Equidistant arrangement of agents on line: Analysis of the algorithm and its generalization

Consideration was given to generalization of one of the formation control algorithms, that of equidistant arrangement of agents over a fixed interval. In distinction to the earlier approaches that are based on the equations of the first order, a second-order algorithm was proposed. It was proved to be stable and with proper selection of the adjusted parameter able to provide a higher rate of convergence in comparison with its first-order counterparts. Relation was demonstrated between the problem of arrangement over an interval and the classical problem of consensus. Examples of the results of modeling were presented.