本論文考慮了全向輪移動機器人的控制問題及其應用。首先，推導了全方位移動機器人的動力學模型，以方便控制設計。在控制器設計中，回授線性化(feedback linearization)用於使系統線性化。然後在線性化系統的基礎上，設計積分型順滑模態(integral sliding mode)控制器進行軌跡追蹤控制，這種控制策略對於模型不確定性和存在於外部的干擾具有良好的強健性。所設計的控制法則會在實驗裝置上實作與測試，透過模擬和實作驗證了控制法則的有效性，並且與經過良好調設後的 PID 控制器進行了性能比較。結果顯示，採用積分型順滑模態控制器的控制系統具有較好的追蹤性能。

在應用方面，首先，本論文建構了一個包括動態立體視覺相機和靜態相機所組成的機器視覺系統，用於擷取動態中的目標物，並導引全向移動機器人攔接目標物。對於機器視覺的系統上，使用了具有深度學習的卡爾曼濾波器(Kalman filter)來降低視覺測量雜訊並且預估目標物的位置和速度，進而預測目標物的未來軌跡和著陸點。經由預測出來的著陸點，透過靜態相機進行全向輪移動機器人導航來完成攔接目標物之目的。機器視覺追蹤演算法一開始先使用數值模擬，然後再對所設計的演算法性能進行了實作驗證。對於全向輪移動機器人的控制上，利用狀態回授線性化控制法並結合 PID 控制器的追蹤法則。最後，此應用在實作上驗證了所設計的系統能夠準確地攔接目標物。

另一應用則考慮了使用全向輪移動機器人為致動器的可配置倒單擺的平衡控制問題。此系統由兩部分組成，倒單擺與全向輪移動機器人。系統中的倒單擺可以配置成旋轉型(rotary inverted pendulum)或球型(spherical inverted pendulum)。目的是控制全向輪移動機器人在平面上提供平移力以平衡球型倒單擺，以及提供旋轉力矩用以平衡旋轉型倒單擺。這兩種系統的詳細動態模型被推導出來後用於控制法則的設計和模擬驗證。基於二階順滑模態(second-order sliding mode)的穩定控制器是為這兩種系統的設計方法。此外，在我們之前的研究中提出的傳統順滑模態控制器和基於垂直平衡點的線性化系統模型之線性二次調節（LQR）控制器也用於性能比較。以模擬和實作驗證了控制法則的有效性。模擬結果顯示，只有二階順滑模態控制器能使系統的倒單擺在垂直位置上有較大初始偏差的情況下穩定。最後，實驗結果顯示，二階順滑模態控制器優於傳統順滑模態控制器和 LQR 控制器。

This dissertation considers the control problems of an omni-directional mobile robot and its applications. First, the dynamic model of an omni-directional mobile robot is derived to facilitate the control design. In the controller design, feedback linearization is used to linearize the system. Then, based on the linearized system, an integral sliding mode controller is then designed for trajectory tracking control. This control strategy is robust to model uncertainties and exogenous disturbances. The designed control laws will be implemented and tested on an experimental setup. The effectiveness of the control law is verified through simulation and experimental studies, and the performance is compared with a well-tuned PID controller. It is shown that the control system with the integral sliding mode controller has better tracking performance.

In applications, a machine vision system composed of a dynamic stereo vision camera and a static camera was constructed. This machine vision system is used to capture the moving target and guide the omni-directional mobile robot to catch the target. For the machine vision system, the Kalman filter with deep learning was used to decrease the visual measurement noises and to estimate the position and velocity of the target, and then predict the future trajectory and touchdown point of the target. Through the predicted touchdown point, the omni-directional mobile robot is navigated by the static camera to complete the purpose of catching the target. The machine vision tracking algorithm was initially simulated numerically, and then the performance of the designed system was verified experimentally. For the control of the omni-directional mobile robot, the state feedback linearization control method combined with the tracking law of the PID controller is used. Finally, this application verifies that the designed system can catch the target accurately.

Another application considers the balance control problems of a configurable inverted pendulum with an omni-directional wheeled mobile robot. This system consists of two parts, an inverted pendulum, and an omni-directional wheel mobile robot. The inverted pendulum in the system can be configured as a rotary inverted pendulum or a spherical inverted pendulum. The objective is to control the omni-directional wheeled mobile robot to provide a translational force on the plane to balance the spherical inverted pendulum and to provide the rotational torque to balance the rotary inverted pendulum. Detailed dynamic models of these two systems are derived for the control strategy design and simulation studies. Stabilizing controllers based on the second-order sliding mode control are designed for both systems. In addition, the conventional sliding mode controllers proposed in our previous work and Linear-Quadratic Regulator (LQR) controllers based on the linearized system models about its upright equilibrium point are also used for performance comparison. The effectiveness of the control strategies is investigated and verified using simulation and experimental studies. The simulation results show that only the second-order sliding mode controller can stabilize the system with a significant initial deviation from the pendulum's upright position. Finally, the experimental results demonstrate that second-order sliding mode control outperforms conventional sliding mode control and LQR control.

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