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Modeling of Inverse Kinematic of 3-DoF Robot, Using Unit Quaternions and Artificial Neural Network

Published online by Cambridge University Press:  08 January 2021

Eusebio Jiménez-López Open the ORCID record for Eusebio Jiménez-López [Opens in a new window] ,
Daniel Servín de la Mora-Pulido ,
Luis Alfonso Reyes-Ávila ,
Raúl Servín de la Mora-Pulido ,
Javier Melendez-Campos  and
Aldo Augusto López-Martínez
Eusebio Jiménez-López*
Affiliation:
Department of Engineering and Technology, Universidad La Salle Noroeste-CIAAM de la Universidad Tecnológica del Sur de Sonora-IIMM, Cd. Obregón, México
Daniel Servín de la Mora-Pulido
Affiliation:
Department of Engineering and Technology, Universidad La Salle Noroeste, Cd. Obregón, México Emails: [email protected], [email protected], [email protected]
Luis Alfonso Reyes-Ávila
Affiliation:
Department of Telematics, Instituto Mexicano del Transporte, Querétaro, México Email: [email protected]
Raúl Servín de la Mora-Pulido
Affiliation:
Department of Engineering and Technology, Universidad La Salle Noroeste, Cd. Obregón, México Emails: [email protected], [email protected], [email protected]
Javier Melendez-Campos
Affiliation:
Department of Engineering and Technology, Universidad La Salle Noroeste, Cd. Obregón, México Emails: [email protected], [email protected], [email protected]
Aldo Augusto López-Martínez
Affiliation:
Department of Automated Systems, CIDESI, Querétaro, México E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper presents a novel method for modeling a 3-degree of freedom open kinematic chain using quaternions algebra and neural network to solve the inverse kinematic problem. The structure of the network was composed of 3 hidden layers with 25 neurons per layer and 1 output layer. The network was trained using the Bayesian regularization backpropagation. The inverse kinematic problem was modeled as a system of six nonlinear equations and six unknowns. Finally, both models were tested using a straight path to compare the results between the Newton–Raphson method and the network training.

