Controlling Dynamic Formations of Mobile Agents Governed by Euler-Lagrange Dynamics

This paper studies the problem of controlling dynamic formations of mobile agents governed by Euler-Lagrange dynamics. Here a formation is said to be dynamic if as time evolves, the desired formation undergoes translation, scaling and rotation. First, a constant-gain formation control algorithm is designed such that all agents can converge to the desired dynamic formation, in which the graphic information is needed for the selection of constant gains. Then, another fully distributed formation control algorithm is further proposed by employing variable-gain control techniques, which enables each agent to be independent of the knowledge of the overall interaction graph needed otherwise in the control gain. Instead of moving with a desired translational velocity, a centroid-tracking formation control algorithm is also proposed such that the centroid of the formation tracks a desired trajectory. The parametric uncertainties are taken into consideration in the proposed formation control algorithms. Finally, simulation examples are provided to validate the effectiveness of the proposed control algorithms.