Leveraging systems and control theory for social robotics: a model-based behavioral control approach to human-robot interaction

Social robots (SRs) are increasingly expected to assist in healthcare, education, and companionship, thereby addressing the growing need for personalized and affordable health and social care. However, sustaining long-term user engagement remains a major challenge for SRs, largely 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 behavioral control of SRs. By identifying the parameters of this model and deploying it within a model-based behavioral steering system, SRs can autonomously adapt their actions to evolving user mental states, enhancing long-term engagement and personalization. To achieve this, we introduce the first integration of a systems-theoretic cognitive model into a closed-loop predictive behavioral control framework for SRs, formulated as a constrained multi-objective optimization problem that enables transparent, cognition-aware adaptation. In experiments with $$\varvec{10}$$ participants interacting with a Nao robot across three chess puzzle sessions ( $$\varvec{45}$$ to $$\varvec{90}$$ minutes each), the identified model achieved a mean squared error (MSE) of $$\varvec{0.067}$$ (i.e., $$\varvec{1.675\%}$$ of the maximum possible MSE) in tracking beliefs, goals, and emotions of participants, and increased engagement by $$\varvec{16\%}$$ ( $$\varvec{p = 0.009}$$ ) compared to a model-free baseline. Post-interaction participant questionnaires further confirmed the perceived engagement and awareness of the model-based controller. Overall, the framework provides a practical pathway toward SRs that autonomously adapt to users in real time, sustain long-term engagement, and ultimately deliver more effective and personalized assistance in domains such as healthcare, education, and companionship.