撓性夾爪（Compliant Gripper）在機械應用領域中有廣泛應用之情景，由於具有適應性強、安全性高、多功能和輕量化、低成本等特點，因此能夠輕易地處理脆弱和不規則形狀的物品。傳統的夾爪設計方法在處理大量網格元素時需要花費昂貴的計算成本，使得許多研究者轉而使用深度學習方法來解決該挑戰。然而，目前大多數的深度學習方法仍需要大量的事先準備的訓練資料，反而增加了整體設計時間，因此本研究提出一個能夠降低計算時間的結合深度學習於拓樸最佳化方法。在進行最佳化設計時，本研究藉由類神經網路模型獲得更細緻（高解析度）之設計結果，根據不同情境使用不同之損失函數（Loss Function），加入投射函數以降低灰階元素數量，並參考穩健性拓樸最佳化方法，同時考慮擴增、縮減與原始設計，避免發生樞紐（Hinge）問題。在模型訓練過程中，採用AMSGrad演算法來更新模型參數，並藉由梯度裁剪（Gradient Clipping）和學習率調整策略，以避免發生梯度爆炸（Gradient Explosion）問題、加速收斂本研究。以四個拓樸最佳化二維標竿問題為例，在考慮相同解析度之設計區間的條件下，傳統拓樸最佳化方法需要210倍之計算時間，且設計結果之應變能較差，增加36%。在撓性夾爪設計部分，與兩個傳統的拓樸最佳化方法相比，本研究之計算時間分別減少93% 與96.5%，且撓性夾爪之包覆性指標和末端之輸出位移數值皆較佳。在撓性夾爪實驗部分，本研究使用3D列印技術製造撓性夾爪，相比於兩個傳統拓樸最佳化演算法所得出之設計結果，本研究在平均分別減少13.01% 和36.36% 輸入力量的同時，平均提升1.89% 和10.15% 之輸出力量，並提高3.7% 和12.2% 之最大負載重量，最後本研究也證明設計之撓性夾爪能夠夾取不同外型或較脆弱之物品，如燈泡、冬粉、雞蛋、洋芋片、蘋果等物品。

Traditional gripper design methods involve high computational costs, especially for large quantities of grid elements. Hence, many researchers have turned to deep learning approaches to tackle this challenge. However, most existing deep learning methods still require a significant amount of pre-prepared training data, which increases the overall design time. To address this issue, this study proposes a hybrid approach that combines deep learning with topology optimization to reduce computational time. During optimization, a neural network model is used to obtain higher-resolution design results. Different loss functions are utilized based on specific contexts and integrating projection functions to reduce the number of grayscale elements. Additionally, robust topology optimization methods are considered, taking into account different designs to prevent hinge-related issues. For model training, gradient clipping and learning rate adjustment strategies are applied to prevent gradient explosion and expedite convergence. To showcase the proposed method's efficacy, four two-dimensional benchmark problems of topology optimization are considered. Taking four two-dimensional benchmark problems of topology optimization as examples, the design results from traditional topology optimization methods show worse strain energy compared to the proposed approach, and it require 210 times the computational time. In the compliant gripper design section, this study demonstrates a significant reduction in computational time of 93% and 96.5% compared to two traditional topology optimization methods. Furthermore, the proposed approach yields improved covering index and output displacement values for the compliant gripper. In the experimental part, the compliant gripper is 3D printed and tested. Compared to the design results obtained from two traditional topology optimization algorithms, the designed compliant gripper proves that the values of output displacement, input force and output force are better, and it can also grip objects with complex or irregular shapes.

[1] Y. Lu, "Industry 4.0: A survey on technologies, applications and open research issues," Journal of industrial information integration, vol. 6, pp. 1-10, 2017.
[2] Onrobot公司網站.https://onrobot.com/.
[3] FESTO公司網站.https://www.festo.com/.
[4] Mindman公司網站.https://mindman.com.tw/.
[5] SRT公司網站.https://softrobottech.com/.
[6] Y. Hao et al., "Universal soft pneumatic robotic gripper with variable effective length," in 2016 35th Chinese control conference (CCC), 2016: IEEE, pp. 6109-6114.
[7] 邱震華, 拓樸與尺寸最佳化於自適性撓性夾爪機械利益最大化設計之研究, 國立成功大學機械工程學系碩士學位論文, 2016.
[8] F. Chen et al., "Topology optimized design, fabrication, and characterization of a soft cable-driven gripper," IEEE Robotics and Automation Letters, vol. 3, no. 3, pp. 2463-2470, 2018.
