廊下ナビゲーションにおけるlegibility再考、通過側の動的表現DPLとSMが有効

Abstract.

We focus on legible robot motion generation in social navigation settings. Legibility in human-robot interaction (HRI) is often described as the property of robot motion that enables an observer to confidently infer the robot’s intent. While mature frameworks exist for generating legible motion in front of static observers, social robot navigation, presents a new challenge: the robot not only must clearly convey its intent; it must do so in a way that ensures human safety in dynamic pedestrian environments where human attention is often divided. With the goal of enabling robots to generate legible motion in dynamic and constrained spaces, we investigate how the choice of representation and the level of human attention shape navigation performance and human impressions. Focusing on the ubiquitous and demanding scenario of hallway navigation, we conduct two controlled user studies involving alternative legibility formulations implemented within a shared model predictive control framework. Study 1 (N=45) investigates the role of intent representation, showing that passing-side legibility—particularly when adaptively updated—leads to smoother human motion and is perceived as more competent and less mentally and physically demanding than destination-based and non-legible baselines. Study 2 (N=45) examines the effect of pedestrian attention, demonstrating that legible motion allows for smooth human motion even under distraction, even if this is not consistently reflected in subjective ratings. Together, these findings suggest that effective legible motion in social robot navigation benefits from interaction-level intent representations that support coordination, with some effects persisting even when human attention is divided. Code is available at https://github.com/fluentrobotics/Legible_MPPI.

1. Introduction

Robots moving in pedestrian spaces like the workplace, the home, and public spaces must do more than simply avoid collisions: they must move in ways that people can intuitively interpret. In social robot navigation (SRN), robots are required to share space with pedestrians and continuously coordinate their motion during close-proximity encounters. In human–human encounters, pedestrians rely on subtle cues such as gaze, orientation, and small path adjustments to infer each other’s intentions and coordinate smooth passages (Wolfinger, 1995; Karp et al., 1977; Goffman, 1966; Goffman, 2009). Robots, however, lack these ingrained social signals. When their motion is difficult to interpret, pedestrians may hesitate, yield unnecessarily, or experience discomfort, leading to inefficient and sometimes unsafe interactions (Mavrogiannis et al., 2023b). This motivates the incorporation of intent signaling directly into robot motion control, particularly in settings where humans and robots must continuously coordinate their actions.

One notable way for encoding communicative signals into robot motion in HRI is through the Legibility framework of Dragan et al. (2013) who define Legibility as the property of motion that enables an observer to quickly and confidently infer the robot’s intent. Early work established that legibility can improve collaboration in manipulation tasks by reducing ambiguity and building trust. For example, Dragan and Srinivasa (2013) showed that legible trajectory planning can make a robot’s intended goal easier to infer. This work inspired a large body of work on understanding how legibility shapes HRI under various settings and domains (Dragan et al., 2013; Dragan and Srinivasa, 2013; Dragan et al., 2015; Kruse et al., 2012; Stulp et al., 2015; Bodden et al., 2018; Mavrogiannis et al., 2018; Taylor et al., 2022; Faria et al., 2024). For example, subsequent studies demonstrated that intent-expressive motion enhances perceived safety and efficiency in shared tasks (Dragan et al., 2015; Kruse et al., 2012; Stulp et al., 2015). Later work recognized the value of legibility for any joint HRI activity (Knepper et al., 2017), discussed the impact of important parameters like the observer’s viewpoint (Nikolaidis et al., 2016; Taylor et al., 2022), and proposed frameworks for transferring the benefits of legibility in other domains (Mavrogiannis et al., 2018; Kruse et al., 2012; Walker et al., 2021).

Despite this rich activity, important limitations arise when legibility is applied to navigation scenarios involving embodied interaction. Much of the existing legibility literature is formulated around simplified settings, in which intent is communicated to passive, static observers who do not spatially interact with the robot (Bodden et al., 2018; Stulp et al., 2015; Dragan et al., 2013). In such settings (e.g., manipulation tasks), legibility is often framed as enabling an observer to infer a robot’s intended goal or final destination from its motion. However, these formulations often break down in embodied navigation: pedestrians do not need to know where others are ultimately headed; they just need to know how to resolve a possible conflict (Mavrogiannis et al., 2018; Wolfinger, 1995). Additionally, prior work often evaluates legibility via studies involving passive watching of robot motion (Kim and Follmer, 2021; Szafir et al., 2014; Taylor et al., 2022; Dragan et al., 2013), overlooking that in real-world navigation, people are both observers and actors who dynamically adapt to the robot’s movements. Existing work on legibility in navigation has also predominantly emphasized open spaces (Mavrogiannis et al., 2022; Taylor et al., 2022; Kruse et al., 2012), while constrained environments such as hallways, which force closer proximity and sharper coordination demands, remain comparatively underexplored. Finally, prior work on legible motion assumes that humans are fully attentive observers (Dragan et al., 2013; Dragan and Srinivasa, 2013; Dragan et al., 2015; Kruse et al., 2012; Stulp et al., 2015; Bodden et al., 2018; Mavrogiannis et al., 2018; Taylor et al., 2022; Faria et al., 2024), yet in many real-world environments, including SRN domains, human attention is often divided across multiple tasks like texting, speaking on the phone, carrying objects, etc. These distractions may limit the extent to which robot motion can influence human behavior.

Motivated by the aforementioned gaps in realizing legible SRN, we ask two questions that to the best of our knowledge have not been sufficiently explored. First, we want to understand how the representations of intent shapes the effectiveness of legible motion in constrained navigation settings. As mentioned, while prior work emphasizes the communication of the robot’s intended destination or an intermediate subgoal, our insight is that navigation under dynamic, crowded, and constrained conditions makes the notion of destination challenging to properly define. Second, we want to understand how human attention influences the impact of legible motion during interaction. Prior work emphasizes fully attentive observers, but SRN domains like train stations, airports, and other public places feature a rich context that divides pedestrian attention.

