本研究旨在透過階層化控制架構使雙足機器人穩定行走。階層化控制架構將機器人控制分為和上層軌跡規劃與下層姿態控制器，並將機器人行走視為雙質量倒單擺系統(dual-mass inverted pendulum, DMIP)運動。上層軌跡規劃根據預先設計理想零力矩點(zero moment point, ZMP)，利用預觀控制(Preview Control)生成機器人身體質心軌跡與擺動腳軌跡。下層姿態控制器混合運動學與動力學控制，其中運動學控制包含利用髖、膝關節將機器人動態定錨為DMIP系統與控制擺動腳跟隨擺動腳軌跡；而動力學控制利用安裝於踝關節之串聯彈性致動器(series elastic actuator, SEA)做力矩伺服控制，使機器人身體質心跟隨身體質心軌跡。本研究將此控制架構實現於實驗室開發之雙足機器人，並利用模擬、實驗驗證機器人穩定行走之性能。

This thesis proposes a hierarchical control structure for the stable walking of bipedal robots. The hierarchical control structure consists of a high-level walking pattern planner and a low-level motion controller. Assuming the robot behaves like a dual-mass inverted pendulum (DMIP) system, the high-level walking pattern planner uses preview control to generate the robot’s CoM and swing-foot trajectories based on the predefined zero moment point (ZMP). On the other hand, the low-level controller performs hybrid kinematic-dynamic control in which the kinematic part controls the velocity-servos at relevant joints to anchor robot dynamics as a DMIP system and to make the swing foot follow the planned trajectory, and the dynamic part controls the ankle torques generated by series elastic actuators to achieve the CoM tracking. The control structure is implemented on a bipedal robot built in-house. Simulations and experiments verify the robot’s stable walking performance.

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vi
表目錄 viii
符號表 1
1. 緒論 3
1.1 研究動機與目的 3
1.2 文獻回顧 6
2. 硬體架構 9
2.1 機構設計 9
2.2 串聯彈性致動器(Series Elastic Actuator, SEA) 10
2.3 機電架構 15
3. 雙足機器人模型與底層控制 18
3.1 系統控制架構 18
3.2 動力學模型 19
3.2.1 線性倒單擺模型(LIPM) 19
3.2.2 雙質量倒單擺模型(DMIP) 21
3.3 運動學模型與姿態控制 22
3.3.1 順向運動學 23
3.3.2 逆向運動學與姿態控制 25
3.4 混合運動學與動力學控制 32
3.4.1 ZMP與腳踝間的關係 32
3.4.2 踝關節力矩控制器 33
4. 行走軌跡規劃 37
4.1 擺動腳軌跡設計 38
4.2 預觀控制(Preview Control) 42
4.3 質心軌跡生成 44
4.4 加入擺動腳影響之質心軌跡修正 47
5. 實驗結果 52
5.1 底層控制器測試 52
5.2 平衡實驗 54
5.3 行走測試 58
6. 結論與未來工作 63
6.1 結論 63
6.2 未來工作 64
7. 參考文獻 67

