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.

Fri Nov 19 14:29:33 MET 1999