Abstract:Electric Vertical Take-Off and Landing (eVTOL) aircraft, pivotal to Advanced Air Mobility (AAM), are emerging as a transformative transportation paradigm with the potential to redefine urban and regional mobility. While these systems offer unprecedented efficiency in transporting people and goods, they rely heavily on computation capability, safety-critical operations such as real-time navigation, environmental sensing, and trajectory tracking--necessitating robust offboard computational support. A widely adopted solution involves offloading these tasks to terrestrial base stations (BSs) along the flight path. However, air-to-ground connectivity is often constrained by spectrum conflicts with terrestrial users, which poses a significant challenge to maintaining reliable task execution. Cognitive radio (CR) techniques offer promising capabilities for dynamic spectrum access, making them a natural fit for addressing this issue. Existing studies often overlook the time-varying nature of BS resources, such as spectrum availability and CPU cycles, which leads to inaccurate trajectory planning, suboptimal offloading success rates, excessive energy consumption, and operational delays. To address these challenges, we propose a trajectory optimization framework for eVTOL swarms that maximizes task offloading success probability while minimizing both energy consumption and resource competition (e.g., spectrum and CPU cycles) with primary terrestrial users. The proposed algorithm integrates a Multi-Armed Bandit (MAB) model to dynamically estimate BS resource availability and a Monte Carlo Tree Search (MCTS) algorithm to determine optimal offloading decisions, selecting both the BSs and access time windows that align with energy and temporal constraints.