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Explicit dynamics of redundant parallel cable robots


Precise model-based control of parallel robots necessitates an analytically accurate and consolidated model of the robotic platform. Lack of accuracy in modeling causes lots of dynamic uncertainties. This fact can result in higher control gains and efforts. Furthermore, imposing modification for optimization purposes is implausible without the derivation of an exact model. Hence, in this paper an elaborative kinematical and dynamical model of redundant cable-driven parallel robots is studied. In fact, a general procedure for modeling of cable-actuated parallel robots is presented to tackle down the difficulties for model-based control. The presented dynamic modeling approach rigorously enumerates the kinematics of robot winches and pulleys. The intrinsic behavior of cables is represented with a linear spring and damper having variable mass and constant density in the workspace. To this end, sagging in cables is neglected as a computationally intractable effect with insignificant impact on robot’s dynamics. Next, model validation is carried out within an experimental study of a redundant cable-driven parallel robot, the RoboCab which is designed and manufactured in Advanced Robotics and Automated Systems (ARAS) Lab. Experimental results reveal the merits and capabilities of proposed model to capture the explicit dynamics of robot. Results also demonstrate the high rate of flexibility and applicability of model for dealing with diverse control applications.

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  1. 1.

    Mustafa, S.K., Yang, G., Yeo, S.H., Lin, W., Chen, I.M.: Self-calibration of a biologically inspired 7 dof cable-driven robotic arm. IEEE/ASME Trans. Mechatron. 13(1), 66–75 (2008)

    Article  Google Scholar 

  2. 2.

    Cui, X., Chen, W., Jin, X., Agrawal, S .K.: Design of a 7-dof cable-driven arm exoskeleton (carex-7) and a controller for dexterous motion training or assistance. IEEE/ASME Trans. Mechatron. PP(99), 1–1 (2016)

    Google Scholar 

  3. 3.

    Moses, M.S., Murphy, R.J., Kutzer, M.D.M., Armand, M.: Modeling cable and guide channel interaction in a high-strength cable-driven continuum manipulator. IEEE/ASME Trans. Mechatron. 20(6), 2876–2889 (2015)

    Article  Google Scholar 

  4. 4.

    Lau, D., Eden, J., Oetomo, D., Halgamuge, S.K.: Musculoskeletal static workspace analysis of the human shoulder as a cable-driven robot. IEEE/ASME Trans. Mechatron. 20(2), 978–984 (2015)

    Article  Google Scholar 

  5. 5.

    Campeau-Lecours, A., Foucault, S., Lalibert, T., Mayer-St-Onge, B., Gosselin, C.: A cable-suspended intelligent crane assist device for the intuitive manipulation of large payloads. IEEE/ASME Trans. Mechatron. 21(4), 2073–2084 (2016)

    Article  Google Scholar 

  6. 6.

    Shiang, W.-J., Cannon, D., Gorman, J.: Dynamic analysis of the cable array robotic crane. In: Proceedings of the 1999 IEEE International Conference on Robotics and Automation, vol. 4, pp. 2495–2500. IEEE (1999)

  7. 7.

    Mousavi, M., Ghanbari, M., Nasr, A., Moosavian, S. A. A., Zarafshan, P.: Sensory feedback performance improvement on robocab: An experimental approach to wire-driven parallel manipulator. In: 2016 4th International Conference on Robotics and Mechatronics (ICROM), pp. 477–482. IEEE (2016)

  8. 8.

    Ghanbari, M., Mousavi, M. R., Moosavian, S. A. A., Nasr, A., Zarafshan, P.: Experimental analysis of an optimal redundancy resolution scheme in a cable-driven parallel robot. In: 2017 5th International Conference on Robotics and Mechatronics (ICROM). IEEE (2017)

  9. 9.

    Nasr, A., Moosavian, S. A. A.: Multi-criteria design of 6-dof fully-constrained cable driven redundant parallel manipulator. In: 2015 3rd RSI International Conference on Robotics and Mechatronics (ICROM), pp. 001–006 (2015)

  10. 10.

    Jamshidifar, H., Khajepour, A., Fidan, B., Rushton, M.: Kinematically-constrained redundant cable-driven parallel robots: modeling, redundancy analysis and stiffness optimization. IEEE/ASME Trans. Mechatron. PP(99), 1–1 (2016)

    Google Scholar 

  11. 11.

