  We formulate the double exchange (DE) model for systems with $t_{2g}$ orbital
degeneracy, relevant for hole-doped cubic vanadates. In the relevant regime of
strong on-site Coulomb repulsion $U$ we solve the model using two distinct
mean-field approximations: Hartree-Fock, and mean-field applied to the
formulation of the model in the Kotliar-Ruckenstein slave boson representation.
We show how, due to the relative weakness of the DE mechanism via $t_{2g}$
degenerate orbitals, the anisotropic C-type antiferromagnetic metallic phase
and the orbital liquid state can be stabilized. This is contrasted with the DE
mechanism via $e_g$ degenerate orbitals which stabilizes the ferromagnetic
order in the hole-doped regime of manganites. The obtained results are in
striking agreement with the observed magnetic structures and the collapse of
the orbital order in the doped La$_{1-x}$Sr$_x$VO$_3$, Pr$_{1-x}$Ca$_x$VO$_3$
and Nd$_{1-x}$Sr$_x$VO$_3$.
