Abstract
This paper presents the design of a redundant actuated three-DOF Cable-Suspended Parallel Robot (CSPR) with parallelogram architecture and its minimum jerk trajectory planning method. The moving platform of the designed CSPR is supported by eight redundant cables to enable three translational motion degrees. These cables are organized in four sets arranged in parallelogram configurations, with each set driven synchronously by a single motor. To achieve smooth robot motion and avoid abrupt changes in cable tensions, a trajectory planning method is proposed that utilizes seventh degree polynomial curves for minimum jerk in the Cartesian space of the moving platform. A dynamic simulation model of the redundantly actuated CSPR is developed, and point-to-point simulations are conducted. The simulation results indicate that the optimized trajectories exhibit reduced sudden cable tension changes and decreased position tracking errors. Compared to third degree polynomial and seventh degree polynomial trajectory before optimized, the average trajectory errors decreased by 3.6% and 2.3%, respectively, and the maximum trajectory errors are below 3.2 mm.
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References
Shen, H., Meng, Q., Li, J., et al.: Kinematic sensitivity, parameter identification and calibration of a non-fully symmetric parallel Delta robot. Mech. Mach. Theory 161, 104311 (2021)
Merlet, J.P.: On the workspace of suspended cable-driven parallel robots. In: 2016 IEEE International Conference on Robotics and Automation (ICRA). IEEE, pp.841–846 (2016)
Yu, J., Li, X., Tao, J., et al.: Workspace quality evaluation and optimal design of a redundantly constrained 6-DoF cable-driven parallel manipulator. In: Intelligent Robotics and Applications: 14th International Conference, ICIRA 2021, Yantai, China, 22–25 October 2021, Proceedings, Part I 14. Springer International Publishing, pp. 575–585 (2021)
Pott, A., Mütherich, H., Kraus, W., et al.: IPAnema: a family of cable-driven parallel robots for industrial applications. In: Cable-Driven Parallel Robots, pp. 119–134 (2013)
Zi, B., Lin, J., Qian, S.: Localization, obstacle avoidance planning and control of a cooperative cable parallel robot for multiple mobile cranes. Robot. Comput. Integr. Manuf. 34, 105–123 (2015)
Scalera, L., Gallina, P., Seriani, S., et al.: Cable-based robotic crane (CBRC): design and implementation of overhead traveling cranes based on variable radius drums. IEEE Trans. Robot. 34(2), 474–485 (2018)
Yao, R., Tang, X.Q., Wang, J.S., et al.: Dimensional optimization design of the four-cable-driven parallel manipulator in FAST. IEEE/ASME Trans. Mechatron. 15(6), 932–941 (2010)
Tang, X.Q., Yao, R.: Dimensional design on the six-cable driven parallel manipulator of FAST. J. Mech. Des. 133(11), 111012 (2011)
Wang, L., Sheng, Y., Qiu, Y.Y., et al.: Design and implementation of the control device for a cable-driven camera robot. Appl. Mech. Mater. 373, 225–230 (2013)
Wang, X.G., Ma, S.Y., Lin, Q.: Hybrid pose/tension control based on stiffness optimization of cable-driven parallel mechanism in wind tunnel test. In: 2016 2nd International Conference on Control, Automation and Robotics (ICCAR), Hong Kong, China, April 28–30, pp. 75–79 (2016)
Zi, B., Qian, S.: Design, Analysis and Control of Cable-Suspended Parallel Robots and It’s Applications, pp. 978–981. Springer (2017). https://doi.org/10.1007/978-981-10-1753-7
Vu, D.S., Barnett, E., Gosselin, C.: Experimental validation of a three-degree-of-freedom cable-suspended parallel robot for spatial translation with constant orientation. J. Mech. Robot. 11(2), 024502 (2013)
Trevisani, A.: Underconstrained planar cable-direct-driven robots: a trajectory planning method ensuring positive and bounded cable tensions Mechatronics 20(1), 113–127 (2010)
Xiang, Y., Li, Q., Jiang, X.: Dynamic rotational trajectory planning of a cable-driven parallel robot for passing through singular orientations. Mech. Mach. Theory 158, 104223 (2021)
Ueland, E., Sauder, T., Skjetne, R.: Optimal force allocation for overconstrained cable-driven parallel robots: Continuously differentiable solutions with assessment of computational efficiency. IEEE Trans. Robot. 37(2), 659–666 (2020)
Gosselin, C., Foucault, S.: Dynamic point-to-point trajectory planning of a two-DOF cable-suspended parallel robot. IEEE Trans. Robot. 30(3), 728–736 (2014)
Gasparetto, A., Zanotto, V.: A technique for time-jerk optimal planning of robot trajectories. Robot. Comput. Integr. Manuf. 24, 415–426 (2008)
Kong, M., Ji, C., Chen, Z., et al.: Smooth and near time-optimal trajectory planning of robotic manipulator with smooth constraint based on cubic B-spline. In: 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO). IEEE, pp. 2328–2333 (2013)
Seki, H., Tadakuma, S.: Minimum jerk control of power assisting robot on human arm behavior characteristic. In: 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No. 04CH37583). IEEE, pp. 722–727 (2004)
Visioli, A.: Trajectory planning of robot manipulators by using algebraic and trigonometric splines. Robotica 18, 611–631 (2000)
Huang, M.S., Hsu, Y.L., Fung, R.F.: Minimum-energy point-to-point trajectory planning for a motor-toggle servomechanism. IEEE/ASME Trans. Mechatron. 17, 337–344 (2012)
Fang, S., Ma, X., Zhao, Y., et al.: Trajectory planning for seven-DOF robotic arm based on quintic polynormial. In: 2019 11th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC). IEEE, pp. 198–201 (2019)
Xie, Z., Wu, P., Ren, P.: A comparative study on the pick-and-place trajectories for a delta robot. In: Proceedings of the ASME Design Engineering Technical Conferences American Society of Mechanical Engineers Digital Collection (2016)
Chang, B.H., Hori, Y.: Trajectory design considering derivative of jerk for head-positioning of disk drive system with mechanical vibration. IEEE/ASME Trans. Mechatron. 11(3), 273–279 (2006)
Kucuk, S.: Optimal trajectory generation algorithm for serial and parallel manipulators. Robot. Comput. Integr. Manuf. 48, 219–232 (2017)
Acknowledgment
The work was supported by the Foundation for the National Natural Science Foundation of China (Grant No.52105024 and 52305011) and the Open Project of State Key Laboratory of Robotics and System (HIT) (Grant No. SKLRS-2023-KF-23 and SKLRS-2024-KF-06).
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Xiang, S., Lu, W., Bian, W., Wei, Z., Sun, C., Liu, Z. (2025). Minimum Jerk Trajectory Planning for a Redundant Actuated Three-DOF Cable-Suspended Parallel Robot with Parallelogram Architecture. In: Lan, X., Mei, X., Jiang, C., Zhao, F., Tian, Z. (eds) Intelligent Robotics and Applications. ICIRA 2024. Lecture Notes in Computer Science(), vol 15201. Springer, Singapore. https://doi.org/10.1007/978-981-96-0771-6_13
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DOI: https://doi.org/10.1007/978-981-96-0771-6_13
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