Stability sensitivity of a completely restrained 3-DOF cable-driven parallel robot with four long-span cables
LIU Peng1,2, QIAO Xinzhou1
1. School of Mechanical Engineering, Xi'an University of Science and Technology, Xi'an 710054, China; 2. Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi'an 710000, China
Abstract：The stability of a completely restrained 3-DOF cable-driven parallel robot with four long-span cables, due to the flexibility and unidirectional restraint characteristics of the cables, as well as the influence of the large-span cable sags, faces severe challenges. This paper establishes the stability evaluation model and stability sensitivity analysis model for the robot, explores and analyzes the influence of the end-effector positions and the cable tensions on the stability of the robot. Firstly, based on kinematics and dynamics model of the robot, the stability position influence factor and the cable tension influence factor are proposed, and furthermore, the stability evaluation model is established. Secondly, the gray correlation analysis method is used to establish the stability sensitivity analysis model for the robot, and it is proposed to use the correlation degree to study and measure the influence degree of the end-effector positions and cable tensions on the stability of the robot. Finally, the established stability evaluation model and sensitivity analysis model are simulated for a cable-driven camera robot with four long-span cables. The research results show that the stability of the camera robot is more sensitive to cable tension influence factors. Among them, the stability has the smallest correlation to the y-direction displacement of the camera platform. This research provides guidance for the robust optimization design of the motion trajectory and motion control for the robot.
刘鹏, 乔心州. 大跨度完全约束空间3-DOF柔索驱动并联机器人稳定性灵敏度研究[J]. 清华大学学报（自然科学版）, 2022, 62(9): 1548-1558.
LIU Peng, QIAO Xinzhou. Stability sensitivity of a completely restrained 3-DOF cable-driven parallel robot with four long-span cables. Journal of Tsinghua University(Science and Technology), 2022, 62(9): 1548-1558.
[1] 崔志伟, 唐晓强, 侯森浩, 等. 索驱动并联机器人可控刚度特性[J]. 清华大学学报(自然科学版), 2018, 58(2): 204-211. CUI Z W, TANG X Q, HOU S H, et al. Characteristics of controllable stiffness for cable-driven parallel robots[J]. Journal of Tsinghua University (Science and Technology), 2018, 58(2): 204-211. (in Chinese) [2] TANG X Q. An overview of the development for cable-driven parallel manipulator[J]. Advances in Mechanical Engineering, 2014, 6: 823028. [3] VERHOEVEN R. Analysis of the workspace of tendon-based Stewart platforms[D]. Duisburg: Gerhard-Mercator-University, 2004. [4] YAO R, ZHU W B, SUN C H, et al. Pose planning for the feed support system of FAST[J]. Advances in Mechanical Engineering, 2014, 6: 209167. [5] 张立勋, 李来禄, 姜锡泽, 等. 柔索驱动的宇航员深蹲训练机器人力控与实验研究[J]. 机器人, 2017, 39(5): 733-741. ZHANG L X, LI L L, JIANG X Z, et al. Force control and experimental study of a cable-driven robot for astronaut deep squat training[J]. Robot, 2017, 39(5): 733-741. (in Chinese) [6] BARNETT E, GOSSELIN C. Large-scale 3D printing with a cable-suspended robot[J]. Additive Manufacturing, 2015, 7: 27-44. [7] WANG X G, PENG M J, HU Z H, et al. Feasibility investigation of large-scale model suspended by cable-driven parallel robot in hypersonic wind tunnel test[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2017, 231(13): 2375-2383. [8] AMARE Z, ZI B, QIAN S, et al. Three-dimensional static and dynamic stiffness analyses of the cable-driven parallel robot with non-negligible cable mass and elasticity[J]. Mechanics Based Design of Structures and Machines, 2018, 46(4): 455-482. [9] CHAWLA I, PATHAK P M, NOTASH L, et al. Workspace analysis and design of large-scale cable-driven printing robot considering cable mass and mobile platform orientation[J]. Mechanism and Machine Theory, 2021, 165: 104426. [10] BEHZADIPOUR S, KHAJEPOUR A. Stiffness of cable-based parallel manipulators with application to stability analysis[J]. Journal of Mechanical Design, 2006, 128(1): 303-310. [11] BOSSCHER P M. Disturbance robustness measures and wrench-feasibile workspace generation techniques for cable-driven robots[D]. Atlanta: Georgia Institute of Technology, 2004. [12] LIU P, QIU Y Y, SU Y, et al. On the minimum cable tensions for the cable-based parallel robots[J]. Journal of Applied Mathematics, 2014: 350492. [13] LIU P, QIU Y Y, SU Y. A new hybrid force-position measure approach on the stability for a camera robot[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016, 230(14): 2508-2516. [14] 赵志刚, 王砚麟, 李劲松. 