.. _hybrid:

Hybrid Avoid Obstacles and Go-to-Goal
----------------------------------------

When an obstacle is near by, but not an immediate threat for a collision,
then the robot does not need to go directly away from the obstacle as the
:ref:`AvoidObstacle` behavior would, but it should veer to the side of the
obstacle while moving towards the goal. The hybrid algorithm calculates an
weighted angle heading that favors :math:`\alpha_g` when :math:`\alpha_{ao}`
is small while favoring larger values of :math:`\alpha_{ao}`.

The input to the behavior is the set of angles:

* Angle to goal in the global coordinate frame, :math:`\phi_g`.

* The avoid obstacle angle in the local coordinate frame, :math:`\alpha_{ao}`,
  which comes from the sonar data.

* The robot's orientation in the global coordinate frame, :math:`\theta`.

* The threshold angle, :math:`Max_{\alpha\_Hybrid}`, 
  for switching to the :ref:`AvoidObstacle` behavior.

The variable that we call :math:`h` is the weighting variable.

.. math:: 
   :label: blended-h

   h = \left\{ \begin{array}{ll}
       \frac{|\alpha_{ao}|}{Max_{\alpha\_Hybrid}} & 
                   \mbox{if} \: |\alpha_{ao}| < Max_{\alpha\_Hybrid} \\
       1    &   \mbox{otherwise}
            \end{array}
       \right.

.. math:: \alpha = h \cdot \alpha_{ao} + (1 - h) \cdot  \alpha_g

.. math:: \alpha = h \cdot \alpha_{ao} + (1 - h) \cdot (\phi_g - \theta)

Thus, for :math:`|\alpha_{ao}| \geq Max_{\alpha\_Hybrid}`, we have pure
collision avoidance:

.. math:: \alpha = \alpha_{ao}