Comparative Study of Different Metaheuristics for the Trajectory Planning of a Robotic Arm

In this paper, seven different metaheuristic optimization algorithms developed between 2005 and 2012 are applied to optimize the robot trajectory for a three-revolute (3R) robotic arm. These algorithms include the artificial bee colony (ABC) algorithm, biogeography-based optimization, gravitational search algorithm, cuckoo search algorithm (CS), firefly algorithm, bat algorithm, and teaching-learning-based optimization (TLBO). This work presents the optimization problem with the objective to plan a trajectory, which can minimize joint travelling time, joint travelling distance, and total joint Cartesian lengths, simultaneously. Nine different design variables are considered for the intermediate joint angles, joint velocities, the end-effector angle for the final configuration, the time from initial to intermediate configuration, and the time from intermediate to final configuration. Two different experiments are conducted to investigate the effect of different considered metaheuristics: 1) for the free workspace and 2) for the workspace with obstacle. All these algorithms are compared based on the algorithm ability to find the best solutions, mean solutions, standard deviation, computational effort, and the convergence of the solutions. Statistical investigation is also performed by using the Friedman rank test and the Holm-Sidak multiple comparison t-test to check the significance of the algorithm for its suitability to the robot trajectory optimization problems. The results show the significance of TLBO, ABC, and CS for the robot trajectory optimization problems.

[1]  Anima Naik,et al.  Data Clustering Based on Teaching-Learning-Based Optimization , 2011, SEMCCO.

[2]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[3]  Vedat Toğan,et al.  Design of planar steel frames using Teaching–Learning Based Optimization , 2012 .

[4]  Bernd Eggers,et al.  Introduction To Robotics Analysis Systems Applications , 2016 .

[5]  Abhijit S. Pandya,et al.  3D affine registration using teaching-learning based optimization , 2013 .

[6]  Bijaya K. Panigrahi,et al.  Application of Multi-Objective Teaching-Learning-Based Algorithm to an Economic Load Dispatch Problem with Incommensurable Objectives , 2011, SEMCCO.

[7]  J. Solano,et al.  Generation of collision-free paths, a genetic approach , 1993 .

[8]  Dan Simon,et al.  Analysis of migration models of biogeography-based optimization using Markov theory , 2011, Eng. Appl. Artif. Intell..

[9]  Hossein Nezamabadi-pour,et al.  BGSA: binary gravitational search algorithm , 2010, Natural Computing.

[10]  Amir Hossein Gandomi,et al.  Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect , 2012, Appl. Soft Comput..

[11]  Jean-Louis Deneubourg,et al.  Ants, buses and robots-self-organization of transportation systems , 1994, Proceedings of PerAc '94. From Perception to Action.

[12]  Amir Hossein Gandomi,et al.  Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems , 2011, Engineering with Computers.

[13]  Francis L. Merat,et al.  Introduction to robotics: Mechanics and control , 1987, IEEE J. Robotics Autom..

[14]  M.E. El-Hawary,et al.  A novel genetic algorithm searching approach for dynamic constrained multicast routing , 2003, CCECE 2003 - Canadian Conference on Electrical and Computer Engineering. Toward a Caring and Humane Technology (Cat. No.03CH37436).

[15]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[16]  Li Wang,et al.  Obstacle-avoidance Path Planning for Soccer Robots Using Particle Swarm Optimization , 2006, 2006 IEEE International Conference on Robotics and Biomimetics.

[17]  Qidan Zhu,et al.  Robot Path Planning Based on Artificial Potential Field Approach with Simulated Annealing , 2006, Sixth International Conference on Intelligent Systems Design and Applications.

[18]  Dan Simon,et al.  Variations of biogeography-based optimization and Markov analysis , 2013, Inf. Sci..

[19]  Narendra Ahuja,et al.  Gross motion planning—a survey , 1992, CSUR.

[20]  Y. Davidor,et al.  Robot programming with a genetic algorithm , 1990, COMPEURO'90: Proceedings of the 1990 IEEE International Conference on Computer Systems and Software Engineering@m_Systems Engineering Aspects of Complex Computerized Systems.

