本文介紹了 HEXA 並聯式機器人的結構，並提出了運動學和動力學問題。運動學
和動力學方程是基於 HEXA 機器人模型建立的。逆運動學和動力學方程的解是詳細
解析推導的。相反，正向運動學問題是通過應用人工神經網絡來解決的。同時，正
向動力學問題的解決方案只是給出了一種方法，而不是具體的解決方案。串聯式機
械手臂的虛擬力感測器方法可以用來確定施加到機器人系統上的外力。基於上述方
法，提出了一種能指示並聯式機器人機械手臂是否發生碰撞的方法。該方法利用了
上一節中推導出的逆動力學解。視覺系統持續監控 HEXA 機器人系統以跟踪末端執
行器的姿態。如果發生碰撞，該視覺系統負責確定接觸點位置。遞歸牛頓-歐拉算法
用於計算導致碰撞的接觸力。逆運動學和動力學的解決方案在 MATLAB 中編程。與
視覺系統相關的問題，如圖像處理和卷積神經網絡，也在 MATLAB 中處理。傳感器
通過 RS232 串行通信協議直接連接到電腦。實驗工作在一個真實的機器人系統上進
行，以驗證所提出方法的有效性。控制 HEXA 機器人的終端器在工作空間中的軌跡
上移動。由于外力作用在終端器、手臂和杆子上，在這個機器人系统中發生了碰撞。
當碰撞開始發生並且外力達到最大值時，就會檢測到碰撞。接觸點的位置也已確定。
計算接觸力並與力感測器的測量值進行比較。

This thesis introduces the configuration of the Hexa parallel robot and presents kinematics and dynamics problems. Kinematics and dynamics equations are built based on the model of the Hexa robot. Solutions to inverse kinematics and dynamics equations are derived analytically in detail. On the contrary, forward kinematics problems are resolved by applying artificial neural networks. Meanwhile, the solution to the forward dynamics problem is only presented with a method, not a specific solution. A virtual force sensor approach for serial manipulators is presented to determine the external force applied to the robot system. Based on mentioned above method, an approach is promoted to indicate whether any collision occurs on the parallel robot manipulators or not. This method exploits the inverse dynamics solution derived in the previous section. A vision system continuously monitors the Hexa robot system to track the pose of the end-effector. If a collision occurs, this vision system is responsible for determining the contact point location. The Recursive Newton-Euler Algorithm is applied to compute a contact force that causes a collision. Solutions to inverse kinematics and dynamics are programmed in MATLAB. Problems related to the vision system, such as image processing and convolutional neural networks, are also processed in MATLAB. Sensors are connected directly to the computer by RS232 serial communication protocol. Experimental work is performed on a real robot system to verify the effectiveness of the presented approach. The Hexa robot is controlled to move the active plate on a trajectory in the workspace. Collisions occurred in this robot system due to external forces acting on the active plate, an arm, and a rod. Collisions are detected when they occur and when external forces reach their maximum value. The contact point location is also determined. The contact forces are computed and compared with the measured value from force sensors.

[1] J. P. Merlet and C. Gosselin, “Parallel Mechanisms and Robots,” in Springer
Handbook of Robotics, Berlin, Heidelberg: Springer Berlin Heidelberg, 2008, pp.
269–285.
[2] F. Pierrot, P. Dauchez, and A. Fournier, “HEXA: a Fast Six-DOF Fully Parallel
Robot,” in Fifth International Conference on Advanced Robotics ’Robots in
Unstructured Environments, Dec. 1991, pp. 1158–1163 vol.2, doi :
10.1109/ICAR.1991.240399.
[3] B. P. Huynh, C. W. Wu, and Y. L. Kuo, “Force/Position Hybrid Control for a Hexa
Robot Using Gradient Descent Iterative Learning Control Algorithm,” IEEE Access,
vol. 7, pp. 72329–72342, 2019, doi: 10.1109/ACCESS.2019.2920020.
[4] S. C. T. Filho and E. L. L. Cabral, “Kinematics and Workspace Analysis of a Parallel
Architecture Robot : the Hexa,” in ABCM Symposium Series in Mechatronics, 2005,
vol. 2, pp. 158–165.
[5] M. Dehghani, M. Ahmadi, A. Khayatian, M. Eghtesad, and M. Farid, “Neural
Network Solution for Forward Kinematics Problem of HEXA Parallel Robot,” in
2008 American Control Conference, Jun. 2008, vol. 60, no. 2, pp. 4214–4219, doi:
10.1109/ACC.2008.4587155.
