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Design optimization of a cable-based parallel tracking system by using evolutionary algorithms

Published online by Cambridge University Press:  05 March 2014

Eusebio E. Hernandez ,
S.-I. Valdez ,
M. Ceccarelli ,
A. Hernandez  and
S. Botello
Eusebio E. Hernandez*
Affiliation:
National Polytechnic Institute, ESIME-UPT, Section of Graduate Studies and Research, Mexico City, Mexico
S.-I. Valdez
Affiliation:
Center for Research in Mathematics (CIMAT), Department of Computer Science, Guanajuato City, Mexico
M. Ceccarelli
Affiliation:
Laboratory of Robotics and Mechatronics, University of Cassino, Cassino (Fr), Italy
A. Hernandez
Affiliation:
Center for Research in Mathematics (CIMAT), Department of Computer Science, Guanajuato City, Mexico
S. Botello
Affiliation:
Center for Research in Mathematics (CIMAT), Department of Computer Science, Guanajuato City, Mexico
*
*Corresponding author. E-mail: euhernandezm@ipn.mx
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Summary

In this paper, an optimization design of a 6 DOF parallel measuring system is analyzed. First, a closed form direct kinematics formulation based on Cayley–Menger determinants is considered in the objective function, in order to measure the manipulator singularities, then an estimation of distribution algorithm is proposed to solve the optimization problem. It is shown that the evolutionary algorithm can find close to optimal solutions for minimum pose error estimation. Additionally, these global optimizers significantly reduce the computational burden in comparison with exhaustive search and other global optimization techniques. The sensitivity of the pose error estimation in the prescribed robots' workspace is analyzed and used to guide a designer in choosing the best structural configuration. Numerical examples are discussed to show the feasibility of the proposed optimization methodology.