To approach these central questions, we embed alternative formulations of legible motion into a model predictive control framework and evaluate them across two comparative studies on a hallway setting. Study 1 (N=45) explores the impact of intent representation on robot navigation as well as human navigation and impressions. Study 2 (N=45) examines the value of legible motion under distraction. Unlike prior work that considers distraction primarily as a robustness check for visibility or timing effects (Taylor, 2024), we treat human attention as a central experimental variable and examine how it shapes the influence of legible motion on behavior and perception. Across both studies, we analyze subjective perceptions of competence, comfort, and effort, alongside objective measures of trajectory smoothness and human acceleration. Together, these studies provide initial empirical insights into key factors influencing the effectiveness of legible motion in SRN, with particular emphasis on intent representation and human attention in dynamic, constrained interactions. In summary, this work makes the following contributions:

• We formulate and compare alternative intent representations for legible motion in social robot navigation, contrasting destination-based formulations with interaction-level coordination in constrained environments.
• We embed different legibility formulations within a shared model predictive control framework, enabling controlled comparison that isolates the effects of intent representation and adaptability.
• We examine human attention as a moderating factor by introducing distraction as an experimental variable and characterizing its impact on the effectiveness of legible motion.
• We empirically evaluate legible motion under embodied, close-proximity interaction through two controlled hallway studies, analyzing both human navigation behavior and subjective perception.

A short note discussing this work appeared as a four-page Late-Breaking Report (LBR) in the Companion Proceedings of the 21st ACM/IEEE International Conference on Human–Robot Interaction (HRI 2026). The present manuscript discusses the same two user studies but in a more in-depth fashion, motivating the investigation based on an extended literature review, providing a rigorous mathematical formulation, a comprehensive analysis of objective and subjective measures collected during the studies, and extended discussions of our takeaways. In particular, we add a Foundations section that formalizes legible social navigation, presenting a unified model predictive control formulation, a model of human intent inference and attention, and an explicit distinction between legibility and predictability. Second, beyond the subjective ratings reported previously, we introduce objective, trajectory-based measures of legibility, namely conflict-resolution time, which captures how early an incoming user commits to a passing side, and robot responsibility, which captures the robot’s share of the avoidance, and analyze both across all conditions in both studies. Third, we add a Discussion section that develops the design implications of our findings and examines the effect of potential confounds, such as adherence to passing-side conventions, on the observed differences. The journal version further provides fuller statistical reporting, open-ended participant responses, and additional figures illustrating qualitative behavioral differences across conditions.

2. Related Work

We review recent work on SRN and legible motion in HRI, as well as more directly relevant work on legible SRN and our evaluation domain of navigation in hallways.

Social robot navigation. Earlier work on social robot navigation (Rösmann et al., 2016; van den Berg et al., 2011) largely treated humans as moving obstacles, missing the inherently interactive nature of human navigation. Interaction-aware methods instead model mutual adaptation, treating humans as intelligent agents perceiving and reacting to the motion of others (Trautman et al., 2015; Mavrogiannis et al., 2022). This view has been realized both in learning-based policies trained in simulated crowds or from human demonstrations (Chen et al., 2017; Cuan et al., 2022; Kathuria et al., 2025) and in model-based planners that fold predicted human motion into the robot’s optimization (Sun et al., 2021; Mavrogiannis et al., 2023a). Beyond avoiding collisions, these methods increasingly seek motion that is efficient, comfortable, and consistent with social norms such as personal space and passing-side conventions (Wolfinger, 1995; Mavrogiannis et al., 2023b). Across these methods, however, interaction is most often framed in a single direction, with the robot inferring human intent in order to resolve conflicts safely and efficiently.

A growing body of work recognizes that navigation is also bidirectional communication, in which the robot’s own motion conveys its intent to those around it (Mavrogiannis et al., 2022; Mavrogiannis et al., 2023b). When robot motion is easy to interpret, pedestrians coordinate more smoothly and perceive the robot as safer (Mavrogiannis et al., 2023b), motivating methods that not only read human intent but actively express the robot’s own (Mavrogiannis et al., 2022; Che et al., 2020).

Legible motion. Prior work has highlighted the potential of robot intent expressiveness for enabling seamless HRI (Satake et al., 2009; Dugas et al., 2020; Dragan et al., 2013; Mavrogiannis et al., 2022), through the use of modalities like gestures (Hart et al., 2014; Dugas et al., 2020), lights (Angelopoulos et al., 2022), and motion (Dragan et al., 2013; Bastarache et al., 2023; Taylor et al., 2022; Mavrogiannis et al., 2022; Walker et al., 2021). The latter, commonly referred to as legible motion, has gained significant attention due to its potential to convey robot intent directly encoded within the robot’s otherwise task-oriented motion, without necessarily requiring dedicated signaling components. Formulations of legibility typically frame it as an inference problem: trajectories are planned so that partial observations maximize the observer’s posterior over the robot’s intended goal or action (Dragan et al., 2013; Dragan and Srinivasa, 2013; Bronars et al., 2024). Recent work has further extended this idea to sequential decision-making tasks from single goals (Faria et al., 2024). Empirical studies have demonstrated that legible motion improves collaboration by reducing ambiguity, enhancing efficiency, and fostering trust and safety in joint tasks (Stulp et al., 2015; Dragan et al., 2015; Lichtenthäler et al., 2012). However, evaluating legible motion is a challenge in itself. In many studies, users watch non-interactive robot demonstrations, either in person or on video, and infer robot goals, sometimes rating confidence (Dragan et al., 2013; Kim and Follmer, 2021; Szafir et al., 2014; Taylor et al., 2022; Wallkotter et al., 2022). For example, Taylor (2024) examined how visibility and timing shape the effectiveness of legible motion, primarily in simulation and static-observer settings. While informative for studying perceptual inference, these paradigms abstract away the reciprocal nature of interaction present in many HRI scenarios, including social robot navigation, where pedestrians both observe and adapt their motion (Trautman et al., 2015; Mavrogiannis et al., 2023b). This highlights the need for embodied experiments in complex scenarios such as narrow hallways, where misunderstandings can escalate into stand-offs (Mavrogiannis et al., 2023a; Stratton et al., 2024; Fujioka et al., 2024), in contrast to prior work emphasizing relatively open spaces where complexity plays little role (Mavrogiannis et al., 2022; Taylor et al., 2022; Kruse et al., 2012).

Legible motion in social navigation. Extending legibility (Dragan and Srinivasa, 2013; Bodden et al., 2018; Stulp et al., 2015) to pedestrian-rich environments introduces unique challenges, as social navigation often hinges less on inferring final targets—as conventionally done in collaborative manipulation—and more on social conventions for resolving encounters (Wolfinger, 1995; Mavrogiannis et al., 2022). Because such encounters are a form of joint action coordinated implicitly through motion (Knepper et al., 2017), early work argued that robots moving among people should shape their trajectories to be intent-expressive rather than merely goal-directed (Kruse et al., 2012; Lichtenthäler and Kirsch, 2013). Fujioka et al. (2024) estimate human understanding online and adapt communicative signals encoded into robot motion online. Mavrogiannis et al. (2018) introduced Social Momentum (SM), in which the robot exaggerates its passing side to clearly signal its preferred avoidance strategy to co-navigating pedestrians. In a similar hallway-passing setting, Cathcart et al. (2023) use nonlinear opinion dynamics to let the robot rapidly and visibly commit to a passing side, breaking the deadlocks that arise when intent stays ambiguous. Bastarache et al. (2023) optimized trajectories that remain interpretable to nearby humans while ensuring predictability. Taylor et al. (2022) and Nikolaidis et al. (2016) incorporate visibility constraints into legible robot motion planning, making sure that intent-expressive motion remains within a person’s field of view. Beyond expressing intent, Geldenbott and Leung (2024) couple legibility with an equitable sharing of collision-avoidance effort, linking how a robot signals its intent to how much of the avoidance burden it assumes. Legible SRN methods differ in how robot intent is represented and conveyed, ranging from destination-based goals to interaction-centric cues such as passing side. However, the comparative effects of these design choices on human motion and perception in embodied pedestrian encounters remain insufficiently understood.

Hallway navigation. Hallway navigation is ubiquitous, motivating the incorporation of hallways into the design of user studies on SRN (Pacchierotti et al., 2006a; Pacchierotti et al., 2006b; Lu and Smart, 2013). Unlike open spaces, hallways introduce geometric constraints amplifying the need for agile, readable robot motion. Prior work in hallway navigation emphasized proxemics and side-passing conventions. Pacchierotti et al. (2006a) proposed strategies where robots initiate avoidance early, shifting to the culturally appropriate side and yielding clearly to pedestrians. In follow-up work, they quantified human comfort for different passing distances, showing that distances that were too close invaded personal space, while excessively wide detours appeared inefficient (Pacchierotti et al., 2006b). Lu and Smart (2013) framed hallway navigation as a costmap-based problem where robots balance actions like yielding, slowing, or parking, and examined gaze as an additional cue. Inspired by these early investigations, our work introduces the feature of intent expressiveness into hallway navigation, analyzing when legibility cues matter, and how to generate them.

3. Foundations

We mathematically formalize our problem domain of legible SRN and motivate our research questions.

3.1. Domain

Social robot navigation. We consider a robot r navigating in a workspace \mathcal{W}\subseteq\mathbb{R}^{2}, among static obstacles \mathcal{O}\subset\mathcal{W} and n\geq 1 co-navigating humans. At each discrete time step t, the robot is in state s^{r}_{t}, and human i is in state s^{i}_{t}. The robot is a dynamical system, evolving according to s^{r}_{t+1}=f(s^{r}_{t},u_{t}), where u is a control action, drawn from a space of controls \mathcal{U}. Each human observes the robot and each other, and adapts their navigation according to an unknown policy \pi_{i}. The goal of the robot is to reach a destination d\in\mathcal{W}, while respecting the safety and comfort of co-navigating humans.

Human inference in social robot navigation. Studies on human action understanding suggest that humans tend to associate observed actions of others with possible goals in a given context (Csibra and Gergely, 2007; Baker et al., 2009). This can be observed in pedestrian domains as well, where humans engage in a form of negotiation over a socially acceptable way to resolve possible navigational conflicts (Wolfinger, 1995). For social navigation, we model this type of human inference as

\mathcal{I}:\mathcal{S}\to\mathcal{G}\mbox{,}

where \mathcal{S} is a space of robot trajectories, and \mathcal{G} represents a space of robot intentions. In practice, we assume that a human observes a partial robot trajectory s^{r}_{a:b}=(s^{r}_{a},\dots,s^{r}_{b}), from time a to time b, and infers its intent as a belief \mathcal{I}(s^{r}_{a:b})=P(g\mid s^{r}_{a:b}), where g\in\mathcal{G} is the robot’s navigational intent. While navigational intent is often modeled as the robot’s intended destination d (Kruse et al., 2012; Lichtenthäler and Kirsch, 2013; Taylor et al., 2022; Amirian et al., 2024; Dragan et al., 2013), other options are possible (e.g., passing side, planned path, etc). Legible robot motion. Following prior work (Dragan et al., 2013), we refer to legibility as the property of robot motion that enables an observer to quickly and confidently infer the robot’s intent. In a navigation setting within a shared context M, a robot may enable pedestrians to correctly infer its true intent g^{*} through motion s^{r}_{a:b}, extracted by solving the following optimization problem:

{s^{r}_{a:b}}^{*}\leftarrow\arg\max_{\mathcal{S}}\;P(g=g^{*}\mid s^{r}_{a:b},M)\mbox{.}

Here, by context M, we refer to any information that conditions this inference, such as the map, past robot and pedestrian behavior, or task-related cues, and it is where richer context would enter in a more general system. In our implementation, this inference uses only the candidate intent set \mathcal{G}, the cost C of the observed trajectory

Legibility is often discussed in relation with and contrasted from predictability (Dragan et al., 2013), the property of motion that matches what an observer expects of an agent heading toward a known intent. Legible motion is the trajectory that maximizes the posterior, \arg\max_{\mathcal{S}}P(g^{*}\mid s^{r}_{a:b}) (eq. (2)), whereas predictable motion maximizes the likelihood, \arg\max_{\mathcal{S}}P(s^{r}_{a:b}\mid g^{*}). By Bayes’ rule, P(g\mid s^{r}_{a:b})\propto P(s^{r}_{a:b}\mid g)\,P(g), so the two coincide when efficient motion toward g^{*} is unlikely under every other intent, P(s^{r}_{a:b}\mid g)\approx 0 for g\neq g^{*}, leaving g^{*} as the most probable explanation of the observed motion. In navigation this can arise when intent is the destination. A corridor is one such case, where the efficient path toward one endpoint is incompatible with the other, so the predictable motion is also the most legible.

