Inverse Kinematics of a Redundant Manipulator Robot Using Constrained Optimization

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1137)


Redundant manipulative robots are characterized by greater manipulability improving performance but complicating inverse kinematics, on the other hand, optimization techniques allow solving complex problems in robotics applications with greater efficiency. This paper presents the inverse kinematics of a redundant manipulative robot with four degrees of freedom to track a desired trajectory, and considering constraint in manipulability. The optimization problem is proposed using the quadratic position errors of the operative end and the constraint is established by a manipulability index, for this the kinematic model of the robot is determined. The results show the points of singularity of the robot and the performance of the proposal implemented, observing the positional errors and the manipulability for each point of the trajectory. In addition, the optimization is evaluated for two desired manipulability values. Finally, it is concluded that the implemented method optimizes the inverse kinematics to track the desired path while constraining the manipulability.


Inverse kinematics Constrained optimization Manipulability Trajectory tracking 


  1. 1.
    Glogowski, P., Lemmerz, K., Schulte, L., Barthelmey, A., Hypki, A., Kuhlenkötter, B., Deuse, J.: Task-based simulation tool for human-robot collaboration within assembly systems. In: Tagungsband des 2. Kongresses Montage Handhabung Industrieroboter (2017)Google Scholar
  2. 2.
    Staicu, S.: Dynamics of Parallel Robots. Springer Nature Customer Service Center Gmbh (2019)Google Scholar
  3. 3.
    Kyrarini, M., Haseeb, M.A., Ristić-Durrant, D., Gräser, A.: Robot learning of industrial assembly task via human demonstrations. Auton. Robots 43, 239–257 (2019). Scholar
  4. 4.
    Zaplana, I., Basanez, L.: A novel closed-form solution for the inverse kinematics of redundant manipulators through workspace analysis. Mech. Mach. Theory 121, 829–843 (2018). Scholar
  5. 5.
    Kofinas, N., Orfanoudakis, E., Lagoudakis, M.G.: Complete analytical forward and inverse kinematics for the NAO humanoid robot. J. Intell. Robot. Syst. 77, 251–264 (2015). Scholar
  6. 6.
    Iliukhin, V.N., Mitkovskii, K.B., Bizyanova, D.A., Akopyan, A.A.: The modeling of inverse kinematics for 5 DOF manipulator. Procedia Eng. 176, 498–505 (2017). Scholar
  7. 7.
    Kim, S., Xu, W., Ren, H.: Inverse kinematics with a geometrical approximation for multi-segment flexible curvilinear robots (2019). Scholar
  8. 8.
    Chiaverini, S., Oriolo, G., Walker, I.D.: Kinematically redundant manipulators. In: Springer Handbook of Robotics (2008). Scholar
  9. 9.
    Varela-Aldas, J., Andaluz, V.H., Chicaiza, F.A.: Modelling and control of a mobile manipulator for trajectory tracking. In: Proceedings of the - 3rd International Conference on Information, Systems and Computer Science, INCISCOS 2018, pp. 69–74 (2018).
  10. 10.
    Jin, L., Li, S., La, H.M., Luo, X.: Manipulability optimization of redundant manipulators using dynamic neural networks. IEEE Trans. Ind. Electron. 64, 4710–4720 (2017). Scholar
  11. 11.
    Li, K.-L., Yang, W.-T., Chan, K.-Y., Lin, P.-C.: An optimization technique for identifying robot manipulator parameters under uncertainty. Springerplus 5, 1771 (2016). Scholar
  12. 12.
    Azad, M., Babič, J., Mistry, M.: Effects of the weighting matrix on dynamic manipulability of robots. Auton. Robots 43, 1867–1879 (2019). Scholar
  13. 13.
    Hwang, S., Kim, H., Choi, Y., Shin, K., Han, C.: Design optimization method for 7 DOF robot manipulator using performance indices. Int. J. Precis. Eng. Manuf. 18, 293–299 (2017). Scholar
  14. 14.
    Husak, E., Karabegović, I.: Heuristic optimization methods in industrial robotics. In: Advanced Technologies, Systems, and Applications II (2018)Google Scholar
  15. 15.
    Liu, W., Chen, D., Steil, J.: Analytical inverse kinematics solver for anthropomorphic 7-DOF redundant manipulators with human-like configuration constraints. J. Intell. Robot. Syst. 86, 63–79 (2017). Scholar
  16. 16.
    Wan, J., Wu, H., Ma, R., Zhang, L.: A study on avoiding joint limits for inverse kinematics of redundant manipulators using improved clamping weighted least-norm method. J. Mech. Sci. Technol. 32, 1367–1378 (2018). Scholar
  17. 17.
    Ferrentino, E., Chiacchio, P.: Redundancy parametrization in globally-optimal inverse kinematics. In: Advances in Robot Kinematics 2018 (2019)Google Scholar
  18. 18.
    Wan, Y., Kou, Y., Liang, X.: Closed-loop inverse kinematic analysis of redundant manipulators with joint limits. In: Advances in Mechanical Design (2018)Google Scholar
  19. 19.
    Kelemen, M., Virgala, I., Lipták, T., Miková, Ľ., Filakovský, F., Bulej, V.: A novel approach for a inverse kinematics solution of a redundant manipulator (2018). Scholar
  20. 20.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Heidelberg (2006)zbMATHGoogle Scholar

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Authors and Affiliations

  1. 1.SISAu Research GroupUniversidad IndoaméricaAmbatoEcuador
  2. 2.Departamento de Eléctrica y ElectrónicaUniversidad de las Fuerzas Armadas – ESPESangolquíEcuador
  3. 3.Facultad de Ingeniería en Sistemas, Electrónica e IndustrialUniversidad Técnica de AmbatoAmbatoEcuador

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