We investigate the transport of active matter in the presence of a disordered square lattice of asymmetric obstacles, which is built by removing a fraction of them from the initial full lattice. We consider no external field. We observe a spontaneous inversion of the net particle current, compared to the usual sense of such a current reported in the literature, if the obstacle (half-circle) has the same diameter of the unit cell of the square lattice. If this diameter is smaller, there is no inversion. We show a calculation that reproduces our numerical results, based on the argument that such effects are a consequence of the imbalance of particles traveling in the positive and the negative directions due to traps formed by the obstacles: for positive travelers the traps are the spaces between neighboring obstacles, while for negative travelers, they are the flat side of the obstacles. PACS numbers: 87.80.Fe, 47.63.Gd, 87.15.hj, 05.40.-a f -0.02 0 0.02 0.04 0.06 0.08 J J x -φ = 0.732 J x -φ = 0.244 J y -φ = 0.732 J y -φ = 0.244 FIG. 4: The x and y components of the mean particle current, Jx and Jy, as a function of f for distinct values of the area fraction φ. We consider wedges as obstacles. The aperture angle of the wedges is 90 • .