本論文旨在將倒單擺系統結合全向移動機器人，以建構二維倒單擺平衡暨軌跡追蹤控制系統。論文主要分兩部分;(一)首先將以Euler-Lagrange方法建立倒單擺系統之動態數學模型，並針對此模型利用線性輸出調節控制法則與非線性輸出調節控制法則，設計平衡暨軌跡追蹤控制器。(二)由摩擦力觀點推導全向移動機器人數學模型，並透過MATLAB/Simulink軟體模擬光學編碼器因滑動造成軌跡誤差情形，再由光學編碼器與慣性感測器結合擴展型卡門濾波器，對全向移動機器人位置與姿態進行濾波並作為回授訊號進行軌跡追蹤控制，使滑動造成的軌跡誤差下降。在實作上，本系統使用德州儀器公司(Texas Instruments, TI)所生產的數位訊號處理器TMS320F2812做為控制核心以實現所有控制法則，並配合周邊介面電路，進而完成倒單擺平衡暨軌跡追蹤控制與以慣性導航之軌跡追蹤控制。

The objective of this thesis is to design tracking control for a spherical inverted pendulum system with an omnidirectional mobile robot. There are two parts in this thesis: First, the Euler-Lagrange method is used to derive the dynamic model of the spherical inverted pendulum system.the linear output regulation control law and nonlinear output regulation control law are designed for balance and tracking control of this system. Second, the dynamic model of the omnidirectional mobile robot with friction is derived. MATLAB/Simulink software is used to simulate the situation of slippage when feedback signals are provided by encoders. To improve the tracking performance an extended Kalman filter is used for predicting the position and attitude with an inertial measurement unit and encoders. In the experiments, the designed controllers are implemented on a digital signal processor (TMS320F2812) produced by Texas Instruments. Finally, combining the digital signal processor with the relevant peripheral interface circuits, balance and tracking control of the spherical inverted pendulum system actuated by an omnidirectional mobile robot is achieved.

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