Article Outline
Glossary
Definition of the Subject
Introduction
Distributed Algorithms on Networks of Processors
Distributed Algorithms for Robotic Networks
Bibliographical Notes
Future Directions
Acknowledgments
Bibliography
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note that the description of the LCR algorithm given here is slightly different from the classic one as presented in [57].
Abbreviations
- Cooperative control :
-
In recent years, the study of groups of robots and multi-agent systems has received a lot of attention. This interest has been driven by the envisioned applications of these systems in scientific and commercial domains. From a systems and control theoretic perspective, the challenges in cooperative control revolve around the analysis and design of distributed coordination algorithms that integrate the individual capabilities of the agents to achieve a desired coordination task.
- Distributed algorithm :
-
In a network composed of multiple agents, a coordination algorithm specifies a set of instructions for each agent that prescribe what to sense, what to communicate and to whom, how to process the information received, and how to move and interact with the environment. In order to be scalable, coordination algorithms need to rely as much as possible on local interactions between neighboring agents.
- Complexity measures :
-
Coordination algorithms are designed to enable networks of agents achieve a desired task. Since different algorithms can be designed to achieve the same task, performance metrics are necessary to classify them. Complexity measures provide a way to characterize the properties of coordination algorithms such as completion time, cost of communication, energy consumption, and memory requirements.
- Averaging algorithms :
-
Distributed coordination algorithms that perform weighted averages of the information received from neighboring agents are called averaging algorithms. Under suitable connectivity assumptions on the communication topology, averaging algorithms achieve agreement, i. e., the state of all agents approaches the same value. In certain cases, the agreement value can be explicitly determined as a function of the initial state of all agents.
- Leader election :
-
In leader election problems, the objective of a network of processors is to elect a leader. All processors have a variable “leader” initially set to unknown. The leader‐election task is solved when only one processor has set the variable “leader” to true, and all other processors have set it to false.
- LCR algorithm :
-
The classic Le Lann–Chang–Roberts (LCR) algorithm solves the leader election task on a static network with the ring communication topology. Initially, each agent transmits its unique identifier to its neighbors. At each communication round, each agent compares the largest identifier received from other agents with its own identifier. If the received identifier is larger than its own, the agent declares itself a non‐leader, and transmits it in the next communication round to its neighbors. If the received identifier is smaller than its own, the agent does nothing. Finally, if the received identifier is equal to its own, it declares itself a leader. The LCR algorithm achieves leader election with linear time complexity and quadratic total communication complexity, respectively.
- Agree‐and‐pursue algorithm :
-
Coordination algorithms for robotic networks combine the features of distributed algorithms for networks of processors with the sensing and control capabilities of the robots. The agree‐and‐pursue motion coordination algorithm is an example of this fusion. Multiple robotic agents moving on a circle seek to agree on a common direction of motion while at the same achieving an equally‐spaced distribution along the circle. The agree‐and‐pursue algorithm achieves both tasks combining ideas from leader election on a changing communication topology with basic control primitives such as “follow your closest neighbor in your direction of motion.”