[6] S. C. T. Filho and E. L. L. Cabral, “Dynamics and Jacobian Analysis of a Parallel
Architecture Robot: the Hexa,” in ABCM Symposium Series in Mechatronics, 2005,
vol. 2, pp. 166–173.
[7] X. Wang and Y. Tian, “Inverse Dynamics of Hexa Parallel Robot Based on the
Lagrangian Equations of First Type,” in 2010 International Conference on Mechanic
Automation and Control Engineering, Jun. 2010, pp. 3712–3716, doi:
10.1109/MACE.2010.5535969.
[8] S. A. B. Birjandi, J. Kuhn, and S. Haddadin, “Observer-Extended Direct Method for
Collision Monitoring in Robot Manipulators Using Proprioception and IMU
Sensing,” IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 954–961, Apr.
2020, doi: 10.1109/LRA.2020.2967287.
[9] S. A. B. Birjandi and S. Haddadin, “Model-Adaptive High-Speed Collision Detection for Serial-Chain Robot Manipulators,” IEEE Robotics and Automation Letters, vol.
5, no. 4, pp. 6544–6551, Oct. 2020, doi: 10.1109/LRA.2020.3015187.
[10] Z. Qiu and R. Ozawa, “A Sensorless Collision Detection Approach Based on Virtual
Contact Points,” in Proceedings - IEEE International Conference on Robotics and
Automation, Sep. 2018, pp. 7639–7645, doi: 10.1109/ICRA.2018.8460219.
[11] Y. Tian, Z. Chen, T. Jia, A. Wang, and L. Li, “Sensorless Collision Detection and
Contact Force Estimation for Collaborative Robots Based on Torque Observer,” in
2016 IEEE International Conference on Robotics and Biomimetics (ROBIO), Dec.
2016, pp. 946–951, doi: 10.1109/ROBIO.2016.7866446.
[12] Y. Yao, Y. Shen, Y. Lu, and C. Zhuang, “Sensorless Collision Detection Method for
Robots with Uncertain Dynamics Based on Fuzzy Logics,” in 2020 IEEE
International Conference on Mechatronics and Automation, ICMA 2020, Oct. 2020,
pp. 413–418, doi: 10.1109/ICMA49215.2020.9233749.
[13] W. Mcmahan, J. M. Romano, and K. J. Kuchenbecker, “Using Accelerometers to
Localize Tactile Contact Events on a Robot Arm,” in Proceedings of Workshop on
Advances in Tactile Sensing and Touch-Based Human-Robot Interaction, ACM/IEEE
International Conference on Human-Robot Interaction, 2012.
[14] M. Fritzsche, J. Saenz, and F. Penzlin, “A Large Scale Tactile Sensor for Safe Mobile
Robot Manipulation,” in 2016 11th ACM/IEEE International Conference on HumanRobot Interaction (HRI), Mar. 2016, vol. 2016-April, pp. 427–428, doi:
10.1109/HRI.2016.7451789.
[15] M. Fritzsche, N. Elkmann, and E. Schulenburg, “Tactile Sensing: A Key Technology
for Safe Physical Human Robot Interaction,” in Proceedings of the 6th International
Conference on Human-Robot Interaction - HRI ’11, 2011, p. 139, doi:
10.1145/1957656.1957700.
[16] G. Cannata, M. Maggiali, G. Metta, and G. Sandini, “An Embedded Artificial Skin
for Humanoid Robots,” in IEEE International Conference on Multisensor Fusion and
Integration for Intelligent Systems, 2008, pp. 434–438, doi:
10.1109/MFI.2008.4648033.
[17] S. H. Yen, P. C. Tang, Y. C. Lin, and C. Y. Lin, “Development of a Virtual Force
Sensor for a Low-Cost Collaborative Robot and Applications to Safety Control,” Sensors (Switzerland), vol. 19, no. 11, Jun. 2019, doi: 10.3390/s19112603.
[18] E. Magrini, F. Flacco, and A. De Luca, “Estimation of Contact Forces using a Virtual
Force Sensor,” in IEEE International Conference on Intelligent Robots and Systems,
Oct. 2014, pp. 2126–2133, doi: 10.1109/IROS.2014.6942848.
[19] D. Popov, A. Klimchik, and N. Mavridis, “Collision Detection, Localization &
Classification for Industrial Robots with Joint Torque Sensors,” in 2017 26th IEEE
International Symposium on Robot and Human Interactive Communication (ROMAN), Aug. 2017, pp. 838–843, doi: 10.1109/ROMAN.2017.8172400.