    Korayem, M.H., Tourajizadeh, H., Zehfroosh, A., Korayem, A.H.: Optimal path planning of a cable-suspended robot with moving boundary using optimal feedback linearization approach. Nonlinear Dyn. 78(2), 1515–1543 (2014).

    MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Korayem, M.H., Zehfroosh, A., Tourajizadeh, H., Manteghi, S.: Optimal motion planning of non-linear dynamic systems in the presence of obstacles and moving boundaries using sdre: application on cable-suspended robot. Nonlinear Dyn. 76(2), 1423–1441 (2014).

    Article  MATH  Google Scholar 

  13. 13.

    Oh, S.-R., Mankala, K., Agrawal, S.K., Albus, J.S.: A dual-stage planar cable robot: dynamic modeling and design of a robust controller with positive inputs. J. Mech. Des. 127(4), 612–620 (2005)

    Article  Google Scholar 

  14. 14.

    Qian, S., Zi, B., Ding, H.: Dynamics and trajectory tracking control of cooperative multiple mobile cranes. Nonlinear Dyn. 83(1), 89–108 (2016)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Triantafyllou, M.: The dynamics of translating cables. J. Sound Vib. 103(2), 171–182 (1985)

    Article  Google Scholar 

  16. 16.

    Jeong, J.W., Kim, S.H., Kwak, Y.K.: Kinematics and workspace analysis of a parallel wire mechanism for measuring a robot pose. Mech. Mach. Theory 34(6), 825–841 (1999)

    Article  Google Scholar 

  17. 17.

    Karoumi, R.: Some modeling aspects in the nonlinear finite element analysis of cable supported bridges. Comput. Struct. 71(4), 397–412 (1999)

    Article  Google Scholar 

  18. 18.

    Kozak, K., Zhou, Q., Wang, J.: Static analysis of cable-driven manipulators with non-negligible cable mass. IEEE Trans. Robot. 22(3), 425–433 (2006)

    Article  Google Scholar 

  19. 19.

    Zi, B., Duan, B., Du, J., Bao, H.: Dynamic modeling and active control of a cable-suspended parallel robot. Mechatronics 18(1), 1–12 (2008)

    Article  Google Scholar 

  20. 20.

    Yao, R., Tang, X., Wang, J., Huang, P.: Dimensional optimization design of the four-cable-driven parallel manipulator in fast. IEEE/ASME Trans. Mechatron. 15(6), 932–941 (2010)

    Google Scholar 

  21. 21.

    Bedoustani, Y. B., Taghirad, H. D., Aref, M. M.: Dynamics analysis of a redundant parallel manipulator driven by elastic cables. In: 2008 10th International Conference on Control, Automation, Robotics and Vision, ICARCV 2008, pp. 536–542. IEEE (2008)

  22. 22.

    Emmens, A.R., Spanjer, S.A.J., Herder, J.L.: Modeling and control of a large-span redundant surface constrained cable robot with a vision sensor on the platform. In: Bruckmann, T. (ed.) Cable-Driven Parallel Robots, pp. 249–260. Springer, Berlin (2015)

    Chapter  Google Scholar 

  23. 23.

    Lau, D., Eden, J., Tan, Y., Oetomo, D.: Caspr: A comprehensive cable-robot analysis and simulation platform for the research of cable-driven parallel robots. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct 2016, pp. 3004–3011 (2016)

  24. 24.

    Shao, Z.-F., Tang, X., Wang, L.-P., Chen, X.: Dynamic modeling and wind vibration control of the feed support system in fast. Nonlinear Dyn. 67(2), 965–985 (2012)

    MathSciNet  Article  Google Scholar 

  25. 25.

    Meunier, G., Boulet, B., Nahon, M.: Control of an overactuated cable-driven parallel mechanism for a radio telescope application. IEEE Trans. Control Syst. Technol. 17(5), 1043–1054 (2009)

    Article  Google Scholar 

  26. 26.

    Su, Y., Qiu, Y., Liu, P.: Optimal cable tension distribution of the high-speed redundant driven camera robots considering cable sag and inertia effects. Adv. Mech. Eng. 6, 729020 (2014)

    Article  Google Scholar 

  27. 27.

    Qiu, Y., Duan, B., Wei, Q., Nan, R., Peng, B.: Optimal distribution of the cable tensions and structural vibration control of the cable-cabin flexible structure. Struct. Eng. Mech. 14(1), 39–56 (2002)

    Article  Google Scholar 

  28. 28.

