Document Type : Research Articles
Authors
Engineering Faculty, Electrical Department, Ferdowsi University of Mashhad
Abstract
In this paper, we propose the problem of connectivity maintenance for a group of robots that are connected with wireless communication. The communication between the agents is modeled by a fading channel, and the exchange of information is possible at permissible distances. The distributed controller is designed to maintain the global connectivity of the network communication graph. On the other hand, obtaining the best communication quality between agents is the definition of good network connectivity. Therefore, the Laplacian matrix is defined as a weighted graph according to the communication parameters. Initially, the controller uses the supergradation algorithm to remake the network Laplacian matrix for having a bigger second eigenvalue. While each agent in the network only has access to the neighbor's information. The control algorithm uses a multi-agent estimator to find the eigenvector corresponding to the second small eigenvalue. The formation problem has been considered in the second step after the reference topology has been obtained. Because of the nonlinear dynamics of the agents, the sliding mode controller has been used for this purpose. This robust controller could be a suitable choice due to the modeling uncertainty and sensor measurement uncertainty. Finally, an example of multi-agent robots is provided to evaluate the algorithm.
Keywords
Main Subjects
[2] S. Martínez and F. Bullo, "Optimal sensor placement and motion coordination for target tracking," Automatica, vol. 42, pp. 661-668, 2006/04/01/ 2006.
[3] M. Otte, M. J. Kuhlman, and D. Sofge, "Auctions for multi-robot task allocation in communication limited environments," Autonomous Robots, vol. 44, pp. 547-584, 2020/03/01 2020.
[4] E. Olcay, J. Bodeit, and B. Lohmann, "Sensor-based Exploration of an Unknown Area with Multiple Mobile Agents," IFAC-PapersOnLine, vol. 53, pp. 9621-9627, 2020/01/01/ 2020.
[5] S. Rahili, J. Lu, W. Ren, and U. M. Al-Saggaf, "Distributed Coverage Control of Mobile Sensor Networks in Unknown Environment Using Game Theory: Algorithms and Experiments," IEEE Transactions on Mobile Computing, vol. 17, pp. 1303-1313, 2018.
[6] J. Cortes, S. Martínez, and F. Bullo, "Robust Rendezvous for Mobile Autonomous Agents via Proximity Graphs in Arbitrary Dimensions," Automatic Control, IEEE Transactions on, vol. 51, pp. 1289-1298, 09/01 2006.
[7] S. Ponda, L. Johnson, A. Kopeikin, H.-L. Choi, and J. How, "Distributed Planning Strategies to Ensure Network Connectivity for Dynamic Heterogeneous Teams," Selected Areas in Communications, IEEE Journal on, vol. 30, pp. 861-869, 06/01 2012.
[8] H. Su, X. Wang, and G. Chen, "A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements," International Journal of Control, vol. 82, pp. 1334-1343, 2009/07/01 2009.
[9] D. Zelazo, A. Franchi, P. Allgöwer, H. Bülthoff, and P. Giordano, “Rigidity Maintenance Control for Multi-Robot Systems,” 2012.
[10] D. Zelazo, A. Franchi, H. H. Bülthoff, and P. Robuffo Giordano, "Decentralized rigidity maintenance control with range measurements for multi-robot systems," The International Journal of Robotics Research, vol. 34, pp. 105-128, 2015/01/01 2014.
[11] L. Zhang, J. Wang, Z. Lin, L. Lin, Y. Chen, and B. He, "Distributed Cooperative Obstacle Avoidance for Mobile Robots Using Independent Virtual Center Points," Journal of Intelligent & Robotic Systems, vol. 98, pp. 791-805, 2020/06/01 2020.
[12] K. Khateri, M. Pourgholi, M. Montazeri, and L. Sabattini, "Effect of Stubborn Agents on Bounded Confidence Opinion Dynamic systems: Unanimity in Presence of Stubborn Agents," in 2019 27th Iranian Conference on Electrical Engineering (ICEE), 2019, pp. 875-880.
