  Various quantum gravity approaches that extend beyond the standard model
predict Lorentz Invariance and Charge-Parity-Time Violation at energies
approaching the Planck scale. These models frequently predict a wavelength
dependent speed of light, which would result in time delays between promptly
emitted photons at different energies, as well as a wavelength-dependent
rotation of the plane of linear polarization for photons resulting from vacuum
birefringence. Here, we describe a pilot program with an automated system of
small telescopes that can simultaneously conduct high cadence optical
photometry and polarimetry of Active Galactic Nuclei (AGN) in multiple
passbands. We use these observations as a proof-of-principle to demonstrate how
such data can be used to test various Lorentz Violation models, including
special cases of the Standard Model Extension (SME). In our initial campaign
with this system, the Array Photo Polarimeter, we observed two AGN sources,
including BL Lacertae at redshift z = 0.069, and S5 B0716+714 at z = 0.31. We
demonstrate that optical polarimetry with a broadband Luminance filter combined
with simultaneous $I_c$-band observations yields SME parameter constraints that
are up to ~10 and ~30 times more sensitive than with a standard $I_c$-band
filter, for SME models with mass dimension d = 5 and d = 6, respectively. Using
only a small system of telescopes with an effective 0.45-m aperture, we further
demonstrate d = 5 constraints for individual lines of sight that are within a
factor of ~1-10 in sensitivity to comparable constraints from optical
polarimetry with a 3.6-m telescope. Such an approach could significantly
improve existing SME constraints via a polarimetric all-sky survey of AGN with
multiple 1-meter class telescopes.