    Du, J., Bao, H., Cui, C., Duan, X.: Nonlinear pd control of a long-span cable-supporting manipulator in quasi-static motion. J. Dyn. Syst. Meas. Control 134(1), 011022 (2012)

    Article  Google Scholar 

  29. 29.

    dit Sandretto, J.A., Trombettoni, G., Daney, D.: Confirmation of hypothesis on cable properties for cable-driven robots. In: Viadero-Rueda, F., Ceccarelli, M. (eds.) New Trends in Mechanism and Machine Science, pp. 85–93. Springer, Berlin (2013)

    Chapter  Google Scholar 

  30. 30.

    Kraus, W., Schmidt, V., Rajendra, P., Pott, A.: System identification and cable force control for a cable-driven parallel robot with industrial servo drives. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), May 2014, pp. 5921–5926 (2014)

  31. 31.

    Luongo, A., Zulli, D.: Mathematical Models of Beams and Cables. Wiley, New York (2013)

    Book  Google Scholar 

  32. 32.

    Irvine, H.M., Irvine, M.: Cable Structures. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  33. 33.

    Nguyen, D. Q., Gouttefarde, M., Company, O., Pierrot, F.: On the simplifications of cable model in static analysis of large-dimension cable-driven parallel robots. In: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 928–934. IEEE (2013)

  34. 34.

    Merlet, J.-P., Alexandre-dit Sandretto, J.: The forward kinematics of cable-driven parallel robots with sagging cables. In: Bruckmann, T. (ed.) Cable-Driven Parallel Robots, pp. 3–15. Springer, Berlin (2015)

    Chapter  Google Scholar 

  35. 35.

    Gouttefarde, M., Nguyen, D.Q., Baradat, C.: Kinetostatic analysis of cable-driven parallel robots with consideration of sagging and pulleys. In: Lenarcic, J. (ed.) Advances in Robot Kinematics, pp. 213–221. Springer, Berlin (2014)

    Chapter  Google Scholar 

  36. 36.

    Khosravi, M.A., Taghirad, H.D.: Dynamic modeling and control of parallel robots with elastic cables: singular perturbation approach. IEEE Trans. Robot. 30(3), 694–704 (2014)

    Article  Google Scholar 

  37. 37.

    Babaghasabha, R., Khosravi, M.A., Taghirad, H.D.: Adaptive robust control of fully constrained cable robots: singular perturbation approach. Nonlinear Dyn. 85(1), 607–620 (2016)

    MathSciNet  Article  Google Scholar 

  38. 38.

    Miermeister, P., Kraus, W., Lan, T., Pott, A.: An elastic cable model for cable-driven parallel robots including hysteresis effects. In: Bruckmann, T. (ed.) Cable-Driven Parallel Robots, pp. 17–28. Springer, Berlin (2015)

    Chapter  Google Scholar 

  39. 39.

    Nasr, A., Moosavian, S.A.A.: Multi-objective optimization design of spatial cable-driven parallel robot equipped with a serial manipulator. Modares Mech. Eng. 16(1), 29–40 (2016)

    Google Scholar 

  40. 40.

    Ghanbari, M., Moosavi, M.R., Moosavian, S.A.A., Zarafshan, P.: Modeling, optimal path planning and tracking control of a cable driven redundant parallel robot. Modares Mech. Eng. 17(4), 67–77 (2017). (in Persian)

    Google Scholar 

  41. 41.

    Ismail, M., Lahouar, S., Romdhane, L.: Collision-free and dynamically feasible trajectory of a hybrid cable serial robot with two passive links. Robot. Auton. Syst. 80, 24–33 (2016)

    Article  Google Scholar 

  42. 42.

    Cheng, C., Xu, W., Shang, J.: Optimal distribution of the actuating torques for a redundantly actuated masticatory robot with two higher kinematic pairs. Nonlinear Dyn. 79(2), 1235–1255 (2015)

    Article  Google Scholar 

  43. 43.

    Lin, J., Liao, G.-T.: Design and oscillation suppression control for cable-suspended robot. In: American Control Conference (ACC), American Automatic Control Council (AACC) 2016, pp. 3014–3019 (2016)

  44. 44.

    Khalaji, A.K., Moosavian, S.A.A.: Robust adaptive controller for a tractor-trailer mobile robot. IEEE/ASME Trans. Mechatron. 19(3), 943–953 (2014)

    Article  Google Scholar 

  45. 45.

    Khalaji, A. Keymasi, Moosavian, S. A. A.: Dynamic modeling and tracking control of a car with n trailers. Multibody Syst. Dyn. 37(2), 211–225 (2016).

    MathSciNet  Article  Google Scholar 

  46. 46.

    Moosavian, S.A.A., Pourreza, A., Alipour, K.: Kinematics and dynamics of a hybrid serial–parallel mobile robot. In: IEEE International Conference on Robotics and Automation: ICRA’09. IEEE 2009, pp. 1358–1363 (2009)

  47. 47.

    Staicu, S.: Dynamics modelling of a stewart-based hybrid parallel robot. Adv. Robot. 29(14), 929–938 (2015)

    Article  Google Scholar 

  48. 48.

    Khalil, W., Guegan, S.: Inverse and direct dynamic modeling of Gough–Stewart robots. IEEE Trans. Robot. 20(4), 754–761 (2004)

    Article  Google Scholar 

  49. 49.

    Moosavian, S.A.A., Papadopoulos, E.: Explicit dynamics of space free-flyers with multiple manipulators via spacemaple. Adv. Robot. 18(2), 223–244 (2004)

    Article  Google Scholar 

  50. 50.

    Zarafshan, P., Moosavian, S.A.A.: Dynamics modelling and hybrid suppression control of space robots performing cooperative object manipulation. Commun. Nonlinear Sci. Numer. Simul. 18(10), 2807–2824 (2013)

    MathSciNet  Article  Google Scholar 

  51. 51.

    Liu, M.-J., Li, C.-X., Li, C.-N.: Dynamics analysis of the gough-stewart platform manipulator. IEEE Trans. Robot. Autom. 16(1), 94–98 (2000)

    Article  Google Scholar 

  52. 52.

    Shapiro, R.: Direct linear transformation method for three-dimensional cinematography. Res. Q. Am. Alliance Health Phys. Educ. Recreat. 49(2), 197–205 (1978)

    Article  Google Scholar 

  53. 53.

    Oh, S.-R., Mankala, K.K., Agrawal, S.K., Albus, J.S.: Dynamic modeling and robust controller design of a two-stage parallel cable robot. Multibody Syst. Dyn. 13(4), 385–399 (2005)

    MathSciNet  Article  Google Scholar 

  54. 54.

    Merlet, J.-P.: Simulation of discrete-time controlled cable-driven parallel robots on a trajectory. IEEE Trans. Robot. 33, 675–688 (2017)

    Article  Google Scholar 

  55. 55.

    Dion-Gauvin, P., Gosselin, C.: Trajectory planning for the static to dynamic transition of point-mass cable-suspended parallel mechanisms. Mech. Mach. Theory 113, 158–178 (2017)

    Article  Google Scholar 

  56. 56.

    Zhang, N., Shang, W., Cong, S.: Geometry-based trajectory planning of a 3–3 cable-suspended parallel robot. IEEE Trans. Robot. 33(2), 484–491 (2017)

    Article  Google Scholar 

  57. 57.

    Miermeister, P., Lächele, M., Boss, R., Masone, C., Schenk, C., Tesch, J., Kerger, M., Teufel, H., Pott, A., Bülthoff, H. H.: The cablerobot simulator large scale motion platform based on cable robot technology. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3024–3029. IEEE (2016)

  58. 58.

    Jamshidifar, H., Khajepour, A., Fidan, B., Rushton, M.: Kinematically-constrained redundant cable-driven parallel robots: modeling, redundancy analysis, and stiffness optimization. IEEE/ASME Trans. Mechatron. 22(2), 921–930 (2017)

    Article  Google Scholar 

  59. 59.

    Gosselin, C., Schreiber, L.-T.: Kinematically redundant spatial parallel mechanisms for singularity avoidance and large orientational workspace. IEEE Trans. Robot. 32(2), 286–300 (2016)

    Article  Google Scholar 

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Correspondence to Payam Zarafshan.

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Mousavi, M.R., Ghanbari, M., Moosavian, S.A.A. et al. Explicit dynamics of redundant parallel cable robots. Nonlinear Dyn 94, 2077–2096 (2018).

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  • Cable-driven parallel robots
  • Explicit dynamics
  • Elastic cables
  • Redundancy
  • Variable mass modeling