  In this paper we consider a random walk of a particle in $\mathbb{R}^d$.
Convergence of different transformations of trajectories of random flights with
Poisson switching moments has been obtained by Davydov and Konakov, as well as
diffusion approximation of the process has been built. The goal of this paper
is to prove stronger convergence in terms of the Wasserstein distance. Three
types of transformations are considered: cases of exponential and
super-exponential growth of a switching moment transformation function are
quite simple, and the result follows from the fact that the limit processes
belong to the unit ball. In the case of the power growth the estimation is more
complicated and follows from combinatorial reasoning and properties of the
Wasserstein metric.