[1] K. Kaneko, K. Harada, F. Kanehiro, G. Miyamori, and K. Akachi, "Humanoid robot HRP-3," in 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2008: IEEE, pp. 2471-2478.
[2] I.-W. Park, J.-Y. Kim, J. Lee, and J.-H. Oh, "Mechanical design of humanoid robot platform KHR-3 (KAIST humanoid robot 3: HUBO)," in 5th IEEE-RAS International Conference on Humanoid Robots, 2005., 2005: IEEE, pp. 321-326.
[3] B. Dynamics. "More Parkour Atlas." https://www.youtube.com/watch?v=_sBBaNYex3E (accessed.
[4] A. Robotics, "Cassie." [Online]. Available: https://www.agilityrobotics.com/#our-vision.
[5] "DARPA Robotics Challenge." [Online]. Available: https://en.wikipedia.org/wiki/DARPA_Robotics_Challenge.
[6] B. G. Katz, "A low cost modular actuator for dynamic robots," Master’s thesis, Massachusetts Institute of Technology, 2018.
[7] Z. Li, N. G. Tsagarakis, and D. G. Caldwell, "Walking pattern generation for a humanoid robot with compliant joints," Autonomous Robots, vol. 35, no. 1, pp. 1-14, 2013.
[8] 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, 1995, vol. 1: IEEE, pp. 399-406.
[9] M. Hutter et al., "Anymal-a highly mobile and dynamic quadrupedal robot," in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2016: IEEE, pp. 38-44.
[10] 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.
[11] M. Vukobratovic, B. Borovac, D. Surla, and D. Stokic, Biped locomotion: dynamics, stability, control and application. Springer Science & Business Media, 2012.
[12] S. Kajita, H. Hirukawa, K. Harada, and K. Yokoi, Introduction to humanoid robotics. Springer, 2014.
[13] 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.
[14] 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.
[15] S. Kajita et al., "Biped walking stabilization based on linear inverted pendulum tracking," in 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2010: IEEE, pp. 4489-4496.
[16] J. H. Park and K. D. Kim, "Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control," in Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No. 98CH36146), 1998, vol. 4: IEEE, pp. 3528-3533.
[17] A. Albert and W. Gerth, "Analytic path planning algorithms for bipedal robots without a trunk," Journal of Intelligent and Robotic Systems, vol. 36, no. 2, pp. 109-127, 2003.
[18] G. Ficht and S. Behnke, "Fast Whole-Body Motion Control of Humanoid Robots with Inertia Constraints," in 2020 IEEE International Conference on Robotics and Automation (ICRA), 2020: IEEE, pp. 6597-6603.
[19] T.-T. Lee, "Trajectory planning and control of a 3-link biped robot," in Proceedings. 1988 IEEE International Conference on Robotics and Automation, 1988: IEEE, pp. 820-823.
[20] K. Ono and R. Liu, "Optimal biped walking locomotion solved by trajectory planning method," J. Dyn. Sys., Meas., Control, vol. 124, no. 4, pp. 554-565, 2002.
[21] K. i. Nagasaka, H. Inoue, and M. Inaba, "Dynamic walking pattern generation for a humanoid robot based on optimal gradient method," in IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No. 99CH37028), 1999, vol. 6: IEEE, pp. 908-913.
[22] 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," 清華大學動力機械工程學系碩士學位論文, pp. 1-55, 2017.
[23] 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," 清華大學動力機械工程學系碩士學位論文, pp. 1-68, 2018.
[24] C. Tatsch, A. Ahmadi, F. Bottega, J. Tani, and R. da Silva Guerra, "Dimitri: an Open-Source Humanoid Robot with Compliant Joint," Journal of Intelligent & Robotic Systems, vol. 91, no. 2, pp. 291-300, 2018.
[25] TDS TPU 95A v3.010 ZH(TW), Ultimaker, 05/16 2017. [Online]. Available: https://support.ultimaker.com/hc/en-us/articles/360012664440-Ultimaker-TPU-95A-TDS
[26] STM32F446RE., STMicroelectronics. [Online]. Available: https://www.st.com/en/evaluation-tools/nucleo-f446re.html
[27] Dynamixel MX-106T., ROBOTIS. [Online]. Available: https://emanual.robotis.com/docs/en/dxl/mx/mx-106-2/
[28] AS5145B Rotary Sensor Datasheet, ams. [Online]. Available: https://ams.com/zh/as5145b
[29] MTi 600-series Datasheet, Xsens. [Online]. Available: https://www.xsens.com/products/mti-600-series
[30] C.-F. Huang, B.-H. Dai, and T.-J. Yeh, "Determination of motor torque for power-assist electric bicycles using observer-based sensor fusion," Journal of Dynamic Systems, Measurement, and Control, vol. 140, no. 7, 2018.
[31] S. R. Buss, "Introduction to inverse kinematics with jacobian transpose, pseudoinverse and damped least squares methods," IEEE Journal of Robotics and Automation, vol. 17, no. 1-19, p. 16, 2004.
[32] 黃凱辰, "基於雙質量倒單擺動態之雙足機器人速度/力矩混成控制與步態規劃," 清華大學動力機械工程學系碩士學位論文, pp. 1-87, 2020.
[33] 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.