本研究提出一具備不同剛性之單節連續體所組成之三節段連續體機器人，每一個單節連續體使用有四條可獨立控制的繩索，因此設計之三節段共使用到12條可繩索來控制姿態。由於考慮到重力和負載效應，最高剛性之節段連接於基座，最小剛性之節段設置於末端節段；此外，基座與中間節段採5碟片設計，而末端節段採較多之7碟片設計，其中兩碟片間以萬向接頭進行連接以提高整體結構之強度。因此，以不同剛性分布與加長末端長度之設計能兼具到手臂運作穩定性以及末端動作敏捷性。除了不同節段剛性與長度組合機構設計外，本研究提出以萬向接頭模型為基礎之運動空間與姿態的解法。此一方法假設每一節段是理想的圓弧線段，使得每一節段中連結各碟片之萬向接頭上的兩聯接軸的偏離角度假設為相等，並以Denavit–Hartenberg （D-H）計算各碟片之空間位置，並進而以碟片上繩索孔位求得所有線段長度，並考慮碟片厚度與節段連接件長度，求出在特定姿態下所需要之繩索長度控制量。此一計算方法之求解亦與常用與定曲率模型公式進行不同姿態下繩索長度控制量的比較，以驗證本文所提出方法之有效性。最後，本研究設計不同程度彎曲的連續體機器人姿態，並萬向接頭模型與片段定曲率模型兩種方式計算出的繩索長度控制量作為手臂控制的輸入參數，接著用NDI光學定位系統量測出實際手臂末端點直線距離誤差與姿態角誤差。以萬向接頭模型和片段定曲率模型操作下的手臂末端點座標進行誤差分析。以萬向接頭模型為方法獲得的直線距離誤差範圍為-0.8218毫米到190.6217毫米。而以片段定曲率模型為方法獲得的直線距離誤差範圍為-138.746毫米到-23.5247毫米、由於大多數連續體機器人機構用定曲率運動學求解繩長，而本文提出以萬向接頭來求解繩長，具備新穎性。

This study presents a continuum robot, and it consists of three continuum segments with different stiffness settings. Each continuum segment is controlled four cables; hence, there are 12 cables used for controlling the pose of the proposed continuum robot. To consider the gravity and payload effects, the highest stiffness segment is arranged to be connected to the base; the smallest stiffness segment is arranged as the connection to the end effector. Moreover, the base and medium segments are designed as 5 disks; the end segment is formed as 7 disks. The intra disk motions are formed by universals joint in each segment. Furthermore, the design in different stiffnesses and lengths significantly improve the whole robot body structure strength and the dexterity at of the end effector.
In addition to the mechanical design, this study proposes a universals joint based kinematics approach. This approach assumes that the shape of each segment is an ideal circular arc segment, and the yaw angle and pitch angle are respectively the same in all segments. Hence, the Denavit–Hartenberg (D-H) presentation of combined universal joints can be applied to calculate the spatial position and pose of each disk. By calculating the cable hole positions on the disks, disk thickness and intra-segment connection length, the required cable lengths can be evaluated to perform a specific continuum robot shape and pose. The proposed method is also compared with conventional piecewise constant curvature method for feasibility analysis.
Finally, this study designs the posture of a continuum robot with different degrees of bending using the cable length control amount calculated by the universal joint model and the segmental constant curvature model as the input parameter of arms control and then uses the NDI optical positioning system to measure the actual linear distance error and attitude angle error of robot end-effector. The error analysis is carried out with the robot end-effector coordinates and attitude angle under the operation of the universal joint and the piecewise constant curvature method. The linear distance error range obtained by the universal joint method is -0.8218 mm to 190.6217 mm. The linear distance error range obtained by the method of the segmental curvature model is -138.7462 mm to -23.5247 mm.
Most of continuum robots used piecewise constant curvature method to obtain the cable lengths; however, this study proposes a university joint model approach to find the cable lengths. This approach could be a newly feasibly solution in controlling a continuum robot.

參考文獻
[1] Y. Liu, Z. Ge, S. Yang, I. D. Walker, and Z. Ju, "Elephant’s Trunk Robot: An Extremely Versatile Under-Actuated Continuum Robot Driven By A Single Motor," Journal of Mechanisms and Robotics, vol. 11, no. 5, p. 051008, 2019.
[2] I. D. Walker et al., "Continuum Robot Arms Inspired By Cephalopods," in Unmanned Ground Vehicle Technology VII, 2005, vol. 5804: SPIE, pp. 303-314.