[13] C. D. G. G. Royle, C. Godsil, and G. F. Royle, Algebraic Graph Theory: Springer, 2001.
[14] R. Dai and M. Mesbahi, "Optimal topology design for dynamic networks," in 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011, pp. 1280-1285.
[15] M. C. D. Gennaro and A. Jadbabaie, "Decentralized Control of Connectivity for Multi-Agent Systems," in Proceedings of the 45th IEEE Conference on Decision and Control, 2006, pp. 3628-3633.
[16] P. Yang, R. A. Freeman, G. J. Gordon, K. M. Lynch, S. S. Srinivasa, and R. Sukthankar, "Decentralized estimation and control of graph connectivity for mobile sensor networks," Automatica, vol. 46, pp. 390-396, 2010/02/01/ 2010.
[17] D. Kempe and F. McSherry, "A decentralized algorithm for spectral analysis," Journal of Computer and System Sciences, vol. 74, pp. 70-83, 2008/02/01/ 2008.
[18] X. Xue, X. Yue, and J. Yuan, "Connectivity preservation and collision avoidance control for spacecraft formation flying in the presence of multiple obstacles," Advances in Space Research, 2020/06/06/ 2020.
[19] S. J. Yoo and B. S. Park, "Connectivity-Preserving Approach for Distributed Adaptive Synchronized Tracking of Networked Uncertain Nonholonomic Mobile Robots," IEEE Transactions on Cybernetics, vol. 48, pp. 2598-2608, 2018.
[20] C. P. Bechlioulis and K. J. Kyriakopoulos, "Robust model-free formation control with prescribed performance and connectivity maintenance for nonlinear multi-agent systems," in 53rd IEEE Conference on Decision and Control, 2014, pp. 4509-4514.
[21] R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Transactions on automatic control, vol. 49, pp. 1520-1533, 2004.
[22] Y. Zhang and Y.-P. Tian, "Allowable delay bound for consensus of linear multi-agent systems with communication delay," International Journal of Systems Science, vol. 45, pp. 2172-2181, 2014/10/03 2014.
[23] A. Nejadvali, R. Esfanjani, A. Farnam, and G. Crevecoeur, "Delay dependent criteria for the consensus of second-order multi-agent systems subject to communication delay," IET Control Theory and Applications, vol. 15, pp. 1-10, 05/07 2021.
[24] R. Mu and A. Wei, "Consensus disturbance rejection for linear multi-agent systems based on output feedback," in 2019 Chinese Control Conference (CCC), 2019, pp. 6094-6099.
[25] R. Carli, G. Como, P. Frasca, and F. Garin, "Distributed averaging on digital erasure networks," Automatica, vol. 47,pp. 115-121, 01/31 2011.
[26] J. Mou, Q. He, Z. Xia, and J. Wang, "Consensus of the Distributed Multiagent System with the Framework of the Small-World Network," Mathematical Problems in Engineering, vol. 2021, p. 6193508, 2021/02/15 2021.
[27] E. Carrillo, S. Yeotikar, S. Nayak, M. K. M. Jaffar, S. Azarm, J. W. Herrmann, et al., "Communication-Aware Multi-Agent Metareasoning for Decentralized Task Allocation,"IEEE Access, vol. 9, pp. 98712-98730, 2021.
[28] X. Gu, T. Jia, and Y. Niu, "Consensus tracking for multi-agent systems subject to channel fading: a sliding mode control method," International Journal of Systems Science, vol. 51, pp. 1-9, 07/30 2020.
[29] S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, "Gossip algorithms: design, analysis and applications," in Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies., 2005, pp. 1653-1664 vol. 3.
[30] J. Li, Y. Niu and Y. Zou, "Sliding Mode Control for Networked Control System Under Fading Channels," 2019 IEEE Conference on Control Technology and Applications (CCTA), Hong Kong, China, 2019, pp. 561-566.
)