  We study the transport properties of a system of active particles moving at
constant speed in an heterogeneous two-dimensional space. The spatial
heterogeneity is modeled by a random distribution of obstacles, which the
active particles avoid. Obstacle avoidance is characterized by the particle
turning speed $\gamma$. We show, through simulations and analytical
calculations, that the mean square displacement of particles exhibits two
regimes as function of the density of obstacles $\rho_o$ and $\gamma$. We find
that at low values of $\gamma$, particle motion is diffusive and characterized
by a diffusion coefficient that displays a minimum at an intermediate obstacle
density $\rho_o$. We observe that in high obstacle density regions and for
large $\gamma$ values, spontaneous trapping of active particles occurs. We show
that such trapping leads to genuine subdiffusive motion of the active
particles. We indicate how these findings can be used to fabricate a filter of
active particles.
