Consensus Building in Human-robot Co-learning via Bias Controlled Nonlinear Opinion Dynamics and Non-verbal Communication through Robotic Eyes

TL;DR

This work tackles the challenge of achieving mutual consensus in human-robot co-learning by introducing a bias-controlled nonlinear opinion dynamics framework complemented by nonverbal robotic eye gaze. A dynamic bias updating rule guides the robot’s internal opinion toward agreement, while eye gaze visually communicates intent to influence the human partner, enabling a bidirectional closed-loop interaction. The approach is analyzed theoretically via bifurcation and nullcline analyses and validated experimentally with 51 participants in a two-choice task, showing rapid progression from dissensus to consensus and growing trust as cues intensify. The results highlight the practical potential of visually signaled intents and bias-aware control to enhance collaboration and reduce cognitive load in real-world human-robot teams, while outlining pathways for extending to multi-choice and diverse settings.

Abstract

Consensus between humans and robots is crucial as robotic agents become more prevalent and deeply integrated into our daily lives. This integration presents both unprecedented opportunities and notable challenges for effective collaboration. However, the active guidance of human actions and their integration in co-learning processes, where humans and robots mutually learn from each other, remains under-explored. This article demonstrates how consensus between human and robot opinions can be established by modeling decision-making processes as non-linear opinion dynamics. We utilize dynamic bias as a control parameter to steer the robot's opinion toward consensus and employ visual cues via a robotic eye gaze to guide human decisions. These non-verbal cues communicate the robot's future intentions, gradually guiding human decisions to align with them. To design robot behavior for consensus, we integrate a human opinion observation algorithm with the robot's opinion formation, controlling its actions based on that formed opinion. Experiments with $51$ participants ($N=51$) in a two-choice decision-making task show that effective consensus and trust can be established in a human--robot co-learning setting by guiding human decisions through nonverbal robotic cues and using bias-controlled opinion dynamics to shape robot behavior. Finally, we provide detailed information on the perceived cognitive load and the behavior of robotic eyes based on user feedback and post-experiment interviews.

Figures (8)

• Figure 1: (a) Experimental setup for a two-agent, two-choice decision-making task between a human and a robot (with human consent obtained for image use). The setup includes red and blue buzzers as two options for the human and robot to press, a robotic eye, a camera sensor, and a screen that continuously displays the participant's score. (b) Robotic eye apparatus for nonverbal communication via eye gaze.
• Figure 2: Pre-experiment instructions for participants, including steps for removing hand accessories, the initial standing position with allowed stepping marks, hand positioning, and the use of a mechanical clicker for cognitive load. Illustrations of 'Don't dos' such as switching after crossing the decision line, non-straight hand motion, and switching too quickly. (Human consent obtained for image use)
• Figure 3: (a) Parameter sweep over $\left(b_r, b_h\right)$, highlighting consensus (yellow) and dissensus (blue) regions. (b) Zero-level contours of $\Delta_1, \Delta_2$ in the $\left(z_r, z_h\right)$ plane for $b_r=b_h= \pm(u+1)$ illustrate the number of equilibrium solutions.
• Figure 4: (a) Illustration of the calculation of the angle $\theta$ and distance $d$ for human opinion observation, showing how the robot captures and interprets the human's decision-making process. (b) Illustration of a comprehensive mental model integrating human internal opinion dynamics, observed opinion dynamics, and the robot's non-linear opinion dynamics, demonstrating how the decision-making process is anticipated during interaction.
• Figure 5: Illustration of the human participant's view of the robot eye gaze, robotic arm, and buzzer across different trials. (a) In 1st to 3rd trials, the robot remains neutral, consistently selecting the opposite buzzer color to demonstrate disagreement. (b) In 4th trial, the robot eye gaze is directed towards the blue buzzer, signaling a shift towards alignment. (c) In 5th trial, the robot intensifies its gaze towards the red buzzer (d) In 6th trial, the gaze remains fixed on the red buzzer (e) In 7th trial, the gaze returns to the blue buzzer (f) In 8th trial, the robotic eye gaze intensifies towards the red buzzer, marking the final and most pronounced visual clues. From 4th to 8th trials, the robot progressively strengthens its gaze towards the selected option, affecting human's decision-making process.

Theorems & Definitions (1)

• Definition 3.1