本研究旨在探討具可變剛性關節的二連桿機器人創新飛躍抓枝運動步態設計與其實現上之可能性。我們首先藉由觀察運動員於爬桿間進行擺盪、飛躍與抓握等動作，將其化簡為二連桿動態系統並設計機器人飛躍抓枝步態。其中第一個階段為(1)擺盪階段，主要為藉由下肢連桿左右擺盪以便累積足夠能量進入後續階段。再者為(2)姿態調整階段，機器人於擺盪過程中需將二連桿調整至類似大於符號(>)的身體姿態作為起飛姿態，以便提供下肢連桿更大的擺盪範圍、增加身軀連桿可抓握之距離。當符合設定之起飛姿態條件後，機器人便進入接下來的(3)飛躍與著陸階段；在飛躍時我們期望能即時旋轉下肢連桿、帶動身軀連桿甩動後，使機器人於著陸時二連桿可以小於符號(<)的身體姿態抓握目標桿件，如此將能量延續至下一次的飛躍抓枝運動步態。我們以拉格朗日方程式推導二連桿機器人在不同階段中的動態數學模型進行數值模擬驗證所設計步態的可行性。模擬結果顯示擺盪階段中加入往覆式的剛性變化可以提高儲能效率，顯示擺盪階段對於整體運動步態實現的重要性。因此我們根據擺盪階段期間(1)有無剛性變化與(2)夾爪有無緊抓握桿件進行數組飛躍抓枝步態實驗。實驗結果顯示所挑選的設計參數可使機器人順利飛躍 21 mm 的間距，且整體運動流程大致符合所提出之大於符號變成小於符號二連桿姿態變化趨勢。在本研究中擺盪階段所嘗試的關節剛性變化設計似乎對於整體的飛躍距離影響有限，未來可進行最佳化的剛性變化探討並善用可變關節於著陸時的衝擊力抑制以利提高飛躍抓枝效能。

This thesis presents a new locomotion style of ricochetal brachiation and investigates the feasibility of this locomotion using a two-link robot equipped with variable stiffness joint. By observing the various phases of movement of athletes climbing between handholders of a ladder, we propose a locomotion style comprising three phases: (1) swing phase; (2) posture adjustment phase; and (3) leaping and landing phase. The objective of the first phase is to accumulate enough energy to move on the succeeding phases by swinging the lowerlimb link. During this swing motion, the next phase is to adjust the two-link posture as similar as possible to the symbol of “ > ”, in which the robot reaches such take-off posture that is able to offer a larger lower-limb link swing range and thus increase the chance of holding the target bar using the body link. After meeting the preset condition of leaping, in the following phase the robot is commanded to instantly rotate the lower-limb link while rotating the body link at the same time, so that the robot can attain a two-link posture that is similar to the symbol of “ > ” to grasp the target bar for easier landing. The robot dynamics is first derived for different phases to explore the feasibility of the proposed locomotion. Simulation results indicate that adding repeating joint stiffness change to the swing phase truly improves the energy accumulation efficiency. Several swing tests are conducted to evaluate the effects of (1) stiffness change and (2) gripper holding condition for ricochetal brachiation. The experimental results demonstrate that the designed robot with preliminary parameter settings can perform successful leaping motion with a flight distance of 21 mm. Moreover, the snapshots of body posture in the experiments tend to match the proposed robot posture changing from “ > ” to “ < ”. The variable stiffness profile used for swing motion seems to have limited effects on the overall leaping distance. In the future an optimal stiffness profile during swing motion could be further designed and the variable stiffness joint is definitely worthy to be applied to attenuate the impact at the landing phase.

[1] K. Song and C. Hsu, "A compliance control design for safe motion of a robotic manipulator," in 2011 9th World Congress on Intelligent Control and Automation, 21-25 June 2011 2011, pp. 920-925, doi: 10.1109/WCICA.2011.5970650.

[2] G. A. Pratt and M. M. Williamson, "Series elastic actuators," in Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots, 5-9 Aug. 1995 1995, vol. 1, pp. 399-406 vol.1, doi: 10.1109/IROS.1995.525827.

[3] 吳健平, "可變剛性致動器開發與飛躍抓枝機器人著陸效能改良之應用," 國立 台灣科技大學機械學系碩士學位論文 , 2019.

[4] 田詠傑, "橫向抓枝機器人之設計與實作 " 國立台灣科技大學機械學系碩士論 文 , 2019.

[5] 楊宗翰, "橫向飛躍抓枝機器人之設計改良與運動控制研究 " 國立台灣科技大 學機械學系碩士論文 , 2018.

[6] C. Zhang, W. Zou, L. Ma, and Z. Wang, "Biologically inspired jumping robots: A comprehensive review," Robotics and Autonomous Systems, vol. 124, p. 103362, 2020/02/01/ 2020, doi: https://doi.org/10.1016/j.robot.2019.103362.

[7] R. Niiyama, A. Nagakubo, and Y. Kuniyoshi, "Mowgli: A Bipedal Jumping and Landing Robot with an Artificial Musculoskeletal System," in Proceedings 2007 IEEE International Conference on Robotics and Automation, 10-14 April 2007 2007, pp. 2546-2551, doi: 10.1109/ROBOT.2007.363848.