Control for legible social robot navigation. A flexible control paradigm that allows for the integration of legibility alongside standard considerations of safety and efficiency is model predictive control (MPC). MPC treats control as a receding-horizon optimization of the form:

\begin{split}u^{*}_{t:T}&=\arg\min_{u\in\mathcal{U}}\sum_{t}^{T-1}J(s^{r}_{t+1},s^{1:n}_{t+1})\\
&s.t.\ s^{r}_{t+1}=f(s^{r}_{t},u_{t})\\
&\qquad s^{1:n}_{t+1}=F(s^{r}_{t-h:t},s^{1:n}_{t-h:t})\mbox{,}\end{split}

where J is a cost function, F is human model predicting future human motion given state history over a window h, and T is a control horizon. We consider a composite cost J=a_{F}J_{F}+a_{L}J_{L}, comprising: a functional cost (J_{F}) that captures human safety, efficiency, and obstacle avoidance as a weighted sum; a legibility cost (J_{L}) that promotes early and confident communication of the robot’s intent. The legibility term motivates the selection of actions maximizing of P(g=g^{*}\mid s^{r}_{a:b},M) from eq. (2) and is defined as

J_{L}(s^{r}_{t+1})=-w_{t}\,P(g=g^{*}\mid s^{r}_{t:t+1},M)\mbox{,}

where w_{t} decays linearly over time, placing greater weight on earlier timesteps to encourage prompt intent disambiguation, consistent with prior work on legible motion (Dragan et al., 2013). Intuitively, J_{L} is low when the robot quickly biases an observer’s belief toward the correct intent, and large when the robot’s actions fail to provide early evidence of its goal.

3.2. Modeling the Pedestrian’s Belief

Following prior work (Dragan et al., 2013), we model a pedestrian’s belief over the robot’s intent by evaluating how well robot motion aligns with each candidate intent g~\in~\mathcal{G}, assuming the robot is optimizing a function C(s^{r}_{a:b},g) representing the cost of reaching intent g given the trajectory s^{r}_{a:b}. We express this belief as a probability:

P(g=g^{*}\mid s^{r}_{a:b},M)=\frac{\exp\left(-\frac{1}{\lambda}C(s^{r}_{a:b},g^{*})\right)}{\sum_{g^{\prime}\in\mathcal{G}}\exp\left(-\frac{1}{\lambda}C(s^{r}_{a:b},g^{\prime})\right)}\mbox{.}

Pedestrian inattention. The parameter \lambda, part of the robot’s contextual understanding M, represents human inattention, which occurs when pedestrians are texting, conversing, carrying an object, or multitasking (Wickens, 2008; Strayer and Drews, 2007; Horrey et al., 2006). This modeling decision is consistent with the concept of bounded rationality (Gershman et al., 2015; Griffiths et al., 2015), which is often employed in human modeling across a range of domains (Wang et al., 2022; Genewein et al., 2015; Xu et al., 2024; Ortega et al., 2015). Higher values of \lambda reflect reduced attention, resulting in diffuse, uncertain beliefs. When \lambda\to\infty, the pedestrian is maximally distracted, unable to reason about robot intents, i.e., a uniform belief over all candidate goals:

\lim_{\lambda\to\infty}P(g\mid s^{r}_{a:b},M)=\frac{1}{|\mathcal{G}|}\mbox{.}

In contrast, lower \lambda values yield confident, near-deterministic inferences. When \lambda\to 0^{+}, the pedestrian’s inference is maximally confident that the intent of minimal cost is the true robot intent, i.e., the belief collapses to a point mass on the minimal-cost goal:

\lim_{\lambda\to 0^{+}}P(g\mid s^{r}_{a:b},M)=\begin{cases}1&\text{if }g=\arg\min_{g^{\prime}\in\mathcal{G}}C(s^{r}_{a:b},g^{\prime})\\
0&\text{otherwise}\mbox{.}\end{cases}

3.3. Challenges in Generating Legible Motion for SRN

Navigation domains in industrial, private, and public spaces feature rich context (e.g., geometric constraints, dense crowds, variable human internal state), motivating a deeper understanding of the role and relevance of legible robot motion. To this end, we approach the following research questions:

Q1. How does intent representation shape legible SRN? In the legibility framework of Dragan et al. (2013), intent refers to the robot’s goal in the task space, i.e., the physical pose of a bottle that the robot intends to grasp. Much of the work on legible motion for SRN adopts a similar notion of intent: the robot aims to generate motion that is legible with respect to its destination (Kruse et al., 2012; Lichtenthäler and Kirsch, 2013; Taylor et al., 2022; Amirian et al., 2024). While this can be a practical assumption for simplified environments like sparsely populated open spaces, we expect that it does not scale to realistic environments with geometric constraints, rich contexts, and dense crowds. Under such settings, pedestrians are not concerned with where others are going but rather how they could seamlessly avoid conflicts (Wolfinger, 1995), for example whether they would be passing each other on the left or the right side. Additionally, in earlier legibility work (Kruse et al., 2012; Lichtenthäler and Kirsch, 2013; Taylor et al., 2022; Amirian et al., 2024), the true intent g^{*} is treated as fixed. For example, in the work of Dragan et al. (2013), when going for the right bottle, the robot needs to be consistently legible with respect to the right bottle. However, the dynamic nature of pedestrian domains may impact the validity of the assumption of fixed intent: pedestrians may modify their navigation intent to resolve conflicts with others. For instance, they might head toward an intermediate waypoint near their true destination.

