  This work addresses the problem of vehicle path planning in the presence of
obstacles and uncertainties, which is a fundamental problem in robotics.
  While many path planning algorithms have been proposed for decades, many of
them have dealt with only deterministic environments or only open-loop
uncertainty, i.e., the uncertainty of the system state is not controlled and,
typically, increases with time due to exogenous disturbances, which leads to
the design of potentially conservative nominal paths.
  In order to deal with disturbances and reduce uncertainty, generally, a
lower-level feedback controller is used.
  We conjecture that, if a path planner can consider the closed-loop evolution
of the system uncertainty, it can compute less conservative but still feasible
paths.
  To this end, in this work we develop a new approach that is based on optimal
covariance steering, which explicitly steers the state covariance for
stochastic linear systems with additive noise under non-convex state chance
constraints.
  The proposed framework is verified using simple numerical simulations.
