  We study planar random motions with finite velocities, of norm $c>0$, along
orthogonal directions and changing at the instants of occurrence of a
non-homogeneous Poisson process with rate function $\lambda(t),\ t\ge0$. We
focus on the distribution of the current position $\bigl(X(t), Y(t)\bigr),\
t\ge0$, in the case where the motion has orthogonal deviations and where also
reflection is admitted. In all the cases the process is located within the
closed square $S_{ct}=\{(x,y)\in \mathbb{R}^2\,:\,|x|+|y|\le ct\}$ and we
obtain the probability law inside $S_{ct}$, on the edge $\partial S_{ct}$ and
on the other possible singularities, by studying the partial differential
equations governing all the distributions examined. A fundamental result is
that the vector process $\bigl(X(t), Y(t)\bigr)$ is probabilistically
equivalent to a linear transformation of two (independent or dependent)
one-dimensional symmetric telegraph processes with rate function proportional
to $\lambda(t)$ and velocity $c/2$. Finally, we extend the results to a wider
class of orthogonal-type evolutions.
