Formation control of nonholonomic mobile robots using implicit polynomials and elliptic Fourier descriptors

This paper presents a novel method for the formation control of a group of nonholonomic mobile robots using implicit and parametric descriptions of the desired formation shape. The formation control strategy employs implicit polynomial (IP) representations to generate potential fields for achieving the desired formation and the elliptical Fourier descriptors (EFD) to maintain the formation once achieved. Coordination of the robots is modeled by linear springs between each robot and its two nearest neighbors. Advantages of this new method are increased flexibility in the formation shape, scalability to different swarm sizes and easy implementation. The shape formation control is first developed for point particle robots and then extended to nonholonomic mobile robots. Several simulations with robot groups of different sizes are presented to validate our proposed approach.

Anahtar Kelimeler:

Formation, Coordination, Autonomous, Nonholonomic, Implicit Polynomials, Elliptic Fourier Descriptors

Formation control of nonholonomic mobile robots using implicit polynomials and elliptic Fourier descriptors

Keywords:

Formation, Coordination, Autonomous, Nonholonomic, Implicit Polynomials, Elliptic Fourier Descriptors,

PDF

___

D. Fox, W. Burgard, H. Kruppa, S. Thrun, “A Probabilistic Approach to Collaborative Multi-Robot Localization,” Auton. Robots, vol. 8, no. 3, pp.325-344, 2000
J. Feddema, D. Schoenwald, “Decentralized Control of Cooperative Robotic Vehicles, ” Proceedings of SPIE, Orlando, Florida, pp.852-864, 2001
K. Hayashi, Y. Yokokohji, T. Yoshikawa ve W. Moreno, “Tele-existence Vision System with Image Stabilization for Rescue Robots,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, 2005
A. Birk, S. Carpin, “Merging Occupancy Grid Maps From Multiple Robots,” Proceedings of the IEEE, vol. 94, no.7, pp.1384-1297, 2006
T. Maneewam, P. Rittipravat, “Sorting Objects by Multiple Robots Using Voronoi Separation and Fuzzy Control,” Proceedings of the 2003 IEEWRSJ Intl. Conference on Intelligent Robots and Systems, Las Vegas, Nevada, 2003
T. Sugar, V. Kumar, “Control and Coordination of Multiple Mobile Robots in Manipulation and Material Handling Tasks,” ExperimentalRobotics VI: Lecture Notes in Control and Information Sciences, vol. 250, pp.15-24, New York: Springer-Verlag, 2000
P. Johnson, J. Bay, “Distributed control of simulated autonomous mobile robot collectives in pay load transporta- tion,”, Autonomous Robot, pp.43-64, 1995.
T. Balch, M. Hybinette, “Social Potentials for Scalable Multi-Robot Formations,” Proceedings of IEEE International Conference on Robotics and Automation, pp.85-94, 2000
H. Yamaguchi, “A cooperative hunting behavior by mobile robot troops,” Intl. J. Robotics Research, pp.931-940, 1999.
T. Balch, R.Arkin, “Behavior-based formation control for multirobotic teams,” IEEE Transactions on Robotics and Autonomation, pp.926-934, 1998.
J. P. Ostrowski, J. Desai ve V. Kumar, “Controlling formations of multiple mobile robots,” Proc. IEEE Int. Conf. Robot Automat., pp.2864-2869, 1998.
P. Song, V. Kumar, “A potential Şeld based approach to multi-robot manipulation,” Roc. of the 2002 IEEE Int. Conference on Robotics and Automation, pp.870-876, 2002.
H. Yalcin, M. Unel, W. Wolovich, “Implicitization of Parametric Curves by Matrix Annihilation,” International Journal of Computer Vision vol. 54, no.1/2/3, pp.105-115, 2003
W. Kang, N. Xi, Y. Zhao, J. Tan, Y. Wang, “Formation Control of Multiple Autonomous Vehicles: Theory and Experimentation,” Proceeding,. IFAC 15th Triennial World Congress, pp.1155-1160, 2002
L. Barnes, W. Alvis, M. Fields, K. Valavanis, W. Moreno, “Heterogeneous Swarm Formation Control Using Bivariate Normal Functions to Generate Potential Fields,” Proceedings of the IEEE Workshop on Distributed Intelligent Systems: Collective Intelligence and Its Applications, 2006
Y. H. Esin, M. Unel, M. Yildiz, “Formation Control of Multiple Robots Using Parametric and Implicit Represen- tations,” Proceedings of the ICIC’08, Lecture Notes in Computer Science, Springer-Verlag, Berlin, pp. 558-565, 2008.
F.P. Kuhl, C.R. Giardina, “Elliptic Fourier Features of a Closed Contour,” Computer Graphics and Image Process- ing, vol. 18, pp.236-258, 1982.
C. Samson, K. Ait-Abderrahim, “Feedback Stabilization of a Nonholonomic Wheeled Mobile Robot,” Proceedings of the IEEE/RSJ International Workshop on Intelligent Robots and Systems, pp.1242-12470, 1991.
C. Samson, K. Ait-Abderrahim, “Feedback Control of a Nonholonomic Wheeled Cart in Cartesian Space,” Pro- ceedings of the IEEE International Conference on Robotics and Automation, pp.1136-1141, 1991.
C. Samson, “Trajectory tracking for nonholonomic vehicles: overview and case study,” Proceedings of the Fourth International Workshop on Robot Motion and Control, pp.139-153, 2004.