[21]  Hossein Nezamabadi-pour,et al.  Filter modeling using gravitational search algorithm , 2011, Eng. Appl. Artif. Intell..

[22]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

[23]  Hiroshi Yokoi,et al.  Development of a motion planning system for an agricultural mobile robot , 1999, SICE '99. Proceedings of the 38th SICE Annual Conference. International Session Papers (IEEE Cat. No.99TH8456).

[24]  R. Venkata Rao,et al.  Mechanical Design Optimization Using Advanced Optimization Techniques , 2012 .

[25]  Dan Simon,et al.  Biogeography-Based Optimization , 2022 .

[26]  R. Venkata Rao,et al.  Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems , 2011, Comput. Aided Des..

[27]  Pratyusha Rakshit,et al.  Multi-robot path-planning using artificial bee colony optimization algorithm , 2011, 2011 Third World Congress on Nature and Biologically Inspired Computing.

[28]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[29]  Xin-She Yang,et al.  Bat algorithm for multi-objective optimisation , 2011, Int. J. Bio Inspired Comput..

[30]  Taher Niknam,et al.  $\theta$-Multiobjective Teaching–Learning-Based Optimization for Dynamic Economic Emission Dispatch , 2012, IEEE Systems Journal.

[31]  Xin-She Yang,et al.  A New Metaheuristic Bat-Inspired Algorithm , 2010, NICSO.

[32]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[33]  Bruce H. Krogh,et al.  The use of simulated annealing to solve the mobile manipulator path planning problem , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[34]  Vimal J. Savsani,et al.  Optimized trajectory planning of a robotic arm using teaching learning based optimization (TLBO) and artificial bee colony (ABC) optimization techniques , 2013, 2013 IEEE International Systems Conference (SysCon).

[35]  Xin-She Yang,et al.  Engineering optimisation by cuckoo search , 2010, Int. J. Math. Model. Numer. Optimisation.

[36]  Dervis Karaboga,et al.  Artificial Bee Colony (ABC) Optimization Algorithm for Solving Constrained Optimization Problems , 2007, IFSA.

[37]  R. Venkata Rao,et al.  Teaching-Learning-Based Optimization: An optimization method for continuous non-linear large scale problems , 2012, Inf. Sci..

[38]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[39]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[40]  Xin-She Yang,et al.  Bat algorithm: a novel approach for global engineering optimization , 2012, 1211.6663.

[41]  S. Holm.  A Simple Sequentially Rejective Multiple Test Procedure , 1979 .

[42]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[43]  Ying-Tung Hsiao,et al.  Ant colony optimization for best path planning , 2004, IEEE International Symposium on Communications and Information Technology, 2004. ISCIT 2004..

[44]  De-Bao Sun,et al.  Path planning for mobile robot using the particle swarm optimization with mutation operator , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

[45]  N.K. Taylor,et al.  Articulated Robot Motion Planning Using Ant Colony Optimisation , 2006, 2006 3rd International IEEE Conference Intelligent Systems.

[46]  Dan Simon,et al.  A dynamic system model of biogeography-based optimization , 2011, Appl. Soft Comput..

[47]  David E. Goldberg,et al.  Inverse kinematics of redundant robots using genetic algorithms , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[48]  Qing Li,et al.  Optimum Path Planning for Mobile Robots Based on a Hybrid Genetic Algorithm , 2006, 2006 Sixth International Conference on Hybrid Intelligent Systems (HIS'06).

[49]  Xin-She Yang,et al.  Firefly Algorithms for Multimodal Optimization , 2009, SAGA.

[50]  Xin-She Yang,et al.  Firefly Algorithm, Lévy Flights and Global Optimization , 2010, SGAI Conf..

[51]  Jin-Hui Zhu,et al.  Obstacle avoidance with multi-objective optimization by PSO in dynamic environment , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[52]  Ellips Masehian,et al.  Classic and Heuristic Approaches in Robot Motion Planning A Chronological Review , 2007 .

[53]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[54]  Bahaa I. Kazem,et al.  Motion Planning for a Robot Arm by Using Genetic Algorithm , 2008 .