本研究提出的跡規劃方法，可以使機器人在平面上實現任意步態行走，包括前進、後退、轉彎和原地踏步等動作。我們的方法規劃了骨盆、支撐腳掌和擺動腳掌的六自由度軌跡（包括三個位置和三個姿態）。骨盆軌跡基於零力矩點（ZMP）設計和預觀控制生成；擺動腳軌跡通過多項式插值進行規劃；姿態軌跡則主要考慮航向角（Yaw Angle）的變化。除了軌跡規劃，本研究先以純運動學控制驗證軌跡與預期目標一致，接著通過運動學與動力學混合控制實現雙足機器人的行走。基於上述架構，我們在MATLAB Simscape中進行物理環境的模擬，並使用實驗室的機器人做實驗，進一步確認軌跡的可行性與控制方法的可靠性。

The trajectory planning method proposed in this thesis enables a robot to perform arbitrary gait movements on a plane, including forward walking, backward walking, turning, and in-place stepping. Our approach involves planning six-degree-of-freedom trajectories for the pelvis, supporting foot, and swinging foot (including three positions and three orientations). The pelvis trajectory is generated based on Zero Moment Point (ZMP) design and preview control; the swinging foot trajectory is planned using polynomial interpolation; and the posture trajectory primarily considers changes in the yaw angle. In addition to trajectory planning, this study first uses pure kinematic control to verify the consistency of the trajectory with the intended target, and then realizes bipedal robot walking through hybrid kinematic-dynamic control. Based on this framework, we conducted simulations in the MATLAB Simscape environment and performed experiments with a laboratory robot to further confirm the feasibility of the trajectory and the reliability of the control method.

[1] "FANUC M-1000iA." FANUC America Corporation. https://www.fanucamerica.com/products/robots/series/m-1000ia (accessed 12/13, 2023).
[2] "送餐機器人." Hong Chiang Technology Co., LTD. https://www.hong-chiang.com.tw/zh-TW/category/K.html (accessed 12/13, 2023).
[3] "AI & Robotics." Tesla. https://www.tesla.com/AI (accessed 12/13, 2023).
[4] K. Kim, P. Spieler, E.-S. Lupu, A. Ramezani, and S.-J. Chung, "A bipedal walking robot that can fly, slackline, and skateboard," Science Robotics, vol. 6, no. 59, p. eabf8136, 2021.
[5] V. Scott Dresser, Amazon Robotics. "Amazon announces 2 new ways it's using robots to assist employees and deliver for customers." Amazon Robotics. https://www.aboutamazon.com/news/operations/amazon-introduces-new-robotics-solutions (accessed June 25, 2024).
[6] U. o. website. "Unitree." Unitree official website. https://www.unitree.com/ (accessed June 25, 2024).
[7] U. Robotics. "Introducing Unitree H1: Its First General-purpose Humanoid Robot| Embodied AI Price below $90k." https://youtu.be/GtPs_ygfaEA?si=_yp0GxNtmj8rCmc8 (accessed June 25, 2024).
[8] C. Zhang, W. Xiao, T. He, and G. Shi, "WoCoCo: Learning Whole-Body Humanoid Control with Sequential Contacts," arXiv preprint arXiv:2406.06005, 2024.
[9] T. He et al., "Learning human-to-humanoid real-time whole-body teleoperation," arXiv preprint arXiv:2403.04436, 2024.
[10] A. Takanishi, M. Ishida, Y. Yamazaki, and I. Kato, "The realization of dynamic walking by the biped walking robot wl-10 rd," Journal of the Robotics Society of Japan, vol. 3, no. 4, pp. 325-336, 1985.
[11] S. Kajita, F. Kanehiro, K. Kaneko, K. Yokoi, and H. Hirukawa, "The 3D linear inverted pendulum mode: A simple modeling for a biped walking pattern generation," in Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No. 01CH37180), 2001, vol. 1: IEEE, pp. 239-246.
[12] C. Stanton, A. Bogdanovych, and E. Ratanasena, "Teleoperation of a humanoid robot using full-body motion capture, example movements, and machine learning," in Proc. Australasian Conference on Robotics and Automation, 2012, vol. 8, p. 51.
[13] S. Kajita et al., "Biped walking pattern generation by using preview control of zero-moment point," in 2003 IEEE international conference on robotics and automation (Cat. No. 03CH37422), 2003, vol. 2: IEEE, pp. 1620-1626.
[14] 蔡禾庭, "整合重心估測與力矩控制於提昇雙足機器人行走穩定性," 碩士, 動力機械工程學系, 國立清華大學, 新竹市, 2017. [Online]. Available: https://hdl.handle.net/11296/vmjprx
[15] 鄭逸倫, "整合力矩控制與重心估測並利用增強式學習提升雙足機器人行走穩定性," 碩士, 動力機械工程學系, 國立清華大學, 新竹市, 2018. [Online]. Available: https://hdl.handle.net/11296/7yfthz
[16] 殷昭駿, "基於預觀控制之步態規劃於運動學與動力學混成控制之雙足機器人," 碩士, 動力機械工程學系, 國立清華大學, 新竹市, 2021. [Online]. Available: https://hdl.handle.net/11296/pjs823
[17] 邱笠維, "應用強化學習於混成控制雙足機器人之步態規劃," 碩士, 動力機械工程學系, 國立清華大學, 新竹市, 2022. [Online]. Available: https://hdl.handle.net/11296/e2sd3w
[18] 楊景苡, "運動學與動力學混成控制雙足機器人之蹺蹺板平衡研究," 碩士, 動力機械工程學系, 國立清華大學, 新竹市, 2023. [Online]. Available: https://hdl.handle.net/11296/zw6bu5
[19] "DYNAMIXEL Protocol 2.0." ROBOTICS. https://emanual.robotis.com/docs/en/dxl/protocol2/ (accessed December 11, 2023).
[20] S. Kajita, H. Hirukawa, K. Harada, and K. Yokoi, Introduction to humanoid robotics. Springer, 2014.
[21] M. Vukobratovic, B. Borovac, D. Surla, and D. Stokic, Biped locomotion: dynamics, stability, control and application. Springer Science & Business Media, 2012.
[22] M. Vukobratović and B. Borovac, "Zero-moment point—thirty five years of its life," International journal of humanoid robotics, vol. 1, no. 01, pp. 157-173, 2004.
[23] M. Vukobratović and J. Stepanenko, "On the stability of anthropomorphic systems," Mathematical biosciences, vol. 15, no. 1-2, pp. 1-37, 1972.
[24] D. T. Greenwood, "Advanced dynamics," (No Title), 2003.
[25] T. Katayama, T. Ohki, T. Inoue, and T. Kato, "Design of an optimal controller for a discrete-time system subject to previewable demand," International Journal of Control, vol. 41, no. 3, pp. 677-699, 1985.