In this thesis, we consider the trajectory planning of an autonomous vehicle to cross an intersection within a given time interval. The vehicle communicates its sensordata to a central coordinator which then computes the trajectory for the given time horizon and sends it back to the vehicle. We consider a realistic scenario in which the communication links are unreliable, the evolution of the state has noise (e.g., due to the model simplification and environmental disturbances), and the observationis noisy (e.g., due to noisy sensing and/or delayed information). The intersection crossing is modeled as a chance constraint problem and the stochastic noise evolution is restricted by a terminal constraint. The communication impairments are modeled as packet drop probabilities and Kalman estimation techniques are used for predicting the states in the presence of state and observation noises. A robust sub-optimalsolution is obtained using convex optimization methods which ensures that the intersection is crossed by the vehicle in the given time interval with very low chance of failure.