Vehicle platooning using connected and automated vehicles (CAVs) has attracted considerable attention. In this paper, we address the problem of optimal coordination of CAV platoons at a highway on-ramp merging scenario. We present a single-level constrained optimal control framework that optimizes the fuel economy and travel time of the platoons while satisfying the state, control, and safety constraints. We also explore the effect of delayed communication among the CAV platoons and propose a robust coordination framework to enforce lateral and rear-end collision avoidance constraints in the presence of bounded delays. We provide a closed-form analytical solution to the optimal control problem with safety guarantees that can be implemented in real time. Finally, we validate the effectiveness of the proposed control framework using a high-fidelity commercial simulation environment.