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The zero-temperature ground-state (GS) properties and phase diagram of afrustrated spin-1 $J_{1}$--$J_{2}$ Heisenberg model on the checkerboard squarelattice are studied, using the coupled cluster method. We consider the casewhere the nearest-neighbour exchange bonds have strength $J_{1}>0$ and thenext-nearest-neighbour exchange bonds present (viz., in the checkerboardpattern of the planar pyrochlore) have strength $J_{2} \equiv \kappa J_{1}>0$.We find significant differences from both the spin-1/2 and classical versionsof the model. We find that the spin-1 model has a first phase transition at$\kappa_{c_{1}} \approx 1.00 \pm 0.01$ (as does the classical model at$\kappa_{{\rm cl}}=1$) between two antiferromagnetic phases, viz., aquasiclassical N\'{e}el phase (for $\kappa < \kappa_{c_{1}}$) and one of theinfinitely degenerate family of quasiclassical phases (for $\kappa >\kappa_{c_{1}}$) that exists in the classical model for $\kappa > \kappa_{{\rmcl}}$, which is now chosen by the {\it order by disorder} mechanism as(probably) the "doubled N\'{e}el" (or N\'{e}el$^{\ast}$) state. By contrast,none of this family survives quantum fluctuations to form a stable GS phase inthe spin-1/2 case. We also find evidence for a second quantum critical point at$\kappa_{c_{2}} \approx 2.0 \pm 0.5$ in the spin-1 model, such that for $\kappa> \kappa_{c_{2}}$ the quasiclassical (N\'{e}el$^{\ast}$) ordering melts and anonclassical phase appears, which, on the basis of preliminary evidence,appears unlikely to have crossed-dimer valence-bond crystalline (CDVBC)ordering, as in the spin-1/2 case. Unlike in the spin-1/2 case, where theN\'{e}el and CDVBC phases are separated by a phase with plaquette valence-bondcrystalline (PVBC) ordering, we find very preliminary evidence for such a PVBCstate in the spin-1 model for all $\kappa > \kappa_{c_{2}}$.

A frustrated spin-1 $J_{1}$--$J_{2}$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model