Abstract
In this paper, a heuristic method based on Firefly Algorithm is proposed for inverse kinematics problems in articulated robotics. The proposal is called, IK-FA. Solving inverse kinematics, IK, consists in finding a set of joint-positions allowing a specific point of the system to achieve a target position. In IK-FA, the Fireflies positions are assumed to be a possible solution for joints elementary motions. For a robotic system with a known forward kinematic model, IK-Fireflies, is used to generate iteratively a set of joint motions, then the forward kinematic model of the system is used to compute the relative Cartesian positions of a specific end-segment, and to compare it to the needed target position. This is a heuristic approach for solving inverse kinematics without computing the inverse model. IK-FA tends to minimize the distance to a target position, the fitness function could be established as the distance between the obtained forward positions and the desired one, it is subject to minimization. In this paper IK-FA is tested over a 3 links articulated planar system, the evaluation is based on statistical analysis of the convergence and the solution quality for 100 tests. The impact of key FA parameters is also investigated with a focus on the impact of the number of fireflies, the impact of the maximum iteration number and also the impact of (α, β, γ, δ) parameters. For a given set of valuable parameters, the heuristic converges to a static fitness value within a fix maximum number of iterations. IK-FA has a fair convergence time, for the tested configuration, the average was about 2.3394 × 10−3 seconds with a position error fitness around 3.116 × 10−8 for 100 tests. The algorithm showed also evidence of robustness over the target position, since for all conducted tests with a random target position IK-FA achieved a solution with a position error lower or equal to 5.4722 × 10−9.
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References
Ammar, B., Chouikhi, N., Alimi, A.M., Chérif, F., Rezzoug, N., Gorce, P.: Learning to walk using a recurrent neural network with time delay. In: Artificial Neural Networks and Machine Learning–ICANN, pp. 511–518. Springer, Heidelberg (2013)
Asfour, T., Dillmann, R.: Human-like motion of a humanoid robot arm based on a closed-form solution of the inverse kinematics problem. In: Intelligent Robots and Systems (IROS 2003), vol. 2, pp. 1407–1412 (2003)
Azevedo, C., Andreff, N., Arias, S.: BIPedal walking: from gait design to experimental analysis. Mechatronics 14(6), 639–665 (2004)
Buckley, K.A., Simon H., Brian C.H.T.: Solution of inverse kinematics problems of a highly kinematically redundant manipulator using genetic algorithms. IET, pp. 264–269 (1997)
Buss, S.R.: Introduction to inverse kinematics with jacobian transpose, pseudoinverse and damped least squares methods. IEEE J. Robot. Autom. 17 (2004)
Çavdar, T., Mohammad, M., Milani, R.A.: A new heuristic approach for inverse kinematics of robot arms. Adv. Sci. Lett. 19(1), 329–333 (2013)
Chiaverini, S., Siciliano, B., Egeland, O.: Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator. IEEE Trans. Control Syst. Technol. 2(2), 123–134 (1994)
De Jong, K.A., Spears, W.M.: An analysis of the interacting roles of population size and crossover in genetic algorithms. In: Parallel Problem Solving from Nature, pp. 38–47. Springer, Heidelberg (1991)
Dorigo, M., Birattari, M., Stutzle, T.: Ant colony optimization. IEEE Comput. Intell. Mag. 1(4), 28–39 (2006)
Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, vol. 1, pp. 39–43 (1995)
Eberhart, R.C., Shi, Y.: Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 Congress on Evolutionary Computation, vol. 1, pp. 81–86 (2001)
Edison, E., Shima, T.: Integrated task assignment and path optimization for cooperating uninhabited aerial vehicles using genetic algorithms. Comput. Oper. Res. 38(1), 340–356 (2011)
Juang, J.G.: Fuzzy neural network approaches for robotic gait synthesis. IEEE Trans. Syst. Man Cybern. B Cybern. 30(4), 594–601 (2000)
Karaboga, D., Gorkemli, B., Ozturk, C., Karaboga, N.: A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif. Intell. Rev. 1–37 (2012)
Kuffner, J., Nishiwaki, K., Kagami, S., Inaba, M., Inoue, H.: Motion planning for humanoid robots. In: Robotics Research, pp. 365–374. Springer, Heidelberg (2005)
Kulpa, R., Multon, F.: Fast inverse kinematics and kinetics solver for human-like figures. In: Proceedings of Humanoids, pp. 38–43 (2005)
Lander, J., CONTENT, G.: Making kine more flexible. Game Developer Mag. 1, 15–22 (1998)
Łukasik, S., Żak, S.: Firefly algorithm for continuous constrained optimization tasks. Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems, pp. 97–106. Springer, Heidelberg (2009)
MATLAB Statistics Toolbox User’s Guide (2014). The MathWorks Inc. http:www.mathworks.com/help/pdf_doc/stats/stats.pdf
Mohamad, M.M., Taylor, N.K., Dunnigan, M.W.: Articulated robot motion planning using ant colony optimisation. In: 3rd International IEEE Conference on Intelligent Systems, pp. 690–695 (2006)