[3] W. M. Kier, "The Functional Morphology Of The Musculature of Squid (Loliginidae) Arms And Tentacles," Journal of Morphology, vol. 172, no. 2, pp. 179-192, 1982.
[4] M. Tanaka and K. Tanaka, "Control Of A Snake Robot For Ascending And Descending Steps," IEEE Transactions on Robotics, vol. 31, no. 2, pp. 511-520, 2015.
[5] A. M. Andruska and K. S. Peterson, "Control Of A Snake-Like Robot In An Elastically Deformable Channel," IEEE/ASME Transactions on Mechatronics, vol. 13, no. 2, pp. 219-227, 2008.
[6] G. Qin et al., "A Snake-Inspired Layer-Driven Continuum Robot," Soft Robotics, vol. 9, no. 4, pp. 788-797, 2022.
[7] Y.-J. Kim, S. Cheng, S. Kim, and K. Iagnemma, "A Stiffness-Adjustable Hyperredundant Manipulator Using A Variable Neutral-Line Mechanism For Minimally Invasive Surgery," IEEE transactions on robotics, vol. 30, no. 2, pp. 382-395, 2013.
[8] F. Alambeigi et al., "On The Use Of A Continuum Manipulator And A Bendable Medical Screw For Minimally Invasive Interventions In Orthopedic Surgery," IEEE transactions on medical robotics and bionics, vol. 1, no. 1, pp. 14-21, 2019.
[9] R. J. Webster, J. M. Romano, and N. J. Cowan, "Mechanics Of Precurved-Tube Continuum Robots," IEEE Transactions on Robotics, vol. 25, no. 1, pp. 67-78, 2008.
[10] J. Burgner-Kahrs, D. C. Rucker, and H. Choset, "Continuum Robots For Medical Applications: A Survey," IEEE Transactions on Robotics, vol. 31, no. 6, pp. 1261-1280, 2015.
[11] H. El-Hussieny et al., "Development And Evaluation Of An Intuitive Flexible Interface For Teleoperating Soft Growing Robots," in 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018: IEEE, pp. 4995-5002.
[12] M. M. Coad et al., "Vine Robots: Design, Releoperation, And Deployment For Navigation And Exploration," IEEE Robotics & Automation Magazine, vol. 27, no. 3, pp. 120-132, 2019.
[13] D. B. Camarillo, C. R. Carlson, and J. K. Salisbury, "Configuration Tracking For Continuum Manipulators With Coupled Tendon Drive," IEEE transactions on robotics, vol. 25, no. 4, pp. 798-808, 2009.
[14] N. Ayadi, M. Turki, R. Ghribi, and N. Derbel, "Identification And Development Of A Real-Time Motion Control For A Mobile Robot's DC Gear Motor," International Journal of Computer Applications in Technology, vol. 55, no. 1, pp. 61-69, 2017.
[15] R. J. Webster III and B. A. Jones, "Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review," The International Journal of Robotics Research, vol. 29, no. 13, pp. 1661-1683, 2010.
[16] T. Mahl, A. Hildebrandt, and O. Sawodny, "A Variable Curvature Continuum Kinematics For Kinematic Control Of The Bionic Handling Assistant," IEEE transactions on robotics, vol. 30, no. 4, pp. 935-949, 2014.
[17] T. Ren, Y. Li, M. Xu, Y. Li, C. Xiong, and Y. Chen, "A Novel Tendon-Driven Soft Actuator With Self-Pumping Property," Soft Robotics, vol. 7, no. 2, pp. 130-139, 2020.
[18] Z. Li, H. Ren, P. W. Y. Chiu, R. Du, and H. Yu, "A Novel Constrained Wire-Driven Flexible Mechanism And Its Kinematic Analysis," Mechanism and Machine Theory, vol. 95, pp. 59-75, 2016.
[19] W. Hu and G. Alici, "Bioinspired Three-Dimensional-Printed Helical Soft Pneumatic Actuators And Their Characterization," Soft robotics, vol. 7, no. 3, pp. 267-282, 2020.
[20] Y. Kim, S. S. Cheng, and J. P. Desai, "Active Stiffness Tuning Of A Spring-Based Continuum Robot For MRI-Guided Neurosurgery," IEEE Transactions on Robotics, vol. 34, no. 1, pp. 18-28, 2017.
