Leveraging Systems and Control Theory for Social Robotics: A Model-Based Behavioral Control Approach to Human-Robot Interaction

TL;DR

This work addresses the challenge of sustaining engagement in social robots by introducing a model-based control framework that embeds the Mathematical Model of Mind (MMM) to infer evolving beliefs, goals, and emotions. The MMM is augmented for control with discrete-time perception, cognition, and decision-making modules and is identified for individual users using a warm-start multi-stage process. Embedded in a closed-loop controller, the MMM guides robot actions (e.g., puzzle difficulty, rewards) to optimize engagement while respecting interaction constraints; a case study with 10 participants using a Nao robot solving chess puzzles demonstrates predictive accuracy (MSE ≈ 0.067) and a 16% improvement in engagement over a model-free baseline. The findings suggest that model-based control grounded in Theory of Mind can enhance transparency, adaptation, and user experience in human-robot interactions, with practical implications for healthcare, education, and companionship applications and avenues for future work on novelty effects, long-term estimation, and richer engagement metrics.

Abstract

Social robots (SRs) should autonomously interact with humans, while exhibiting proper social behaviors associated to their role. By contributing to health-care, education, and companionship, SRs will enhance life quality. However, personalization and sustaining user engagement remain a challenge for SRs, due to their limited understanding of human mental states. Accordingly, we leverage a recently introduced mathematical dynamic model of human perception, cognition, and decision-making for SRs. Identifying the parameters of this model and deploying it in behavioral steering system of SRs allows to effectively personalize the responses of SRs to evolving mental states of their users, enhancing long-term engagement and personalization. Our approach uniquely enables autonomous adaptability of SRs by modeling the dynamics of invisible mental states, significantly contributing to the transparency and awareness of SRs. We validated our model-based control system in experiments with 10 participants who interacted with a Nao robot over three chess puzzle sessions, 45 - 90 minutes each. The identified model achieved a mean squared error (MSE) of 0.067 (i.e., 1.675% of the maximum possible MSE) in tracking beliefs, goals, and emotions of participants. Compared to a model-free controller that did not track mental states of participants, our approach increased engagement by 16% on average. Post-interaction feedback of participants (provided via dedicated questionnaires) further confirmed the perceived engagement and awareness of the model-driven robot. These results highlight the unique potential of model-based approaches and control theory in advancing human-SR interactions.

Figures (17)

• Figure 1: Perception module.
• Figure 2: Cognition module.
• Figure 3: Decision-making module.
• Figure 4: The two configurations used in the two-stage identification of the model (RLD stands for real-life data and RPK for rationally perceived knowledge). The coupled configuration includes both the perception and cognition modules, while the decoupled configuration includes only the perception module.
• Figure 5: Block diagram of the model-based controller of the social robot using the ToM model.

Theorems & Definitions (5)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5