[9] 陳揚, 多重材料拓樸最佳化於3D列印自適性撓性夾爪設計之研究, 國立成功大學機械工程學系碩士學位論文, 2020.
[10] S. Perai, "Methodology of compliant mechanisms and its current developments in applications: a review," American Journal of Applied Sciences, vol. 4, no. 3, pp. 160-167, 2007.
[11] L. L. Howell and A. Midha, "A loop-closure theory for the analysis and synthesis of compliant mechanisms," 1996.
[12] L. L. Howell, "Compliant mechanisms," in 21st Century Kinematics: The 2012 NSF Workshop, 2013: Springer, pp. 189-216.
[13] A. Kaveh and S. Talatahari, "Size optimization of space trusses using Big Bang–Big Crunch algorithm," Computers & structures, vol. 87, no. 17-18, pp. 1129-1140, 2009.
[14] R. T. Haftka and R. V. Grandhi, "Structural shape optimization—a survey," Computer methods in applied mechanics and engineering, vol. 57, no. 1, pp. 91-106, 1986.
[15] E. Andreassen, A. Clausen, M. Schevenels, B. S. Lazarov, and O. Sigmund, "Efficient topology optimization in MATLAB using 88 lines of code," Structural and Multidisciplinary Optimization, vol. 43, pp. 1-16, 2011.
[16] H. A. Eschenauer and N. Olhoff, "Topology optimization of continuum structures: a review," Appl. Mech. Rev., vol. 54, no. 4, pp. 331-390, 2001.
[17] M. P. Bendsøe and N. Kikuchi, "Generating optimal topologies in structural design using a homogenization method," Computer methods in applied mechanics and engineering, vol. 71, no. 2, pp. 197-224, 1988.
[18] M. P. Bendsøe and O. Sigmund, "Material interpolation schemes in topology optimization," Archive of applied mechanics, vol. 69, pp. 635-654, 1999.
[19] X. Huang and Y. Xie, "Evolutionary topology optimization of continuum structures with an additional displacement constraint," Structural and multidisciplinary optimization, vol. 40, no. 1-6, pp. 409-416, 2010.
[20] O. Sigmund, "A 99 line topology optimization code written in Matlab," Structural and multidisciplinary optimization, vol. 21, pp. 120-127, 2001.
[21] O. Sigmund, "On the design of compliant mechanisms using topology optimization," Journal of Structural Mechanics, vol. 25, no. 4, pp. 493-524, 1997.
[22] K. Svanberg, "MMA and GCMMA-two methods for nonlinear optimization," Optimization and Systems Theory, vol. 1, pp. 1-15, 2007.
[23] H. Adeli, "Neural networks in civil engineering: 1989–2000," Computer‐Aided Civil and Infrastructure Engineering, vol. 16, no. 2, pp. 126-142, 2001.
[24] R. Vargas, A. Mosavi, and R. Ruiz, "Deep learning: a review," 2018.
[25] B. Mahesh, "Machine learning algorithms-a review," International Journal of Science and Research (IJSR).[Internet], vol. 9, pp. 381-386, 2020.
[26] P. Cunningham, M. Cord, and S. J. Delany, "Supervised learning," Machine learning techniques for multimedia: case studies on organization and retrieval, pp. 21-49, 2008.
[27] H. B. Barlow, "Unsupervised learning," Neural computation, vol. 1, no. 3, pp. 295-311, 1989.
[28] M. H. Sazli, "A brief review of feed-forward neural networks," Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, vol. 50, no. 01, 2006.
[29] A. Ajit, K. Acharya, and A. Samanta, "A review of convolutional neural networks," in 2020 international conference on emerging trends in information technology and engineering (ic-ETITE), 2020: IEEE, pp. 1-5.
[30] Y. Yu, X. Si, C. Hu, and J. Zhang, "A review of recurrent neural networks: LSTM cells and network architectures," Neural computation, vol. 31, no. 7, pp. 1235-1270, 2019.
[31] G. E. Henter, J. Lorenzo-Trueba, X. Wang, and J. Yamagishi, "Deep encoder-decoder models for unsupervised learning of controllable speech synthesis," arXiv preprint arXiv:1807.11470, 2018.
[32] K. P. Sinaga and M.-S. Yang, "Unsupervised K-means clustering algorithm," IEEE access, vol. 8, pp. 80716-80727, 2020.
[33] H. Sasaki and H. Igarashi, "Topology optimization accelerated by deep learning," IEEE Transactions on Magnetics, vol. 55, no. 6, pp. 1-5, 2019.
