To update the belief when the robot moves, we have to specify the
action model 
. Based on the assumption of normally
distributed errors in translation and rotation, we use a mixture of
two independent, zero-centered Gaussian distributions whose tails
are cut off [Burgard et al.
1996]. The variances of these distributions are
proportional to the length of the measured motion.
Figure 3 illustrates the resulting densities for two
example paths if the robot's belief starts with a Dirac distribution.
Both distributions are three-dimensional (in 
-space) and Figure 3 shows their 2D
projections into 
-space.
