A Multi-objective Differential Evolution Algorithm for Robot Inverse Kinematics
|International Journal of Computer Science and Engineering|
|© 2016 by SSRG - IJCSE Journal|
|Volume 3 Issue 11|
|Year of Publication : 2016|
|Authors : Enrique Rodriguez, Baidya Nath Saha, Jesús Romero-Hdz, David Ortega|
How to Cite?
Enrique Rodriguez, Baidya Nath Saha, Jesús Romero-Hdz, David Ortega, "A Multi-objective Differential Evolution Algorithm for Robot Inverse Kinematics," SSRG International Journal of Computer Science and Engineering , vol. 3, no. 11, pp. 61-69, 2016. Crossref, https://doi.org/10.14445/23488387/IJCSE-V3I11P113
This paper presents the robot inverse kinematics solution for four Degrees of Freedom (DOF) through Differential Evolution (DE) algorithm. DE can handle real numbers (float, double) which leads more powerful than Genetic Algorithm (GA). We propose a multi-objective fitness function that makes an attempt to minimize the positional error and maximum angular displacement of the robot joints. Maximum angular displacement based fitness function adopt the constraints on different unrealistic rotational movement of the manipulator. We employ an equitable treatment of both fitness functions while maximizing these two over generations that iteratively selects the optimal weights of these two fitness functions automatically. Trigonometric mutation and binomial crossover improve the performance of the conventional DE technique. We compared the results of proposed multi-objective DE with GA and Algebraic Method (AM). Proposed multi-objective DE algorithm obtains less positional error than conventional DE, GA and AM while meeting the rotational constraints of the manipulator’s joints.
A Multi-objective Differential Evolution Algorithm for Robot Inverse Kinematics.
 J. G. Ramírez-Torres, G. Toscano-Pulido, A. Ramírez-Saldívar, and A. Hernández-Ramírez, “A complete closed-form solution to the inverse kinematics problem for the P2Arm manipulator robot,” Proc. - 2010 IEEE Electron. Robot. Automot. Mech. Conf. CERMA 2010, pp. 372–377, 2010.
 M. A. Mikulski and T. Szkodny, “Remote control and monitoring of AX-12 robotic arm based on windows communication foundation,” Adv. Intell. Soft Comput., vol. 103, pp. 77–83, 2011.
 E. P. Lana, B. V Adorno, and C. J. Tierra-Criollo, “Assistance Task Using a Manipulator Robot and User Kinematics Feedback,” XI Simpósio Bras. Automação Intel., pp. 1–6, 2013.
 H. Sultan and E. M. Schwartz, “Robotic Arm Manipulator Control for SG5-UT,” vol. 00, no. 407, pp. 1–5, 2007.
 J. Q. Gan, E. Oyama, E. M. Rosales, and H. Hu, “A complete analytical solution to the inverse kinematics of the Pioneer 2 robotic arm,” Robotica, vol. 23, no. 1, pp. 123–129, 2005.
 P. Corke, Robotics, Vision and Control - Fundamental Algorithms in MATLAB. 2011.
 J. K. Parker, a. R. Khoogar, and D. E. Goldberg, “Inverse Kinematics of Redundant Robots Using Genetic Algorithms,” Proc. IEEE Int. Conf. Robot. Autom., pp. 271–276, 1989.
 F. Y. C. Albert, S. P. Koh, S. K. Tiong, C. P. Chen, and F. W. Yap, “Inverse kinematic solution in handling 3R manipulator via real-time genetic algorithm,” Proc. - Int. Symp. Inf. Technol. 2008, ITSim, vol. 4, 2008.
 C. González, D. Blanco, and L. Moreno, “A memetic approach to the inverse kinematics problem,” 2012 IEEE Int. Conf. Mechatronics Autom. ICMA 2012, pp. 180–185, 2012.
 X. S. Wang, M. L. Hao, and Y. H. Cheng, “On the use of differential evolution for forward kinematics of parallel manipulators,” Appl. Math. Comput., vol. 205, no. 2, pp. 760–769, 2008.
 A. Henning, “Approximate Inverse Kinematics Using a Database,” 2014.
 A. A. Mohammed and M. Sunar, “Kinematics Modeling of a 4-DOF Robotic Arm,” pp. 87–91, 2015.
 Z. Sui, L. Jiang, Y. Tian, and W. Jiang, “Proceedings of the 2015 Chinese Intelligent Automation Conference,” vol. 338, no. 5988, pp. 151–161, 2015.
 N. N. Son, H. P. H. Anh, and T. Dinh Chau, “Inverse kinematics solution for robot manipulator based on adaptive MIMO neural network model optimized by hybrid differential evolution algorithm,” 2014 IEEE Int. Conf. Robot. Biomimetics, IEEE ROBIO 2014, pp. 2019–2024, 2014.
 R. N. Jazar, Theory of Applied Robotics: Kinematics, Dynamics, and Control. 2010.
 Y. X. and M. Gen, Introduction to evolutionary algorithms. Springer-Verlag London, 2010.
 H. Aytug and G. J. Koehler, “Stopping criteria for finite length genetic algorithms,” INFORMS J. Comput., vol. 8, no. 2, pp. 183–191, 1996.
 H. Aytug and G. J. Koehler, “New stopping criterion for genetic algorithms,” Eur. J. Oper. Res., vol. 126, no. 3, pp. 662–674, 2000.
 M. Studniarski, “Stopping criteria for genetic algorithms with application to multiobjective optimization,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 6238 LNCS, no. PART 1, pp. 697–706, 2010.
 H. Y. Fan and J. Lampinen, “A trigonometric mutation operation to differential evolution,” J. Glob. Optim., vol. 27, no. 1, pp. 105–129, 2003.
 M. Gabli, E. M. Jaara, and E. B. Mermri, “A Genetic Algorithm Approach for an Equitable Treatment of Objective Functions in Multi-objective Optimization Problems,” no. May, 2014.
 Y. D. Zhao and X. X. Qiao, “Research on optimal multiple sequence alignment,” Proc. Int. Conf. E-bus. E-Government, ICEE 2010, pp. 5500–5505, 2010.