[20] A. De Luca, A. Albu-Schaffer, S. Haddadin, and G. Hirzinger, “Collision Detection
and Safe Reaction with the DLR-III Lightweight Manipulator Arm,” in 2006
IEEE/RSJ International Conference on Intelligent Robots and Systems, Oct. 2006, pp.
1623–1630, doi: 10.1109/IROS.2006.282053.
[21] F. Flacco, A. Paolillo, and A. Kheddar, “Residual-Based Contacts Estimation for
Humanoid Robots,” in 2016 IEEE-RAS 16th International Conference on Humanoid
Robots (Humanoids), Nov. 2016, pp. 409–415, doi:
10.1109/HUMANOIDS.2016.7803308.
[22] J. Vorndamme, M. Schappler, and S. Haddadin, “Collision Detection, Isolation and
Identification for Humanoids,” in 2017 IEEE International Conference on Robotics
and Automation (ICRA), May 2017, pp. 4754–4761, doi:
10.1109/ICRA.2017.7989552.
[23] J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, “You Only Look Once: Unified,
Real-Time Object Detection,” in 2016 IEEE Conference on Computer Vision and
Pattern Recognition (CVPR), Jun. 2016, pp. 779–788, doi: 10.1109/CVPR.2016.91.
[24] D. M. Ebert and D. D. Henrich, “Safe Human-Robot-Cooperation: Image-based
collision detection for Industrial Robots,” in IEEE/RSJ International Conference on
Intelligent Robots and System, vol. 2, pp. 1826–1831, doi:
10.1109/IRDS.2002.1044021.
[25] Rahul and B. B. Nair, “Camera-Based Object Detection, Identification and Distance
Estimation,” in 2018 2nd International Conference on Micro-Electronics and
Telecommunication Engineering (ICMETE), Sep. 2018, pp. 203–205, doi:
10.1109/ICMETE.2018.00052.
[26] Y. Mito, M. Morimoto, and K. Fujii, “An Object Detection and Extraction Method
Using Stereo Camera,” in 2006 World Automation Congress, Jul. 2006, pp. 1–6, doi:
10.1109/WAC.2006.375746.
[27] S. F. Lin and S. H. Huang, “Moving Object Detection from a Moving Stereo Camera
via Depth Information and Visual Odometry,” in 2018 IEEE International
Conference on Applied System Invention (ICASI), Apr. 2018, pp. 437–440, doi:
10.1109/ICASI.2018.8394278.
[28] A. S. Mohan and R. Resmi, “Video Image Processing for Moving Object Detection
and Segmentation using Background Subtraction,” in 2014 First International
Conference on Computational Systems and Communications (ICCSC), Dec. 2014, pp.
288–292, doi: 10.1109/COMPSC.2014.7032664.
[29] A. Petrovskaya, J. Park, and O. Khatib, “Probabilistic Estimation of Whole Body
Contacts for Multi-Contact Robot Control,” in Proceedings 2007 IEEE International
Conference on Robotics and Automation, Apr. 2007, pp. 568–573, doi:
10.1109/ROBOT.2007.363047.
[30] F. Dimeas, L. D. Avendaño-Valencia, and N. Aspragathos, “Human - Robot Collision
Detection and Identification Based on Fuzzy and Time Series Modelling,” Robotica,
vol. 33, no. 9, pp. 1886–1898, Nov. 2015, doi: 10.1017/S0263574714001143.
[31] W. Khalil, “Dynamic Modeling of Robots Using Recursive Newton-Euler
Techniques,” in ICINCO 2010 - Proceedings of the 7th International Conference on
Informatics in Control, Automation and Robotics (2010), 2010.
[32] C. Guarino Lo Bianco, “Evaluation of Generalized Force Derivatives by Means of a
Recursive Newton–Euler Approach,” IEEE Trans. Robot., vol. 25, no. 4, pp. 954–
959, Aug. 2009, doi: 10.1109/TRO.2009.2024787.
[33] R. Featherstone and D. Orin, “Robot Dynamics: Equations and algorithms,” in
Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on
Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065), 2000, vol.
1, pp. 826–834, doi: 10.1109/ROBOT.2000.844153.
[34] R. Featherstone and D. E. Orin, “Dynamics,” in Engineering Science, 6th ed, vol. 4,
no. 12, Berlin, Heidelberg: Routledge, 2015, pp. 63–70.