  We tackle the problem of trajectory planning in an environment comprised of a
set of obstacles with uncertain time-varying locations. The uncertainties are
modeled using widely accepted Gaussian distributions, resulting in a
chance-constrained program. Contrary to previous approaches however, we do not
assume perfect knowledge of the moments of the distribution, and instead
estimate them through finite samples available from either sensors or past
data. We derive tight concentration bounds on the error of these estimates to
sufficiently tighten the chance-constraint program. As such, we provide
provable guarantees on satisfaction of the chance-constraints corresponding to
the nominal yet unknown moments. We illustrate our results with two autonomous
vehicle trajectory planning case studies.
