From Interaction to Relationship: Multidimensional Interaction Model for Human-Robot Systems

Abstract

Current HRI models provide valuable insights into multimodal communication, interaction taxonomies, and temporal changes such as trust or engagement. However, these approaches remain largely interaction-centric and do not adequately explain how repeated multimodal interactions develop into lasting human-robot relationships. This work identified three structural gaps in existing HRI theory: interaction-centric modeling, multimodality without relationship integration, and dynamic aspects in relationship development. To address these limitations, we introduce the Multidimensional Interaction Model (MIM ${ }^{3})$. The model integrates three key dimensions: multimodal behavior, meaning-sensitive adaptation, and temporal accumulation. Multimodality captures the bidirectional exchange of sensory signals between humans and robots. Meaning-sensitive adaptation describes how information is interpreted across hierarchical representational levels, and temporal accumulation explains the stabilization of expectations and roles during repeated human-robot encounters. MIM ${ }^{3}$ offers a structured perspective on how interaction evolves into relationship providing a theoretical basis for the development of long-term human-robot systems that enable stable, predictable, and socially meaningful interaction. The model is used as an analytical framework to classify current project examples involving service robots.