  We present a detailed study of the cosmic star formation history over $90$
per cent of cosmic time ($0\lesssim z\lesssim4$), using deep, radio continuum
observations that probe star formation activity independent of dust. The Low
Frequency Array Two Metre Sky Survey has imaged three well-studied
extragalactic fields, Elais-N1, Bo\"otes and the Lockman Hole, reaching
$\sim20\,\mu\rm{Jy/beam}$ rms sensitivity at $150\,\rm{MHz}$. The availability
of high-quality ancillary data from ultraviolet to far-infrared wavelengths has
enabled accurate photometric redshifts and the robust separation of
radio-bright AGN from their star-forming counterparts. We capitalise on this
unique combination of deep, wide fields and robustly-selected star-forming
galaxies to construct radio luminosity functions and derive the cosmic star
formation rate density. We carefully constrain and correct for scatter in the
$L_{150\,\rm{MHz}}-\rm{SFR}$ relation, which we find to be $\sim0.3\,\rm{dex}$.
Our derived star formation rate density lies between previous measurements at
all redshifts studied. We derive higher star formation rate densities between
$z\sim0$ and $z\sim3$ than are typically inferred from short wavelength
emission; at earlier times, this discrepancy is reduced. Our measurements are
generally in good agreement with far-infrared and radio-based studies, with
small offsets resulting from differing star formation rate calibrations.
