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.