Abstract
We consider a weighted communication graph in a network of mobile robots, and its associated Laplacian whose entries depend on the pairwise distance between the robots.We propose a heuristic distributed solution for the maximization of the algebraic connectivity of the graph by moving the robots to appropriate positions. Our approach is optimization-based and can be extended to handle various constraints, such as the robots’ dynamics. Our proposed distributed solution uses local algorithms that utilize information only from nearby neighboring robots. Numerical simulations show the applicability and effectiveness of the algorithm and indicate that in certain cases the proposed distributed solution can perform better than the centralized version.
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Bhatta, P., Fiorelli, E., Lekien, F., Leonard, N.E., Paley, D.A., Zhang, F., Bachmayer, R., Davis, R.E., Fratantoni, D.M., Sepulchre, R.: Coordination of an Underwater Glider Fleet for Adaptive Sampling. In: Proceedings of the International Workshop on Underwater Robotics, Genoa, Italy, pp. 61–69 (2005)
Izzo, D., Pettazzi, L.: Autonomous and Distributed Motion Planning for Satellite Swarm. Journal of Guidance, Control and Dynamics 30(2), 449–459 (2007)
Lau, H.Y.K., Ko, A.W.Y.: Coordination of Cooperative Search and Rescue Robots for Disaster Relief. In: Proceedings of IFAC World Congress, Seul, Korea, July 6-11 (2008)
Casbeer, D.W., Li, S., Beard, R.W., Mehra, R.K.: Forest Fire Monitoring With Multiple Small UAVs. In: Proceedings of the ACC, Portland, OR, USA, June 8-10 (2005)
Mathews, G., Durrant-Whyte, H.: Decentralised Optimal Control for Reconnaissance. In: Proceedings of the Conference on Information, Decision and Control, Adelaide, Australia, February 12-14 (2007)
Bullo, F., Cortés, J., Martínez, S.: Distributed Control of Robotic Networks. Applied Mathematics Series. Princeton University Press (2008)
Keviczky, T., Johansson, K.H.: A Study on Distributed Model Predictive Consensus. In: Proceedings of IFAC World Congress, Seul, Korea, July 6-11 (2008)
Ren, W., Beard, R.: Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications. Springer, London (2008)
Olfati-Saber, R., Murray, R.: Consensus Problems in Networks of Agents with Switching Topology and Time-Delays. IEEE Transactions on Automatic Control 49(9), 1520–1533 (2004)
Olfati-Saber, R., Fax, J.A., Murray, R.: Consensus and Cooperation in Networked Multi-Agent Systems. Proceeding of IEEE 95(1), 215–233 (2007)
Anisi, D.A., Hu, X., Ögren, P.: Connectivity Constrained Multi-UGV Surveillance. In: Proceedings of the 17th IFAC World Congress, Seoul, Korea (July 2008)
Derenick, J., Spletzer, J., Hsieh, A.: An Optimal Approach to Collaborative Target Tracking with Performance Guarantees. Journal of Int. Rob. Syst. 56, 47–67 (2009)
Grocholsky, B., Makarenko, A., Durrant-Whyte, H.: Information-Theoretic Coordinated Control of Multiple Sensor Platforms. In: Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan, September 14-19 (2003)
Chung, T.H., Gupta, V., Burdick, J.W., Murray, R.M.: On a Decentralized Active Sensing Strategy using Mobile Sensor Platforms in a Network. In: Proceedings of the 43rd IEEE Conference on Decision and Control, Paradise Island, the Bahamas, December 14-17 (2004)
Martínez, S., Bullo, F.: Optimal sensor placement and motion coordination for target tracking. Automatica 42, 661–668 (2006)
Olfati-Saber, R.: Distributed Tracking for Mobile Sensor Networks with Information-Driven Mobility. In: Proceedings of the American Control Conference, New York City, USA (2007)
De Gennaro, M.C., Jadbabaie, A.: Decentralized Control of Connectivity for Multi-Agent Systems. In: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, USA, December 13-15 (2006)
Zavlanos, M.M., Pappas, G.J.: Distributed Connectivity Control of Mobile Networks. In: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, December 12-14 (2007)
Schuresko, M., Cortés, J.: Distributed Motion Constraints for Algebraic Connectivity of Robotic Networks. Journal of Intelligent Robotics Systems 56, 99–126 (2009)
Kim, Y., Mesbahi, M.: On Maximizing the Second Smallest Eigenvalue of a State-Dependent Graph Laplacian. IEEE Transactions of Automatic Control 51(1), 116–120 (2006)
Boyd, S.: Convex Optimization of Graph Laplacian Eigenvalues. In: Proceedings of the International Congress of Mathematicians, Madrid, Spain, pp. 1311–1319 (2006)
Cohen, E., Kaplan, H.: Spatially-decaying Aggregation over a Network. Journal of Computer and System Sciences 73, 265–288 (2007)
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Simonetto, A., Keviczky, T., Babuška, R. (2013). Distributed Algebraic Connectivity Maximization for Robotic Networks: A Heuristic Approach. In: Martinoli, A., et al. Distributed Autonomous Robotic Systems. Springer Tracts in Advanced Robotics, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32723-0_20
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DOI: https://doi.org/10.1007/978-3-642-32723-0_20
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