This paper presents a Vehicle-Platoon-Aware Bi-Level Optimization Algorithm for Autonomous Intersection Management (VPA-AIM) to coordinate the merging of Connected and Automated Vehicles (CAVs) at unsignalized intersections. The constraint-coupled bi-level optimization is operated with a limited view of incoming traffic using the rolling horizon procedure to reduce computational complexity. In each decision step, the platoon formation scheme is incorporated into an upper-level traffic scheduling model as decision variables to pursue an optimal schedule from a systemic view. Meanwhile, the passing sequence and timeslots of vehicles are jointly optimized with the platoon configuration scheme by virtue of real-time traffic states to improve operational efficiency and fairness. After that, a lower-level trajectory planning model will generate dynamically-feasible and energy-efficient trajectories according to the given schedule and coupling constraints with the objective of improving space utilization to prevent spillbacks. Moreover, the quantifiable connection between the makespan of traffic scheduling schemes and the occurrence of spillbacks is established while demonstrating that the cooperative platoon formation strategy is effective in avoiding and mitigating spillbacks in normal and saturated traffic states. Additionally, the proposed algorithm can be extended to mixed traffic scenarios with high penetration market rate of CAVs based on the assumption of tracking errors of Human Driven Vehicles (HDVs) trajectories. Numerical experiments are conducted on extensive scenarios with different traffic densities, where the Constraint Programming (CP) technique is used to produce the optimal schedule. Experimental results indicate the superiority of the proposed approach in optimality and stability with reasonable sub-second computation time for real-life applications.