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研究生:邵士航
研究生(外文):Shih-Hang Shao
論文名稱:單球機器人的向量分層控制
論文名稱(外文):Vector Hierarchical Control of a Ballbot
指導教授:黃啟光黃啟光引用關係
指導教授(外文):Chi-Kuang Hwang
學位類別:碩士
校院名稱:中華大學
系所名稱:電機工程學系碩士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:92
中文關鍵詞:單球機器人級聯控制分層控制向量分層控制座標轉換分層控制
外文關鍵詞:ballbotmodelCCHCVHC
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在本論文中所開發的單球機器人,是由一顆球、一個身體以及三個全向輪排成三角形所組成,所以單球機器人可以在二維平面上自由移動也可以在定點上旋轉。傳統的分層滑模控制(HSMC)和聯級滑模控制(CSMC)是用來控制欠驅動非線性系統,我們修改了基本的切換方法,用一個簡單的正數而不需要做切換,但它們的原始結構將會被保留。
基本的子系統是由原始的變數以及其推導的正數所組成,然而下一個與其它的正數也能夠根據聯級或是分層結構來建立。尤其重要的是,每個子系統通常被分配有一個子系統控制輸入,其目的是獲得穩定的子系統,除了含有其他子系統的控制輸入殘留項,換句話說,它是一個非線性回授用來消除所有相關的非線性函數。
本論文只能保證一個穩定的最終分層子系統或聯級子系統,但原始變數的穩定性不能得到保證。本論文所提控制方法中,首先介紹一個聯級控制與兩個分層控制以及一個向量分層控制,然後呈現有考慮座標轉換的分層控制(CHC)以及兩個向量型(VCHCs)。對於姿態和點到點的控制問題,將從模擬中驗證其可行性,並且比較它們之間的性能差異。

A ballbot is consisted of a ball, a body, and three Omni wheels which have been arranged triangle form, so the ballbot can move freely in two-dimension plane with a spinning ability at fixed point. Conventional hierarchical sliding mode control (HSMC) and cascaded sliding mode control (CSMC) are utilized to control under-actuated nonlinear systems. We modify their essential switching scheme as a simple positive constant without any switching, but we kept their structure. The fundamental subsystem is the combination of the original variable and its derivative with a positive constant. Then the next one with the other positive constant can also be created according to the cascaded structure or hierarchical structure.
Each subsystem normally is assigned with a subsystem control input which is designed to achieve a stable subsystem except a remainder containing the other subsystem control inputs. In other words, it is a nonlinear feedback to cancel all the associated nonlinear functions. We can only guarantee a stable final hierarchical or cascaded subsystem, but the stability of the original variables cannot be ensured. We start with a cascaded control (CC), two hierarchical controls (HC), and one vector hierarchical control (VHC). Then by considering the coordinate transformation, two coordinate transformation hierarchical controls (CHC) and their vector type VCHCs algorithms have also presented in the thesis. For regulation and point-to-point problems, simulations have been conducted to verify their feasibility and to compare their performance.

摘 要 ii
ABSTRACT iii
誌謝 iv
目錄 v
圖目錄 vi
表目錄 ix
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 1
1.3 論文架構 2
第二章 單球機器人數學模型 3
2.1 數學模型敘述 3
2.2 動力學方程式推導 6
第三章 控制方法 9
3.1 聯級控制(CC)與分層控制(HC) 9
3.2 座標分層控制 (CHC) 17
第四章 模擬與討論 21
4.1 姿態控制 21
4.2 點對點控制 22
第五章 結論與未來展望 86
附錄 87
參考文獻 91


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[2] A. K. Mampetta, “Automatic transition of ballbot from statically stable state to dynamically stable state”, Master’s thesis, Carnegie Mellon University, Pittsburgh, PA, Report CMU-R1-TR-01-00,2006.
[3] U. Nagarajian, G. A. Kantor, and R. Hollis, “Trajectory planning and control of an under-actuated dynamically stable single spherical wheel robot”, Proceedings IEEE international conference on Robotics and Automation, May 12-17, 2009.
[4] U. Nagarajian, A. Mampetta, G. A. Kntor, and Ralph Hollis, “State transition, balancing, station keeping , and yaw control for a dynamically stable single spherical wheel mobile robot”, Proceedings IEEE international conference on Robotics and Automation, Kobe international conference center, Kobe, Japan, May 12-17, 2009.
[5] Lauwers. T. B., Kantor. G. A., and Hollis R. L., “The ballbot: An omnidirectional
balancing mobile robot”, The International Journal of Robotics Research, pp. 0(0) 1–14., 2013.
[6] Wu. C. W., Hwang C. K., “A Novel Ball Driven by Omni Wheels”, ICMLC Int. Conf. on Machine Learning and Cybernetics, pp. 3800-3803., 2008.
[7] M Kumagai., Ochiai T., “Development of a Robot Balancing on a Ball”, Int. Conf. on Control, Automation and Systems, pp.433-438., 2008.
[8] M Kumagai.,R.Hollis, “Development of a three-dimensional ball rotation sensing system using optical mouse sensors,” in Robotics and Automation, IEEE International Conference on, pp. 5038 –5043. , May 2011.
[9] P. Fankhauser and C. Gwerder, “Modeling and Control of a Ballbot,” Bachelor thesis, ETH Zurich, June 2010.
[10] Fantoni I., Lozano R., Spong M. W., “Energy Based Control of the Pendubot”, IEEE Trans. on Automatic Control, Vol. 45, No. 4, pp. 725-729., 2000.
[11] Shyu. K. K., Jen. C. L., Shang. L. J., “Sliding Mode Control for an Under-actuated Overhead Crane System”, IECON 32nd Annual Conf. on IEEE Industrial Electronics, pp. 412-417., 2006.
[12] Wang. W., Yi. J., Zhao. D., Liu. D., “Design of a Stable Sliding Mode Controller for a Class of Second-order Under-actuated Systems”, IEEE Proc. Control Theory, Vol.151, No.6, pp. 683-690., 2004.
[13] J. Yi. and W. Wang, “Cascade sliding-mode controller for large-scale under-actuated systems”, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.301-306. ,2005
[14] C. W. Chiu, C. H. Wang, C. K. Hwang “Hierarchical Sliding Mode Control of a Spherical Robots Driven by Omni Wheels“ ,Proceedings of the IEEE International Conference on Machine Learning and Cybernetics, Xian, 15-17 July, 2012, pp. 1613-1616.
[15] K.S. Huang, Y. H. Lin, K. B. Lin, B. K. Lee, C. K. Hwang “Cascade Sliding Mode Control of a Spherical Robots Driven by Omni Wheels“ , Proceedings of the IEEE International Conference on Machine Learning and Cybernetics, Xian, 15-17 July, 2012, pp. 1607-161

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