A univariate marginal distribution algorithm based on extreme elitism and its application to the robotic inverse displacement problem

In this paper, a univariate marginal distribution algorithm in continuous domain (UMDAC) based on extreme elitism (EEUMDAC) is proposed for solving the inverse displacement problem (IDP) of robotic manipulators. This algorithm highlights the effect of a few top best solutions to form a primary evolution direction and obtains a fast convergence rate. Then it is implemented to determine the IDP of a 4-degree-of-freedom (DOF) Barrett WAM robotic arm. After that, the algorithm is combined with differential evolution (EEUMDAC-DE) to solve the IDP of a 7-DOF Barrett WAM robotic arm. In addition, three other heuristic optimization algorithms (enhanced leader particle swarm optimization, intersect mutation differential evolution, and evolution strategies) are applied to find the IDP solution of the 7-DOF arm and their performance is compared with that of EEUMDAC-DE.

[1]  Yan Kang,et al.  An Improved Estimation of Distribution Algorithm for Dynamic Voltage Scaling Problem in Heterogeneous System , 2014 .

[2]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[3]  Huosheng Hu,et al.  A complete analytical solution to the inverse kinematics of the Pioneer 2 robotic arm , 2005, Robotica.

[4]  Stefano Carpin,et al.  Kinematics and Calibration for a Robot Comprised of Two Barrett WAMs and a Point Grey Bumblebee2 Stereo Camera , 2012 .

[5]  Y. Ho,et al.  Simple Explanation of the No-Free-Lunch Theorem and Its Implications , 2002 .

[6]  Serdar Kucuk,et al.  Inverse kinematics solutions for industrial robot manipulators with offset wrists , 2014 .

[7]  Yong Gao,et al.  Space Complexity of Estimation of Distribution Algorithms , 2005, Evolutionary Computation.

[8]  Kerim Çetinkaya,et al.  Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator , 2015, Neural Computing and Applications.

[9]  Rasit Köker,et al.  A genetic algorithm approach to a neural-network-based inverse kinematics solution of robotic manipulators based on error minimization , 2013, Inf. Sci..

[10]  H. J. Estrada-García,et al.  Automatic Image Segmentation Using Active Contours with Univariate Marginal Distribution , 2013 .

[11]  Thomas Bäck,et al.  An Overview of Evolutionary Algorithms for Parameter Optimization , 1993, Evolutionary Computation.

[12]  Liang Gao,et al.  A differential evolution algorithm with intersect mutation operator , 2013, Appl. Soft Comput..

[13]  Martin Pelikan,et al.  An introduction and survey of estimation of distribution algorithms , 2011, Swarm Evol. Comput..

[14]  Muhammad Naeem,et al.  An application of univariate marginal distribution algorithm in MIMO communication systems , 2010 .

[15]  Patryk Filipiak,et al.  Univariate Marginal Distribution Algorithm with Markov Chain Predictor in Continuous Dynamic Environments , 2014, IDEAL.

[16]  Shital S. Chiddarwar,et al.  Comparison of RBF and MLP neural networks to solve inverse kinematic problem for 6R serial robot by a fusion approach , 2010, Eng. Appl. Artif. Intell..

[17]  I. Vasilyev,et al.  Analytical solution to inverse kinematic problem for 6-DOF robot-manipulator , 2010 .

[18]  Heinz Mühlenbein,et al.  Convergence Theory and Applications of the Factorized Distribution Algorithm , 2015, CIT 2015.

[19]  Chih-Cheng Chen,et al.  A combined optimization method for solving the inverse kinematics problems of mechanical manipulators , 1991, IEEE Trans. Robotics Autom..

[20]  Pedro Larrañaga,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

[21]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[22]  A. Rezaee Jordehi,et al.  Enhanced leader PSO (ELPSO): A new PSO variant for solving global optimisation problems , 2015, Appl. Soft Comput..

[23]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[24]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[25]  T. Gotthans,et al.  Design of Passive Analog Electronic Circuits Using Hybrid Modified UMDA algorithm , 2015 .

[26]  Guoyong Zhang,et al.  A hybrid Univariate Marginal Distribution Algorithm for dynamic economic dispatch of units considering valve-point effects and ramp rates , 2015 .

[28]  Kazuhiro Kosuge,et al.  Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits and Its Application to Redundancy Resolution , 2008, IEEE Transactions on Robotics.

[29]  Sankar Nath Shome,et al.  Inverse Kinematics of Redundant Manipulator using Interval Newton Method , 2015 .

[30]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[31]  D. Goldberg,et al.  BOA: the Bayesian optimization algorithm , 1999 .

[32]  Pedro Larrañaga,et al.  Optimization in Continuous Domains by Learning and Simulation of Gaussian Networks , 2000 .

[33]  Tian Huang,et al.  A new numerical algorithm for the inverse position analysis of all serial manipulators , 2005, Robotica.

[34]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .