Arc-transitive antipodal distance-regular graphs of diameter three related to $PSL_d(q)$

In this paper, we investigate antipodal distance-regular graphs of diameter three and valency $q(q^{d-1}-1)/(q-1)$ with arc-transitive automorphism group which induces an almost simple permutation group on the antipodal classes with the socle isomorphic to $PSL_d(q),$ where $ d\ge 3$. We find that such a graph is necessarily bipartite.