  Bipedal robots are essentially unstable because of their complex kinematics
as well as high dimensional state space dynamics, hence control and generation
of stable walking is a complex subject and still one of the active topics in
the robotic community. Nowadays, there are many humanoids performing stable
walking, but fewer show effective push recovery under pushes.
  In this paper, we firstly review more common used abstract dynamics models
for a humanoid robot which are based on the inverted pendulum and show how
these models can be used to provide walking for a humanoid robot and also how a
hierarchical control structure could fade the complexities of a humanoid
walking. Secondly, the reviewed models are compared together not only in an
analytical manner but also by performing several numerical simulations in a
push recovery scenario using \mbox{MATLAB}. These theoretical and simulation
studies quantitatively compare these models regarding regaining balance. The
results showed that the enhanced version of Linear Inverted Pendulum Plus
Flywheel is the ablest dynamics model to regain the stability of the robot even
in very challenging situations.