Bibliography
Alighanbari M, How JP (2006) Robust decentralized task assignment for cooperative UAVs. In: AIAA conference on guidance, navigation and control, Keystone, CO, August 2006
Ando H, Oasa Y, Suzuki I, Yamashita M (1999) Distributed memoryless point convergence algorithm for mobile robots with limited visibility. Trans IEEE Robotics Autom 15(5):818–828
Angeli D, Bliman PA (2006) Stability of leaderless discrete‐time multi-agent systems. Math Control Signal Syst 18(4):293–322
Arai T, Pagello E, Parker LE (2002) Guest editorial: Advances in multirobot systems. Trans IEEE Robotics Autom 18(5):655–661
Arkin RC (1998) Behavior‐Based Robotics. MIT Press, Cambridge, MA
Arslan G, Marden JR, Shamma JS (2007) Autonomous vehicle‐target assignment: A game theoretic formulation. J ASME Dyn Syst Meas Control 129(5):584–596
Barlow GW (1974) Hexagonal territories. Anim Behav 22:876–878
Bauso D, Giarré L, Pesenti R (2006) Nonlinear protocols for optimal distributed consensus in networks of dynamic agents. Syst Control Lett 55(11):918–928
Belta C, Kumar V (2004) Abstraction and control for groups of robots. Trans IEEE Robotics 20(5):865–875
Bertsekas DP, Castañón DA (1991) Parallel synchronous and asynchronous implementations of the auction algorithm. Parallel Comput 17:707–732
Bertsekas DP, Castañón DA (1993) Parallel primal‐dual methods for the minimum cost flow problem. Comput Optim Appl 2(4):317–336
Blondel VD, Hendrickx JM, Olshevsky A, Tsitsiklis JN (2005) Convergence in multiagent coordination, consensus, and flocking. In: IEEE conference on decision and control and european control conference, Seville, Spain, December 2005, pp 2996–3000
Boinski S, Campbell AF (1995) Use of trill vocalizations to coordinate troop movement among whitefaced capuchins – a 2nd field-test. Behaviour 132:875–901
Bruckstein AM, Cohen N, Efrat A (1991) Ants, crickets, and frogs in cyclic pursuit. Technical Report CIS 9105, Center for Intelligent Systems, Technion, Haifa, Israel. http://www.cs.technion.ac.il/tech-reports
Bullo F (2006) Notes on multi-agent motion coordination: Models and algorithms. In: Antsaklis PJ, Tabuada P (eds) Network Embedded Sensing and Control, Proceedings of NESC'05 Worskhop. Lecture Notes in Control and Information Sciences, vol 331. Springer, New York, pp 3–8
Cao M, Morse AS, Anderson BDO (2008) Reaching a consensus in a dynamically changing environment – convergence rates, measurement delays and asynchronous events. J SIAM Control Optim 47(2):601–623
Carli R, Fagnani F, Speranzon A, Zampieri S (2008) Communication constraints in the average consensus problem. Automatica 44(3):671–684
Castañón DA, Wu C (2003) Distributed algorithms for dynamic reassignment. In: IEEE conference on decision and control. Maui, HI, December 2003, pp 13–18
Chatterjee S, Seneta E (1977) Towards consensus: Some convergence theorems on repeated averaging. J Appl Probab 14(1):89–97
Cogburn R (1984) The ergodic theory of Markov chains in random environments. Z Wahrscheinlichkeitstheorie Geb 66(1):109–128
Conradt L, Roper TJ (2003) Group decision‐making in animals. Nature 421(6919):155–158
Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to Algorithms, 2nd edn. Press MIT, Cambridge, MA
Cortés J (2008) Distributed algorithms for reaching consensus on general functions. Automatica 44(3):726–737
Cortés J, Bullo F (2005) Coordination and geometric optimization via distributed dynamical systems. J SIAM Control Optim 44(5):1543–1574
Cortés J, Martínez S, Bullo F (2005) Spatially‐distributed coverage optimization and control with limited‐range interactions. Control ESAIM Optim Calc Var 11:691–719
Cortés J, Martínez S, Bullo F (2006) Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. Trans IEEE Autom Control 51(8):1289–1298
Cortés J, Martínez S, Karatas T, Bullo F (2004) Coverage control for mobile sensing networks. IEEE Trans Autom Control 20(2):243–255