[8] S. H. Hyon and T. Mita, "Development of a biologically inspired hopping robot"Kenken"," in Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292), 11-15 May 2002 2002, vol. 4, pp. 3984-3991 vol.4, doi: 10.1109/ROBOT.2002.1014356.

[9] U. Scarfogliero, C. Stefanini, and P. Dario, "A bioinspired concept for high efficiency locomotion in micro robots: the jumping Robot Grillo," in Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., 15-19 May 2006 2006, pp. 4037-4042, doi: 10.1109/ROBOT.2006.1642322.

[10] J. Zhao, W. Yan, N. Xi, M. W. Mutka, and L. Xiao, "A miniature 25 grams running and jumping robot," in 2014 IEEE International Conference on Robotics and Automation (ICRA), 31 May-7 June 2014 2014, pp. 5115-5120, doi: 10.1109/ICRA.2014.6907609.

[11] V. Zaitsev, O. Gvirsman, U. B. Hanan, A. Weiss, A. Ayali, and G. Kosa, "Locustinspired miniature jumping robot," in 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 28 Sept.-2 Oct. 2015 2015, pp. 553-558, doi: 8910.1109/IROS.2015.7353426.

[12] G. Kenneally, A. De, and D. E. Koditschek, "Design Principles for a Family of Direct-Drive Legged Robots," IEEE Robotics and Automation Letters, vol. 1, no. 2, pp. 900-907, 2016, doi: 10.1109/LRA.2016.2528294.

[13] D. W. Haldane, J. K. Yim, and R. S. Fearing, "Repetitive extreme-acceleration (14g) spatial jumping with Salto-1P," in 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 24-28 Sept. 2017 2017, pp. 3345-3351, doi: 10.1109/IROS.2017.8206172.

[14] G. Jung et al., "JumpRoACH: A Trajectory-Adjustable Integrated Jumping– Crawling Robot," IEEE/ASME Transactions on Mechatronics, vol. 24, no. 3, pp. 947-958, 2019, doi: 10.1109/TMECH.2019.2907743.

[15] S. Bergbreiter and K. S. J. Pister, "Design of an Autonomous Jumping Microrobot," in Proceedings 2007 IEEE International Conference on Robotics and Automation, 10-14 April 2007 2007, pp. 447-453, doi: 10.1109/ROBOT.2007.363827.

[16] M. Wang, X.-z. Zang, J.-z. Fan, and J. Zhao, "Biological Jumping Mechanism Analysis and Modeling for Frog Robot," Journal of Bionic Engineering, vol. 5, no. 3, pp. 181-188, 2008/09/01/ 2008, doi: https://doi.org/10.1016/S16726529(08)60023-2.

[17] M. Noh, S. Kim, S. An, J. Koh, and K. Cho, "Flea-Inspired Catapult Mechanism for Miniature Jumping Robots," IEEE Transactions on Robotics, vol. 28, no. 5, pp. 10071018, 2012, doi: 10.1109/TRO.2012.2198510.

[18] D. Wei and W. Ge, "Research on one Bio-inspired Jumping Locomotion Robot for Search and Rescue," International Journal of Advanced Robotic Systems, vol. 11, 10/16 2014, doi: 10.5772/58819.

[19] M. Woodward and M. Sitti, "MultiMo-Bat: A biologically inspired integrated jumping-gliding robot," The International Journal of Robotics Research, vol. 33, pp. 1511-1529, 10/01 2014, doi: 10.1177/0278364914541301.

[20] J.-S. Koh et al., "Jumping on water: Surface tension–dominated jumping of water striders and robotic insects," Science, vol. 349, no. 6247, pp. 517-521, 2015.

[21] U. Scarfogliero, C. Stefanini, and P. Dario, "Design and Development of the LongJumping "Grillo" Mini Robot," in Proceedings 2007 IEEE International Conference on Robotics and Automation, 10-14 April 2007 2007, pp. 467-472, doi: 10.1109/ROBOT.2007.363830.

[22] M. Kovac, M. Fuchs, A. Guignard, J. Zufferey, and D. Floreano, "A miniature 7g jumping robot," in 2008 IEEE International Conference on Robotics and Automation, 19-23 May 2008 2008, pp. 373-378, doi: 10.1109/ROBOT.2008.4543236.

[23] J. Zhao et al., "MSU Jumper: A Single-Motor-Actuated Miniature Steerable Jumping Robot," IEEE Transactions on Robotics, vol. 29, no. 3, pp. 602-614, 2013, doi: 10.1109/TRO.2013.2249371.

[24] J. M. Calderón, W. Moreno, and A. Weitzenfeld, "Fuzzy variable stiffness in landing phase for jumping robot," in Innovations in bio-inspired computing and applications: Springer, 2016, pp. 511-522.

[25] G. A. Cardona, W. Moreno, A. Weitzenfeld, and J. M. Calderon, "Reduction of impact force in falling robots using variable stiffness," in SoutheastCon 2016, 2016: IEEE, pp. 1-6.

