This paper presents an advanced robotic automation framework that combines an impedance-based compliance controller with an imitation learning network for high-precision peg-in-hole assembly. The framework is characterized by three key features. First, it employs an impedance-based compliance controller to ensure stable contact. This approach enables the robot to adapt flexibly to external contact forces, functioning like a spring-damper system to prevent potential damage. Second, domain randomization is applied to both geometric and visual properties within a high-fidelity simulation environment. This strategy effectively narrows the reality gap, enhancing robustness against environmental uncertainties and visual disturbances. Third, the framework utilizes an action-chunking-transformer (ACT) network to predict precise action sequences based on multimodal data, reducing compounding errors in trajectory generation and improving assembly success rates. Each feature is supported by specific advancements, such as real-time force feedback integration, diverse simulation scenario generation, and multimodal sensor fusion. Extensive experiments conducted in various unseen environments demonstrate the framework's effectiveness, confirming its suitability for complex assembly tasks that require high adaptability and precision under diverse conditions.