Q2. How does human distraction impact benefits of legible SRN? The combination of functional and legible costs in eq. (3) highlights a fundamental tradeoff: legible motion can be at odds with functional efficiency (Dragan et al., 2013). A variety of contextual factors could impact this tradeoff, including crowd density, spatial constraints, or human attentiveness. In this work, we focus on the latter. Prior work on legible motion in HRI assumes that the observer is fully engaged and attentive to robot behavior (Dragan et al., 2013; Nikolaidis et al., 2016; Taylor et al., 2022; Bronars et al., 2024; Wallkotter et al., 2022), a situation corresponding to small \lambda. In realistic pedestrian domains, however, human attention is often limited. Here, we want to understand how the legible SRN framework discussed in Sec. 3.2 impacts navigation performance and human impressions when pedestrians around the robot are distracted, a situation expressed via larger \lambda values. Under distraction, pedestrians may have limited capacity to register communicative signals broadcasted by the robot. We anticipate that in such cases, vividly legible motion cues that allow humans to rapidly disambiguate the robot’s immediate intent despite limited attention may reduce confusion and support safe conflict resolution. Approaching this question will help inform the design of SRN algorithms that adaptively balance efficiency and legibility.

4. How does Intent Representation Shape Legible SRN

We present an IRB-approved lab study (HUM00268645) investigating how the intent representation underlying legible motion generation impacts navigation performance and user impressions (Q1).

4.1. Experiment Design

Experimental setup. The study took place in a hallway of size 2\,\mathrm{m}\times 5.8\,\mathrm{m}, constructed with room dividers inside the lab (see Fig. 1). An easel pad was placed at each hallway end. We used the Hello Robot Stretch 2 mobile platform. An overhead camera (Insta360) recorded RGB video if the user gave consent. A motion capture system (OptiTrack) was used to localize the robot and the users. The full experimental apparatus is shown in Fig. 2. All navigation algorithms were implemented using a state-of-the-art MPC framework (Williams et al., 2017). Human motion prediction, F in eq. (3), was modeled as a constant velocity (CV) propagation, following extensive prior work (Kollmitz et al., 2015; Liu et al., 2023; Singamaneni et al., 2021; Poddar et al., 2023; Schöller et al., 2020). The MPC horizon was set to 10 steps with a time step of 0.3\,\mathrm{s}, and controllers operated at 20 Hz. Procedure. Upon arriving in the lab, users provided informed consent, possibly opting out of video recording and data publishing. They were then given instructions, going over the task and the robot’s role, before participating in a trial round in which the robot remained stationary. They then completed five trials involving hallway navigation alongside the robot. Each trial lasted approximately 80 seconds. Right after each trial, users completed a questionnaire soliciting their reflections over their interactions with the robot. They then went through a debriefing form, provided demographic information and prior experience with robotics, and were compensated $20. Each complete session lasted no more than 40 minutes.

Task description. Users were told that the study concerned human impressions of robot navigation algorithms but were not given its specific objectives. They were instructed to imagine that they were workers in a factory performing a mock “factory inspection” task. Completing an inspection task involved the user placing a colored sticker on an easel pad. To justify the robot’s presence, users were told that it was monitoring their inspection and recording the sticker colors. In each study session, a user completed five trials, each corresponding to a different experimental condition, i.e., a different algorithm executed by the robot. In each trial, the user traversed the hallway back and forth six times to place six stickers across the two easel pads. Throughout the trial, the robot also traversed back and forth along the hallway, always moving against the user’s direction, engaging on head-on encounters with them. Upon reaching its destination, the robot executed a brief turning maneuver to reorient itself toward the opposite end of the hallway. To ensure repeatable human-robot encounters, we synchronized human and robot motion by instructing users to only turn around and move to the opposite easel after they hear a gong sound, signaling that the robot was ready to move. Because the robot’s nominal speed was slower than participants (0.33~m/s), its navigation destinations were positioned closer than the human stations, ensuring that both agents reached their respective ends within comparable timeframes.

4.2. Conditions

Each participant completed five trials in a within-subjects design. In each trial, the robot executed a different navigation algorithm, with algorithm order counterbalanced using a Balanced Latin Square to mitigate ordering effects. All five strategies were implemented within the same model predictive control (MPC) framework, differing only in how the robot’s intent is represented and conveyed. We evaluate the following strategies:

Goal-based legibility (GL). Here, the space of intent, \mathcal{G}, is modeled as the set of the two hallway endpoints, with g^{*}=d, i.e., corresponding to the robot’s intended destination, similar to prior legibility implementations Kruse et al. (2012); Dragan et al. (2013). The pedestrian’s belief in eq. (5) is computed using a Euclidean distance-based cost C. Intuitively, this algorithm is favoring actions that consistently communicate the robot’s intended destination. Because both endpoints lie along the corridor axis, efficient motion toward the destination is also the legible motion, and GL thus corresponds to the case where legibility and predictability collapse.

Passing-side legibility (PL). Here, \mathcal{G} consists of artificial subgoals placed to the left and right of the hallway endpoints (d), effectively creating the notion of passing-side interactions. By steering toward one of these offsets, the robot conveys its intended side of passage. The robot’s true intent g^{*} is assigned at random before the trial and held fixed for each encounter. The cost C is identical to GL, and left/right assignments are balanced across trials for all participants.

Dynamic passing side legibility (DPL). Here, \mathcal{G} is defined as in PL, but g^{*} is dynamically adapted at run time. Specifically, the robot selects the passing side associated with the lower predicted probability of being chosen by the human, based on CV predictions of the human’s motion. These probabilities are computed using the same Bayesian inference framework employed earlier for goal inference in legibility, i.e., P(g\mid s^{i}_{0:t}), but here applied to the human’s observed trajectory s^{i}_{0:t} rather than the robot’s, to infer the human’s preferred passing side.

