並聯式機構的解析動力學因為其高度非線性與機構間的耦合性，使得解析動力學的求解較為困難，並且解析模型仍需線性化以降低計算的複雜度，方能放入運動控制當中。此外，相較於動力學，並聯式機構的運動學解析模型通常較容易求解。因此，本文將以並聯式機構的運動學模型來引導訓練逆向動力學的類神經網路，並運用類神經網路非線性擬合與計算快速的特性，來彌補解析模型的在求解與運算上的劣勢。本文首先會介紹本文所使用的3-UPU並聯式機構構型，並定義相關參數後進行運動學推導以利於後續模型的建立。而後透過多組運動學方程式與CAD檔建立Simulink的剛體動力學模型，並利用Simscape計算出機構的逆向動力學數值解。此外，為了確保資料的正確性，本文亦利用Adams建立相同的模型交叉驗證其數值解。透過定義多組週期函數，得到端效器在工作空間中涵蓋不同速度、加速度及馬達出力的點資料，並作為數據驅動與物理引導的類神經網路模型之訓練資料。除了理想的模擬資料外，本文利用雷射追蹤儀安裝位置與其感測器的線性重複精度訂定噪音資料，並做為強健性測試使用。最終，在同樣的網路結構下，透過對逆向運動學引導之模型與數據驅動模型的預測結果比較，證實了在加入物理模型後的機器學習模型在內差能力、外插能力、通用能力、及強健性皆優於一般的數據驅動模型。此外，論文中所提及的相關程式碼與資料集將開源於個人的GitHub頁面[1]。

The analytical derivation of dynamic model for parallel kinematic manipulators can be challenging owing to high nonlinearity and strong coupling between each joint. Besides, the analytical dynamic model requires linearization before being implemented to control scheme which certainly losses its nonlinearity. In addition, compared to dynamic model, the analytical kinematic model is relatively simple to be derived. Thus, by utilizing the nonlinear fitting and fast computational characteristics of neural network, this study proposed a novel machine learning model, termed Physics-Guided Neural Network, in order to guide the inverse dynamic model training process with kinematic model. This study first introduces a 3-UPU PKM and defines the parameters related to the derivation of kinematics, so that the Simulink model is established by several blocks including inverse kinematics, CAD model, and data post-processing. Then, a spiral trajectory is performed to verify the correctness of the model. With the aid of Simulink Simscape, the inverse dynamics data of PKM is generated. Therefore, multiple periodic trajectory data that contains different velocity, and acceleration of the end-effector is imported to Python IDE in order to train inverse dynamic model with data-driven neural network (DDNN) and physics-guided neural network (PGNN). Different from DDNN, PGNN uses physics-based loss functions in the learning objective of neural network to ensure the model prediction is guided by physics model. In addition, this study utilizes the mounting position of laser tracker and the linear repeatability of its sensor to generate noise data with physics consistency. Through the analysis in different aspects, kinematics model guided neural network is proved to have better performance on convergence, interpolation capability, extrapolation capability, generalization capability, and robustness than traditional data-driven neural network. All the codes and datasets used in this study have been made available on this link https://github.com/PhoniExZoe/PGNN.

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