Brief paper: A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems

Authors:
Dimos V. Dimarogonas;Kostas J. Kyriakopoulos
Affiliations:
Automatic Control Lab., School of Electrical Eng., Royal Institute of Technology, SE-100 44, Stockholm, Sweden;Control Systems Laboratory, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou 15780, Greece
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

In this paper, a feedback control strategy that achieves convergence of a multi-agent system to a desired formation configuration is proposed for both the cases of agents with single integrator and nonholonomic unicycle-type kinematics. When inter-agent objectives that specify the desired formation cannot occur simultaneously in the state space the desired formation is infeasible. It is shown that under certain assumptions, formation infeasibility forces the agents' velocity vectors to a common value at steady state. This provides a connection between formation infeasibility and flocking behavior for the multi-agent system. We finally also obtain an analytic expression of the common velocity vector in the case of formation infeasibility.