<p>As the technology for unmanned aerial vehicles matures, new platforms equipped with flexible arms and new applications, particularly for physical interactions with an unstructured environment, have emerged to leverage and expand their inherent aerial capabilities. The primary purpose of this research is to develop a proper interaction control method for the recently introduced dual-arm aerial continuum manipulation system. The paper contributes by designing a learning-based controller integrated into visual servo control framework to increase the system's robustness against parametric and nonparametric uncertainties. For verification purpose, the challenging task of peg-in-hole operation is considered. The proposed controller implicitly incorporates image-based visual servoing, impedance control, and adaptive sliding-mode control under a unified learning control framework. Simulation results demonstrate the efficacy of the proposed technique.</p>