多机器人协调吊运系统力位姿混合运动稳定性评价方法[J]. 哈尔滨工程大学学报, 2018, 39(1): 148-155. ZHAO Z G, WANG Y L, LI J S. Appraise of dynamical stability of multi-robots cooperatively lifting system based on hybrid force-position-pose approach[J]. Journal of Harbin Engineering University, 2018, 39(1): 148-155. (in Chinese) [15] 杜敬利, 段学超, 保宏. 考虑柔索垂度影响的索支撑系统静刚度[J]. 机械工程学报, 2010, 46(17): 29-34. DU J L, DUAN X C, BAO H. Static stiffness of a cable-supporting system with the cable sag effects considered[J]. Journal of Mechanical Engineering, 2010, 46(17): 29-34. (in Chinese) [16] LIU P, QIU Y Y. Tension optimization for a cable-driven parallel robot with non-negligible cable mass[J]. The Open Automation and Control Systems Journal, 2015, 7: 1973-1980. [17] 刘顺青, 洪宝宁, 徐奋强, 等. 高液限土边坡稳定性影响因素的敏感性研究[J]. 防灾减灾工程学报, 2014, 34(5): 589-596. LIU S Q, HONG B N, XU F Q, et al. Sensitivity studies on factors influencing stability of high liquid limit soil slope[J]. Journal of Disaster Prevention and Mitigation Engineering, 2014, 34(5): 589-596. (in Chinese) [18] 李元松, 王玉, 朱冬林, 等. 边坡稳定性评价方法研究现状与发展趋势[J]. 武汉工程大学学报, 2021, 43(4): 428-435. LI Y S, WANG Y, ZHU D L, et al. Research status and developmental trends of slope stability evaluation method[J]. Journal of Wuhan Institute of Technology, 2021, 43(4): 428-435. (in Chinese) [19] 刘春, 杜俊生, 王敬堃. 基于灰色关联分析理论的边坡稳定性预测[J]. 地下空间与工程学报, 2017, 13(5): 1424-1430. LIU C, DU J S, Wang J K. Prediction of slope stability based on gray relational analysis theory[J]. Chinese Journal of Underground Space and Engineering, 2017, 13(5): 1424-1430. (in Chinese) [20] WANG X N, YANG W C, GE Y, et al. The influence of shrinkage-reducing agent solution properties on shrinkage of cementitious composite using grey correlation analysis[J]. Construction and Building Materials, 2020, 264: 120194. [21] SU Y, QIU Y Y, LIU P. Optimal cable tension distribution of the high-speed redundant driven camera robots considering cable sag and inertia effects[J]. Advances in Mechanical Engineering, 2014, 6: 729020. [22] 韦慧玲, 仇原鹰, 盛英. 高速绳牵引摄像机器人的运动稳定控制[J]. 西安电子科技大学学报(自然科学版), 2016, 43(5): 63-69, 104. WEI H L, QIU Y Y, SHENG Y. Motion stable control for cable-driven parallel camera robots with high speeds[J]. Journal of Xidian University (Natural Science), 2016, 43(5): 63-69, 104. (in Chinese) [23] YIN J N, JIANG P, YAO R. An approximately analytical solution method for the cable-driven parallel robot in FAST[J]. Research in Astronomy and Astrophysics, 2021, 21(2): 046. [24] 刘欣. 两种并联机器人的机构性能分析与运动控制研究[D]. 西安: 西安电子科技大学, 2009. LIU X. On the mechanism performance analysis and motion control of the two types of parallel manipulators[D]. Xi'an: Xidian University, 2009. (in Chinese) [25] BEER F P, JOHNSTON JR E R, DEWOLF J T, et al. Mechanics of materials[M]. New York: McGraw-Нill, 2012. [26] MARTYNYUK A A, CHERNIENKO V. A. Estimating the Lyapunov function and stability of motion of a system with equations of motion with an asymptotically expanded right-hand side[J]. International Applied Mechanics, 2021, 57(1): 11-18. [27] DENG J L. Introduction to grey system theory[J]. The Journal of Grey System, 1989(1): 1-24. [28] ZHU L H, ZHAO C, DAI J, Prediction of compressive strength of recycled aggregate concrete based on gray correlation analysis[J]. Construction and Building Materials, 2021, 273: 121750. [29] GAO C L, LI S C, WANG J, et al. The risk assessment of tunnels based on grey correlation and entropy weight method[J]. Geotechnical and Geological Engineering, 2018, 36(3): 1621-1631. [30] WEI H L, QIU Y Y, SU Y. Motion control strategy and stability analysis for high-speed cable-driven camera robots with cable inertia effects[J]. International Journal of Advanced Robotic Systems, 2016, 13(5): 1-9.
2022, Vol. 62 
