# 臺灣博碩士論文加值系統

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 在本篇論文中，我們先回顧一個無漂移系統的片斷運動規劃演算方法，接著我們提出閉迴路控制的設計，在運動歸劃的演算上閉迴路控制的數學工具發展和前者相同。這個設計控制器是使用常數開關控制信號的方法，這個方法的提出可以將一個非線性無漂移系統的狀態帶到任何我們要求的位置且可以讓它的狀態呈現漸進穩定。
 In this thesis, we first review a piecewise motion planning algorithm for driftless nonlinear systems. Then, we propose a closed-loop control design based on the same mathematical tool developed in the motion planning algorithm. The proposed control designs can drive the state of a driftless nonlinear system to any desired position asymptotically, using constantly switching control signals.
 1.Introduction1 2.Differential Geometry3 2.1Controllability Concepts3 2.2Differential Geometry4 2.2.1 Lie Bracket concepts4 2.2.2 Formal Exponential concepts5 3.Open-Loop Control Design11 3.1 Nilpotent systems11 3.1.1 Design the fictitious input 11 3.1.2 Calculate the Philip Hall coordinate 12 3.1.3 Design the true control 13 3.2 Non-nilpotent systems18 3.3 Examples20 4.Closed-Loop Control Design23 4.1 Regulation Control24 4.2 Examples28 4.3 Tracking Control30 4.4 Examples33 5.Conclusion36 Reference74
 L. Gurvits, Z. Li, '''' Smooth time-periodic feedback solutions for nonholonomic motion planning , '''' In Z. Li and J. F. Canny, editors, ''''Nonholonomic motion planning'''', pages. 53-108, Kluwer, 1993.R. M. Murray and S. S. Sastry, '''' Nonholonomic motion planning : Steering using sinusoids, '''' IEEE Transactions on Automatic Control, vol. 38 no. 5, pp. 700-716, 1993.Shankar Sastry, '''' Nonlinear systems : Analysis, Stability, and Control, Springer, 1999.G. A. Lafferriere, '''' A general strategy for computing steering controls of systems without drift, '''' Proceedings of the 30th IEEE Conference on Decision and Control, pp.1115-1120, 1991.G. A. Lafferriere and H. J. Sussmann, ''''A differential geometric approach to motion planning.'''', In Z. Li and J. F. Canny, editors, ''''Nonholonomic motion planning'''', pages. 235-270, Kluwer, 1993.P. Di. Giamberardino, S. Monaco and D. Normand-Cyrot. Piecewise continuous control for a car-like robot: implementation and experimental results. In Proceedings of the IEEE Conference on Decision and Control, pages. 3564-3569, 1996.S. Monaco and D. Normand-Cyrot. On nonlinear digital control. In A. J. Fossard and D. Normand-Cyrot, editors, Nonlinear Systems, Volume 3 : Control, pages 127-155. Chapman and Hall, 1997.G. A. Lafferriere and E. D. Sontag, '''' Remarks on control Lyapunov functions for discontinuous stabilizing feedback, '''' IEEE Conference on Decision and Control, pp.2398-2403, 1991.C. Samson, '''' Velocity and torque feedback control of a nonholonomic cart,'''' Advanced Robot Control, C. Canudas de Wit, editor, LNCIS 162, Springer, pp. 125-151, 1991.C. Samson, '''' Time-varying feedback stabilization of a car-like wheeled mobile robots,'''' International Journal of Robotics Research, vol. 12, no. 1, pp.55-66, 1993.C. Samson and K. Ait-Abderrahim, '''' Feedback stabilization of a nonholonomic wheeled mobile robot,'''' Proceedings of International Conference on Intelligent Robots and Systems (IROS), 1991.A. W. Divelbiss and J. Wen, '''' A global approach to nonholonomic motion planning, '''' Proceeding IEEE Conference on Decision and Control, pp.1597-1602, 1992.Donald, E. Kirk, '''' Optimal control theory : An introduction, ''''M. Fliess, Series de Volterra et series formelles non commutatives. C. R. Academic Science, Paris, Serie A, 280:965-967, 1975.J. M. Coron, '''' Global asymptotic stabilization for controllable systems without drift,'''' Mathematics of Control, Signals and Systems, vol. 5, pp.295-312, 1991.R. M. Murray, '''' Control of nonholonomic systems using chained form,'''' Fields Institute Communications, vol. 1, pp.219-245, 1993.O. J. Sordalen, ''''Exponential stabilization of a car with n trailers,'''' Proceedings of the 32nd IEEE Control and Decison Conference, vol. 1, pp.978-983, 1993.M. Vidyasagar, ''''Nonlinear syatems analysis second edition,'''' pp. 400-414V.S. Varadarajan. Lie Groups, Lie Algebras, and Their Representations. Springer-Verlag, 1984.
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 1 無漂移系統之連續控制設計 2 無漂移系統之部份狀態轉換與穩定化 3 自走車控制

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