Couzin ID, Krause J, Franks NR, Levin SA (2005) Effective leadership and decision‐making in animal groups on the move. Nature 433:513–51
Cybenko G (1989) Dynamic load balancing for distributed memory multiprocessors. J Parallel Distrib Comput 7:279–301
DeGroot MH (1974) Reaching a consensus. J Am Stat Assoc 69(345):118–121
Ferrari‐Trecate G, Buffa A, Gati M (2006) Analysis of coordination in multi-agent systems through partial difference equations. IEEE Trans Autom Control 51(6):1058–1063
Flocchini P, Prencipe G, Santoro N, Widmayer P (2005) Gathering of asynchronous oblivious robots with limited visibility. Theor Comput Sci 337(1–3):147–168
Frazzoli E, Bullo F (2004) Decentralized algorithms for vehicle routing in a stochastic time‐varying environment. In: IEEE conference on decision and control. Paradise Island, Bahamas, December 2004. pp 3357–3363
Freeman RA, Yang P, Lynch KM (2006) Stability and convergence properties of dynamic average consensus estimators. In: IEEE conference on decision and control. San Diego, CA, December 2006, pp 398–403
Gallager RG (1968) Information Theory and Reliable Communication. Wiley, New York
Ganguli A, Cortés J, Bullo F (2005) On rendezvous for visually‐guided agents in a nonconvex polygon. In: IEEE conference on decision and control and european control conference, Seville, December 2005, pp 5686–5691
Ganguli A, Cortés J, Bullo F (2006) Distributed deployment of asynchronous guards in art galleries. In: American control conference, Minneapolis, June 2006, pp 1416–1421
Gazi V, Passino KM (2003) Stability analysis of swarms. IEEE Trans Autom Control 48(4):692–697
Gerkey BP, Mataric MJ (2004) A formal analysis and taxonomy of task allocation in multi-robot systems. Int J Robotics Res 23(9):939–954
Godwin MF, Spry S, Hedrick JK (2006) Distributed collaboration with limited communication using mission state estimates. In: American control conference. Minneapolis, MN, June 2006, pp 2040–2046
Gueron S, Levin SA (1993) Self‐organization of front patterns in large wildebeest herds. J Theor Bio 165:541–552
Gupta P, Kumar PR (2000) The capacity of wireless networks. Trans IEEE Inf Theory 46(2):388–404
Hatano Y, Mesbahi M (2005) Agreement over random networks. Trans IEEE Autom Control 50:1867–1872
Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge, UK
Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. Trans IEEE Autom Control 48(6):988–1001
Justh EW, Krishnaprasad PS (2004) Equilibria and steering laws for planar formations. Syst Control Lett 52(1):25–38
Kashyap A, Başar T, Srikant R (2007) Quantized consensus. Automatica 43(7):1192–1203
Klavins E (2003) Communication complexity of multi-robot systems. In: Boissonnat JD, Burdick JW, Goldberg K, Hutchinson S (eds) Algorithmic foundations of robotics V, vol 7. Springer tracts in advanced robotics. Springer, Berlin
Klavins E, Ghrist R, Lipsky D (2006) A grammatical approach to self‐organizing robotic systems. Trans IEEE Autom Control 51(6):949–962
Klavins E, Murray RM (2004) Distributed algorithms for cooperative control. Pervasive IEEE Comput 3(1):56–65
Landau HJ, Odlyzko AM (1981) Bounds for eigenvalues of certain stochastic matrices. Linear Algebra Appl 38:5–15
Lin J, Morse AS, Anderson BDO (2004) The multi-agent rendezvous problem: An extended summary. In: Kumar V, Leonard NE, Morse AS (eds) Proceedings of the 2003 block island workshop on cooperative control, ser. Lecture notes in control and information sciences, vol 309. Springer, New York, pp 257–282
Lin Z, Broucke M, Francis B (2004) Local control strategies for groups of mobile autonomous agents. IEEE Trans Autom Control 49(4):622–629
Lin Z, Francis B, Maggiore M (2005) Necessary and sufficient graphical conditions for formation control of unicycles. Trans IEEE Autom Control 50(1):121–127
Lin Z, Francis B, Maggiore M (2007) State agreement for continuous‐time coupled nonlinear systems. J SIAM Control Optim 46(1):288–307
