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中文摘要：
针对一般父驱动机械臂的运动规划和控制问题进行研究。从二阶漂移非完整约束系统的一般控制模型出发，基于李代数扩展理论，提出了二阶非完整约束系统的光滑多项式扩展概念，并进一步提出了一种二阶漂移非完整约束系统控制的指数稳定控制方法。针对欠驱动机械臂中从动关节不多于主动关节的情况，给出了一个指数稳定控制定理，并以平面2R和3R欠驱动机械臂进行了仿真。仿真结果证明了提出的指数稳定控制方法的有效性。
英文摘要：
The motion planning and control of underactuated manipulator are studied. From point of view of second order nonholonomic system, based on the extension theory of Lie Algebra, a new extension based on smooth trigonometrical polynomial is proposed, and a exponentially stable control method is verified for a class of underactuated manipulator with actuated joints not less than the passive ones. A 2R and a 3R underactuated planar manipulators with one unactuated joint respectively are simulated to show some aspects of the research. The simulation results confirm that the proposed theory stabilizes the control systems exponentially.
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