Sequential Control of Attention and Opinion Dynamics in Human–Robot Systems

Sequential Control of Attention and Opinion Dynamics in Human–Robot Systems Giulia d’Addato1,3,4, Luigi Palopoli2,4, Daniele Fontanelli1,4 Abstract—We introduce a control strategy for jointly shaping human attention and opinion in interaction with a robot. Attention is captured by a modulation variable governed by spatial factors, such as distance and relative heading, while opinion evolves through nonlinear social dynamics. The proposed sequential strategy unfolds in three phases. First, the robot uses geometry to adjust human attention, thereby increasing her/his receptivity. Next, it steers the coupled opinions into the basin of attraction of the desired equilibrium by temporarily modifying its own dynamics. Finally, once aligned, the system naturally converges under unforced dynamics. This framework bridges the gap between motion planning and opinion dynamics, showing how spatial behaviour can be exploited to regulate both attention and consensus in human–robot interaction. Index Terms—Human-robot interaction, nonlinear opinion dynamics, attention shaping, sequential control, social influence. I. INTRODUCTION Mobile robots are increasingly being deployed in environments shared with people, such as hospitals, airports, warehouses, and shopping centers, where successful navigation requires more than just avoiding collisions. Humans coordinate movement through nonverbal signals, such as body orientation and proxemics. Socially aware navigation seeks to incorporate these cues, enabling robots to move predictably and to cooperate smoothly with nearby people [1]. Opinion dynamics models, originally developed for social networks and later applied to multi-robot settings, offer a concise representation of how internal preferences evolve in coordinated decisions (e.g. directional consensus) [2], [3]. However, existing approaches rely on passive or reactive behaviour, where robots adapt to human motion or seek consensus without explicitly accounting for attention as a prerequisite for influence. In contrast, our work gives the robot an active, initiative-taking role by using motion not only to adapt to people, but also to elicit and regulate human attention. This proactive modulation of attention enhances the robot’s ability to shape opinion dynamics, enabling smoother and more cooperative navigation in shared environments. This work is supported by the EU – NextGenerationEU (PNRR), through the National Ph.D. Program in Autonomous Systems (DAuSy, D93C23000470005), and by Future AI Research (FAIR, PE00000013). 1Department of Industrial Engineering, Universit` a di Trento, Trento, Italy. [email protected]. 2Department of Information Engineering and Computer Science, Universit` a di Trento, Trento, Italy. 3Department of Electrical and Information Engineering, Politecnico di Bari, Bari, Italy. 4IDRA Labs @ University of Trento. We propose a three-phase sequential control strategy in which the robot: (i) actively shapes spatial engagement to raise the level of human attention; (ii) temporarily alters its own update law to steer joint human-robot opinions into the basin of a desired equilibrium; and (iii) reverts to unforced dynamics, allowing the system to converge naturally. This formulation explicitly links motion planning and social influence: motion is a tool to induce receptivity, and receptivity is then leveraged to achieve reliable opinion steering. The approach can be validated using stability arguments and basinof-attraction estimates, and its feasibility can be demonstrated through simulations. II. PROBLEM FORMULATION AND PROPOSED SOLUTION Drawing inspiration from the opinion-attention framework of [2] and [3], we model both humans and robots as agents whose internal states evolve through symmetric nonlinear dynamics. Each opinion variable, zhfor the human and zr for the robot, is influenced by self-dynamics and by the counterpart’s opinion, weighted by an attention variable. Here, the opinion zrepresents a directional preference: its sign encodes the orientation (e.g., left if z < 0, right if z > 0), while its magnitude reflects the strength of the preference. The coupled dynamics are given by: ˙zh=−dhzh+uhtanh(αhzh+γhzr+bh) ˙zr=−drzr+urtanh(αrzr+γrzh+br)(1) with dh, dr>0denoting the resistance to opinion change, αh, αrthe self-influence terms, γh, γrthe cross-influence weights, and bh, brthe biases capturing intrinsic predispositions or external factors. For the robot, the attention is assumed to remain constantly high, i.e., ur= 1. Human attention uh∈[umin, umax]is instead regulated by spatial cues: τh˙uh=−uh+g(κh, χ;Rh), with g(κh, χ;Rh) = umin + (umax −umin)(Rhκh)n (Rhκh)n+χn. Here χ=p(xr−xh)2+ (yr−yh)2is the inter-agent distance, κh= cos(θh−θr)measures heading alignment, and Rhacts as a critical distance threshold. Attention increases when the robot approaches the human and aligns its heading. The nonlinear structure of (1) admits three equilibria: one unstable equilibrium at the origin, and two stable equilibria corresponding to the possible consensus outcomes. Our objective is to design a control strategy that drives the system towards a desired equilibrium ˆ zwith minimal intervention, by first inducing high human attention through motion and then exploiting the resulting receptive state to steer opinions. 