Abstract
In this paper, we develop a suite of motion planning strategies suitable for large-scale sensor networks. These solve the problem of reconfiguring the network to a new shape while minimizing either the total distance traveled by the nodes or the maximum distance traveled by any node. Three network paradigms are investigated: centralized, computationally distributed, and decentralized. For the centralized case, optimal solutions are obtained in O(m) time in practice using a logarithmic-barrier method. Key to this complexity is transforming the Karush-Kuhn-Tucker (KKT) matrix associated with the Newton step sub-problem into a mono-banded system solvable in O(m) time. These results are then extended to a distributed approach that allows the computation to be evenly partitioned across the m nodes in exchange for O(m) messages in the overlay network. Finally, we offer a decentralized, hierarchical approach whereby follower nodes are able to solve for their objective positions in O(1) time from observing the headings of a small number (2-4) of leader nodes. This is akin to biological systems (e.g. schools of fish, flocks of birds, etc.) capable of complex formation changes using only local sensor feedback. We expect these results will prove useful in extending the mission lives of large-scale mobile sensor networks.
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References
Compass: Collaborative multiscale processing and architecture for sensornetworks, http://compass.cs.rice.edu/
Networking technology and systems (NeTS). NSF Solicitation 06-516 (December 2005)
Bachmayer, R., Leonard, N.E.: Vehicle networks for gradient descent in a sampled environment. In: Proc. IEEE Conf. on Decision and Control, Las Vegas (December 2002)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge Unviersity Press, Cambridge (2004)
Bruce, J., Veloso, M.: Fast and accurate vision-based pattern detection and identification. In: IEEE International Conference on Robotics and Automation (May 2003)
Butler, Z., Rus, D.: Event-based control for mobile sensor networks. IEEE Pervasive Computing 2(4), 10–18 (2003)
Cortés, J., Martínez, S., Karatas, T., Bullo, F.: Coverage control for mobile sensing networks. IEEE Trans. on Robotics and Automation 20(2), 243–255 (2004)
Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 1969 24th national conference, New York, USA, pp. 157–172 (1969)
Derenick, J., Spletzer, J.: TR LU-CSE-05-029: Optimal shape changes for robot teams. Technical report, Lehigh University (2005)
Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. John Wiley and Sons, Chichester (1998)
Ganguli, A., Susca, S., Martínez, S., Bullo, F., Cortés, J.: On collective motion in sensor networks: sample problems and distributed algorithms. In: Proc. IEEE Conf. on Decision and Control, Seville, Spain, pp. 4239–4244 (December 2005)
Golub, G.H., Loan, C.F.V.: Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)
Govindan, R., et al.: Tenet: An architecture for tiered embedded networks. Technical report, Center for Embedded Networked Sensing (CENS) (November 2005)
Lobo, M., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of second-order cone programming. Linear Algebra and Applications, Special Issue on Linear Algebra in Control, Signals and Image Processing (1998)
MOSEK ApS. The MOSEK Optimization Tools Version 3.2 (Revision 8) User’s Manual and Reference, http://www.mosek.com
Mourikis, A., Roumeliotis, S.: Optimal sensing strategies for mobile robot formations: Resource constrained localization. In: Robotics: Science & Sys., pp. 281–288 (June 2005)
Ögren, P., Leonard, N.: A tractable convergent dynamic window approach to obstacle avoidance. In: IEEE/RSJ IROS, Lausanne, Switzerland, vol. 1 (October 2002)
Press, W., et al.: Numerical Recipes in C. Cambridge University Press, Cambridge (1993)
Saad, Y.: Iterative Methods for Sparse Linear Systems. Society for Industrial and Applied Mathematics. Philadelphia, PA, USA (2003)
Zhang, B., Sukhatme, G.S.: Controlling sensor density using mobility. In: The Second IEEE Workshop on Embedded Networked Sensors, pp. 141–149 (May 2005)
Zhang, F., Goldgeier, M., Krishnaprasad, P.S.: Control of small formations using shape coordinates. In: Proc. IEEE Int. Conf. Robot. Automat., Taipei, vol. 2 (September 2003)
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Derenick, J.C., Mansley, C.R., Spletzer, J.R. (2008). Efficient Motion Planning Strategies for Large-Scale Sensor Networks. In: Akella, S., Amato, N.M., Huang, W.H., Mishra, B. (eds) Algorithmic Foundation of Robotics VII. Springer Tracts in Advanced Robotics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68405-3_28
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DOI: https://doi.org/10.1007/978-3-540-68405-3_28
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