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畢業(yè)設(shè)計(jì)(論文)外文資料翻譯
系 部： 機(jī)械工程系
專 業(yè)： 機(jī)械工程及自動(dòng)化
姓 名：
學(xué) 號(hào)：
外文出處： Advance online publication:
4 August 2006
附 件： 1.外文資料翻譯譯文；2.外文原文。
指導(dǎo)教師評(píng)語(yǔ)：
該生的外文翻譯基本正確，沒(méi)有嚴(yán)重的語(yǔ)法或拼寫錯(cuò)誤，已達(dá)到本科畢業(yè)的水平。
簽名：
年 月 日
附件1：外文資料翻譯譯文
對(duì)移動(dòng)式遙控裝置的智能控制——使用2型模糊理論
摘要：我們針對(duì)單輪移動(dòng)式遙控裝置的動(dòng)態(tài)模型開發(fā)出一種追蹤控制器，這種追蹤控制器是建立在模糊理論的基礎(chǔ)上將運(yùn)動(dòng)控制器和力矩控制器整合起來(lái)的裝置。用計(jì)算機(jī)模擬來(lái)確定追蹤控制器的工作情況和它對(duì)不同航向的實(shí)際用途。
關(guān)鍵詞：智能控制、2型模糊理論、移動(dòng)式遙控裝置
I. 介紹
由于受運(yùn)動(dòng)學(xué)強(qiáng)制約束，移動(dòng)遙控裝置是非完整的系統(tǒng)。描述此約束的恒等式不能夠明確的反映出遙控裝置在局部及整體坐標(biāo)系中的關(guān)系。因此，包括它們?cè)趦?nèi)的控制問(wèn)題吸引了去年控制領(lǐng)域的注意力。
不同的方法被用來(lái)解決運(yùn)動(dòng)控制的問(wèn)題。Kanayama等人針對(duì)一個(gè)非完整的交通工具提出了一個(gè)穩(wěn)定的追蹤控制方案，這種方案使用了Lyapunov功能。Lee等人用還原法和飽和約束來(lái)解決追蹤控制。此外，大多數(shù)被報(bào)道過(guò)的設(shè)計(jì)依賴于智能控制方式如模糊邏輯控制和神經(jīng)式網(wǎng)絡(luò)。
然而上述提到的發(fā)表中大多數(shù)都集中在移動(dòng)式遙控裝置的運(yùn)動(dòng)模塊，即這些模塊是受速度控制的。而很少有發(fā)表關(guān)注到不完整的動(dòng)力系統(tǒng)，即受力和扭矩控制的模塊：布洛克。
在2005年12月15日被視為標(biāo)準(zhǔn)并且在2006年3月5日被公認(rèn)的手稿。這一著作在某種程度上受到DGEST——一個(gè)在Grant 493.05-P下的研究所的支持。研究者們同樣也受到了來(lái)自CONACYT——給予他們研究成果的獎(jiǎng)學(xué)金的支持。
在這篇論文中我展現(xiàn)了一臺(tái)追蹤單輪移動(dòng)式遙控裝置的控制器，這臺(tái)追蹤控制器用了一種控制條件如移動(dòng)遙控裝置的速度達(dá)到了有效速度，還用了一種模糊理論控制器如給實(shí)際遙控裝置提供了必要扭矩。這篇論文的其余部分的結(jié)構(gòu)如下：第二部分和第三部分對(duì)問(wèn)題作了簡(jiǎn)潔描述，包括了單輪車移動(dòng)遙控裝置的運(yùn)動(dòng)和動(dòng)力模塊和對(duì)追蹤控制器的介紹。第四部分用追蹤控制器列舉了些模擬結(jié)果。第五部分做出了結(jié)論。
II. 疑難問(wèn)題陳述
A移動(dòng)控制裝置
這個(gè)被看作單輪移動(dòng)控制器的模型（見(jiàn)圖1），它是由兩個(gè)同軸驅(qū)動(dòng)輪和一個(gè)自由前輪組成。
