Nonlinear Flocking with Fixed Distances.*

We investigate the stability of a class of nonlinear flocking schemes of Cucker-Smale type executed on a finite population of autonomous agents. We use algebraic graph theory tools and derive sufficient conditions for asymptotic convergence for velocity coordination while the flock remains sufficiently connected. In addition, the positions of the agents converge to some predefined relative distances. A simulation example is provided to illustrate our theoretical findings.