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標題: 單球驅動機器人之3D建模與控制設計
3D Modeling and Control Design for a Ballbot
作者: 徐嘉隆
Hsu, Chia-Lung
關鍵字: 單球驅動機器人;Ballbot
出版社: 機械工程學系所
引用: [1] G. A. Bekey, Autonomous Robots: From Biological Inspiration to Implementation and Control, MIT Press, Cambridge, MA, 2005. [2] R. Siegwart and I. R. Nourbakhsh, Introduction to Autonomous Mobile Robots, MIT Press, Cambridge, MA, 2004. [3] G. Campion, G. Bastin, and B. D’Andrea-Novel, “Structural Properties and Classification of Kinematic and Dynamic Models of Wheeled Mobile Robots,” IEEE Trans. on Robotics and Automation, Vol. 12, No. 1, pp. 47-62, 1996. [4] S. Hashimoto, “Humanoid Robots in Waseda University-Hadaly-2 and WABIAN,” IARP(International Advanced Robotics Programme) 1st Int. Workshop on Humanoid and Human Friendly Robotics, Tsukuba, Japan, Oct. 1998. [5] S. H. Collins, M. Wisse, and A. Ruina, ”A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees,” Int. J. of Robotics Research, Vol. 20, No. 7, pp. 607-615, July 2001. [6] 高琦凱,“雙足機器人的設計製作與步態規劃及嵌入式單軸伺服控制器實作”,國立中興大學機械工程研究所,碩士論文,民國九十六年。 [7] 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. [8] 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. [9] E. M. Schearer, Modeling Dynamics and Exploring Control of a Single-Wheeled Dynamically Stable Mobile Robot with Arms, Master Thesis, Carnegie Mellon University, Aug. 2006. [10] 蕭俊祥、黃柏凱, “球型機械人平衡控制與軌跡追蹤”,中國機械工程學會第二十四屆全國學術研討會,論文編號:B17-0046,民國九十六年。 [11] M. W. Spong, S. Hutchinson, and M. Vidyasagar, Robot Modeling and Control, Wiley, New York, 2006. [12] J. J. Craig, Introduction to Robotics: Mechanics and Control, 3rd Ed., Addison-Wesley, Reading, MA, 2005. [13] J. T. Spooner, M. Maggiore, R. Ordonez, K. M. Passino, Stable Adaptive Control and Estimation for Nonlinear Systems, Wiley, New York, 2002.
針對能在地平面往隨意方向前進的單球驅動機器人,本論文推導其完整解析動力學模式,並進行其隨意軌跡(含移動速率 和前進方向 )追蹤控制設計的研究。首先,假設三個滾柱和圓球間完全沒有滑動,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(含圓球與直立桿)的數學模式,包括3D解析動力學模式、順向以及逆向速度運動學方程式。因單球驅動機器人的動力學模式屬於含有內部動態的輸入-輸出可回授線性化 (input-output feedback linearizable) 系統,本論文於控制系統設計時,先選擇一適當的李亞普洛夫候選函數(Lyapunov function candidate),再根據可線性化部分的動力模式,使用反向步進(backstepping)法推導其穩定非線性追蹤控制律。最後並以三階軟楔插入法(cubic spline interpolation)先規劃機器人的期望軌跡,再進行閉迴路控制系統之性能模擬,驗證所提控制策略的有效性。

In this thesis, we consider the modeling and control for a ballbot that can freely move in any direction within range. The whole complex analytical dynamic equations are derived and then used for synthesizing a nonlinear tracking control law for arbitrary trajectory following. Based on the assumption of no slippage between the three rollers and the ball, forward and inverse velocity kinematics equations are derived. After building the complex kinetic energy and potential energy expressions, the analytical 3D dynamic equations are derived via Lagrange's equations. The dynamics model of a ballbot is input-output feedback linearizable. Thus, by choosing an appropriate Lyapunov function candidate, a stable nonlinear control law is derived, based on the linearizable part model, using the backstepping method. Finally, computer simulations are used to illustrate the effectiveness of the suggested control strategy using a desired motion trajectory generated by the cubic spline interpolation method.
其他識別: U0005-1408200818203000
Appears in Collections:機械工程學系所

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