Abstract
This paper addresses the problem of controlling a large number of robots required to accomplish a task as a group. We propose an abstraction based on the definition of a map from the configuration space of the robots to a lower dimensional manifold, whose dimension does not scale with the number of robots. The task to be accomplished by the team suggests a natural feedback control system on the group manifold. We show that, if mean and covariance matrix are chosen as group variables for fully actuated robots, it is possible to design decoupling control laws, i.e., the feedback control for a robot is only dependent on the state of the robot and the state of the group, therefore the communication necessary to accomplish the task is kept to a minimum.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Belta C., Kumar V. (2002) Trajectory design for formations of robots by kinetic energy shaping. In: IEEE International Conference on Robotics and Automation, Washington, DC, 2002
Desai J., Ostrowski J.P., Kumar V. (1998) Controlling formations of multiple mobile robots. In: Proc. IEEE Int. Conf. Robot. Automat., Leuven, Belgium, May, 1998. 2864–2869
Eren T., Belhumeur P.N., Morse A.S. (2002) Closing ranks in vehicle formations based rigidity. In: IEEE Conference on Decision and Control, Las Vegas, NV, December, 2002
Isidori A. (1995) Nonlinear Control Systems, 3rd edn. Springer-Verlag, London
Leonard N.E., Fiorelli E. (2001) Virtual leaders, artificial potentials, and coordinated control of groups. In: 40th IEEE Conference on Decision and Control, Orlando, FL, December, 2001. 2968–2973
Ogren P., Fiorelli E., Leonard N.E. (2002) Formations with a mission: stable coordination of vehicle group maneuvers. In: Proc. Symp. on Mathematical Theory of Networks and Systems, Notre Dame, IN, August, 2002
Olfati-Saber R., Murray R.M. (2002) Distributed cooperative control of multiple vehicle formations using structural potential functions. In: IFAC World Congress, Barcelona, Spain, July, 2002
Tabuada P., Pappas G.J., Lima P. (2001) Feasible formations of multi-agent systems. In: American Control Conference, Arlington, VA, June, 2001
Tanner H., Pappas G.J., Kumar V. (2002) Input-to-state stability on formation graphs. In: Proceedings of the IEEE International Conference on Decision and Control, Las Vegas, NV, December, 2002
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Belta, C., Kumar, V. (2003). Towards Abstraction and Control for Large Groups of Robots. In: Bicchi, A., Prattichizzo, D., Christensen, H.I. (eds) Control Problems in Robotics. Springer Tracts in Advanced Robotics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36224-X_11
Download citation
DOI: https://doi.org/10.1007/3-540-36224-X_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00251-2
Online ISBN: 978-3-540-36224-1
eBook Packages: Springer Book Archive