This paper focuses on developing a control theoretic solution for connected and automated vehicles that can ensure system safety over a given finite time horizon in presence of uncertainty. Safety is the primary concern for most of autonomous systems, especially automated vehicles. Ensuring safety of autonomous vehicles is a challenging task because of the environmental uncertainties and the inherent non-convexity of the problem. We treat the ensured safety problem as a robust constraint satisfaction problem and propose a novel solution involving sampling-based motion planning, successive convexification, and robust tube-based model predictive control (RTMPC) approaches. The proposed control strategy is capable of generating highly maneuvering behaviors of connected and automated vehicles in addition to ensuring system safety despite the uncertainties. Simulation results show the generation of collision-free, smooth and highly maneuverable trajectories from the proposed control framework in dynamic and uncertain environments.