[34] B. Li, C. Huang, X. Li, S. Zheng, and J. Hong, "Non-iterative structural topology optimization using deep learning," Computer-Aided Design, vol. 115, pp. 172-180, 2019.
[35] D. W. Abueidda, S. Koric, and N. A. Sobh, "Topology optimization of 2D structures with nonlinearities using deep learning," Computers & Structures, vol. 237, p. 106283, 2020.
[36] X. Xiao, S. Lian, Z. Luo, and S. Li, "Weighted res-unet for high-quality retina vessel segmentation," in 2018 9th international conference on information technology in medicine and education (ITME), 2018: IEEE, pp. 327-331.
[37] A. Chandrasekhar and K. Suresh, "TOuNN: Topology optimization using neural networks," Structural and Multidisciplinary Optimization, vol. 63, pp. 1135-1149, 2021.
[38] F. Wang, B. S. Lazarov, and O. Sigmund, "On projection methods, convergence and robust formulations in topology optimization," Structural and multidisciplinary optimization, vol. 43, pp. 767-784, 2011.
[39] O. Sigmund, "Manufacturing tolerant topology optimization," Acta Mechanica Sinica, vol. 25, pp. 227-239, 2009.
[40] A. K. Jain, J. Mao, and K. M. Mohiuddin, "Artificial neural networks: A tutorial," Computer, vol. 29, no. 3, pp. 31-44, 1996.
[41] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, "Learning representations by back-propagating errors," nature, vol. 323, no. 6088, pp. 533-536, 1986.
[42] J. He, L. Li, J. Xu, and C. Zheng, "ReLU deep neural networks and linear finite elements," arXiv preprint arXiv:1807.03973, 2018.
[43] K. Shankar, Y. Zhang, Y. Liu, L. Wu, and C.-H. Chen, "Hyperparameter tuning deep learning for diabetic retinopathy fundus image classification," IEEE Access, vol. 8, pp. 118164-118173, 2020.
[44] F. Morin and Y. Bengio, "Hierarchical probabilistic neural network language model," in International workshop on artificial intelligence and statistics, 2005: PMLR, pp. 246-252.
[45] H. Robbins and S. Monro, "A stochastic approximation method," The annals of mathematical statistics, pp. 400-407, 1951.
[46] B. T. Polyak, "Some methods of speeding up the convergence of iteration methods," Ussr computational mathematics and mathematical physics, vol. 4, no. 5, pp. 1-17, 1964.
[47] S. J. Reddi, S. Kale, and S. Kumar, "On the convergence of adam and beyond," arXiv preprint arXiv:1904.09237, 2019.
[48] D. P. Kingma and J. Ba, "Adam: A method for stochastic optimization," arXiv preprint arXiv:1412.6980, 2014.
[49] R. Pascanu, T. Mikolov, and Y. Bengio, "Understanding the exploding gradient problem," CoRR, abs/1211.5063, vol. 2, no. 417, p. 1, 2012.
[50] S. Kanai, Y. Fujiwara, and S. Iwamura, "Preventing gradient explosions in gated recurrent units," Advances in neural information processing systems, vol. 30, 2017.
[51] O. Sigmund, "Morphology-based black and white filters for topology optimization," Structural and Multidisciplinary Optimization, vol. 33, pp. 401-424, 2007.
[52] R. T. Shield and W. Prager, "Optimal structural design for given deflection," Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 21, no. 4, pp. 513-523, 1970.
[53] S. I. Valdez, S. Botello, M. A. Ochoa, J. L. Marroquín, and V. Cardoso, "Topology optimization benchmarks in 2D: Results for minimum compliance and minimum volume in planar stress problems," Archives of Computational Methods in Engineering, vol. 24, pp. 803-839, 2017.
[54] K. Svanberg, "The method of moving asymptotes—a new method for structural optimization," International journal for numerical methods in engineering, vol. 24, no. 2, pp. 359-373, 1987.
[55] C.-H. Liu, F.-M. Chung, Y. Chen, C.-H. Chiu, and T.-L. Chen, "Optimal design of a motor-driven three-finger soft robotic gripper," IEEE/ASME Transactions on Mechatronics, vol. 25, no. 4, pp. 1830-1840, 2020.
[56] 張耕祐, 濾化水平集拓樸最佳化方法於幾何非線性撓性夾爪之研究, 國立成功大學機械工程學系碩士學位論文, 2021.
[57] C.-H. Liu, Y. Chen, and S.-Y. Yang, "Quantification of hyperelastic material parameters for a 3D-Printed thermoplastic elastomer with different infill percentages," Materials Today Communications, vol. 26, p. 101895, 2021.
[58] Optuna套件.https://optuna.org/.