外文翻譯對移動式遙控裝置的智能控制使用2型模糊理論

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1、 畢業(yè)設(shè)計(論文)外文資料翻譯 系　　部： 機械工程系 專 業(yè)： 機械工程及自動化 姓 名： 學(xué) 號： 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)

2、教師評語： 該生的外文翻譯基本正確，沒有嚴(yán)重的語法或拼寫錯誤，已達到本科畢業(yè)的水平。 簽名： 年 月 日 附件1：外文資料翻譯譯文 對移動式遙控裝置的智能控制——使用2型模糊理論 摘要：我們針對單輪移動式遙控裝置的動態(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)上將運動控制器和力矩控制器整合起來的裝置。用計算機模擬來確定追蹤控制器的工作情況和它對不同航向的實際用途。 關(guān)鍵詞：智能控制

3、、2型模糊理論、移動式遙控裝置 I. 介紹 由于受運動學(xué)強制約束，移動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，包括它們在內(nèi)的控制問題吸引了去年控制領(lǐng)域的注意力。 不同的方法被用來解決運動控制的問題。Kanayama等人針對一個非完整的交通工具提出了一個穩(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解決追蹤控制。此外，大多數(shù)被報道過的設(shè)計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)都集中在移動式遙控裝置的運動模塊，即這些模塊是受速度控制的。而很少有發(fā)表關(guān)注到

4、不完整的動力系統(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——一個在Grant 493.05-P下的研究所的支持。研究者們同樣也受到了來自CONACYT——給予他們研究成果的獎學(xué)金的支持。 在這篇論文中我展現(xiàn)了一臺追蹤單輪移動式遙控裝置的控制器，這臺追蹤控制器用了一種控制條件如移動遙控裝置的速度達到了有效速度，還用了一種模糊理論控制器如給實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問題作了簡潔描述，包括了單輪車移動遙控裝置的運動和動力模塊和對追蹤控制器的介紹

5、。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. 疑難問題陳述 A移動控制裝置 這個被看作單輪移動控制器的模型（見圖1），它是由兩個同軸驅(qū)動輪和一個自由前輪組成。 圖1. 旋轉(zhuǎn)移動機械手 運動規(guī)律可見平面5的運動方程式 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)件的移動中心，θ是構(gòu)件朝向和x軸之間的夾角（夾角為逆時針形式）；v為速度矢量，v 和w分別為長度和角速度; τ為輸入矢量，M是一個對稱的正定義的固定零件，R是一個向心的零件,G是重力矢量。等式（1

6、，a）表示移動控制裝置的運動或駕駛系統(tǒng)。注意到防滑條件強加了一個不完整的約束，也就是說這個移動控制裝置只能夠朝著驅(qū)動輪軸線的方向移動。 ycos-xsin=0 (2) 移動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和移動遙控裝置的方向，我們必須設(shè)計出一個控制器使其適用于合適的扭矩諸如測定的位置達到參考位置（由3式表示）。 （3） 為了達到控制目標(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)見圖2 III.運動模塊的控制 我們基于Kanayama等人提議的程序和Nelson等人解決運動模塊的追蹤問題，這由

7、V表示出來。假設(shè)軌跡q達到了（4）式的要求： q= (4) 用遙控器的局部框架（圖1中的移動坐標(biāo)系），錯誤的坐標(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（1，a）實現(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FLC有兩個輸入變量相應(yīng)的引出兩個速度錯誤，分別是長度和角度，且兩個輸出變量，驅(qū)動和旋轉(zhuǎn)輸入扭矩，分別為F和N，他們的作用分別是1的所有

8、直角和2的梯形，且很容易被估算出來。 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，我們利用了萬有引力中心的方法來實現(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 t

9、o 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實現(xiàn)的模擬實驗是用來測試移動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)了對于情況1的模擬結(jié)果。位置和方向錯誤分別見圖5和圖6，錯誤可近似于零。追蹤軌跡（見圖7）也和預(yù)想的及其接近，速度錯誤（見圖8）減小至0，達到了整個模擬過程中1秒內(nèi)的控制目標(biāo)。圖9是測試控制器的模擬簡圖。圖10是三個變

10、量的追蹤錯誤。最后，圖11是遺傳運算法則的演化過程，這個通常用來查找模糊控制器的最佳參數(shù)。 圖 5.位置錯誤參量值。（直線為x，虛線為y） 圖 6.方向錯誤參量值 圖 7.移動遙控裝置運動軌跡 圖 8. 速度錯誤: 實線: 錯誤在e, 虛線:錯誤在 evw 圖 9 控制器的模擬板塊 圖10三個變量的跟蹤錯誤 圖 11 查找最優(yōu)的方案仿真 表2為模糊控制器在25個在不同環(huán)境下所產(chǎn)生的模擬結(jié)果。從這個表中我們同樣選擇了不同的速度和位置參數(shù) 表2 不同模糊控制器實驗仿真 VI.總結(jié) 追蹤控制器是將單輪移動遙控裝置的模糊邏輯控制器與可測

11、定點的穩(wěn)定性和速度軌跡的動力學(xué)整合起來的。計算機模擬結(jié)果確定了這臺控制器可以實現(xiàn)我們的目標(biāo)。在以后的工作中，圖2中的控制結(jié)構(gòu)可以做些擴展，比如說增加些跟蹤的準(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 integr

12、ating 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.