Lumelsky VJ, Harinarayan KR (1997) Decentralized motion planning for multiple mobile robots: the cocktail party model. Auton Robots 4(1):121–135
Lynch NA (1997) Distributed algorithms. Morgan Kaufmann Publishers, San Mateo, CA
Marshall JA, Broucke ME, Francis BA (2004) Formations of vehicles in cyclic pursuit. Trans IEEE Autom Control 49(11):1963–1974
Martínez S, Bullo F, Cortés J, Frazzoli E (2007) On synchronous robotic networks – Part I: Models, tasks and complexity. Trans IEEE Autom Control 52(12):2199–2213
Martinez S, Bullo F, Cortés J, Frazzoli E (2007) On synchronous robotic networks – Part II: Time complexity of rendezvous and deployment algorithms. Trans IEEE Autom Control 52(12):2214–2226
Martínez S, Cortés J, Bullo F (2007) Motion coordination with distributed information. Control IEEE Syst Mag 27(4):75–88
Miller MB, Bassler BL (2001) Quorum sensing in bacteria. Annu Rev Microbiol 55:165–199
Moore BJ, Passino KM (2007) Distributed task assignment for mobile agents. Trans IEEE Autom Control 52(4):749–753
Moreau L (2004) Stability of continuous‐time distributed consensus algorithms, Preprint. Available at http://xxx.arxiv.org/math.OC/0409010
Moreau L (2005) Stability of multiagent systems with time‐dependent communication links. Trans IEEE Autom Control 50(2):169–182
Okubo A (1986) Dynamical aspects of animal grouping: swarms, schools, flocks and herds. Advances in Biophysics 22:1–94
Olfati‐Saber R (2006) Flocking for multi-agent dynamic systems: Algorithms and theory. Trans IEEE Autom Control 51(3):401–420
Olfati‐Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233
Olfati‐Saber R, Franco E, Frazzoli E, Shamma JS (2006) Belief consensus and distributed hypothesis testing in sensor networks. In: Antsaklis PJ, Tabuada P (eds) Network embedded sensing and control. Proceedings of NESC'05 worskhop. Lecture notes in control and information sciences, vol 331. Springer, New York, pp 169–182
Olfati‐Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time‐delays. Trans IEEE Autom Control 49(9):1520–1533
Olshevsky A, Tsitsiklis JN (2007) Convergence speed in distributed consensus and averaging. J SIAM Control Optim
Parrish JK, Viscido SV, Grunbaum D (2002) Self‐organized fish schools: an examination of emergent properties. Biol Bull 202:296–305
Pavone M, Frazzoli E, Bullo F (2007) Decentralized algorithms for stochastic and dynamic vehicle routing with general target distribution. In: IEEE conference on decision and control, New Orleans, LA, December 2007, pp 4869–4874
Peleg D (2000) Distributed computing. A locality‐sensitive approach. Monographs on discrete mathematics and applications. SIAM, Philadelphia, PA
P Ögren, Fiorelli E, Leonard NE (2004) Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment. Trans IEEE Autom Control 49(8):1292–1302
Rathinam S, Sengupta R, Darbha S (2007) A resource allocation algorithm for multi‐vehicle systems with non holonomic constraints. Trans IEEE Autom Sci Eng 4(1):98–104
Ren W, Beard RW (2005) Consensus seeking in multi-agent systems under dynamically changing interaction topologies. Trans IEEE Autom Control 50(5):655–661
Ren W, Beard RW, Atkins EM (2007) Information consensus in multivehicle cooperative control: Collective group behavior through local interaction. Control IEEE Syst Mag 27(2):71–82
Santoro N (2001) Distributed computations by autonomous mobile robots. In: Pacholski L, Ruzicka P (eds) SOFSEM 2001: Conference on current trends in theory and practice of informatics (Piestany, Slovak Republic). Lecture notes in computer science, vol 2234. Springer, New York, pp 110–115
Savkin AV (2004) Coordinated collective motion of groups of autonomous mobile robots: Analysis of Vicsek's model. Trans IEEE Autom Control 49(6):981–982
Savla K, Bullo F, Frazzoli E (2007) Traveling Salesperson Problems for a double integrator. Trans IEEE Autom Control, To appear
Savla K, Frazzoli E, Bullo F (2008) Traveling Salesperson Problems for the Dubins vehicle. Trans IEEE Autom Control 53(9) To appear
