Hyperbolic, rotation invariant moment systems are derived for a non-linear
kinetic description of two-dimensional Vicsek swarming model. The systems also preserve
mass conservation, and numerical experiments show that this approach captures
the key features of the model such as shock waves, contact discontinuities, rarefaction
waves, vortex formations. If the system order increases, the solutions of the moment
systems converge to the solution of the corresponding kinetic equation.