13、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 proble

14、ms 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

15、 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 conc

16、entrated 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,

17、 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 (c

18、orresponding 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 Studie

19、s 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 th

20、e 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 L

21、ewis [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 pape

22、r 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

23、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 conclus

24、ions. 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 m

25、ovement 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

26、 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) represent

27、s 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

28、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 co

29、ntrol 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

30、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

31、 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 c

32、ontrol 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 respect

33、ively), 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.

34、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

35、 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 defuzzific

36、ation 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 POS

37、ITIVE 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 f

38、or 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 con

39、trol 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

40、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:

41、 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.

42、 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 contro

43、ller 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

44、 as to increase the tracking accuracy and the performance level. REFERENCES [1] S. Bentalba, A. El Hajjaji, A. Rachid, Fuzzy Control of a Mobile Robot: A New Approach, Proc. IEEE Int. Conf. On Control Applications, Hartford, CT, pp 69-72, October 1997. [2] A. M. Bloch, S. Drakunov, Tracking in

45、NonHolonomic Dynamic System Via Sliding Modes, Proc. IEEE Conf. On Decision & Control, Brighton, UK, pp 1127-1132, 1991. [3] G. Campion, G. Bastin, B. D’Andrea-Novel, Structural Properties and Classification of Kinematic and Dynamic Models of Wheeled Mobile Robots, IEEE Trans. On Robotics and Auto

46、mation, Vol. 12, No. 1, February 1996. [4] D. Chwa., Sliding-Mode Tracking Control of Nonholonomic Wheeled Mobile Robots in Polar coordinates, IEEE Trans. On Control Syst. Tech. Vol. 12, No. 4, pp 633-644, July 2004. [5] R. Fierro and F.L. Lewis, Control of a Nonholonomic Mobile Robot: Backstepp

47、ing Kinematics into Dynamics. Proc. 34th Conf. on Decision & Control, New Orleans, LA, 1995. [6] R. Fierro, F.L. Lewis, Control of a Nonholonomic Mobile Robot Using Neural Networks, IEEE Trans. On Neural Networks, Vol. 9, No. 4, pp 589 – 600, July 1998. [7] T. Fukao, H. Nakagawa, N. Adachi, Adap

48、tive Tracking Control of a NonHolonomic Mobile Robot, IEEE Trans. On Robotics and Automation, Vol. 16, No. 5, pp. 609-615, October 2000. [8] S. Ishikawa, A Method of Indoor Mobile Robot Navigation by Fuzzy Control, Proc. Int. Conf. Intell. Robot. Syst., Osaka, Japan, pp 1013-1018, 1991. [9] J. S

49、. R. Jang, C.T. Sun, E. Mizutani, Neuro Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice Hall, Upper Sadle River, NJ, 1997. [10] Y. Kanayama, Y. Kimura, F. Miyazaki T. Noguchi, A Stable Tracking Control Method For a Non-Holonomic Mobile Robot, Proc.

50、 IEEE/RSJ Int. Workshop on Intelligent Robots and Systems, Osaka, Japan, pp 1236- 1241, 1991. [11] I. Kolmanovsky, N. H. McClamroch., Developments in Nonholonomic Nontrol Problems, IEEE Control Syst. Mag., Vol. 15, pp. 20–36, December. 1995. [12] T-C Lee, C. H. Lee, C-C Teng, Tracking Control of

51、 Mobile Robots Using the Backsteeping Technique, Proc. 5th. Int. Conf. Contr., Automat., Robot. Vision, Singapore, pp 1715-1719, December 1998. [13] T-C Lee, K. Tai, Tracking Control of Unicycle-Modeled Mobile robots Using a Saturation Feedback Controller, IEEE Trans. On Control Systems Technology

52、, Vol. 9, No. 2, pp 305-318, March 2001. [14] T. H. Lee, F. H. F. Leung, P. K. S. Tam, Position Control for Wheeled Mobile Robot Using a Fuzzy Controller, IEEE pp 525-528, 1999. [15] W. Nelson, I. Cox, Local Path Control for an Autonomous Vehicle, Proc. IEEE Conf. On Robotics and Automation, pp.

53、 1504-1510, 1988. [16] K. M. Passino, S. Yurkovich, “Fuzzy Control”, Addison Wesley Longman, USA 1998. [17] S. Pawlowski, P. Dutkiewicz, K. Kozlowski, W. Wroblewski, Fuzzy Logic Implementation in Mobile Robot Control, 2nd Workshop On Robot Motion and Control, pp 65-70, October 2001. [18] C-C T

54、sai, H-H Lin, C-C Lin, Trajectory Tracking Control of a Laser-Guided Wheeled Mobile Robot, Proc. IEEE Int. Conf. On Control Applications, Taipei, Taiwan, pp 1055-1059, September 2004. [19] K. T. Song, L. H. Sheen, Heuristic fuzzy-neural Network and its application to reactive navigation of a mobil

55、e robot, Fuzzy Sets Systems, Vol. 110, No. 3, pp 331-340, 2000. [20] S. V. Ulyanov, S. Watanabe, V. S. Ulyanov, K. Yamafuji, L. V. Litvintseva, G. G. Rizzotto, Soft Computing for the Intelligent Robust Control of a Robotic Unicycle with a New Physical Measure for Mechanical Controllability, Soft C

56、omputing 2 pp 73 – 88, Springer- Verlag, 1998. 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

57、 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.

58、 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 Logi

59、c, 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, Tij

60、uana, 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’0

61、5. 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 Acade

62、my 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. Lesl

63、ie 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 In

64、stitute 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. L

65、uis 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.