[26] Y. Nagamatsu, T. Shirai, H. Suzuki, Y. Kakiuchi, K. Okada, and M. Inaba, "Distributed torque estimation toward low-latency variable stiffness control for geardriven torque sensorless humanoid," in 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2017: IEEE, pp. 5239-5244.

[27] K. Sekino, S. Sakaino, and T. Tsuji, "Frontal posture control of jumping biped robot using stiffness bias control," in IECON 2017-43rd Annual Conference of the IEEE Industrial Electronics Society, 2017: IEEE, pp. 6727-6732.

[28] B. Vanderborght, N. Tsagarakis, R. Van Ham, I. Thorson, and D. Caldwell, "MACCEPA 2.0: Compliant actuator used for energy efficient hopping robot Chobino1D," Autonomous Robots, vol. 31, pp. 55-65, 07/01 2011, doi: 10.1007/s10514-011-9230-7.

[29] B. Vanderborght et al., "Variable impedance actuators: A review," Robotics and Autonomous Systems, vol. 61, no. 12, pp. 1601-1614, 2013/12/01/ 2013, doi: https://doi.org/10.1016/j.robot.2013.06.009.

[30] M. Weckx et al., "Prototype design of a novel modular two-degree-of-freedom variable stiffness actuator," in 2014 IEEE-RAS International Conference on Humanoid Robots, 2014: IEEE, pp. 33-38.

[31] I. Vanderniepen, R. Van Ham, M. Van Damme, R. Versluys, and D. Lefeber, "Orthopaedic rehabilitation: A powered elbow orthosis using compliant actuation," in 2009 IEEE International Conference on Rehabilitation Robotics, 2009: IEEE, pp. 172-177.

[32] P. Cherelle et al., "The MACCEPA actuation system as torque actuator in the gait rehabilitation robot ALTACRO," in 2010 3rd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, 2010: IEEE, pp. 27-32.

[33] B. Brackx et al., "Design of a modular add-on compliant actuator to convert an orthosis into an assistive exoskeleton," in 5th IEEE RAS/EMBS International Conference on Biomedical Robotics and Biomechatronics, 2014: IEEE, pp. 485-490.

[34] T. Bacek et al., "Conceptual design of a novel variable stiffness actuator for use in lower limb exoskeletons," in 2015 IEEE International Conference on Rehabilitation Robotics (ICORR), 2015: IEEE, pp. 583-588.

[35] R. Versluys, A. Matthys, R. Van Ham, I. Vanderniepen, and D. Lefeber, "Powered ankle-foot system that mimics intact human ankle behavior: Proposal of a new concept," in 2009 IEEE International Conference on Rehabilitation Robotics, 2009: IEEE, pp. 658-662.

[36] M. Moltedo, T. Baček, K. Langlois, K. Junius, B. Vanderborght, and D. Lefeber, "Design and experimental evaluation of a lightweight, high-torque and compliant actuator for an active ankle foot orthosis," in 2017 International Conference on Rehabilitation Robotics (ICORR), 2017: IEEE, pp. 283-288.

[37] R. Van Ham, B. Vanderborght, M. Van Damme, B. Verrelst, and D. Lefeber, "MACCEPA, the mechanically adjustable compliance and controllable equilibrium position actuator: Design and implementation in a biped robot," Robotics and Autonomous Systems, vol. 55, no. 10, pp. 761-768, 2007/10/31/ 2007, doi: https://doi.org/10.1016/j.robot.2007.03.001.

[38] D. Braun, M. Howard, and S. Vijayakumar, "Optimal variable stiffness control: formulation and application to explosive movement tasks," Autonomous Robots, vol. 33, no. 3, pp. 237-253, 2012.

[39] A. Radulescu, J. Nakanishi, D. J. Braun, and S. Vijayakumar, "Optimal Control of Variable Stiffness Policies: Dealing with Switching Dynamics and Model Mismatch," in Geometric and Numerical Foundations of Movements: Springer, 2017, pp. 393-419.

[40] T. Fukuda, H. Hosokai, and Y. Kondo, "Brachiation type of mobile robot," in Fifth International Conference on Advanced Robotics' Robots in Unstructured Environments, 1991: IEEE, pp. 915-920.

[41] J. Nakanishi, T. Fukuda, and D. E. Koditschek, "Preliminary studies of a second generation brachiation robot controller," in Proceedings of International Conference on Robotics and Automation, 1997, vol. 3: IEEE, pp. 2050-2056.

[42] J. Nakanishi, A. Radulescu, D. J. Braun, and S. Vijayakumar, "Spatio-temporal stiffness optimization with switching dynamics," Autonomous Robots, vol. 41, no. 2, pp. 273-291, 2017.

[43] 徐士傑, "可橫向飛躍握枝仿生機器人設計與實作," 國立台灣科技大學機械工 程系碩士論文 , 2016.

[44] "American Ninja Warrior Number 1 Fastest Time. History Has Been Made!," https://www.youtube.com/watch?v=gZkObiYVdN4&t=265s, 2015.

[45] D. Ufford, "Simulation of a 2-link Brachiating Robot with Open-Loop Controllers " Northwestern University 2009