Control of a team of mobile robots based on non-cooperative equilibria with partial coordination

Krzysztof Skrzypczyk

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 1, page 89-97
  • ISSN: 1641-876X

Abstract

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In this work we present an application of the concept of non-cooperative game equilibria to the design of a collision free movement of a team of mobile robots in a dynamic environment. We propose the solution to the problem of feasible control synthesis, based on a partially centralized sensory system. The control strategy based on the concept of non-cooperative game equilibria is well known in the literature. It is highly efficient through phases where the solution is unique. However, even in simple navigation problems, it happens that multiple equilibria occur, which incurs a problem for control synthesis and may lead to erroneous results. In this paper we present a solution to this problem based on the partial centralization idea. The coordinator module is incorporated into the system and becomes active when multiple equilibria are detected. The coordination method includes a 'fair arbiter' for the selection of an appropriate equilibrium solution. Simulation studies of the proposed methodology were carried out for 2, 3 and 5 robots, and their results are presented.

How to cite

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Skrzypczyk, Krzysztof. "Control of a team of mobile robots based on non-cooperative equilibria with partial coordination." International Journal of Applied Mathematics and Computer Science 15.1 (2005): 89-97. <http://eudml.org/doc/207731>.

@article{Skrzypczyk2005,
abstract = {In this work we present an application of the concept of non-cooperative game equilibria to the design of a collision free movement of a team of mobile robots in a dynamic environment. We propose the solution to the problem of feasible control synthesis, based on a partially centralized sensory system. The control strategy based on the concept of non-cooperative game equilibria is well known in the literature. It is highly efficient through phases where the solution is unique. However, even in simple navigation problems, it happens that multiple equilibria occur, which incurs a problem for control synthesis and may lead to erroneous results. In this paper we present a solution to this problem based on the partial centralization idea. The coordinator module is incorporated into the system and becomes active when multiple equilibria are detected. The coordination method includes a 'fair arbiter' for the selection of an appropriate equilibrium solution. Simulation studies of the proposed methodology were carried out for 2, 3 and 5 robots, and their results are presented.},
author = {Skrzypczyk, Krzysztof},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {motion planning; game theory; multi-robot systems},
language = {eng},
number = {1},
pages = {89-97},
title = {Control of a team of mobile robots based on non-cooperative equilibria with partial coordination},
url = {http://eudml.org/doc/207731},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Skrzypczyk, Krzysztof
TI - Control of a team of mobile robots based on non-cooperative equilibria with partial coordination
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 1
SP - 89
EP - 97
AB - In this work we present an application of the concept of non-cooperative game equilibria to the design of a collision free movement of a team of mobile robots in a dynamic environment. We propose the solution to the problem of feasible control synthesis, based on a partially centralized sensory system. The control strategy based on the concept of non-cooperative game equilibria is well known in the literature. It is highly efficient through phases where the solution is unique. However, even in simple navigation problems, it happens that multiple equilibria occur, which incurs a problem for control synthesis and may lead to erroneous results. In this paper we present a solution to this problem based on the partial centralization idea. The coordinator module is incorporated into the system and becomes active when multiple equilibria are detected. The coordination method includes a 'fair arbiter' for the selection of an appropriate equilibrium solution. Simulation studies of the proposed methodology were carried out for 2, 3 and 5 robots, and their results are presented.
LA - eng
KW - motion planning; game theory; multi-robot systems
UR - http://eudml.org/doc/207731
ER -

References

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  8. Koren Y. and Borenstein J: (1991): Potential Field Methods and their Inherent Limitations for Mobile Robot Navigation. - Proc. IEEE Conf. Robotics and Automation, Sacramento, CA, pp. 1398-1404. 
  9. LaValle S. (2000): Robot motion planning: A game-theoretic foundation. - Algorithmica, Vol. 26, No. 3, pp. 430-465. Zbl0993.93028
  10. Li Q. and Payandeh S. (2001): On coordination of robotic agents based on game theory. -(private communication). 
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  12. Maynard Smith J. (1982): Evolution and the Theory of Games. -Cambridge: Cambridge University Press. 

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