Pant, M., Gupta, H., Narayan, G.: Genetic algorithms: a review. In: National conference on frontiers in applied and computational mathematics (FACM-2005), Allied Publishers, p. 225, 04–05 Mar 2005
Pérez-Rodríguez, R., Marcano-Cedeño, A., Costa, Ú., Solana, J., Cáceres, C., Opisso, E., Gómez, E.J.: Inverse kinematics of a 6 DoF human upper limb using ANFIS and ANN for anticipatory actuation in ADL-based physical neurorehabilitation. Expert Syst. Appl. 39(10), 9612–9622 (2012)
Pham, D.T., Castellani, M., and Le Thi, H.A.: Nature-inspired intelligent optimisation using the bees algorithm. In: Transactions on Computational Intelligence XIII, pp. 38–69. Springer, Heidelberg (2014)
Pollard, N.S., Hodgins, J.K., Riley, M.J., Atkeson, C.G.: Adapting human motion for the control of a humanoid robot. In Proceedings of IEEE International Conference on Robotics and Automation, ICRA’02, vol. 2, pp. 1390–1397 (2002)
Rokbani, N., Alimi, A.M.: Inverse kinematics using particle swarm optimization, a statistical analysis. Procedia Eng. 64, 1602–1611 (2013)
Rokbani, N., Alimi, A.M.: IK-PSO, PSO inverse kinematics solver with application to biped gait generation. Int. J. Comput. Appl. 58(22), 33–39 (2012)
Rokbani, N., Alimi, A.M., Cherif, B.A.: Architectural proposal for an intelligent humanoid. In: Procedings of IEEE Conference on Automation and Logistics (2007)
Rokbani, N., Benbousaada, E., Ammar, B., Alimi, A.M.: Biped robot control using particle swarm optimization. In: IEEE International Conference Systems on Man and Cybernetics (SMC), pp. 506–512 (2010)
Rokbani, N., Boussada, E.B., Cherif, B.A., Alimi, A.M.: From gaits to ROBOT, A Hybrid methodology for A biped Walker. Mobile Robotics: Solutions and Challenges. In: Proceedings of Clawar, vol. 12, pp. 685–692 (2009)
Rokbani, N., Cherif B.A., Alimi, A.M.: Toward intelligent biped-humanoids gaits generation. In: Choi, B. (eds.) Humanoids. Chap 14, InTech (2009)
Rokbani, N., Zaidi, A., Alimi, A.M.: Prototyping a biped robot using an educational robotics kit. In: IEEE International Conference on Education and E-learning Innovations. Sousse, Tunisia (2012)
Rutkowski, L., Przybyl, A., Cpalka, K.: Novel online speed profile generation for industrial machine tool based on flexible neuro-fuzzy approximation. IEEE Trans. Industr. Electron. 59(2), 1238–1247 (2012)
Schmidt, V., Müller, B., Pott, A. Solving the forward kinematics of cable-driven parallel robots with neural networks and interval arithmetic. In: Computational Kinematics, pp. 103–110. Springer, Netherlands (2014)
Tchoń, K., Jakubiak, J.: Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of Jacobian inverse kinematics algorithms. Int. J. Control 76(14), 1387–1419 (2003)
Tchon, K., Jakubiak, J.: Jacobian inverse kinematics. In: Advances in Robot Kinematics: Mechanisms and Motion, p. 465 (2006)
Tevatia, G., Schaal, S.: Inverse kinematics for humanoid robots. In: Proceedings of IEEE International Conference on Robotics and Automation, (ICRA’00), pp. 294–299 (2000)
Tolani, D., Goswami, A., Badler, N.I.: Real-time inverse kinematics techniques for anthropomorphic limbs. Graph. Models 62(5), 353–388 (2000)
Van den Bergh, F., Engelbrecht, A.P.: Effects of swarm size on cooperative particle swarm optimizers (2001)
Wang, R.Y., Popović, J.: Real-time hand-tracking with a color glove. In: ACM Transactions on Graphics (TOG), ACM, vol. 28, No. 3, p. 63 (2009)
Xu, Q., Li, Y.: Error analysis and optimal design of a class of translational parallel kinematic machine using particle swarm optimization. Robotica 27(1), 67–78 (2009)
Yang, X.S. (2010). Firefly algorithm, Levy flights and global optimization. In: Research and Development in Intelligent Systems XXVI. Springer, London, 209–218
Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspired Comput. 2(2), 78–84 (2010)
Yang, X.S.: Firefly algorithms for multimodal optimization. In: Stochastic algorithms: foundations and applications, pp. 169–178, Springer, Heidelberg (2009)
Zaidi, A., Rokbani, N., Alimi, A.M.: A hierarchical fuzzy controller for a biped robot. In: Proceedings of ICBR 2013. Sousse, Tunisia ( 2013)
Zaidi, A., Rokbani, N., Alimi, A.M.: Neuro-Fuzzy gait generator for a biped robot. J. Electron. Syst. 2(2), 48–54 (2012)
Zhang, X,.Nelson, C.A.: Multiple-criteria kinematic optimization for the design of spherical serial mechanisms using genetic algorithms. J. Mech. Des. 133(1) (2011)
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The authors would like to acknowledge the financial support of this work by grants from General Direction of Scientific Research (DGRST), Tunisia, under the ARUB program.
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Rokbani, N., Casals, A., Alimi, A.M. (2015). IK-FA, a New Heuristic Inverse Kinematics Solver Using Firefly Algorithm. In: Azar, A., Vaidyanathan, S. (eds) Computational Intelligence Applications in Modeling and Control. Studies in Computational Intelligence, vol 575. Springer, Cham. https://doi.org/10.1007/978-3-319-11017-2_15
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