Novel personalized and affordable approaches are needed in order to provide efficient therapeutic interventions for people with autism spectrum disorder. In this paper, we introduce a new category of socially assistive robots, i.e., socially assistive drones (SADs) for therapeutic interactions with humans. SADs autonomously perform and engage humans in dance movement therapy (DMT), which has proven to be highly effective for people with autism spectrum disorder when it is personalized and adapted carefully. The main focus of this paper is on developing adaptive, personalized, and interactive control approaches based on fuzzy logic, which efficiently deals with nonlinear dynamics and directly introduces the expert (linguistic) knowledge into the control system. The developed approaches are implemented via a small quadcopter in real-life interactions with 10 participants. The results of the case study prove the excellent performance of the SAD in adapting and personalizing its decisions with respect to each user and thus keeping them engaged in the proposed DMT plans.@en