Keywords

Inverse kinematicRobotNeural networkQuaternions
Type
Article
Information
Robotica , Volume 39 , Issue 7 , July 2021 , pp. 1230 - 1250
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Shala, A., Likaj, R., Bruqi, M. and Bajrami, X., “Propulsion effect analysis of 3 DOF robot under gravity,” Proc. Eng. 100, 206–212 (2015).Google Scholar
Stelian, A., Dumitru, A. and Florina, C., “Modeling dynamical behaviour of wobble plate mechanism,” TEHNOMUS. 21, 58–62 (2014).Google Scholar
Li, W., Howison, T. and Angeles, J., “On the use of the dual Euler-Rodrigues parameters in the numerical solution of the inverse-displacement problem,” Mech. Mach. Theory. 125, 21–33 (2018).10.1016/j.mechmachtheory.2017.12.006CrossRefGoogle Scholar
Sarabandi, S. and Thomas, F., “Accurate Computation of Quaternions from Rotations Matrices,” In: International Symposium on Advances in Robot Kinematics (Springer, Cham, 2018) pp. 39–46.Google Scholar
Yang, X., Wu, H. and Chen, Y., “A dual quaternion solution to the forward kinematics of a class of six-DOF parallel robots with full or reductant actuation,” Mech. Mach. Theory. 107, 27–36 (2017).10.1016/j.mechmachtheory.2016.08.003CrossRefGoogle Scholar
Dai, J., “Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections,” Mech. Mach. Theory. 92, 144–152 (2015).10.1016/j.mechmachtheory.2015.03.004CrossRefGoogle Scholar
Reyes, L., “Quaternions: Une Representation Parametrique Systematique Des Rotation Finies. Partie I: Le Cadre Theorique,” In: Rapport de Recherche INRIA Rocquencourt France (1990).Google Scholar
Reyes, L., “Quaternions: Une Representation Parametrique Systematique Des Rotation Finies. Partie II: Quelques Application,” In: Rapport de Recherche INRIA Rocquencourt France (1991).Google Scholar
Cao, Y., Gosselin, C., Ren, P. and Zhou, H., “Orientationability analyses of a special class of the Stewart-Gough parallel manipulators using the unit quaternion representation,” Adv. Robot. 27, 147–158 (2013).10.1080/01691864.2013.751157CrossRefGoogle Scholar
Peng, D., Abdellatif, O. and Yannick, H., “Solid body motion prediction using a unit quaternion-based solver with actuator disk,” Comptes Rendus Mecanique. 346, 1136–1152 (2018).Google Scholar
Wei, W., Fei, L. and Chao, Y., “Calibration method of robot base frame using unit quaternion form,” Precis. Eng. 41, 47–54 (2015).Google Scholar
Xiao, X. and Wan, Z., “An improved symplectic integration for rigid body dynamics in terms of unit quaternions,” Appl. Math. Mech. 35, 1177–1187 (2014).Google Scholar
Mao, C. and Hao, L., “Development of a 3D parallel mechanism robot arm with three vertical-axial pneumatic actuators combined with a stereo vision system,” Sensors. 11, 11476–11494 (2011).Google Scholar
Ying, Z., Xianwen, K., Shimin, W., Duanling, L. and Qizheng, L., “CGA-based approach to direct kinematics of parallel mechanisms with the 3-RS structure,” Mech. Mach. Theory. 124, 162–178 (2018).Google Scholar
Tadano, S., Takeda, R. and Miyagawa, H., “Three dimensional gait analysis using wearable acceleration and gyro sensors based on quaternion calculations,” Sensors. 13, 9321–9343 (2013).10.3390/s130709321CrossRefGoogle ScholarPubMed
Ude, A., “Estimation of cartesian space robot trajectories using unit quaternion space,” Int. J. Adv. Robot. Syst. 11, 1–8 (2014).10.5772/58871CrossRefGoogle Scholar
Fadhil, A., “Proposed algorithm to solve inverse kinematics problem of the robot,” Eur. J. Sci. Res. 149, 376–384 (2018).Google Scholar
Theofanidis, M., Iftekar, S., Cloud, J., Brady, J. and Makedon, F., “Kinematic Estimation with Neural Networks for Robotic Manipulators,” In: International Conference on Artificial Neural Networks (Springer, Cham, 2018) pp. 795–802.Google Scholar
Panchanand, J. and Biswal, B., “A neural network approach for inverse kinematic of a SCARA manipulator,” Int. J. Robot. Automat. (IJRA). 3, 52–61 (2014).Google Scholar
Ahmed, R., Almusawi, J., Canan, L. and Kapucu, S., “A New Artificial Neural Network Approach in Solving Inverse Kinematics of Robotic Arm (Denso VP6242),” In: Computational Intelligence and Neuroscience (2016) pp. 1–10.Google Scholar
Aggarwala, L., Aggarwala, K. and Urbanica, R., “Use of artificial neural networks for the development of an inverse kinematic solution and visual identification of singularity zone(s),” Proc. CIRP. 17, 812–817 (2014).Google Scholar
Hagan, M., Demuth, H., Beale, M. and De Jess, O., Neural Network Design (2nd ed.) (PWS Publishing Co. Boston MA, USA, 2014).Google Scholar
Zijia, L., Brandstötter, M. and Hofbaur, M., “Kinematic Analysis for a Planar Redundant Serial Manipulator,” In: International Symposiu on Multibody Systems and Mechatronics (Springer, Cham, 2017) pp. 97–106.Google Scholar
Gousami, M., Gousami, B. and Ben-Ahmed-Dahou, M., “Dual Quaternions Robotics: A) The 3R Planar Manipulator,” J. Rehabil. Robot. 6, 8–21 (2018).10.12970/2308-8354.2018.06.02CrossRefGoogle Scholar
Zhang, Z., Sun, J. and Wang, Z., “Quaternion Method for the Kinematics Analysis of Parallel Metamorphic Mechanisms,” In: Advances in Reconfigurable Mechanisms and Robots II (Springer, Cham, 2016) pp. 259–274.10.1007/978-3-319-23327-7_23CrossRefGoogle Scholar
Zhensong, N. and Ruikun, W., “6R robot inverse solution algorithm based on quaternion matrix and groebner base,” Advances in Linear Algebra & Matrix Theory 8(1), 33–40 (2018).Google Scholar