2025 I-RIM Conference October 17-19, Rome, Italy ISBN: 9788894580570 =CONCATENATE("10.5281/zenodo.", J35) 77 Proposed Solution: To achieve this, we propose a sequential control strategy combining motion-based attention shaping and opinion steering. The method unfolds in three phases: •Phase A - Attention Shaping: The first step is to increase uhby reducing the relative distance χand aligning the robot’s heading with that of the human. To this end, we adopt a path-following controller inspired by [4], where the human forward trajectory is treated as a virtual path. The robot regulates its angular velocity according to ω= vrγ(χ)−κeθ,with eθ=˜ θ−δ(ly)the attitude error, δ(·) the approaching angle function, and γ(χ)an auxiliary stabilising term. Under mild assumptions on δ(·), this control law guarantees that eθ→0, ensuring alignment of headings, while the translational motion drives χtowards the activation threshold Rh. As a result, both spatial cues evolve towards values that increase uh(χ, ηh), preparing the system for opinion steering. The robot’s orientation then evolves as θr←θr+ω∆t. •Phase B - Opinion Steering: Once human attention level is high enough, the robot temporarily modifies its opinion dynamics to guide the coupled system towards the basin of attraction of the target equilibrium. This can be expressed as ˙zr=−drzr+fdes r(zr),or equivalently by injecting an auxiliary input ˜νrinside the nonlinearity: ˙zr=−drzr+ tanh(νr),˜νr=νr−αrzr−γrzh−br, where the cross-term is temporarily removed to enhance the effectiveness of the desired steering. During this phase, the robot and human headings are updated according to [3]: ˙ θi=kiβisin(tanh(zi)) + ϕi, i ∈ {r, h},(2) where βiscales the deviation angle, kicontrols the intensity of the orientation update and ϕiis the heading angle between the agent’s current and goal directions. •Phase C - Natural Convergence: The auxiliary input is removed, restoring the unforced dynamics (1). The system then converges autonomously to the desired equilibrium under its natural dynamics. The orientation continues to evolve according to (2). III. PRELIMINARY RESULTS We validated the proposed strategy in simulation with a human–robot pair evolving in a 2D plane. As explained in the previous section, the opinion–attention dynamics were embedded in a navigation framework where deviation angles depend on opinions and the human’s motion was simulated as a nominal forward trajectory that adapts its direction according to the evolving opinion states given by (1). Figure 1 illustrates the resulting trajectories, the evolution of opinions and the dynamics of attention. In the initial stage, the robot approaches the human’s path and aligns its heading, causing attention to increase until a threshold is surpassed. Once the human is sufficiently attentive, the robot temporarily adjusts its opinion dynamics to guide the system towards the desired equilibrium. After this step, the auxiliary input is 0123456789 -2 -1 0 1 2 (a) Human and robot trajectories with phase transitions. 0 5 10 15 20 25 30 35 40 -2 -1 0 1 2 3 (b) Opinion evolution. 0 5 10 15 20 25 30 35 40 -2 -1 0 1 2 3 (c) Attention evolution. Fig. 1: Simulation results for the proposed strategy. removed and natural dynamics take over, leading both agents to autonomously converge to consensus. Without this strategy, the human and the robot would simply follow their own preferred directions with no guarantee of reaching a consensus. In this case, however, the robot successfully biases the joint behaviour towards the intended outcome, even if its knowledge of the human’s parameters is not exact. IV. CONCLUSION AND FUTURE WORK We have proposed a sequential, three-phase control strategy for human–robot interaction which combines attention shaping through spatial engagement and opinion steering through social alignment. This approach extends existing opinion dynamics models by highlighting attention as a prerequisite for effective influence, and showing that regulating attention and opinion enables the robot to reliably steer the coupled system towards the desired consensus equilibrium. While our simulations illustrate the feasibility of our approach, future work will include real-world experiments with human participants and extensions to multi-agent interactions. We also intend to explore non-sequential strategies where attention and opinion are jointly modulated, which could facilitate smoother and faster convergence. REFERENCES [1] Singamaneni, Phani Teja, et al. ”A survey on socially aware robot navigation: Taxonomy and future challenges.” The International Journal of Robotics Research 43.10 (2024): 1533-1572. [2] Bizyaeva, Anastasia, Alessio Franci, and Naomi Ehrich Leonard. ”Nonlinear opinion dynamics with tunable sensitivity.” IEEE Transactions on Automatic Control 68.3 (2022): 1415-1430. [3] Cathcart, Charlotte, et al. ”Proactive opinion-driven robot navigation around human movers.” 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2023. [4] Andreetto, Marco, et al. ”Simulating passivity for robotic walkers via authority-sharing.” IEEE Robotics and Automation Letters 3.2 (2018): 1306-1313. 78