Nonlinear Dynamics of Unicycles in Leader-Follower Formation

Abstract: In this paper, a dynamical systems analysis is presented for characterizing the motion of a group of unicycles in leader-follower formation. The equilibrium formations are characterized along with their local stability analysis. It is demonstrated that with the variation in control gain, the collective dynamics might undergo Andronov-Hopf and Fold-Hopf bifurcations. The vigor of quasi-periodicity in the regime of Andronov-Hopf bifurcation and heteroclinic bursts between quasi-periodic and chaotic behavior in the regime of Fold-Hopf bifurcation increases with the number of unicycles. Numerical simulations also suggest the occurrence of global bifurcations involving the destruction of heteroclinic orbit.