本論文旨在將倒單擺系統結合全向移動機器人，並建構二維倒單擺平衡控制系統。論文主要分成兩部分：(一)首先利用Euler-Lagrange方法建立倒單擺系統之動態數學模型，結合全向移動機器人及馬達模型，進而建立全向移動機器人致動二維倒單擺之完整數學模型，並以超螺旋控制法則(super-twisting algorithm, STA)設計二階順滑模態(second-order sliding mode)平衡控制器；(二)利用(一)所推導出數學模型，針對此系統以未解耦合方式設計非線性輸出調節(nonlinear output regulation )控制器，並透過MATLAB/Simulink軟體來進行模擬，驗證計算上的正確性。而本論文中使用磁鐵與霍爾元件來作為倒單擺的角度量測方式，以裝置於單擺上的磁鐵，藉由霍爾元件來感應磁場的變化，進而量測角度。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控制。

The objective of this thesis is to design balance control for a spherical inverted pendulum system with an omnidirectional mobile robot. The contribution of this thesis is twofold. First, the Euler-Lagrange method is used to derive the dynamic model of the spherical inverted pendulum system with an omnidirectional mobile robot. The super-twisting algorithm of the second-order sliding mode control is used to design a balance controller. Secondly, based on the uncoupled nonlinear model, a nonlinear output regulation controller is designed for trajectory tracking. The MATLAB/Simulink software is used for numerical simulation. In the experiments, the angular measurement of the inverted pendulum is based on the Hall sensors and magnets. The magnets are mounted on the pendulum. Hall sensors are used to sense changes in the magnetic field due to angular changes. 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 control of the spherical inverted pendulum system actuated by an omnidirectional mobile robot is achieved.

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