Hostname: page-component-55f67697df-zpzq9 Total loading time: 0 Render date: 2025-05-09T15:56:34.598Z Has data issue: false hasContentIssue false
  • English
  • Français

Decentralized controllers for shape generation with robotic swarms

Published online by Cambridge University Press:  01 September 2008

M. Ani Hsieh ,
Vijay Kumar  and
Luiz Chaimowicz
M. Ani Hsieh*
Affiliation:
GRASP Laboratory, University of Pennsylvania
Vijay Kumar
Affiliation:
GRASP Laboratory, University of Pennsylvania
Luiz Chaimowicz
Affiliation:
Computer Science Department, Universidade Federal de Minas Gerais
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

We address the synthesis of controllers for a swarm of robots to generate a desired two-dimensional geometric pattern specified by a simple closed planar curve with local interactions for avoiding collisions or maintaining specified relative distance constraints. The controllers are decentralized in the sense that the robots do not need to exchange or know each other's state information. Instead, we assume that the robots have sensors allowing them to obtain information about relative positions of neighbors within a known range. We establish stability and convergence properties of the controllers for a certain class of simple closed curves. We illustrate our approach through simulations and consider extensions to more general planar curves.

Keywords

robot swarmsdecentralised controlmotion planning
Type
Article
Information
Robotica , Volume 26 , Issue 5 , September 2008 , pp. 691 - 701
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Britton, N. F., Franks, N. R., Pratt, S. C. and Seeley, T. D., “Deciding on a New Home: How Do Honeybees Agree?,” Proceeding of Royal Society of London B, vol. 269, 2002, pp. 1383–1388.CrossRefGoogle ScholarPubMed
2.Pratt, S. C., “Quorum sensing by encounter rates in the ant temnothorax albipennis,” Behav. Ecolo. 16 (2), (2005) pp. 448–496.Google Scholar
3.Couzin, I. D., Krause, J., James, R., Ruxton, G. D. and Franks, N. R., “Collective memory and spatial sorting in animal groups,” J. Theo. Bio. 218, (2002) pp. 1–11.CrossRefGoogle ScholarPubMed
4.Parrish, J. K., Viscido, S. V. and Grunbaum, D., “Self-organized fish schools: An examination of emergent properties,” Biol. Bull. 202, (2002) pp. 296–305.CrossRefGoogle ScholarPubMed
5.Reynolds, C. W., “Flocks, Herds and Schools: A Distributed Behavioral Model,” Proceedings of the 14th annual conference on Computer Graphics (SIGGRAPH'87), (ACM Press, 1987), Baltimore, Maryland, USA pp. 25–34.CrossRefGoogle Scholar
6.Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I. and Shochet, O., “Novel type of phase transition in a system of self-driven particles,” Phys. Rev. Lett. 75 (6), 1226–1229 (1995).CrossRefGoogle Scholar
7.Jadbabaie, A., Lin, J. and Morse, A., “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Trans. Autom. Control, July 2003 48 (6), pp. 988–1001.CrossRefGoogle Scholar
8.Tanner, H. G., Jadbabaie, A. and Pappas, G. J., “Flocking in fixed and switching networks,” Trans. Autom. Control 52 (5), 863–868 (2007).CrossRefGoogle Scholar
9.Albayrak, O., Line and Circle Formation of Distributed Autonomous Mobile Robots with Limited Sensor Range (PhD thesis, Naval Postgraduate School, Monterey, CA, 1996).Google Scholar
10.Suzuki, I. and Yamashita, M., “Distributed anonymous mobile robots: Formation of geometric patterns,” SIAM J. Comput. 28 (4), 1347–1363 (1999).CrossRefGoogle Scholar
11.Desai, J. P., Ostrowski, J. P. and Kumar, V., “Modeling and control of formations of nonholonomic mobile robots,” IEEE Trans. Robot. Autom. 17 (6), 905–908 (2001).CrossRefGoogle Scholar
12.Fierro, R., Song, P., Das, A. and Kumar, V., “Cooperative control of robot formations,” Cooperative Control and Optimization: Series on Applied Optimization (Murphey, R. and Paradalos, P., eds.) (Kluwer Academic Press, 2002) pp. 79–93.Google Scholar
13.Tanner, H. G. and Kumar, A., Formation Stabilization of Multiple Agents Using Decentralized Navigation Functions. (MIT Press, 2005).CrossRefGoogle Scholar
14.Loizou, S. G. and Kyriakopoulos, K. J., “A feedback based multiagent navigation framework,” Int. J. Syst. Sci. 37 (6), 377–384 (2006).CrossRefGoogle Scholar
15.Ogren, P., Fiorelli, E. and Leonard, N. E., “Formations with a Mission: Stable Coordination of Vehicle Group Maneuvers,” Proceedings of 15th International Symposium on Mathematical Theory of Networks and Systems, Notre Dame, Illinois, USA (Aug. 2002) pp. 267–278.Google Scholar
16.Song, P. and Kumar, V., “A Potential Field Based Approach to Multi-Robot Manipulation,” Proceedings of IEEE International Conference on Robotics and Automation, Washington, DC (May 2002) pp. 1217–1222.Google Scholar