Social Momentum (SM) (Mavrogiannis et al., 2022). Here, \mathcal{G}=\{L,R\}, where L and R represent passing from the left and right, respectively. Unlike PL and DPL, which encode passing-side intent through artificial offset goals, SM reasons about passing directly in the joint human–robot interaction space. This allows us to not fixate our results to the specific notion of generating passing sides using artificial goals. The cost C is defined using the angular momentum of the system: its sign encodes the passing side, while its magnitude reflects confidence (Mavrogiannis et al., 2022). Intuitively, J_{L} rewards trajectories that reinforce the currently emerging passing side. Thus g^{*} is dynamically adapted based on the passing preference of the human.

No legibility (NL). This is vanilla MPC implemented as a non-legible reference algorithm, implemented by setting J_{L}=0. This baseline represents purely functional robot navigation without communicative intent.

4.3. Implementation

The controllers were implemented as ROS 2 nodes using PyTorch. We tuned each controller separately to balance goal progress and collision avoidance while producing its intended navigation behavior. MPPI evaluated 250 sampled trajectories per update over a 10-step horizon with a timestep of 0.3\,\mathrm{s}, and the control loop operated at 20 Hz. Human velocity was estimated from consecutive tracked positions using a 0.05\,\mathrm{s} interval and used for constant-velocity prediction. Table 1 reports the principal coefficients used in the intent objectives and their temporal weighting. Code for this work is available at https://github.com/fluentrobotics/Legible_MPPI.

4.4. Measures

Because human beliefs and inferences about robot intent are inherently latent and cannot be directly observed, we rely on established measures to evaluate how legible motion impacted human motion.

To objectively assess the impact of different algorithms on human behavior, we analyze human motion. We measure human path inefficiency using the Path Irregularity (Human PI) measure (Guzzi et al., 2013), defined as the amount of unnecessary turning per unit path length (\text{rad}/\text{m}), and widely used in SRN research (Mavrogiannis et al., 2019; Mavrogiannis et al., 2018; Gao and Huang, 2022; Tsoi et al., 2024; Biswas et al., 2022). We also measure human motion abruptness using Human Average Acceleration (Human AA), defined as the average acceleration along a user’s full trajectory over a trial, yielding a single scalar value per algorithm per user. Human AA is widely used in SRN literature (Mavrogiannis et al., 2019; Gao and Huang, 2022; Mavrogiannis et al., 2018; Biswas et al., 2022; Zhang et al., 2022) as a proxy for how much robot motion physically challenged a user: higher acceleration indicates more speed changes, indicating greater discomfort.

We also study user impressions collected via questionnaires. We use the Discomfort and Competence subscales of RoSAS (Carpinella et al., 2017), presented in randomized order on 9-point Likert scales. We also use the Mental, Physical, Temporal, Frustration, Performance, and Effort demand scales from NASA-TLX (Hart and Staveland, 1988), presented in a 21-point format. To capture perceived goal clarity, we asked users to rate: (L1) – “The robot will bump into me in the future” (perceived collision risk); (L2) – “I was quickly and accurately able to tell where the robot wants to go” (perceived legibility, based on Dragan et al. (2013)), both presented as 7-point scales. Finally, we collected open-form responses to capture insights not covered by the structured scales.

4.5. Hypotheses

We study how different legibility implementations impact navigation performance and impressions by investigating the following:

H1: “Legible algorithms will be more positively perceived and enable higher user performance." We hypothesize that legible algorithms (GL, SM, PL, DPL) will lead to lower acceleration and more regular paths for the users, compared to non-legible algorithms (NL). We further expect legible algorithms to be rated as more competent and comfortable on the RoSAS scale, and to impose lower workload on users as measured by the NASA TLX, in contrast to non-legible algorithms.

H2: “Legibility over the robot’s passing side will be more positively perceived and enable higher user performance compared to legibility over the robot’s goal." We hypothesize that passing side legibility (PL, DPL, SM) will enable faster and more accurate inference of the robot’s intent than goal-based legibility (GL), as reflected in survey responses. Passing side legibility is also expected to yield smoother trajectories (lower acceleration and more regular paths), and to be perceived as more competent, more comfortable, and less effortful for users compared to goal-based legibility.

H3: “Dynamically adapting the robot’s legibility intent based on user reaction will be more positively perceived and enable higher user performance compared to legibility over a fixed intent." We hypothesize that dynamic adaptation (SM, DPL) will outperform fixed intent legibility (PL) under the same passing side representation. Specifically, dynamic algorithms are expected to produce smoother human motion (lower acceleration and more regular paths), be perceived as more competent and comfortable, and require less effort and workload than fixed intent approaches.

4.6. Analysis

A total of 45 human subjects participated in the study, recruited from a university population through mailing lists. The participants (32 male, 12 female, 1 unidentified) had an average age of 22.42 years (SD = 2.75). On a 5-point Likert scale, they rated their familiarity with robotics technology at an average of 3.68 (SD = 1.03). Qualitative differences across algorithms are shown in Fig. 4.

We modeled the study metrics using linear mixed-effects regression, with algorithms and algorithm order as fixed effects, and random effects for participants to account for repeated measures. Pairwise comparisons between algorithms were corrected using the Benjamini–Hochberg (BH) method.

We present the results organized by hypothesis and grouped by metric type. Table 2 reports subjective RoSAS ratings of Competence and Discomfort whereas Fig. 3 shows objective and workload-related outcomes, including L1 (Fig. 33b), mental demand (Fig. 33c), physical demand (Fig. 33d), and Human AA (Fig. 33a). No statistically significant effects were observed for Human PI, L2, or the NASA-TLX subscales of Performance, Effort, and Temporal Demand.

H1. NL was perceived as significantly less competent than SM and DPL (p<.05), and more likely to bump into participants than SM (L1, p<.05). No significant differences emerged between NL and PL or GL in terms of subjective metrics. NL also elicited higher mental demand and frustration compared to DPL (p<.05). Qualitative responses reinforced these impressions: participants described NL as “hard to predict,” noting that the robot was “almost always in my way” or “super slow to respond”. By contrast, DPL was praised for “giving me space,” and SM for “interacting at the right time”. These remarks align with the higher competence ratings for SM and DPL.

