3-UPU型並聯式機構包含了三組配置相同的連桿，依序由萬向接頭(universal joint)、滑動接頭(prismatic joint)與萬向接頭串接，透過線性驅動三個滑動接頭共同控制末端效應器之運動。為了避免過大的加/減速變化影響加工精度，甚至造成機台受損，在CNC控制器中包含了處理系統運動規劃的插補器(interpolator)與控制系統實際運動的控制器(controller)。目前已有許多文獻探討運動輪廓(motion profile)對機台穩定性的影響，不同於多數文獻僅考量端效器之運動規劃，本研究以本實驗室所開發的3-UPU型並聯式機構為載具，考量其三軸驅動量、加速度與急跳度極限，提出一最佳化之插補器機器學習模型，規劃最佳化運動輪廓。
本文首先推導3-UPU型並聯式機構之運動學，藉由空間向量關係推得順、逆向運動學的解析解，可迅速求得系統線性驅動量與末端效應器座標之關係。接著推導此機構之運動靜力學通式，估算系統容許的端效器加速度極限。最後以PyTorch建立符合此系統之機器學習模型進行運動輪廓的最佳化，並探討模型中的損失函數(loss function)與超參數(hyperparameter)對計算結果的影響。經此機器學習模型最佳化的路徑(path)不僅在端效器中心點呈現平滑而連續的運動輪廓，驅動端的急跳度也在使用者設定的極限值以內，且最大限度的縮短運動總時間，充分發揮此並聯式工具機之性能，並提供了此機台未來投入智慧製造之可能性。

A 3-UPU Parallel Kinematic Mechanism (PKM) contains three identical limbs, each of which is connected by universal joint, prismatic joint and another universal joint in sequence. The end effector is controlled via the linear motion of the prismatic joint of each limb. An interpolator that plans the motion of the system and a controller that maneuvers the motion are included in the CNC system to avoid large acceleration/deceleration which could undermine the machining accuracy or cause machinery damage. Many studies have been focusing on the effect of motion profile to the stability of the machine, but many of which consider only the motion planning of the end effectors. Taking the 3-UPU PKM developed by our laboratory as a research subject, in this study, we proposed a machine learning interpolator that considers kinematics, acceleration, and jerk limits of the three limbs and the motors. We first derived the analytical solution for both forward and inverse kinematics of the 3-UPU PKM, providing us the relationship between the lengths of the limbs and the position of the end effector. Next, we derived the general solution to the kinetostatics that computes the loading of the joints, which
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constrain the optimizing process. Finally, we developed a machine-learned model that optimizes the motion profiles. Discussions about the effects of the design of the loss function are included. This interpolator contains an optimization that considers the constrains and the motions of both the end effector and the actuators, providing a possible precursor for the development of a cyber-physical system.

摘要 ............................................................................................................. I
Abstract ...................................................................................................... II
致謝 .......................................................................................................... IV
目錄 .......................................................................................................... VI
圖表目錄 ................................................................................................ VIII
第1章 緒論 ........................................................................................... 1
1-1. 研究背景 .................................................................................................................. 1
1-2. 文獻回顧 .................................................................................................................. 3
1-2-1. 並聯式機構之發展 ......................................................................................... 3
1-2-2. 插補與運動控制 ............................................................................................. 5
1-3. 研究目的與研究方法 .............................................................................................. 7
第2章 3-UPU型並聯式機構介紹 ....................................................... 9
2-1. 構型介紹與自由度計算 .......................................................................................... 9
2-2. 座標與參數定義 .................................................................................................... 12
2-3. 3-UPU並聯式機構運動學模型 ........................................................................... 15
2-3-1. 逆向運動學 ................................................................................................... 16
2-3-2. 順向運動學 ................................................................................................... 17
2-4. 運動靜力學模型 .................................................................................................... 18
第3章 3-UPU並聯式機構系統加減速規劃 ..................................... 23
3-1. 規劃指定路徑之速度曲線方法 ............................................................................ 24
3-1-1. 梯形加減速規劃(Trapezoidal Velocity Profile) ........................................... 24
3-1-2. S型加減速規劃(S-curve Velocity Profile) .................................................. 26
3-2. 機器學習 ................................................................................................................ 28
VII
3-2-1. PyTorch簡介 ................................................................................................ 29
3-2-2. 最佳化演算法 ............................................................................................... 29
3-3. 3-UPU型並聯式機構系統加減速規劃機器學習模型........................................ 31
3-3-1. 路徑定義 ....................................................................................................... 31
3-3-2. 機器學習模型 ............................................................................................... 32
3-3-3. 機台物理限制條件 ....................................................................................... 37
第4章 結果與討論 ............................................................................. 39
4-1. 給定測試路徑 ........................................................................................................ 39
4-2. 最佳化多種指定路徑加減速之超參數設定與分析 ............................................ 44
4-2-1. 測試路徑A最佳化結果分析 ...................................................................... 45
4-2-2. 測試路徑B最佳化結果分析 ...................................................................... 55
4-2-3. 測試路徑C最佳化結果分析 ...................................................................... 63
第5章 結論與未來工作 ..................................................................... 71
5-1. 結論 ........................................................................................................................ 71
5-2. 未來工作 ................................................................................................................ 73
參考文獻 ................................................................................................... 74

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