We study hard-core dipolar bosons on a square lattice subject to a unidirectional periodic drive that Floquet-engineers anisotropic hopping. Driving along one lattice direction provides a controlled way to suppress transverse tunneling, yielding a kinetically quasi-one-dimensional regime with strongly anisotropic transport within the leading-order high-frequency Floquet effective description. In this limit, the system does not reduce to decoupled chains, due to the long-range in-plane dipolar interaction remains isotropic and couples different chains. Focusing on dipoles polarized perpendicular to the plane, for which the interaction is purely repulsive and isotropic, we use sign-problem-free worm-algorithm quantum Monte Carlo simulations to map the half-filling phase diagram versus kinetic anisotropy and dipolar coupling. We find that increasing kinetic anisotropy systematically lowers the interaction strength required to stabilize checkerboard order, demonstrating that Floquet-induced suppression of transverse motion enhances density ordering. Near the superfluid--checkerboard boundary, finite-size results reveal a narrow transition region where the stiffness drops rapidly while checkerboard correlations rise sharply; Its pronounced sharpening with system size is consistent with a weakly first-order transition rounded by finite-size effects. Away from half filling, on the doped sides of the checkerboard plateau, we identify a narrow checkerboard-supersolid regime with simultaneously finite checkerboard correlations and superfluid stiffness, where the superfluid stiffness is anisotropic but the density pattern is isotropic.
We perform a stability analysis of superfluid (SF) and supersolid (SS) phases of polarized dipolar bosons in two-dimensional optical lattices at high filling factors and zero temperature, and obtain the phase boundaries between SF, checkerboard SS (CSS), striped SS (SSS), and collapse. We show that the phase diagram can be explored through the application of an external field and the tuning of its direction with respect to the optical lattice plane. In particular, we find a transition between the CSS and SSS phases.