Objective metrics corroborated the subjective findings. NL produced significantly higher Human AA than DPL and PL (p<.05) as well as SM (p<.01), indicating more abrupt changes in human motion under NL.

Taken together, these results indicate that legible robot motion has positive effects, but its impact depends on how intent is represented. Passing-side formulations with dynamic adaptation (DPL, SM) received higher competence ratings and elicited lower human average acceleration compared to the non-legible baseline (NL). However, the absence of consistent subjective differences for PL and GL, despite PL showing objective improvement in Human AA, suggests that not all forms of legibility are equally effective. Thus, H1 is only partially supported.

H2. GL was consistently rated as the least competent among the legible conditions. Subjectively, participants rated GL as more likely to collide (L1, p<.01) and less competent than SM and DPL (p<.001), and more discomforting than DPL (p<.05). GL was also associated with significantly higher mental demand, frustration and physical demand compared to DPL and SM (p<.05). Open ended responses echoed this: participants frequently mentioned that GL “ignored my location,” “took the same path I was moving,” and made them feel like they were “about to bump into the robot each time.” These remarks directly capture the higher discomfort observed in the quantitative measures.

Objective measures mirrored these impressions. GL yielded the highest Human AA, reflecting more abrupt, less smooth human motion, whereas DPL, PL, and SM maintained significantly lower values (p<.01), supporting smoother interactions.

These findings suggest that destination-based legibility (GL), as adopted in prior work (Kruse et al., 2012), can be misleading in the hallway setting evaluated here, whereas passing-side formulations with dynamic adaptation (SM, DPL) yield smoother human motion and lower workload. While PL and GL differed in terms of Human AA, subjective differences emerged only between the adaptive passing-side strategies (DPL, SM) and GL. This indicates that adaptation amplified the perceived benefits of passing-side legible motion. Thus, H2 is only partially supported.

H3. PL was rated as significantly less competent than SM and DPL (p<.05) and more likely to collide (L1, p<.05). It also elicited higher discomfort than DPL (p<.05). Open-ended responses reinforced these ratings: while some participants acknowledged that PL “chose a path that wouldn’t collide,” others remarked that it “didn’t adapt to my walking style” or felt “aimless.” These comments capture why, despite passing-side intent representation, PL was still perceived as less competent and more uncomfortable.

Objective metrics provided a more mixed picture. PL showed slightly lower Human AA than DPL but higher than SM, though these differences were not statistically significant.

Taken together, the evidence indicates that given the passing-side intent representation, dynamic adaptation improves perceptions of competence and comfort, however objective measures did not show significant differences. Thus, H3 is partially supported.

Summary. Across all three hypotheses (H1–H3), results converge on a consistent pattern: legible motion improves both perceived competence and the smoothness of human motion, but the effectiveness depends on how intent is represented. Passing-side formulations with dynamic adaptation (DPL, SM) produced the most favorable outcomes, consistently outperforming the baseline (NL) and, in most cases, the static passing-side strategy (PL). In contrast, goal-based legibility (GL) elicited higher workload and less fluent trajectories, making it less suitable for close human–robot navigation. Taken together, the findings indicate that interaction-level representations of intent, combined with dynamic adaptation, are most suitable for legible robot behavior in hallway navigation.

4.7. Exploratory Analysis

In the foundational legibility study of Dragan et al. (2013), legibility was assessed with passive observers. Participants watched recorded reaching motions and, from only the first portion of each trajectory, predicted the robot’s intended goal and rated their confidence, with motion deemed more legible when it elicited earlier and more confident correct predictions. This protocol fits manipulation, where the human only watches, but not our setting, where participants are simultaneously observers and actors who perceive the robot and adjust their own motion in response, and we want to capture their experience of legibility as co-navigators. Our self-report item (L2: "I was quickly and accurately able to tell where the robot wants to go") is the questionnaire analog of this goal-prediction measure, yet it showed no significant differences across conditions. We therefore conducted a post hoc exploratory analysis using two behavioral proxies that recover the same notion of early, confident intent disambiguation from the recorded interaction itself, computed per head-on encounter from the human and robot trajectories and averaged within each trial:

• Conflict-resolution time. Olivier et al. (2012) introduce the Minimal Predicted Distance (MPD), the closest separation the robot and human would reach if both held their current velocity, and Vassallo et al. (2017) track its evolution over an interaction to characterize how a crossing is resolved. For a head-on encounter with human i, let \Delta p_{t}=p^{r}_{t}-p^{i}_{t} and \Delta v_{t}=v^{r}_{t}-v^{i}_{t} be the relative position and velocity of the robot and human (from states s^{r}_{t} and s^{i}_{t}) at step t. The predicted time to closest approach is \tau_{t}=\max\!\big(0,\,-\langle\Delta p_{t},\Delta v_{t}\rangle/\lVert\Delta v_{t}\rVert^{2}\big), giving \mathrm{MPD}_{t}=\lVert\Delta p_{t}+\tau_{t}\,\Delta v_{t}\rVert. We report the conflict-resolution time t_{c}-t^{\ast}, where t_{c} is the closest encounter and t^{\ast}=\min\{\,t\leq t_{c}:\mathrm{MPD}_{t^{\prime}}\geq d_{c}\ \forall\,t^{\prime}\in[t,t_{c}]\,\} is the earliest step from which the predicted clearance stays above a comfort threshold d_{c}. A larger value indicates that the human disambiguated the robot’s passing intent earlier. We set d_{c}=0.8\,\mathrm{m}, a comfortable center-to-center passing distance (Neggers et al., 2022), and confirmed that the ranking remained stable for d_{c}\in[0.6,1.0]\,\mathrm{m}.
• Robot responsibility (R_{\text{robot}}) (Probst et al., 2025). We quantify the conflict at each step as C_{t}=\max\!\big(0,\,1-\mathrm{MPD}_{t}/d_{0}\big), which grows as the predicted clearance drops below the combined agent radius d_{0}. Each step-to-step change in C_{t} is split between the two agents by a counterfactual comparison: the robot’s contribution is how much the conflict changes due to its velocity adjustment, measured against it keeping its previous velocity, and analogously for the human. R_{\text{robot}}\in[0,1] is then the robot’s share of the total conflict reduction, so higher values indicate that the robot performed more of the avoidance.

