Turn-taking is a fundamental aspect of conversation, but current Human-Robot Interaction (HRI) systems often rely on simplistic, silence-based models, leading to unnatural pauses and interruptions. This paper investigates, for the first time, the application of general turn-taking models, specifically TurnGPT and Voice Activity Projection (VAP), to improve conversational dynamics in HRI. These models are trained on human-human dialogue data using self-supervised learning objectives, without requiring domain-specific fine-tuning. We propose methods for using these models in tandem to predict when a robot should begin preparing responses, take turns, and handle potential interruptions. We evaluated the proposed system in a within-subject study against a traditional baseline system, using the Furhat robot with 39 adults in a conversational setting, in combination with a large language model for autonomous response generation. The results show that participants significantly prefer the proposed system, and it significantly reduces response delays and interruptions.