×

zbMATH — the first resource for mathematics

Modified PSO method for robust control of 3RPS parallel manipulators. (English) Zbl 1202.90282
Summary: We propose an effective method to design a modified particle swarm optimization (MPSO) singularity control method for a fully parallel robot manipulator. By adopting MPSO to obtain simple and effective estimated damping values, the result automatically adjusts the damping value around a singular point and greatly improves the accuracy of system responses. This method works by damping accelerations of the end effector, so that accelerations along the degenerated directions are zero at a singular point. These velocities, however, may not be zero in some situations, in which case, fluctuations will be encountered around a singular point. To overcome this drawback, we propose a control scheme that uses both damped acceleration and damped velocity, called the hybrid damped resolved-acceleration control (HDRAC) scheme. The MPSO optimization method can immediately provide optimal damping factors when used in an online application. Our proposed approach offers such superior features as easy implementation, stable convergence characteristics, and good computational efficiency. The main advantage of the HDRAC with MPSO in the 3RPS parallel manipulator control system is that it is not necessary for the system to plan its path for avoiding the singular point; thus, the workspace can be improved. Illustrative examples are provided to show the effectiveness of this HDRAC in practical applications, and experimental results verifying the utility of the proposed control scheme are presented.

MSC:
90C59 Approximation methods and heuristics in mathematical programming
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] K. M. Lee and D. Shah, “Kinematic analysis of three degree of freedom in-parallel actuated manipulator,” in Proceedings of the IEEE International Conference on Robotics and Automation, vol. 4, pp. 354-360, Raleigh, NC, USA, 1987.
[2] K. M. Lee and D. Shah, “Dynamic analysis of three degree of freedom in-parallel actuated manipulator,” in Proceedings of the IEEE International Conference on Robotics and Automation, vol. 4, pp. 361-367, Raleigh, NC, USA, 1988.
[3] Q. Xu and Y. Li, “An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory,” Robotics and Computer-Integrated Manufacturing, vol. 24, no. 3, pp. 402-414, 2008.
[4] Y. Fang and Z. Huang, “Kinematic analysis of 3RPS parallel robotic mechanisms,” Mechanical Science and Technology, vol. 16, no. 1, pp. 82-87, 1997.
[5] Y. Li and Q. Xu, “Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism,” Robotica, vol. 23, no. 2, pp. 219-229, 2005.
[6] Y. Li and Q. Xu, “Kinematic analysis of a 3-PRS parallel manipulator,” Robotics and Computer-Integrated Manufacturing, vol. 23, no. 4, pp. 395-408, 2007.
[7] J. Y. S. Luh, M. W. Walker, and R. P. C. Paul, “Resolved-acceleration control of mechanical manipulators,” IEEE Transactions on Automatic Control, vol. 25, no. 3, pp. 468-474, 1980. · Zbl 0436.93026
[8] S.-L. Wu and S.-K. Lin, “Implementation of damped-rate resolved-acceleration robot control,” Control Engineering Practice, vol. 5, no. 6, pp. 791-800, 1997.
[9] R. Campa, R. Kelly, and E. GarcĂ­a, “On stability of the resolved acceleration control,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA ’01), pp. 3523-3528, May 2001.
[10] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, pp. 1942-1948, IEEE, December 1995.
[11] R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the 6th International Symposium on Micromachine and Human Science, pp. 39-43, Nagoya, Japan, 1995.
[12] J. Kennedy, “Particle swarm: social adaptation of knowledge,” in Proceedings of the 1997 IEEE International Conference on Evolutionary Computation (ICEC ’97), pp. 303-308, April 1997.
[13] S. Naka, T. Genji, T. Yura, and Y. Fukuyama, “A hybrid particle swarm optimization for distribution state estimation,” IEEE Transactions on Power Systems, vol. 18, no. 1, pp. 60-68, 2003.
[14] Y. Shi and R. C. Eberhart, “Empirical study of particle swarm optimization,” in Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1945-1950, IEEE, 1999.
[15] X. Chen and Y. Li, “A modified PSO structure resulting in high exploration ability with convergence guaranteed,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 37, no. 5, pp. 1271-1289, 2007.
[16] C. H. Liu and S. Cheng, “Direct singular positions of 3RPS parallel manipulators,” Journal of Mechanical Design, vol. 126, no. 6, pp. 1006-1016, 2004.
[17] T.-S. Hwang and M.-Y. Liao, “Optimal mechanism design and dynamic analysis of a 3-leg 6-DOF linear motor based parallel manipulator,” Asian Journal of Control, vol. 6, no. 1, pp. 136-144, 2004.
[18] S. A. Joshi and L.-W. Tsai, “Jacobian analysis of limited-DOF parallel manipulators,” Journal of Mechanical Design, vol. 124, no. 2, pp. 254-258, 2002.
[19] C. C. Kao, S. L. Wu, and R. F. Fung, “The 3RPS parallel manipulator motion control in the neighborhood of singularities,” in Proceedings of the International Symposium on Industrial Electronics, Mechatronics and Applications, vol. 1, pp. 165-179, 2007.
[20] W.-M. Lin, F.-S. Cheng, and M.-T. Tsay, “Nonconvex economic dispatch by integrated artificial intelligence,” IEEE Transactions on Power Systems, vol. 16, no. 2, pp. 307-311, 2001.
[21] W.-M. Lin, F.-S. Cheng, and M.-T. Tsay, “An improved tabu search for economic dispatch with multiple minima,” IEEE Transactions on Power Systems, vol. 17, no. 1, pp. 108-112, 2002.
[22] A. A. Maciejewski and C. A. Klein, “Singular value decomposition. Computation and applications to robotics,” International Journal of Robotics Research, vol. 8, no. 6, pp. 63-79, 1989.
[23] J. T. Wen and J. F. O’Brien, “Singularities in three-legged platform-type parallel mechanisms,” IEEE Transactions on Robotics and Automation, vol. 19, no. 4, pp. 720-726, 2003.
[24] K. W. Spring, “Euler parameters and the use of quaternion algebra in the manipulation of finite rotations: a review,” Mechanism and Machine Theory, vol. 21, no. 5, pp. 365-373, 1986.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.