Individuals with autism spectrum disorder (ASD) often face significant challenges in social reciprocity, which involves the mutual exchange of social cues and interactions. This study investigates the potential of using a child-height assistive robot named Rudolf to enhance the social reciprocity skills of children with ASD. The research focused on two main questions: how the robot's semi-autonomous functions influence the enhancement of social reciprocity and how its customizable features elicit and improve these skills. Rudolf was specifically designed to engage children with ASD in a structured, supportive environment, offering tailored interactions to practice social reciprocity. A multiple-probe design was employed over three months to evaluate the robot's impact on the social skills of three participants with ASD. The study revealed significant improvements in the children's social reciprocity, with participants demonstrating increased engagement, trust, and interaction within the robot-assisted environment. The customizable functionalities of Rudolf were particularly effective in eliciting and reinforcing interactive behaviors. This research highlights the potential of assistive robots, like Rudolf, in addressing the unique social challenges faced by individuals with ASD. The findings suggest that such robots, when designed with customizable, child-centered features, can significantly enhance social skills in this population. The study contributes to the development of tailored assistive technologies that improve social integration and overall quality of life for children with ASD.