17.Pereira, G. A. S., Kumar, V., and Campos, M. F. M., “Decentralized algorithms for multi-robot manipulation via caging,” Int. J. Robot. Res. (IJRR), July-August 2004 23, pp. 783–795.CrossRefGoogle Scholar
18.Chaimowicz, L., Michael, N. and Kumar, V., “Controlling Swarms of Robots Using Interpolated Implicit Functions,” Proceedings of the 2005 International Conference on Robotics and Automation (ICRA05), Barcelona, Spain, (2005) pp. 2487–2492.Google Scholar
19.Correll, N., Rutishauser, S. and Martinoli, A., “Comparing Coordination Schemes for Miniature Robotic Swarms: A Case Study in Boundary Coverage of Regular Structures,” Proceedings of 10th International Symposium on Experimental Robotics (ISER) 2006, Rio de Janeiro, Brazil, (2006) pp. 471–480.Google Scholar
20.Correll, N. and Martinoli, A., “System Identification of Self-Organizing Robotic Swarms,” Proceedings of 8th Int. Symposium on Distributed Autonomous Robotic Systems (DARS) 2006, Rio de Janeiro, Brazil (2006) pp. 31–40.Google Scholar
21.Sepulchre, R., Paley, D., and Leonard, N. E., “Stabilization of planar collective motion, part 1. All-to-all communication,” IEEE Trans. Autom. Control 52 (5)811–824 (2005).Google Scholar
22.Paley, D., Leonard, N. E. and Sepulchre, R. J., “Collective Motion of Self-Propelled Particles: Stabilizing Symmetric Formations on Closed Curves,” Proceedings of the 45th IEEE Conference on Decision and Control (Submitted), San Diego, CA, (2006) pp. 5067–5072.Google Scholar
23.Zhang, F. and Leonard, N. E., “Coordinated patterns of unit speed particles on a closed curve,” Syst. Control Lett. 56 (6), 397–407 (2007).CrossRefGoogle Scholar
24.Zhang, F., Fratantoni, D. M., Paley, D., Lund, J. and Leonard, N. E., “Control of coordinated patterns for ocean sampling,” Int. J. Control 80 (7), 1186–1199 (2007).CrossRefGoogle Scholar
25.Bertozzi, A., Kemp, M. and Marthaler, D., “Determining environmental boundaries: Asynchronous communication and physical scales,” Coop. Control, (2004) vol. 309, pp. 25–42.Google Scholar
26.Kerr, W. and Spears, D., “Robotic Simulation of Gases for a Surveillance Task,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2005, Edmonton, Alberta, Canada, (August 2005) pp. 2905–2910.CrossRefGoogle Scholar
27.Belta, C., Pereira, G. A. S. and Kumar, V., “Abstraction and Control of Swarms of Robots,” International Symposium of Robotics Research'03, Sienna, Italy, (2003) pp. 224–233.Google Scholar
28.Chaimowicz, L. and Kumar, V., “Aerial sheperds: Coordination Among Uavs and Swarms of Robots,” Proceedings of the 7th International Symposium on Distributed Autonomous Robotic Systems (DARS2004), Toulouse, France (2004) pp. 231–240.Google Scholar
29.Michael, N., Belta, C., and Kumar, V., “Controlling Three Dimensional Swarms of Robots,” Proceedings of IEEE International Conference on Robotics and Automation (ICRA) 2006, Orlando, FL (April 2006) pp. 964–969.Google Scholar
30.Zhang, F., Goldgeier, M., and Krishnaprasad, P. S., “Control of Small Formations Using Shape Coordinates,” Proceedings of of 2003 International Conference of Robotics and Automation, Taipei, Taiwan (2003) pp. 2510–2515.Google Scholar
31.Spletzer, J. and Fierro, R., “Optimal Positioning Strategies for Shape Changes in Robot Teams,” Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005) pp. 754–759.Google Scholar
32.Nabet, B. and Leonard, N. E., “Shape Control of a Multi-agent System Using Tensegrity Structures,” IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Nagoya, Japan (2006) pp. 329–339.Google Scholar
33.Hsieh, M. A. and Kumar, V., “Pattern Generation with Multiple Robots,” Proceedings of International Conference on Robotics and Automation (ICRA) 2006, Orlando, FL (Apr. 2006) pp. 2442–2447.Google Scholar
34.do Carmo, M. P., Differential Geometry of Curves and Surfaces, Upper Saddle River, New Jersey (Prentic-Hall Inc., 1976).Google Scholar
35.Rimon, E. and Koditschek, D. E., “Exact robot navigation using artificial potential functions,” IEEE Trans. Robot. Autom. 8, 501–518 (1992).CrossRefGoogle Scholar
36.Turk, G. and O'Brien, J. F., “Shape Transformation Using Variational Implicit Functions,” Proceedings of the 26th Annual Conference on Computer Graphics (SIGGRAPH 99), ACM Press/Addison-Wesley Publishing Co., Los Angeles, California, USA (1999) pp. 335–342.Google Scholar
37.Turk, G., Dinh, H. Q., O'Brien, J. F. and Yngve, G., “Implicit Surfaces That Interpolate,” Proceedings of the International Conference on Shape Modeling & Applications, IEEE Computer Society, Geneva, Italy (2001) pp. 62–73.Google Scholar