[21] C. Sun, L. Chen, J. Liu, J. S. Dai, and R. Kang, "A Hybrid Continuum Robot Based On Pneumatic Muscles With Embedded Elastic Rods," Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 234, no. 1, pp. 318-328, 2020.
[22] A. Degani, H. Choset, A. Wolf, and M. A. Zenati, "Highly Articulated Robotic Probe For Minimally Invasive Surgery," in Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., 2006: IEEE, pp. 4167-4172.
[23] M.-H. Hsu, P. T.-T. Nguyen, D.-D. Nguyen, T.-K. Nguyen, and C.-H. Kuo, "Fabrication And Image Servo Tracking Study Of A Continuum Robot Prototype," International Journal of iRobotics, vol. 4, no. 2, pp. 35-41, 2021.
[24] A. Yeshmukhametov, K. Koganezawa, and Y. Yamamoto, "A Novel Discrete Wire-Driven Continuum Robot Arm With Passive Sliding Disc: Design, Kinematics And Passive Tension Control," Robotics, vol. 8, no. 3, p. 51, 2019.
[25] M. W. Hannan and I. D. Walker, "Kinematics And The Implementation Of An Elephant's Trunk Manipulator And Other Continuum Style Robots," Journal of robotic systems, vol. 20, no. 2, pp. 45-63, 2003.
[26] H. D. Yang and A. T. Asbeck, "Design And Characterization Of A Modular Hybrid Continuum Robotic Manipulator," IEEE/ASME Transactions on Mechatronics, vol. 25, no. 6, pp. 2812-2823, 2020.
[27] J. Peng, W. Xu, T. Yang, Z. Hu, and B. Liang, "Dynamic Modeling And Trajectory Tracking Control Method Of Segmented Linkage Cable-Driven Hyper-Redundant Robot," Nonlinear Dynamics, vol. 101, no. 1, pp. 233-253, 2020.
[28] P. Qi, C. Qiu, H. Liu, J. S. Dai, L. D. Seneviratne, and K. Althoefer, "A Novel Continuum Manipulator Design Using Serially Connected Double-Layer Planar Springs," IEEE/ASME Transactions on Mechatronics, vol. 21, no. 3, pp. 1281-1292, 2015.
[29] I. A. Seleem, H. El-Hussieny, S. F. Assal, and H. Ishii, "Development And Stability Analysis Of An Imitation Learning-Based Pose Planning Approach For Multi-Section Continuum Robot," IEEE Access, vol. 8, pp. 99366-99379, 2020.
[30] S. Xu, B. He, Y. Zhou, Z. Wang, and C. Zhang, "A Hybrid Position/Force Control Method For A Continuum Robot With Robotic And Environmental Compliance," IEEE Access, vol. 7, pp. 100467-100479, 2019.
[31] C. Abah, A. L. Orekhov, G. L. Johnston, and N. Simaan, "A Multi-Modal Sensor Array For Human–Robot Interaction And Confined Spaces Exploration Using Continuum Robots," IEEE Sensors Journal, vol. 22, no. 4, pp. 3585-3594, 2021.
[32] D. Alatorre, D. Axinte, and A. Rabani, "Continuum Robot Proprioception: The Ionic Liquid Approach," IEEE Transactions on Robotics, vol. 38, no. 1, pp. 526-535, 2021.
[33] H. Wang, Z. Yan, Y. Gao, W. Wang, and Z. Du, "3-D Force Sensing Strategy Of Laryngeal Continuum Surgical Robot Based On Fiber Bragg Gratings," IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1-10, 2021.
[34] M. Li, R. Kang, S. Geng, and E. Guglielmino, "Design And Control Of A Tendon-Driven Continuum Robot," Transactions of the Institute of Measurement and Control, vol. 40, no. 11, pp. 3263-3272, 2018.
[35] W. Xu, T. Liu, and Y. Li, "Kinematics, Dynamics, And Control Of A Cable-Driven Hyper-Redundant Manipulator," IEEE/ASME Transactions on Mechatronics, vol. 23, no. 4, pp. 1693-1704, 2018.
[36] A. Nagarajan, S. R. Kanna, and V. M. Kumar, "Multibody Dynamic Simulation Of A Hyper Redundant Robotic Manipulator Using ADAMS Ansys Interaction," in 2017 International Conference on Algorithms, Methodology, Models and Applications in Emerging Technologies (ICAMMAET), 2017: IEEE, pp. 1-6.