對(duì)用戶(hù)上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對(duì)任何下載內(nèi)容負(fù)責(zé)。
6. 下載文件中如有侵權(quán)或不適當(dāng)內(nèi)容,請(qǐng)與我們聯(lián)系,我們立即糾正。
7. 本站不保證下載資源的準(zhǔn)確性、安全性和完整性, 同時(shí)也不承擔(dān)用戶(hù)因使用這些下載資源對(duì)自己和他人造成任何形式的傷害或損失。
最新文檔
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)6整理和復(fù)習(xí)2圖形與幾何第7課時(shí)圖形的位置練習(xí)課件新人教版
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)6整理和復(fù)習(xí)2圖形與幾何第1課時(shí)圖形的認(rèn)識(shí)與測(cè)量1平面圖形的認(rèn)識(shí)練習(xí)課件新人教版
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)6整理和復(fù)習(xí)1數(shù)與代數(shù)第10課時(shí)比和比例2作業(yè)課件新人教版
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)4比例1比例的意義和基本性質(zhì)第3課時(shí)解比例練習(xí)課件新人教版
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)3圓柱與圓錐1圓柱第7課時(shí)圓柱的體積3作業(yè)課件新人教版
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)3圓柱與圓錐1圓柱第1節(jié)圓柱的認(rèn)識(shí)作業(yè)課件新人教版
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)2百分?jǐn)?shù)(二)第1節(jié)折扣和成數(shù)作業(yè)課件新人教版
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)1負(fù)數(shù)第1課時(shí)負(fù)數(shù)的初步認(rèn)識(shí)作業(yè)課件新人教版
- 2023年六年級(jí)數(shù)學(xué)上冊(cè)期末復(fù)習(xí)考前模擬期末模擬訓(xùn)練二作業(yè)課件蘇教版
- 2023年六年級(jí)數(shù)學(xué)上冊(cè)期末豐收?qǐng)@作業(yè)課件蘇教版
- 2023年六年級(jí)數(shù)學(xué)上冊(cè)易錯(cuò)清單十二課件新人教版
- 標(biāo)準(zhǔn)工時(shí)講義
- 2021年一年級(jí)語(yǔ)文上冊(cè)第六單元知識(shí)要點(diǎn)習(xí)題課件新人教版
- 2022春一年級(jí)語(yǔ)文下冊(cè)課文5識(shí)字測(cè)評(píng)習(xí)題課件新人教版
- 2023年六年級(jí)數(shù)學(xué)下冊(cè)6整理和復(fù)習(xí)4數(shù)學(xué)思考第1課時(shí)數(shù)學(xué)思考1練習(xí)課件新人教版