Keywords

RoboticsParallel mechanism designTracking systemOptimizationEstimation of distribution algorithms
Type
Articles
Information
Robotica , Volume 33 , Issue 3 , March 2015 , pp. 599 - 610
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Barbosa, M., Pires, E. and Lopes, A., “Optimization of Parallel Manipulators using Evolutionary Algorithms,” In: Soft Computing Models in Industrial and Environmental Applications, 5th International Workshop (SOCO 2010) Advances in Intelligent and Soft Computing, vol. 73 (Corchado, E., Novais, P., Analide, C. and Sedano, J., eds.)(Springer, Berlin, 2010) pp. 79–86.Google Scholar
2.Bosman, P. A. and Thierens, D., “Adaptive Variance Scaling in Continuous Mutli-Objective Estimation-of-Distribution Algorithms,” Proceedings of the 2007 Conference on Genetic and Evolutionary Computation (GECCO '07), ACM (2007) pp. 500–507.Google Scholar
3.Cabrera, J., Castillo, J., Nadal, F., Ortiz, A. and Simón, A., “Synthesis of Mechanisms with Evolutionary Techniques,” In: Proceedings of EUCOMES 08 (Ceccarelli, M. eds.) (Springer, Netherlands, 2009) pp. 167–174.Google Scholar
4.Cai, Y., Sun, X., Xu, H. and Jia, P., “Cross Entropy and Adaptive Variance Scaling in Continuous Eda,” Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO '07), ACM, New York, NY, USA (2007) pp. 609–616.Google Scholar
5.Carbone, G., “Stiffness Performance of Multibody Robotic Systems,” IEEE International Conference on Automation, Quality and Testing, Robotics, vol. 2 (2006) pp. 219–224.Google Scholar
6.Carbone, G. and Ceccarelli, M., “Experimental tests on feasible operation of a finger mechanism in the larm hand,” Mech. Based Des. Struct. Mach. 36 (1), 1–13 (2008).CrossRefGoogle Scholar
7.Ceccarelli, M.. Fundamentals of Mechanics of Robotic Manipulation (Springer, International Series on Microprocessor-Based and Intelligent Systems Engineering, Netherlands, 2004).CrossRefGoogle Scholar
8.Ceccarelli, M., Avila Carrasco, C. and Ottaviano, E., “Error Analysis and Experimental Tests of Catrasys (Cassino Tracking System),” 26th Annual Confjerence of the IEEE Industrial Electronics Society (IECON 2000), vol. 4 (2000) pp. 2371–2376.Google Scholar
9.Chai, K.-S., Young, K. and Tuersley, I., “A practical calibration process using partial information for a commercial stewart platform,” Robotica 20, 315–322 (2002).Google Scholar
10.Chiu, Y.-J. and Perng, M.-H., “Self-calibration of a general hexapod manipulator with enhanced precision in 5-dof motions,” Mech. Mach. Theory 39 (1), 1–23 (2004).CrossRefGoogle Scholar
11.Dong, W. and Yao, X., “Unified eigen analysis on multivariate gaussian based estimation of distribution algorithms,” Inf. Sci. 178 (15), 3000–3023 (2008).Google Scholar
12.Downing, D. M., Samuel, A. E. and Hunt, K. H., “Identification of the special configurations of the octahedral manipulator using the pure condition,” Int. J. Robot. Res. 21, 147–159 (2002).CrossRefGoogle Scholar
13.Hernández-Martínez, E. E., Ceccarelli, M., Carbone, G., López-Cajún, C. S. and Jáuregui-Correa, J. C., “Characterization of a cable-based parallel mechanism for measurement purposes,” Mech. Based Des. Struct. Mach. 38 (1), 25–49 (2010).Google Scholar
14.Jeong, J. W., Kim, S. H., Kwak, Y. K. and Smith, C. C., “Development of a parallel wire mechanism for measuring position and orientation of a robot end-effector,” Mechatronics 8 (8), 845–861 (1998).Google Scholar
15.Li, T. and Ceccarelli, M., “An experimental analysis of human straight walking,” Frontiers Mech. Eng. 8 (1), 95–103 (2013).Google Scholar
16.Omran, A., El-Bayoumi, G., Bayoumi, M. and Kassem, A., “Genetic algorithm based optimal control for a 6-dof non redundant stewart manipulator,” Int. J. Aerosp. Mech. Eng. 2 (2), 73–79 (2008).Google Scholar
17.Ottaviano, E. and Ceccarelli, M., “Numerical and experimental characterization of singularities of a six-wire parallel architecture,” Robotica 25, 315–324 (2007).Google Scholar
18.Ottaviano, E., Ceccarelli, M. and Palmucci, F., “An application of catrasys, a cable-based parallel measuring system for an experimental characterization of human walking,” Robotica 28, 119–133 (2010).Google Scholar
19.Ottaviano, E., Ceccarelli, M., Toti, M. and Carrasco, C., “Catrasys (cassino tracking system): A wire system for experimental evaluation of robot workspace,” J. Robot. Mechatronics 14, 78–87 (2002).Google Scholar
20.Pelikan, M., Goldberg, D. E. and Cantú-Paz, E., “BOA: The Bayesian Optimization Algorithm,” In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-99) vol. I (Banzhaf, W., Daida, J., Eiben, A. E., Garzon, M. H., Honavar, V., Jakiela, M. and Smith, R. E., eds.) (Morgan Kaufmann Publishers, San Fransisco, CA, Orlando, FL, 1999) pp. 525–532.Google Scholar
21.Pelikan, M., Sastry, K. and Cantú-Paz, E. (eds.), Scalable Optimization via Probabilistic Modeling, Studies in Computational Intelligence, vol. 33 (Springer Berlin Heidelberg, 2006).Google Scholar
22.Rauf, A., Pervez, A. and Ryu, J., “Experimental results on kinematic calibration of parallel manipulators using a partial pose measurement device,” IEEE Trans. Robot. 22 (2), 379–384 (2006).CrossRefGoogle Scholar
23.Renaud, P., Andreff, N., Lavest, J.-M. and Dhome, M., “Simplifying the kinematic calibration of parallel mechanisms using vision-based metrology,” IEEE Trans. Robot. 22 (1), 12–22 (2006).CrossRefGoogle Scholar
24.Rolland, L. and Chandra, R., “On Solving the Forward Kinematics of the 6-6 General Parallel Manipulator with an Efficient Evolutionary Algorithm,” In: ROMANSY 18 Robot Design, Dynamics and Control, CISM International Centre for Mechanical Sciences, vol. 524 (Parenti Castelli, V. and Schiehlen, W., eds.) (Springer, Vienna, 2010) pp. 117–124.Google Scholar
25.Shapiro, J. L., “Diversity Loss in General Estimation of Distribution Algorithms,” Proceedings of the 9th international conference on Parallel Problem Solving from Nature (PPSN'06) (Springer-Verlag, Berlin, 2006) pp. 92–101.Google Scholar
26.Thomas, F., Ottaviano, E., Ros, L. and Ceccarelli, M., “Coordinate-Free Formulation of a 3-2-1 Wire-Based Tracking Device Using Cayley–Menger Determinants,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'03) vol. 1 (2003) pp. 355–361.Google Scholar
27.Thomas, F., Ottaviano, E., Ros, L. and Ceccarelli, M., “Performance analysis of a 3-2-1 pose estimation device,” IEEE Trans. Robot. 21 (3), 288–297 (2005).Google Scholar
28.Thomas, F. and Ros, L., “Revisiting trilateration for robot localization,” IEEE Trans. Robot. 21 (1), 93–101 (2005).Google Scholar
29.Valdez, S.-I., Hernández-Aguirre, A. and Botello, S., “Adequate Variance Maintenance in a Normal Eda Via the Potential-Selection Method,” In: EVOLVE-A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II (Schütze, O., Coello, C., Carlos, A., Tantar, A.-A., Tantar, E., Bouvry, P., Del Moral, P. and Legrand, P., eds.) (Springer Berlin Heidelberg, 2013) pp. 221–235.Google Scholar
30.Williams, R., Albus, J. and Bostelman, R., “3d cable-based cartesian metrology system,” J. Robot. Syst. 21, 237–257 (2004).Google Scholar
31.Yuan, B. and Gallagher, M., “On the Importance of Diversity Maintenance in Estimation of Distribution Algorithms,” Proceedings of the 2005 Conference on Genetic and Evolutionary Computation (GECCO'05) (ACM, New York, NY, USA, 2005) pp. 719–726.Google Scholar
32.Zhang, Q. and Mühlenbein, H., “On the convergence of a class of estimation of distribution algorithms,” IEEE Trans. Evolutionary Comput. 8 (2), 127–136 (2004).Google Scholar
33.Zhuang, H., Wu, J. and Huang, W., “Optimal Planning of Robot Calibration Experiments by Genetic Algorithms,” Proceedings od the IEEE International Conference on Robotics and Automation vol. 2 (1996), pp. 981–986.Google Scholar