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An adaptive niching genetic algorithm approach for generating multiple solutions of serial manipulator inverse kinematics with applications to modular robots

Published online by Cambridge University Press:  26 May 2009

Saleh Tabandeh ,
William W. Melek  and
Christopher M. Clark
Saleh Tabandeh*
Affiliation:
Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, CanadaN2L 3G1
William W. Melek
Affiliation:
Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, CanadaN2L 3G1
Christopher M. Clark
Affiliation:
Department of Computer Science, California Polytechnic State University, 1 Grand Avenue, San Luis Obispo, CA 94307-0354, USA
*
*Corresponding author. E-mail: [email protected]
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Summary

Inverse kinematics (IK) is a nonlinear problem that may have multiple solutions. A modified genetic algorithm (GA) for solving the IK of a serial robotic manipulator is presented. The algorithm is capable of finding multiple solutions of the IK through niching methods. Despite the fact that the number and position of solutions in the search space depends on the position and orientation of the end-effector as well as the kinematic configuration (KC) of the robot, the number of GA parameters that must be set by a user are limited to a minimum through the use of an adaptive niching method. The only requirement of the algorithm is the forward kinematics (FK) equations which can be easily obtained from the Denavit–Hartenberg link parameters and joint variables of the robot. For identifying and processing the outputs of the proposed GA, a modified filtering and clustering phase is also added to the algorithm. For the postprocessing stage, a numerical IK solver is used to achieve convergence to the desired accuracy. The algorithm is validated on three KCs of a modular and reconfigurable robot (MRR).

Keywords

Pose estimation and registrationSerial manipulator design and kinematicsMotion planningModular robotsSpace robotics
Type
Article
Information
Robotica , Volume 28 , Issue 4 , July 2010 , pp. 493 - 507
Copyright
Copyright © Cambridge University Press 2009

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References

1.Paul, R. P., Robot Manipulator: Mathematics, Programming and Control (MIT Press, Cambridge, MA, 1981).Google Scholar
2.Tsai, L. and Morgan, A., “Solving the kinematics of the most general six- and five-degree-of-freedom manipulators by continuation methods,” J. Mech. Transm. Autom. Des. 107, 189–200 (1985).Google Scholar
3.Kucuck, S. and Bingul, Z., “The inverse kinematics solutions of fundamental robot manipulators with offset wrist,” IEEE Int. Conf. Mechatronics 197–202, (Jul. 2005).Google Scholar
4.Xie, J., Yan, S. and Qiang, W., “A Method for Solving the Inverse Kinematics Problem of 6-DOF Space Manipulator,” First International Symposium on Systems and Control in Aerospace and Astronautics, Harbin (Jan. 2006) pp. 379–382.Google Scholar
5.Goldenberg, A. A., Benhabib, B. and Fenton, G., “A complete generalized solution to the inverse kinematics of robots,” IEEE J. Robot. Autom. RA-1 (1), 14–20 (Mar. 1985).Google Scholar
6.Goldenberg, A. A. and Lawrence, D. L., “A generalized solution to the inverse kinematics of robotics manipulators,” ASME J. Dyn. Syst., Meas. Control 107, 103–106 (Mar. 1985).CrossRefGoogle Scholar
7.Grudic, G. Z. and Lawrence, P. D., “Iterative inverse kinematics with manipulator configuration control,” IEEE Trans. Robot. Autom. 9 (4), 476–483 (Aug. 1993).CrossRefGoogle Scholar
8.Chen, I.-M. and Yang, G., “Inverse Kinematics for Modular Reconfigurable Robots,” Proceedings of IEEE International Conference on Robotics and Automation, Leuven, Belgium, vol. 2, (May 1998) pp. 1647–1652.Google Scholar
9.Chen, I.-M. and Gao, Y., “Closed-Form Inverse Kinematics Solver for Reconfigurable Robots,” IEEE International Conference on Robotics and Automation, Seoul, Korea, vol. 3, (2001) pp. 2395–2400.Google Scholar
10.Parker, J. K., Khoogar, A. R. and Goldberg, D. E., “Inverse Kinematics of Redundant Robots Using Genetic Algorithm,” IEEE International Conference on Robotics and Cybernetics, Scottsdale, AZ, USA, vol. 1, (1989) pp. 271–276.Google Scholar
11.Buckley, K. A., Hopkins, S. H. and Turton, B. C. H., “Solution of Inverse Kinematics Problems of a Highly Kinematically Redundant Manipulator Using Genetic Algorithms,” Second International Conference on Genetic Algorithms in Engineering: Innovations and Applications, Glasgow, UK (Conf. Publ. No.449), (Sep. 1997) pp. 264–269.Google Scholar
12.Sheng, L., Wan-long, L., Yan-chun, D. and Liang, F., “Forward Kinematics of the Stewart Platform Using Hybrid Immune Genetic Algorithm,” IEEE Conference on Mechatronics and Automation, Bangkok, Thailand (Jun. 2006) pp. 2330–2335.Google Scholar
13.Zhang, Y., Sun, Z. and Yang, T., “Optimal Motion Generation of a Flexible Macro-micro Manipulator System Using Genetic Algorithm and Neural Network,” IEEE Conference on Robotics, Automation and Mechatronics, Bangkok, Thailand (Dec. 2006) pp. 1–6.Google Scholar
14.Chapelle, F., Chocron, O. and Bidaud, Ph., “Genetic Programming for Inverse Kinematics Problem Approximation,” Proceedings of IEEE International Conference on Robotics and Automation, Seoul, Korea, vol. 4, (2001) pp. 3364–3369.Google Scholar
15.Karla, P., Mahapatra, P. B. and Aggarwal, D. K., “On the Solution of Multimodal Robot Inverse Kinematic Function Using Real-coded Genetic Algorithms,” IEEE International Conference on Systems, Man and Cybernetics, Washington, DC, USA, vol. 2, (2003) pp. 1840–1845.Google Scholar
16.Karla, P., Mahapatra, P. B. and Aggarwal, D. K., “On the Comparison of Niching Strategies for Finding the Solution of Multimodal Robot Inverse Kinematics,” IEEE International Conference on Systems, Man and Cybernetics, The Hague, The Netherlands, vol. 6, (2004) pp. 5356–5361.Google Scholar
17.Tabandeh, S., Clark, C. and Melek, W., “A Genetic Algorithm Approach to Solve for Multiple Solutions of Inverse Kinematics Using Adaptive Niching and Clustering,” Proceedings of IEEE World Congress on Computational Intelligence, Vancouver, Canada (July 2006) pp. 1815–1822.Google Scholar
18.Chocron, O. and Bidaud, Ph., “Evolutionnary Algorithms in Kinematic Design of Robotic Systems,” International Conference on Intelligent Robots and Systems, September 7–11, (1997), Grenoble, France, pp. 1111–1117.Google Scholar
19.Corke, P. I., “A robotics toolbox for MATLAB,” IEEE Robot. Autom. Mag. 3 (1), 24–32 (1996).Google Scholar
20.Kuipers, J. B., Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality (Princeton University Press, 1999).Google Scholar
21.Altmann, S. L., Rotations, Quaternions, and Double Groups (Dover Publications, 1986).Google Scholar
22.Sareni, B. and Krähenbühn, L., “Fitness sharing and niching methods revisited”, IEEE Trans. Evol. Comput. 2 (3), 97–106 (Sept. 1998).CrossRefGoogle Scholar
23.Goldberg, D. E. and Richardson, J., “Genetic Algorithms with Sharing for Multimodal Function Optimization”, Proceedings of the 2nd International Conference Genetic Algorithms, Cambridge, Massachusetts, United States (1987) pp. 41–49.Google Scholar
24.Goldberg, D. E. and Wang, L., “Adaptive Niching via Coevolutionary Sharing”, Technical Report, IlliGAL Report No. 97007 (Urbana, IL: University of Illinois at Urbana-Champaign, 1997).Google Scholar
25.Neef, M., Thierens, D. and Arciszewski, H., “A Case Study of a Multiobjective Recombinative Genetic Algortihm with Coevolutionary Sharing,” Proceedings of 1999 Congress on Evolutionary Computation, Washington, DC, USA, vol. 1, (1999).Google Scholar
26.Deb, K. and Agrawal, R. B., “Simulated binary crossover for continuous search space,” Complex Syst. 9 (2), 115–148 (1995).Google Scholar
27.Deb, K. and Goyal, M., “A combined genetic adaptive search (GeneAS) for engineering design,” Comput. Sci. Inform. 26 (4), 30–45 (1995).Google Scholar
28.Chiu, S., “Fuzzy model identification based on cluster estimation,” J. Intell. Fuzzy Syst. 2 (3), 268–278 (Sep. 1994).Google Scholar
29.Rudolph, G., “Evolutioary Search Under Partially Ordered Sets,” Technical Report No. CI-67/99 (Dortmund, Germany: Department of Computer Science/LS11, University of Dortmund).Google Scholar
30.Zitzler, E., Deb, K. and Thiele, L., “Comparison of multiobjective evolutionary algorithms: Empirical results,” Evol. Comput. 8 (2), 173–195 (Feb. 1999).Google Scholar
31.Li, Z., Melek, W. and Clark, C., “Development and Characterization of a Modular and Reconfigurable Robot,” Proceedings of the International Conference on Changeable, Agile, Reconfigurable and Virtual Production, Toronto, Canada (Jul. 2007).Google Scholar