Research on Multi-rotor Aerial Vehicles (MAVs) has experienced remarkable advancements over the past two decades, propelling the field forward at an accelerated pace. Through the implementation of motion control and the integration of specialized mechanisms, researchers have unlocked the potential of MAVs to perform a wide range of tasks in diverse scenarios. Notably, the literature has highlighted the distinctive attributes of MAVs that endow them with a competitive edge in physical interaction when compared to other robotic systems. In this survey, we present a categorization of the various types of physical interactions in which MAVs are involved, supported by comprehensive case studies. We examine the approaches employed by researchers to address different challenges using MAVs and their applications, including the development of different types of controllers to handle uncertainties inherent in these interactions. By conducting a thorough analysis of the strengths and limitations associated with different methodologies, as well as engaging in discussions about potential enhancements, this survey aims to illuminate the path for future research focusing on MAVs with high actuation capabilities.
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