圖1. 旋轉(zhuǎn)移動(dòng)機(jī)械手
運(yùn)動(dòng)規(guī)律可見(jiàn)平面5的運(yùn)動(dòng)方程式
q&=
M(q)&+V(q,q)v+G(q)= (1)
q= q是描述控制器位置的坐標(biāo)矢量，（x，y）是笛卡爾坐標(biāo)，它指出了構(gòu)件的移動(dòng)中心，θ是構(gòu)件朝向和x軸之間的夾角（夾角為逆時(shí)針形式）；v為速度矢量，v 和w分別為長(zhǎng)度和角速度; τ為輸入矢量，M是一個(gè)對(duì)稱的正定義的固定零件，R是一個(gè)向心的零件,G是重力矢量。等式（1，a）表示移動(dòng)控制裝置的運(yùn)動(dòng)或駕駛系統(tǒng)。注意到防滑條件強(qiáng)加了一個(gè)不完整的約束，也就是說(shuō)這個(gè)移動(dòng)控制裝置只能夠朝著驅(qū)動(dòng)輪軸線的方向移動(dòng)。
ycos-xsin=0 (2)
移動(dòng)遙控裝置式的追蹤控制器構(gòu)造如下：一條特定的預(yù)想軌跡q和移動(dòng)遙控裝置的方向，我們必須設(shè)計(jì)出一個(gè)控制器使其適用于合適的扭矩諸如測(cè)定的位置達(dá)到參考位置（由3式表示）。
（3）
為了達(dá)到控制目標(biāo)，我們基于5的步驟，我們得到τ(t)利用模糊邏輯控制器（FLC）控制著輪系(1.a)。追蹤控制器的大體結(jié)構(gòu)見(jiàn)圖2
III.運(yùn)動(dòng)模塊的控制
我們基于Kanayama等人提議的程序和Nelson等人解決運(yùn)動(dòng)模塊的追蹤問(wèn)題，這由V表示出來(lái)。假設(shè)軌跡q達(dá)到了（4）式的要求：
q= (4)
用遙控器的局部框架（圖1中的移動(dòng)坐標(biāo)系），錯(cuò)誤的坐標(biāo)可被定義為：
e=T(q-q), ==(5)
輔助速度控制著輸入量，其可以對(duì)（1，a）實(shí)現(xiàn)追蹤。表示如下：
v=f(e,v), =(6)
其中k1, k2 and k3是連續(xù)的正整數(shù)
IV.模糊邏輯控制器
模糊邏輯控制器的目的是找出控制輸入量τ 如實(shí)際速度矢量v和速度矢量vc之間的關(guān)系
（7）
就像圖2中所顯示的一樣，根本上說(shuō)FLC有兩個(gè)輸入變量相應(yīng)的引出兩個(gè)速度錯(cuò)誤，分別是長(zhǎng)度和角度，且兩個(gè)輸出變量，驅(qū)動(dòng)和旋轉(zhuǎn)輸入扭矩，分別為F和N，他們的作用分別是1的所有直角和2的梯形，且很容易被估算出來(lái)。
圖3和圖4描繪了N,C,P代表的模糊方框中的MFS結(jié)合了每一個(gè)輸入和輸出變量，這些變量都被包括在范圍[-1,1]中
圖2. 追蹤控制結(jié)構(gòu)
圖3. 輸入可變電壓 ev 和 ew
圖 4. 輸出的F和N
FLC中包含9條控制著輸入和輸出關(guān)系的直線，這采用了Mamdani形式的推論引擎，我們利用了萬(wàn)有引力中心的方法來(lái)實(shí)現(xiàn)非模糊程序。在表格1中，我們表現(xiàn)了一種直線形式：
Rule i: 假如ev 是 G1 ，ew 是G2 那么F 是G3 ，N 是G4
Where G1..G4 are the fuzzy set associated to each variable and i= 1 ... 9.
表1 模糊尺組
In Table I, N means NEGATIVE, P means POSITIVE and C means ZERO.