Savla K, Notarstefano G, Bullo F (2007) Maintaining limited‐range connectivity among second‐order agents. J SIAM Control Optim, To appear
Schumacher C, Chandler PR, Rasmussen SJ, Walker D (2003) Task allocation for wide area search munitions with variable path length. In: American control conference, Denver, CO, pp 3472–3477
Seeley TD, Buhrman SC (1999) Group decision‐making in swarms of honey bees. Behav Eco Sociobiol 45:19–31
Sepulchre R, Paley D, Leonard NE (2007) Stabilization of planar collective motion: All-to-all communication. Trans IEEE Autom Control 52:811–824
Sharma V, Savchenko M, Frazzoli E, Voulgaris P (2005) Time complexity of sensor‐based vehicle routing. In: Thrun S, Sukhatme G, Schaal S, Brock O (eds) Robotics: Science and systems. Press MIT, Cambridge, MA, pp 297–304
Sharma V, Savchenko M, Frazzoli E, Voulgaris P (2007) Transfer time complexity of conflict‐free vehicle routing with no communications. Int J Robotics Res 26(3):255–272
Sinclair AR (1977) The african buffalo, study a of resource limitation of population. The University of Chicago Press, Chicago, IL
Smith SL, Broucke ME, Francis BA (2005) A hierarchical cyclic pursuit scheme for vehicle networks. Automatica 41(6):1045–1053
Smith SL, Bullo F (2007) Monotonic target assignment for robotic networks. Trans IEEE Autom Control, Submitted, To appear
Spanos DP, Olfati‐Saber R, Murray RM (2005) Approximate distributed Kalman filtering in sensor networks with quantifiable performance. In: Symposium on information processing of sensor networks (IPSN). Los Angeles, CA, April 2005. pp 133–139
Stewart KJ, Harcourt AH (1994) Gorillas vocalizations during rest periods – signals of impending departure. Behaviour 130:29–40
Suzuki I, Yamashita M (1999) Distributed anonymous mobile robots: Formation of geometric patterns. J SIAM Comput 28(4):1347–1363
Tahbaz‐Salehi A, Jadbabaie A (2008) Consensus over random networks. Trans IEEE Autom Control 53(3):791–795
Tanner HG, Jadbabaie A, Pappas GJ (2007) Flocking in fixed and switching networks. Trans IEEE Autom Control 52(5):863–868
Tsitsiklis JN (1984) Problems in decentralized decision making and computation. Dissertation, Laboratory for Information and Decision Systems, MIT, Nov. Technical Report LIDS-TH-1424
Tsitsiklis JN, Bertsekas DP, Athans M (1986) Distributed asynchronous deterministic and stochastic gradient optimization algorithms. Trans IEEE Autom Control 31(9):803–812
Uny Y Cao, Fukunaga AS, Kahng A (1997) Cooperative mobile robotics: Antecedents and directions. Auton Robots 4(1):7–27
Wu CW (2006) Synchronization and convergence of linear dynamics in random directed networks. Trans IEEE Autom Control 51(7):1207–1210
Xiao L, Boyd S, Lall S (2005) A scheme for asynchronous distributed sensor fusion based on average consensus. In: Symposium on information processing of sensor networks (IPSN). Los Angeles, CA, April 2005. pp 63–70
Zavlanos M, Pappas G (2007) Dynamic assignment in distributed motion planning with local information. In: American control conference. New York, July 2007, pp 1173–1178
Zavlanos MM, Pappas GJ (2005) Controlling connectivity of dynamic graphs. In: IEEE conference on decision and control and european control conference. Seville, Spain, December 2005, pp 6388–6393
Acknowledgments
This material is based upon work supported in part by NSF CAREER Award CMS‐0643679, NSF CAREER Award ECS‐0546871, and AFOSR MURI Award FA9550-07-1-0528.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag
About this entry
Cite this entry
Bullo, F., Cortés, J., Martínez, S. (2012). Robotic Networks, Distributed Algorithms for. In: Meyers, R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1806-1_94
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1806-1_94
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1805-4
Online ISBN: 978-1-4614-1806-1
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering