Dynamics and Control of a Robotic Arm Having Four Links


The manipulator control is an important problem in robotics. To work out this problem, a correct dynamic model for the robot manipulator must be in hand. Hence, this work first presents the dynamic model of an existing 4-DOF robot manipulator based on the Euler–Lagrange principle, utilizing the body Jacobian of each link and the generalized inertia matrix. Furthermore, essential properties of the dynamic model are analyzed for the purpose of control. Then, a PID controller is designed to control the position of the robot by decoupling the dynamic model. To achieve a good performance, the differential evolution algorithm is used for the selection of parameters of the PID controller. Feedback linearization scheme is also utilized for the position and trajectory tracking control of the manipulator. The obtained results reveal that the PID control coupled with the differential evolution algorithm and the feedback linearization control enhance the performance of the robotic manipulator. It is also found out that increasing masses of manipulator links do not affect the performance of the PID position control, but higher control torques are required in these cases.

This is a preview of subscription content, log in to check access.


  1. 1.

    Jazar, R.N.: Theory of Applied Robotics. Springer US, Boston (2010). doi:10.1007/978-1-4419-1750-8

  2. 2.

    Kostic, D.; de Jager, B.; Steinbuch, M.; Hensen, R.: Modeling and identification for high performance robot control: an RRR-robotic arm case study. IEEE Trans. Control Syst. Technol. 12(6), 904–919 (2004)

    Article  Google Scholar 

  3. 3.

    Long, Z.M.; Guo, S.Q.; Chen, G.J.; Yin, B.L.: Modeling and simulation for the articulated robotic arm test system of the combination drive. Appl. Mech. Mater. 151, 480–483 (2012). doi:10.4028/www.scientific.net/AMM.151.480

  4. 4.

    Wallin, P.J.: Robotics in the food industry: an update. Trends Food Sci. Technol. 8(6), 193–198 (1997). http://www.sciencedirect.com/science/article/pii/S092422449701042X

  5. 5.

    Meike, D.; Ribickis, L.: Energy effcient use of robotics in the automobile industry. In: 2011 15th International Conference on Advanced Robotics (ICAR), pp. 507–511, Jun (2011)

  6. 6.

    Erzincanli, F.; Sharp, J.M.: A classi_cation system for robotic food handling. Food Control. 8(4), 191–197 (1997). http://www.sciencedirect.com/science/article/pii/S0956713597000480

  7. 7.

    Ouerfelli, M.; Kumar, V.; Harwin, W.S.: Methods for kinematic modeling of biological and robotic systems. Med. Eng. Phys. vol. 22(7), 509–520 (2000). http://www.sciencedirect.com/science/article/pii/S1350453300000631

  8. 8.

    Krasilnikyants, E.V.; Varkov, A.A.; Tyutikov, V.V.: Robot manipulator control system. Autom. Remote Control 74(9), 1589–1598 (2013). doi:10.1134/S0005117913090154

    Article  Google Scholar 

  9. 9.

    Yadav, P.S.; Singh, N.: Robust control of two link rigid manipulator. http://www.ijiee.org/vol5/530-A0016.pdf

  10. 10.

    Xia, Q.X.; Yu, Y.Q.; Liu, Q.B.: Fuzzy control for underactuated manipulator. Appl. Mech. Mater. 397–400, 1490–1493 (2013). doi:10.4028/www.scientific.net/AMM.397-400.1490

  11. 11.

    Soylemez, M.; Gokasan, M.; Bogosyan, O.: Position control of a single-link robot-arm using a multi-loop PI controller. In: Proceedings of 2003 IEEE Conference on Control Applications, CCA 2003, vol. 2, pp. 1001–1006, Jun (2003)

  12. 12.

    Piltan, F.; Bayat, R.; Aghayari, F.; Boroomand, B.: Design error-based linear model-free evaluation performance computed torque controller. Int. J. Robot. Autom. 3(3), 151–166 (2012). http://www.researchgate.net/profile/FarzinPiltan3/publication/263969238DesignError-basedLinearModel-freeEvaluationPerformanceComputedTorqueController/links/00b4953c7749e749ec000000.pdf

  13. 13.

    Piltan, F.; Sulaiman, N.; Marhaban, M.H.; Nowzary, A.; Tohidian, M.: Design of FPGA-based sliding mode controller for robot manipulator. Int. J. Robot. Autom. 2(3), 173–194 (2011). http://www.academia.edu/download/30900697/IJRAV2I3.pdf#page=52

  14. 14.

    Al-Khayyt, S.Z.S.: Tuning PID controller by neural network for robot manipulator trajectory tracking. Al-Khwarizmi Eng. J. 8(1), 19–28 (2013). http://aliraq.ws/LionImages/News/69953.pdf

  15. 15.

    Receanu, D.: Modeling and simulation of the nonlinear computed torque control in simulink/MATLAB for an industrial robot. SL Struct. Longev. 10(2), 95–106 (2013). doi:10.3970/sl.2013.010.095.pdf

  16. 16.


  17. 17.

    Arunachalam, V.: Optimization using di_erential evolution (2008). http://ir.lib.uwo.ca/wrrr/22/

  18. 18.

    Taher, S.A.; Afsari, S.A.: Optimal location and sizing of UPQC in distribution networks using differential evolution algorithm. Math. Problems Eng. 2012, 1–20 (2012). http://www.hindawi.com/journals/mpe/2012/838629/

  19. 19.

    Corke, P.: A robotics toolbox for MATLAB. IEEE Robot. Autom. Mag. 3(1), 24–32 (1996)

  20. 20.

    Corke, P.I.: A computer tool for simulation and analysis: the robotics toolbox for MATLAB. In: Proceedings of National Conference Australian Robot Association, pp. 319–330 (1995). http://www.pessoal.utfpr.edu.br/winderson/arquivos/ARA95.pdf

  21. 21.

    Fahimi, F.: Autonomous Robots. Springer US, Boston (2009). http://link.springer.com/10.1007/978-0-387-09538-7

Download references

Author information



Corresponding author

Correspondence to H. M. Al-Qahtani.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Al-Qahtani, H.M., Mohammed, A.A. & Sunar, M. Dynamics and Control of a Robotic Arm Having Four Links. Arab J Sci Eng 42, 1841–1852 (2017). https://doi.org/10.1007/s13369-016-2324-y

Download citation


  • Robot control
  • PID
  • Differential evolution
  • Feedback linearization