  We introduce and discuss two nonlinear perturbed extensions of the
Cucker-Smale model with asymmetric coupling weights. The first model assumes a
finite collection of autonomous agents aiming to perform a consensus process in
the presence of identical internal dynamics. The second model describes a
similar population of agents that perform velocity alignment with the
restriction of collision-free orbits. Although qualitatively different, we
explain how these two non-trivial types of perturbations are analyzed under a
unified framework. Rigorous analysis is conducted towards establishing new
sufficient conditions for asymptotic flocking to a synchronized motion.
Applications of our results are compared with simulations to illustrate the
effectiveness of our theoretical estimates.
