鑑於傳統機械臂控制發展上，面對處理系統含有未知不確定項的情況下，適應控制法則需將系統轉換成線性參數化的形式，然後計算出複雜的regressor矩陣之困擾，與限制未知參數需為非時變之缺點，本論文利用函數近似的技巧，在免除計算regressor矩陣的前提之下，依機械臂在自由空間運動與受限空間運動之分，各別針對剛性與撓性關節機械臂提出適應與適應阻抗控制器，以改善傳統機械臂適應控制的缺陷，而在每一主題之下，又各細分為考慮與未考慮驅動器電氣特性的狀況。亦即本論文提出以下的無regressor矩陣計算之機械臂適應控制器：
1. 剛性機械臂之適應控制器
2. 電氣驅動剛性機械臂之適應控制器
3. 撓性關節機械臂之適應控制器
4. 撓性關節電氣驅動機械臂之適應控制器
5. 剛性機械臂之適應阻抗控制器
6. 電氣驅動剛性機械臂之適應阻抗控制器
7. 撓性關節機械臂之適應阻抗控制器
8. 撓性關節電氣驅動機械臂之適應阻抗控制器
而本文所探討的撓性關節電氣驅動機械臂，截至目前為止，鮮少有文獻加以提出研究，原因是此系統的每一軸皆為五階系統，當在考慮n軸的機械臂時，將需要利用到5n階的微分方程式來描述整個動態行為，如此複雜的串接式機械臂系統，大大的增加了控制器設計的困難度。若在加以考慮系統含有未知的時變參數時，更使得此控制問題面臨了高難度的挑戰性。而本文針對此複雜的系統所提出的適應與適應阻抗控制器，為解決此高難度控制問題的先驅。
本文所提出的無regressor矩陣計算之機械臂適應控制器，顧名思義，最大的貢獻便是在實現的過程當中，解決了傳統上適應控制法則需計算regressor矩陣之困擾，針對各式複雜的機械臂在面對系統含有未知時變參數的問題時，先進行有系統性的整理分類之後，再發展出統一的設計架構，使得控制器能更容易的實現。而本文所提出的控制器設計，除了皆輔有Lyapunov-like穩定性分析，以確保閉迴路系統的穩定度，證明輸出誤差皆得以有漸進收斂的結果之外，進一步的，亦針對追蹤誤差的暫態邊界進行暫態響應的分析，以確保各控制器的暫態性能。各控制器皆以兩軸機械臂為範例，並利用電腦模擬的方式來驗證其功效與可行性。

In traditional adaptive control strategies for robot manipulators, the uncertainties should be linearly parameterizable into a regressor form. This is because traditional adaptive control strategies have a common assumption that the uncertain parameters should be constant or slowly time varying. However, derivation of the regressor matrix is tedious. It will become far more complex when more joints are considered. To deal with this problem, this dissertation utilized the function approximation technique to represent time-varying uncertainties in some finite combinations of orthogonal basis. Under consideration of joint flexibility and/or actuator dynamics, several regressor-free adaptive control strategies for robot manipulators are proposed as:
1. Adaptive control for rigid robots
2. Adaptive control for electrically-driven rigid robots
3. Adaptive control for flexible-joint robots
4. Adaptive control for flexible-joint electrically-driven robots
5. Adaptive impedance control for rigid robots
6. Adaptive impedance control for electrically-driven rigid robots
7. Adaptive impedance control for flexible-joint robots
8. Adaptive impedance control for flexible-joint electrically-driven robots
To the best of our knowledge, this is the first research focus on the adaptive control and adaptive impedance control of robot manipulators with consideration of joint flexibility and actuator dynamics. Controller design for this problem is difficult, because each joint of the robot has to be described by a 5th-order cascade differential equation.
In this dissertation, a systematic procedure is proposed to circumvent various configurations of robot manipulators with time-varying uncertainties. The controller design is free from real-time calculation of the regressor matrix in every sampling period which is necessary in most of the robot adaptive control strategies. The basic idea is to represent system time-varying uncertainties using finite combinations of basis functions with some unknown constant weighting vectors. Closed-loop stability and boundedness of internal signals are proved by the Lyapunov-like analysis with consideration of the function approximation error. In addition, the upper bounds of tracking errors in the transient state are also derived. A 2 DOF planar manipulator is used in the computer simulation to verify the effectiveness of the proposed controllers.

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