本論文是針對我們現有實驗用的六軸平台做其運動分析與控制，首先我們推導平台的逆向運動學，並利用Newton-Raphson數值法與類神經網路學習的方式來處理平台順向運動學運算的問題。使用Newton數值法於順向運動學運算雖然可以得到很好的精度，但其每次運算所需的疊代次數為數次至數百次，也就是說我們無法得知其每次運算所需的時間為何，而運用類神經網路學習的方式則可以有效降低計算時間且所需的運算時間固定。在類神經網路學習方面，我們分別使用BPN和實驗室發展的SONFIN來學習平台順向運動學的運算，由兩者的模擬結果，我們可以觀察出應用SONFIN於順向運動學運算的誤差量較小，即其偍供較佳的運算精度。
在完成六軸平台的運動學分析，我們即可對平台做實際控制，除了現有的PI型硬體位置控制器外，我們設計了一個PD-like型的模糊位置控制器，以提供較佳的運動響應與位置精度。接著我們分析六軸平台的動力學，以計算出在不同的平台位置姿態下，各油壓致動器所需提供的力為何，以期能對於六軸平台的模型建構與控制器設計有所幫助。另外，針對平台機構可能遇到的奇異點問題，我們是使用路徑規劃的方式來迴避運動中的奇異曲面。在本論文中共提出三種奇異點路徑規避法，分別為最佳化奇異點規避法、曲面梯度奇異點規避法與近似最佳化即時奇異點規避法。使用最佳化規避法雖然擁有較高的位置精度，但其運算時間較長。而曲面梯度規避法的演算架構簡單、計算量小，但其位置精度則較差。而我們提出的近似最佳化即時奇異點規避法即是結合前兩種方法的優點，其動作原理為利用SONFIN學習最佳化規避法的搜尋方向，再以曲面梯度規避法的演算架構來尋找適當的取代路徑。

The aim of our research is the motion analysis and control of a six-degree experimental motion platform. At first, we analyze the inverse kinematics of a six-degree motion platform. Then we solve the forward kinematics problem by the Newton-Raphson numerical method and the neural networks. Adopting the Newton-Raphson numerical method for the forward kinematics problem can achieve good accuracy, but it needs several to hundred numbers of iterations in every calculation. The use of neural networks for the forward kinematics problem can solve this problem, because it takes less and constant time in every calculation. We adopt the BPN and SONFIN for the forward kinematics problem and compare their simulation results. We can observe that SONFIN offers better accuracy than BPN.
After finishing the kinematics analysis of the six-degree motion platform, we design controllers to control it practically. In addition to the original PI-type hardware position controller, we design a PD-like type fuzzy position controller to improve the motion response and position accuracy. We also analyze the dynamics of platform to compute the force of actuators needed to offer in different platform motion and pose. We hope this analysis can help us on the modeling of a six-degree platform and the design of controller. Finally, we adopt the path planning method for avoiding the manifold of singularity during the motion of platform. We propose three kinds of singularity-free path planning methods in this thesis. They are the optimal, gradient and approximate optimal singularity-free path planning methods. Although the optimal method can offer better position accuracy, it takes longer computing time than the gradient one. The approximate optimal method adopts and fuses the spirit of the optimal and gradient method. It uses SONFIN to learn the search direction of optimal method first, then searches the alternate path based on the gradient method.

中文摘要 i
英文摘要 ii
目錄 iii
圖列 v
表列 vii
第一章 簡介與文獻回顧 1
1.1 六軸平台( Stewart Platform )簡介 1
1.2 實驗設備系統介紹 2
第二章 具自我建構能力之類神經模糊推論網路 4
2.1 SONFIN的架構( structure ) 4
2.2 SONFIN的學習演算法( learning algorithm ) 7
2.2.1 輸入、輸出空間的分割 8
2.2.2 模糊法則的建構 10
2.2.3 推論部分架構的確認 11
2.2.4 網路參數的確認 12
第三章 六軸平台運動學分析 14
3.1 空間座標定義 14
3.2 逆向運動學推導( Inverse Kinematics ) 15
3.3 順向運動學探討( Forward Kinematics ) 16
3.3.1 數值方法( Newton-Raphson ) 17
3.3.2 類神經綱路學習法( Neural Network ) 19
3.4 模擬結果( Simulation Results ) 21
第四章 控制系統架構 30
4.1 控制系統架構 30
4.2 軌跡規劃( Trajectory Planning ) 31
4.3 模糊控制法( Fuzzy Control ) 34
4.3.1 PD-like模糊控制器 35
4.4 實驗結果( Experiment Results ) 37
第五章 六軸平台動力學分析 41
5.1 致動器的慣性力分析 41
5.2 六軸平台的動力學分析 44
5.3 模擬結果( Simulation Results ) .47
第六章 路徑中奇異點規避法 49
6.1 六軸平台奇異點( Singularity )的問題 49
6.2奇異點路徑規避法( Singularity-Free Path Planning ) 51
6.2.1 最佳化( Optimal )奇異點規避法 53
6.2.2 曲面梯度( Gradient )奇異點規避法 54
6.2.3 近似最佳化即時奇異點規避法 56
6.3 模擬結果( Simulation Results ) 57
第七章 結論與展望 68
參考文獻 69

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