  Planar run-and-tumble walks with orthogonal directions of motion are
considered. After formulating the problem with generic transition probabilities
among the orientational states, we focus on the symmetric case, giving general
expressions of the probability distribution function (in the Laplace-Fourier
domain), the mean square displacement and the effective diffusion constant in
terms of transition rate parameters. As case studies we treat and discuss two
classes of motion, alternate/forward and isotropic/backward, obtaining, when
possible, analytic expressions of probability distribution functions in the
space-time domain. We discuss at the end also the case of cyclic motion.
Reduced (enhanced) effective diffusivity, with respect to the standard 2D
active motion, is observed in the cyclic and backward (forward) cases.
