  In this paper, we extend a framework that we developed earlier for
coordination of connected and automated vehicles (CAVs) at a signal-free
intersection to incorporate uncertainty. We formulate a deterministic motion
planning problem the solution of which guarantees that none of the constraints
in the system becomes active. Considering the uncertainty in the CAVs'
trajectories, we reformulate the motion planning problem as a probabilistic
problem, the solution of which guarantees that constraints in the system are
satisfied within a threshold. Using the noisy observations of actual time
trajectories and leveraging the Gaussian process regression, we obtain bounded
confidence intervals for deviations from the nominal trajectories of CAVs.
Incorporating these confidence intervals, each CAV aims at solving the
probabilistic motion planning problem in a robust approach. We demonstrate the
effectiveness of our proposed framework through a numerical simulation.
