About

   Even though there has been an interest in controlling large-scale dynamical systems composed of multiple mobile agents for more than a decade, we are witnessing a surge of results in cooperative and formation control especially in the last several years. The framework of networked multi-agent systems has variety of applications such as air traffic control [7], intelligent highways [8], multiple robots carrying out cooperative tasks [9], coordinated control of satellites for earth observation [10], RoboCup Soccer [11], to cite but a few examples and references. The main reasons for this growth is due to the fact that formations can implement instruments which are unfeasible to implement monolithically.
   Furthermore, formation behaviors can also be found in nature during flocking and schooling which benefit the animals that use formation in various ways. Each animal in a heard, for instance, benefits by minimizing its encounter with predators [1].

Recent and future projects around the world

  1. EO-1 (Earth Observing), a land imaging satellite, maintained an almost exact orbit 1 minute behind Landsat 7 so that their images of the ground can be compared. Although both spacecraft were in the same orbit, roughly 700km overhead, their different shapes and masses made EO-1 to adjust its orbit from time to time, which was done using the help from the land station, i.e., the formation was a semi autonomous one [2].
  2. ST3 (Space Technology 3), developed by JPL, combines the images from two small telescopes flying in formation to produce images almost as good as those of a very expensive giant telescope.
  3. LISA, a giant interferometer built using spacecraft separated by distance by ESA, will look for ripples in space called gravity waves, which are produced when black holes collapse [3].
  4. TechSat 21, a set of three micro satellites flying in formation to operate as a "virtual satellite," is being developed by Air Force Research Laboratory (AFRL) [4].
  5. Orion-Emerald - first on-orbit demonstration of precise relative navigation using carrier phase differential GPS [12].

Challenges

   The agent (for example, a spacecraft) must be able to determine its state as well as the states of the other agents in the formation. They must be able to calculate their paths and decide whether they are drifting apart. If any adjustments are necessary, they must be able to work them out themselves.
   Even in the face of intermittent communication failures, the formation should still be stable to some extent.

Research abstract - Influence of the communication channel failure in the stability of the formation

   Real world multi-agent systems, especially the formations done in space, usually experience abrupt changes in their communication infrastructure due to a number of reasons such as component failure, solar wind, etc. In this research we take a system represented by a double integrator model [6] and derive stability conditions under intermittent communication collapses.
   We first analyzed the stability of the formation without communication channel collapses, where we introduced a Schur-like decomposition [5] technique and proved that a formation consisting of identical agents can be analyzed for stability by analyzing the stability of a single agent with the same dynamics modified only by the largest eigenvalue of the Laplacian matrix representing the interconnection.
   Then using the same decomposition technique, we derived conditions in the form of a linear matrix inequality for the formation to be second-moment stable (mean-square stable).
   Finally, through a simulation of 4 identical agents moving in a formation over a one dimensional space we showed the validity of our derived results.

Future work

   We are interested in deriving conditions for stability under variable channel collapse probability, for example, the channel collapse probability being an increasing function of the relative distance, which is a much realistic case.
   We are also interested in deriving conditions for stability under the presence of time delay in the communication network.

Reference

  1. Hand book of behavioral neurobiology, vol. 3- Social behavior and communication 354-382
  2. New Scientist - 25 September 1999 - Catherine Zandonella
  3. http://www.esa.int/esaCP/index.html
  4. TECHSAT 21 AND REVOLUTIONIZING SPACE MISSIONS USING MICRO SATELLITES -Maurice Martin, Steve Kilberg
  5. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Trans. Autom. Contr., vol. 49, no. 9, pp. 1495-1476, 2005.
  6. T. Hayakawa, T. Matsuzawa, and S. Hara "Formation control of multi-agent systems with sampled information"
  7. C. Tomlin, G. Pappas, and S. Sastry, "Conflict resolution for air traffic management: a study in multiagent hybrid systems," IEEE Trans. Autom. Contr., vol. 43, no. 4, pp. 509-521, 1998.
  8. J. Z. Hernandez, S. Ossowski, and A. Garcia-Serrano, "Multiagent architectures for intelligent traffic management systems," Transportation Research Part C: Emerging Technologies, vol. 10, no. 5-6, pp. 473-506, 2002.
  9. E. Pagello, A. DfAngeloc, F. Monteselloa, F. Garellia, and C. Ferraria, "Cooperative behaviors in multi-robot systems through implicit communication," Robotics and Autonomous Systems, vol. 29, no. 1, pp. 65-77, 1999.
  10. P. Silvestrin, "Control and navigation aspects of the new Earth observation missions of the European Space Agency," Annual Reviews in Control, vol. 29, no. 2, pp. 247-260, 2005.
  11. RoboCup Official Site, http://www.robocup.org/
  12. P. Ferguson, F. Busse, B. Engberg, J. How, M. Tillerson, N. Pohlman, A. Richards, and R. Twiggs, "formation flying experiments on the orion-emerald mission," AIAA Space 2001 Conference and Exposition - Albuquerque, New Mexico, August 28 - 30, 2001.

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