V.模擬結(jié)果
在Matalb實(shí)現(xiàn)的模擬實(shí)驗(yàn)是用來(lái)測(cè)試移動(dòng)式遙控裝置的追蹤控制器（在（1）中已有定義）。我們認(rèn)為初始位置q和 初始速度v。在圖5到圖8中，我們體現(xiàn)了對(duì)于情況1的模擬結(jié)果。位置和方向錯(cuò)誤分別見(jiàn)圖5和圖6，錯(cuò)誤可近似于零。追蹤軌跡（見(jiàn)圖7）也和預(yù)想的及其接近，速度錯(cuò)誤（見(jiàn)圖8）減小至0，達(dá)到了整個(gè)模擬過(guò)程中1秒內(nèi)的控制目標(biāo)。圖9是測(cè)試控制器的模擬簡(jiǎn)圖。圖10是三個(gè)變量的追蹤錯(cuò)誤。最后，圖11是遺傳運(yùn)算法則的演化過(guò)程，這個(gè)通常用來(lái)查找模糊控制器的最佳參數(shù)。
圖 5.位置錯(cuò)誤參量值。（直線為x，虛線為y）
圖 6.方向錯(cuò)誤參量值
圖 7.移動(dòng)遙控裝置運(yùn)動(dòng)軌跡
圖 8. 速度錯(cuò)誤: 實(shí)線: 錯(cuò)誤在e, 虛線:錯(cuò)誤在 evw
圖 9 控制器的模擬板塊
圖10三個(gè)變量的跟蹤錯(cuò)誤
圖 11 查找最優(yōu)的方案仿真
表2為模糊控制器在25個(gè)在不同環(huán)境下所產(chǎn)生的模擬結(jié)果。從這個(gè)表中我們同樣選擇了不同的速度和位置參數(shù)
表2 不同模糊控制器實(shí)驗(yàn)仿真
VI.總結(jié)
追蹤控制器是將單輪移動(dòng)遙控裝置的模糊邏輯控制器與可測(cè)定點(diǎn)的穩(wěn)定性和速度軌跡的動(dòng)力學(xué)整合起來(lái)的。計(jì)算機(jī)模擬結(jié)果確定了這臺(tái)控制器可以實(shí)現(xiàn)我們的目標(biāo)。在以后的工作中，圖2中的控制結(jié)構(gòu)可以做些擴(kuò)展，比如說(shuō)增加些跟蹤的準(zhǔn)確性或工作性能。
附件2：外文原文
Intelligent Control of an Autonomous Mobile Robot using Type-2 Fuzzy Logic
Abstract— We develop a tracking controller for the dynamic model of unicycle mobile robot by integrating a kinematic controller and a torque controller based on Fuzzy Logic Theory. Computer simulations are presented confirming the performance of the tracking controller and its application to different navigation problems.
Index Terms—Intelligent Control, Type-2 Fuzzy Logic, Mobile Robots.
I. INTRODUCTION
Mobile robots are nonholonomic systems due to the constraints imposed on their kinematics. The equations describing the constraints cannot be integrated simbolically to obtain explicit relationships between robot positions in local and global coordinate’s frames. Hence, control problems involve them have attracted attention in the control community in the last years [11].
Different methods have been applied to solve motion control problems. Kanayama et al. [10] propose a stable tracking control method for a nonholonomic vehicle using a Lyapunov function. Lee et al. [12] solved tracking control using backstepping and in [13] with saturation constraints. Furthermore, most reported designs rely on intelligent control approaches such as Fuzzy Logic Control [1][8][14][17][18][20] and Neural Networks [6][19].
However the majority of the publications mentioned above, has concentrated on kinematics models of mobile robots, which are controlled by the velocity input, while less attention has been paid to the control problems of nonholonomic dynamic systems, where forces and torques are the true inputs: Bloch
Manuscript received December 15, 2005 qnd accepted on April 5, 2006. This work was supported in part by the Research Council of DGEST under Grant 493.05-P. The students also were supported by CONACYT with scholarships for their graduate studies.
Oscar Castillo is with the Division of Graduate Studies and Research in Tijuana Institute of Technology, Mexico (corresponding author phone: 52664-623-6318; fax: 52664-623-6318; e-mail: ocastillo@tectijuana.mx).
Patricia Melin is with the Division of Graduate Studies and Research in Tijuana Institute of Technology, Mexico (e-mail: harias@tectijuana.mx).
Arnulfo Alanis is with the Division of Graduate Studies and Research in Tijuana Institute of Technology, Mexico (e-mail: pmelin@tectijuana.mx)
Leslie Astudillo is a graduate student in Computer Science with the Division of Graduate Studies and Research in Tijuana Institute of Technology, Mexico (e-mail: pmelin@tectijuana.mx)
Jose Soria is a with the Division of Graduate Studies and Research in Tijuana Institute of Technology, Mexico (e-mail: jsoria@ucsd.edu).
Luis Aguilar is with CITEDI-IPN Tijuana, Mexico(e-mail:laguilar@citedi.mx)
and Drakunov [2] and Chwa [4], used a sliding mode control to the tracking control problem. Fierro and Lewis [5] propose a dynamical extension that makes possible the integration of kinematic and torque controller for a nonholonomic mobile robot. Fukao et al. [7], introduced an adaptive tracking controller for the dynamic model of mobile robot with unknown parameters using backstepping.
In this paper we present a tracking controller for the dynamic model of a unicycle mobile robot, using a control law such that the mobile robot velocities reach the given velocity inputs, and a fuzzy logic controller such that provided the required torques for the actual mobile robot. The rest of this paper is organized as follows. Sections II and III describe the formulation problem, which include: the kinematic and dynamic model of the unicycle mobile robot and introduces the tracking controller. Section IV illustrates the simulation results using the tracking controller. The section V gives the conclusions.
II. PROBLEM FORMULATION
A. The Mobile Robot
The model considered is a unicycle mobile robot (see Fig. 1), it consist of two driving wheels mounted on the same axis and a front free wheel [3].
Fig. 1.
Fig. 1. Wheeled mobile robot.
The motion can be described with equation (1) of movement in a plane [5]:
Q&=
M(q)&+V(q,q)v+G(q)= (1)
Where q=is the vector of generalized coordinates which describes the robot position, (x,y) are the cartesian coordinates, which denote the mobile center of mass and θ is the angle between the heading direction and the x-axis(which is taken counterclockwise form);v= is the vector of velocities, v and w are the linear and angular velocities respectively; is the input vector,M(q)R is a symmetric and positive-definite inertia matrix, V(q,q)Ris the centripetal and Coriolis matrix,G(q)R is the gravitational vector. Equation (1.a) represents the kinematics or steering system of a mobile robot. Notice that the no-slip condition imposed a non-holonomic constraint described by (2), that it means that the mobile robot can only move in the direction normal to the axis of the driving wheels.
ycos-xsin=0 (2)
B. Tracking Controller of Mobile Robot Our control objective is established as follows: Given a desired trajectory qd(t) and orientation of mobile robot we must design a controller that apply adequate torque τ such that the measured positions q(t) achieve the desired reference qd(t) represented as (3):
（3）
To reach the control objective, we are based in the procedure of [5], we deriving a τ(t) of a specific vc(t) that controls the steering system (1.a) using a Fuzzy Logic Controller (FLC). A general structure of tracking control system is presented in the Fig. 2.
III. CONTROL OF THE KINEMATIC MODEL
We are based on the procedure proposed by Kanayama et al. [10] and Nelson et al. [15] to solve the tracking problem for the kinematic model, this is denoted as vc(t). Suppose the desired trajectory qd satisfies (4):
q= (4)
Using the robot local frame (the moving coordinate system x-y in figure 1), the error coordinates can be defined as (5):
e=T(q-q), ==(5)
And the auxiliary velocity control input that achieves tracking for (1.a) is given by (6):
v=f(e,v), =(6)
Where k1, k2 and k3 are positive constants.
IV. FUZZY LOGIC CONTROLLER
The purpose of the Fuzzy Logic Controller (FLC) is to find a control input τ such that the current velocity vector v to reach the velocity vector vc this is denoted as (7):
（7）
As is shown in Fig. 2, basically the FLC have 2 inputs variables corresponding the velocity errors obtained of (7) (denoted as ev and ew: linear and angular velocity errors respectively), and 2 outputs variables, the driving and rotational input torques τ (denoted by F and N respectively). The membership functions (MF)[9] are defined by 1 triangular and 2 trapezoidal functions for each variable involved due to the fact are easy to implement computationally.
Fig. 3 and Fig. 4 depicts the MFs in which N, C, P represent the fuzzy sets [9] (Negative, Zero and Positive respectively) associated to each input and output variable, where the universe of discourse is normalized into [-1,1] range.
Fig. 2. Tracking control structure
Fig. 3. Membership function of the input variables ev and ew
Fig. 4. Membership functions of the output variables F and N.
The rule set of FLC contain 9 rules which governing the input-output relationship of the FLC and this adopts the Mamdani-style inference engine [16], and we use the center of gravity method to realize defuzzification procedure. In Table I, we present the rule set whose format is established as follows:
Rule i: If ev is G1 and ew is G2 then F is G3 and N is G4
Where G1..G4 are the fuzzy set associated to each variable and i= 1 ... 9.
TABLE 1
FUZZY RULE SET
In Table I, N means NEGATIVE, P means POSITIVE and C means ZERO.
V. SIMULATION RESULTS
Simulations have been done in Matlab? to test the tracking controller of the mobile robot defined in (1). We consider the initial position q(0) = (0, 0, 0) and initial velocity v(0) = (0,0). From Fig. 5 to Fig. 8 we show the results of the simulation for the case 1. Position and orientation errors are depicted in the Fig. 5 and Fig. 6 respectively, as can be observed the errors are sufficient close to zero, the trajectory tracked (see Fig. 7) is very close to the desired, and the velocity errors shown in Fig. 8 decrease to zero, achieving the control objective in less than 1 second of the whole simulation. We show in Fig. 9 the Simulink block diagram to test the controller. We also show in Fig. 10 the tracking errors in the three variables. Finally, we show in Fig. 11 the evolution of the genetic algorithm that was used to find the optimal parameters for the fuzzy controller.
Fig. 5. Positions error with respect to the reference values. Solid: error in x, dotted: error in y.
Fig. 6. Orientation error with respect to the reference values.
Fig. 7. Mobile Robot Trajectory.
Fig. 8. Velocity errors: Solid: error in e, dotted: error in evw
Fig. 9 Simulink block diagram of the controller.
Fig. 10 Tracking errors in the three variables.
Fig. 11 Evolution of GA for finding optimal Controller
In Table II we show simulation results for 25 experiments with different conditions for the gains of the fuzzy controller. We can also appreciate from this table that different reference velocities and positions were considered.
TABLE II
SIMULATION RESULTS FOR DIFFERENT EXPERIMENTS WITH THE FUZZY CONTROLLER.
VI. CONCLUSIONS
We described the development of a tracking controller integrating a fuzzy logic controller for a unicycle mobile robot with known dynamics, which can be applied for both, point stabilization and trajectory tracking. Computer simulation results confirm that the controller can achieve our objective. As future work, several extensions can be made to the control structure of Fig. 2, such as to increase the tracking accuracy and the performance level.
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Oscar Castillo is a Professor of Computer Science in the Graduate Division, Tijuana Institute of Technology, Tijuana, Mexico. In addition, he is serving as Research Director of Computer Science and head of the research group on fuzzy logic and genetic algorithms. Currently, he is President of HAFSA (Hispanic American Fuzzy Systems Association) and Vice-President of IFSA (International Fuzzy Systems Association) in charge of publicity. Prof. Castillo is also Vice-Chair of the Mexican Chapter of the Computational Intelligence Society (IEEE). Prof. Castillo is also General Chair of the IFSA 2007 World Congress to be held in Cancun, Mexico. He also belongs to the Technical Committee on Fuzzy Systems of IEEE and to the Task Force on “Extensions to Type-1 Fuzzy Systems”. His research interests are in Type-2 Fuzzy Logic, Intuitionistic Fuzzy Logic, Fuzzy Control, Neuro-Fuzzy and Genetic-Fuzzy hybrid approaches. He has published over 50 journal papers, 5 authored books, 10 edited books, and 160 papers in conference proceedings.
Patricia Melin is a Professor of Computer Science in the Graduate Division, Tijuana Institute of Technology, Tijuana, Mexico. In addition, she is serving as Director of Graduate Studies in Computer Science and head of the research group on fuzzy logic and neural networks. Currently, she is Vice President of HAFSA (Hispanic American Fuzzy Systems Association) and Program Chair of International Conference FNG’05. Prof. Melin is also Chair of the Mexican Chapter of the Computational Intelligence Society (IEEE). She is also Program Chair of the IFSA 2007 World Congress to be held in Cancun, Mexico. She also belongs to the Committee of Women in Computational Intelligence of the IEEE and to the New York Academy of Sciences. Her research interests are in Type-2 Fuzzy Logic, Modular Neural Networks, Pattern Recognition, Fuzzy Control, Neuro-Fuzzy and Genetic-Fuzzy hybrid approaches. She has published over 50 journal papers, 5 authored books, 8 edited books, and 140 papers in conference proceedings.
Leslie Astudillo is a graduate student in Computer Science with the Division of Graduate Studies and Research in Tijuana Institute of Technology, Mexico. She has published 2 papers in Conference Proceedings.
Arnulfo Alanis is a Professor with the Division of Graduate Studies and Research in Tijuana Institute of Technology, Mexico. He has published 2 Journal papers and 15 Conference Proceedings papers.
Jose Soria is a Professor with the Division of Graduate Studies and Research in Tijuana Institute of Technology, Mexico. He has published 4 Journal papers and 5 Conference Proceedings papers.
Luis Aguilar is a Professor with the Center for Research in Digital Systems in Tijuana, Mexico. He has published 5 Journal papers and 15 Conference Proceedings papers. He is member of the National System of Researchers of Mexico, and member of IEEE. He is member of the IEEE Computational Intelligence-Chapter Mexico, and member of the Hispanic American Fuzzy Systems Association. He is also member of the International Program Committees of several Conferences, and reviewers of several International Journals.