The paper introduces a novel framework for safe and autonomous aerial physical interaction in industrial settings. It comprises two main components: a neural network-based target detection system enhanced with edge computing for reduced onboard computational load, and a control barrier function (CBF)-based controller for safe and precise maneuvering. The target detection system is trained on a dataset under challenging visual conditions and evaluated for accuracy across various unseen data with changing lighting conditions. Depth features are utilized for target pose estimation, with the entire detection framework offloaded into low-latency edge computing. The CBF-based controller enables the UAV to converge safely to the target for precise contact. Simulated evaluations of both the controller and target detection are presented, alongside an analysis of real-world detection performance.