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標題: 考慮滑動之單球驅動機器人建模與TS模糊及適應模糊控制
Modeling, Stable TS Fuzzy and Adaptive Fuzzy Controls for a Ballbot with Slip Effect
作者: 李孟原
Lee, Meng-Yuan
關鍵字: TS;TS模糊;Fuzzy;Control;Adaptive;Uncertainty;模糊控制;適應控制;不確定性
出版社: 機械工程學系所
引用: [1] T. B. Lauwers, G. A. Kantor, and R. L. Hollis, “A Dynamically Stable Single-Wheeled Mobile Robot with Inverse Mouse-Ball Drive,” IEEE Int. Conf. Robotics and Automation, pp. 2884-2889, 2006. [2] T. B. Lauwers, G. A. Kantor, and R. L. Hollis, “One is Enough,” 12th Int. Symp. Robotics Research, San Francisco, CA, Oct. 12-15, 2005. [3] 徐嘉隆,“單球驅動機器人之3D建模與控制設計”,國立中興大學機械工程研究所碩士論文,民國九十七年。 [4] D. Stonier, S.-H. Cho, S.-L. Choi, N. S. Kuppuswamy, and J.-H. Kim, “Nonlinear Slip Dynamics For an Omniwheel Mobile Robot Platform,” IEEE Int. Conf. Robotics and Automation, Roma, Italy, pp. 2367-2372, April 2007. [5] D. Wang and C. B. Low, “Modeling and Analysis of Skidding and Slipping in Wheeled Mobile Robots: Control Design Perspective,” IEEE Trans. on Robotics, Vol. 24, No. 3, pp. 676-687, June 2008. [6] H. O. Wang, K. Tanaka, and M. F. Griffin, “An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues,” IEEE Trans. on Fuzzy Systems, Vol. 4, No. 1, pp.14-23, Feb. 1996. [7] K. Tanaka, and H. O. Wang, Fuzzy Control Systems Design and Analysis, Addison-Wesley, Reading, NY, 2001. [8] C.-C. Shing, P.-L. Hsu, and S.-S. Yeh, “T-S Fuzzy Path Controller Design for the Omnidirectional Mobile Robot,” 32nd Annual Conf. on IEEE Industrial Electronics, pp. 4142-4146, Nov. 6-10, 2006. [9] C.-C. Sun, H.-Y. Chung, and W.-J. Chang, “Design the T-S Fuzzy Controller for a Class of T-S Fuzzy Models via Genetic Algorithm,” IEEE Int. Conf. on Fuzzy Systems, Vol.1, pp. 278-283, May 12-17, 2002. [10] 黃仕璟,“三軸磁浮軸承之模糊建模與強健適應控制-使用線性矩陣不等式法”,國立中興大學機械工程學系博士論文,民國九十三年。 [11] 莊仁豪,“全向式三輪機器人之動力學模式與適應控制設計”,國立中興大學機械工程學系碩士論文,民國九十七年。 [12] 廖秉德,“含磁滯估測器之三軸壓電致動平台穩定適應模糊控制設計”,國立中興大學機械工程學系碩士論文,民國九十七年。 [13] J. J. Craig, Introduction to Robotics: Mechanics and Control, 3rd Ed., Addison-Wesley, Reading, MA, 2005. [14] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, pp. 338-353, 1965. [15] L.-X. Wang, A Course in Fuzzy Systems and Control, Prentice Hall, 1997.
本論文針對能在地面往隨意方向前進的單球驅動機器人,推導其完整解析動力學模式及近似TS模糊模式,並提出其TS模糊控制律和非線性穩定適應模糊控制律。考慮三個滾柱和圓球間,以及圓球和地面間均有滑動速度和摩擦力的影響,於建立完整的動能、位能表示式後,利用拉格蘭奇(Lagrange)方程式推導出整體機器人系統的數學模式。本文TS模糊控制器的設計,乃使用並行分散補償 (PDC, parallel distributed compensation) 方式,以Lyapunov穩定理論推導能求解控制增益的線性矩陣不等式(LMI)。另外,再根據可線性化部分的動力模式,利用Lyapunov穩定理論推導單球驅動機器人的非線性穩定適應模糊控制律,其中包含非線性阻尼項和模糊近似器,以及含 修正項之參數調適律。最後以電腦模擬印證所提控制律確能讓機器人同時達到隨意軌跡追蹤和直立桿維持平衡直立不倒之控制目的。

In this thesis, we consider the modeling and control for a ballbot that can freely move in any direction within range. Consider that there exist slipping, skidding, and friction both between the three rollers and the ball, and between the ball and the ground. After building the complex kinetic energy and potential energy expressions, the analytical 3D dynamic equations are derived via Lagrange's equations. Then, an approximate TS fuzzy model is derived, and the corresponding TS fuzzy controller is synthesized based on PDC concept via Lyapunov stability theory. The derived LMI's can be solved using the LMI control toolbox. Furthermore, a nonlinear stable adaptive fuzzy controller is derived based on the linearizable part model via Lyapunov method. The proposed nonlinear adaptive control law includes a nonlinear damping term and a fuzzy function approximator using a parameter adaptation law with -modification. Finally, computer simulations are used to illustrate the effectiveness of the suggested control strategies using a desired motion trajectory generated by the cubic spline interpolation method.
其他識別: U0005-1808200918250700
Appears in Collections:機械工程學系所

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