The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Graph rigidity and distributed formation stabilization of multi-vehicle systems
Abstract
We provide a graph theoretical framework that allows us to formally define formations of multiple vehicles and the issues arising in uniqueness of graph realizations and its connection to stability of formations. The notion of graph rigidity is crucial in identifying the shape variables of a formation and an appropriate potential function associated with the formation. This allows formulation of meaningful optimization or nonlinear control problems for formation stabilization/tacking, in addition to formal representation of split, rejoin, and reconfiguration maneuvers for multi-vehicle formations. We introduce an algebra that consists of performing some basic operations on graphs which allow creation of larger rigid-by-construction graphs by combining smaller rigid subgraphs. This is particularly useful in performing and representing rejoin/split maneuvers of multiple formations in a distributed fashion.
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Citations
Cites
Information Flow and Cooperative Control of Vehicle Formations
Fax, J. A., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834433 · Cited by 4,579
Self-citation(1992) · Lecture Notes in Computer Science · doi:10.1007/bfb0022433 · Cited by 3,955
Exact robot navigation using artificial potential functions
Rimon, E., & Koditschek, D. E. (1992) · IEEE Transactions on Robotics and Automation · doi:10.1109/70.163777 · Cited by 1,835
Virtual leaders, artificial potentials and coordinated control of groups
Leonard, N. E., & Fiorelli, E. (2003) · Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) · doi:10.1109/cdc.2001.980728 · Cited by 1,262
On graphs and rigidity of plane skeletal structures
Laman, G. (1970) · Journal of Engineering Mathematics · doi:10.1007/bf01534980 · Cited by 1,043
DISTRIBUTED COOPERATIVE CONTROL OF MULTIPLE VEHICLE FORMATIONS USING STRUCTURAL POTENTIAL FUNCTIONS
Olfati-Saber, R., & Murray, R. M. (2002) · IFAC Proceedings Volumes · doi:10.3182/20020721-6-es-1901.00244 · Cited by 663
Self-citationAn Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game
Jacobs, D. J., & Hendrickson, B. (1997) · Journal of Computational Physics · doi:10.1006/jcph.1997.5809 · Cited by 388
Formation Flying Control of Multiple Spacecraft via Graphs, Matrix Inequalities, and Switching
Mesbahi, M., & Hadaegh, F. Y. (2001) · Journal of Guidance, Control, and Dynamics · doi:10.2514/2.4721 · Cited by 320
Graver, J., Servatius, B., & Servatius, H. (1993) · Graduate Studies in Mathematics · doi:10.1090/gsm/002 · Cited by 315
Almost all simply connected closed surfaces are rigid
Gluck, H. (1975) · Lecture Notes in Mathematics · doi:10.1007/bfb0066118 · Cited by 283
On Generic Rigidity in the Plane
Lovász, L., & Yemini, Y. (1982) · SIAM Journal on Algebraic Discrete Methods · doi:10.1137/0603009 · Cited by 271
INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS
Fax, J. A., & Murray, R. M. (2002) · IFAC Proceedings Volumes · doi:10.3182/20020721-6-es-1901.00100 · Cited by 195
Self-citationRoth, B. (1981) · The American Mathematical Monthly · doi:10.1080/00029890.1981.11995175 · Cited by 164
Cited by
Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788
Self-citationConsensus and Cooperation in Networked Multi-Agent Systems
Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2006.887293 · Cited by 10,522
Self-citationCoverage Control for Mobile Sensing Networks
Cortes, J., Martinez, S., Karatas, T., & Bullo, F. (2004) · IEEE Transactions on Robotics and Automation · doi:10.1109/tra.2004.824698 · Cited by 2,710
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms
Bullo, F., Cortés, J., & Martínez, S. (2009) · Princeton University Press eBooks · doi:10.1515/9781400831470 · Cited by 1,509
Consensus protocols for networks of dynamic agents
Saber, R. O., & Murray, R. M. (2004) · Proceedings of the 2003 American Control Conference, 2003. · doi:10.1109/acc.2003.1239709 · Cited by 901
Self-citation
Metadata
- Authors
- Olfati-Saber, R., & Murray, R. M.
- Venue
- Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
- Publisher
- IEEE
- Published
- 2003-08-27
- Volume
- 3
- Pages
- 2965-2971
- ISSN
- 0191-2216 (ISSN-L)
- OpenAlex
- W1483882723
- Cited by
- 368
- References
- 13
- FWCI
- 10.79
- Type
- conference paper
- Language
- en
- Open access
- closed
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