We analyze both metrics with the same linear mixed-effects model used for our other measures. Both differed significantly across conditions (Table 3). Conflict-resolution time was longest under the passing-side strategies (SM, DPL, PL), indicating that humans committed to a passing side earlier, and shortest under goal-based legibility (GL) and the non-legible baseline (NL), where comfortable clearance emerged only just before the closest encounter and the passing intent stayed ambiguous until late in the approach. Robot responsibility followed the same ordering, with the robot performing the largest share of the avoidance under SM and DPL and the smallest under GL.

These behavioral differences mirror our subjective and motion results: the adaptive passing-side strategies (SM, DPL) that resolved conflicts earliest and bore the most avoidance were also rated more competent and yielded smoother human motion, whereas goal-based legibility behaved much like the non-legible baseline. The intended differences in legibility were thus expressed in coordination behavior, reinforcing that the benefit of legible motion depends on how intent is represented and adapted to the human.

5. How Human Distraction Impacts Benefits of Legible SRN

In our IRB-approved Study 2, we investigate the role of legible motion under distraction (Q2). The distraction factor was implemented as a between-subjects manipulation: the no-distraction data were directly reused from Study 1, and a new cohort of participants was assigned to the distraction condition in Study 2.

5.1. Study Design

We used the same task setup as Study 1, where users performed the mock inspection task of placing colored stickers on easels while navigating on a hallway alongside the robot.

Distraction task. Besides navigating, users simultaneously completed a verbal comprehension task: listening to an audio passage and answering related multiple-choice questions on a mobile device (see Fig. 5). This form of distraction was motivated by prior research on distracted pedestrian walking behaviors (Bazzi and Cacace, 2023; Luo et al., 2023). The audio materials were modeled after standardized English comprehension passages (e.g., TOEFL listening sections) to provide a consistent cognitive challenge across users. Each passage was narrated at a rate of 90 words per minute and at a fixed volume level. In a pilot study with five participants, all were able to follow navigation instructions while answering the comprehension questions and reported the dual-task setup as manageable, indicating that the distraction was effective without being overwhelming.

Procedure. Users completed consent forms, read instructions, and participated in a practice round. They then completed three trials involving hallway navigation alongside the robot, while concurrently completing the distraction task. Each trial lasted approximately 80 seconds. Right after each trial, users completed a questionnaire with our subjective measures. They then went through a debriefing form and were compensated $15. The full session lasted up to 30 minutes.

Conditions. We used a within-subjects design where in each trial the robot ran a different algorithm: Dynamic Passing-side Legibility (DPL), Social Momentum (SM), and No Legibility (NL). DPL and SM were chosen as the top legible performers from Study 1, whereas NL serves as a non-legible reference. Similar to Study 1, condition order was counter-balanced using Balanced Latin Square.

Hypothesis H4: “Legible algorithms will be more positively perceived and enable higher user performance in the presence of cognitive distraction, compared to respective ratings and performance under no distraction." We expect that distraction will make the navigation task more challenging to complete, making legible motion essential for conflict resolution. When users are solely focused on navigation, they may split the responsibility for collision avoidance with the robot. In contrast, when their attention is divided, we expect the navigation task to become more challenging, and anticipate that even subtle communicative signals from the robot’s part will facilitate navigation.

5.2. Analysis

A total of 45 participants (28 male, 17 female; M_{age}=23.55, SD_{age}=4.05) took part in Study 2. On average, they reported robotics familiarity of 3.40 (SD=0.91) on a 5-point Likert scale. To validate the distraction manipulation, we compared self-reported mental demand and walking metrics across conditions. Participants reported significantly higher mental demand under distraction (8.58\pm 0.72) than no-distraction (4.14\pm 0.60), confirming that the manipulation increased cognitive load (t(241.9)=-8.87,p<.001). Task performance further supported this, with 91.1% participants scoring perfectly. Robot acceleration was higher under distraction (1.70\pm 0.51~m/s^{2} vs. 1.34\pm 0.21~m/s^{2}), indicating more abrupt adjustments when participants were less attentive. Finally, distraction reduced average walking velocity (0.960\pm 0.02 vs. 1.11\pm 0.01, t(244.23)=8.71;p<.001), further supporting the validity of the manipulation.

We compare algorithms under distraction using a linear mixed-effects regression model with the same specification as Study 1. We did not find significant differences between algorithms under distraction in terms of subjective measures. However, Human AA was lower when the robot was running legible algorithms (DPL, SM) than for NL (Table 4), with the NL-SM difference reaching statistical significance (p<.05). The reduction in Human AA from legible algorithms relative to the non-legible baseline was similar across distraction and no-distraction conditions (drawn from Study 1), and differences in algorithm sets were handled by incorporating repeated measures through participant random intercepts.

H4. We test H4 by fitting linear mixed-effects models with fixed effects of Algorithm, Distraction level, and their interaction, and random intercepts for participants. Likelihood ratio tests comparing models with and without the interaction term showed no evidence that distraction altered the performance of any algorithm for any of the metrics. Thus, H4 was not supported: legible algorithms did not enable significantly higher performance and impressions under distraction compared to the non-distraction setting, based on models restricted to algorithms present in both conditions.

5.3. Exploratory Analysis

We explore our collected dataset to uncover a deeper understanding of how distraction impacted the effects of legible motion for users.

Distraction reduced variability in subjective ratings. Residual variance in competence and discomfort ratings was lower under distraction (competence: 1.24 vs. 1.01; discomfort: 0.71 vs. 0.46). AIC and likelihood ratio tests favored a homoskedastic over heteroskedastic model (\DeltaAIC = 1.5; \chi^{2}(2)=2.47;p=.29), indicating that variance was reduced overall rather than driven by specific algorithms. This indicates that once participant, baselines, and order effects were controlled for, algorithms explained little additional variance in competence or discomfort ratings. In practice, participants under distraction seemed to provide more uniform evaluations (e.g., “the robot was fine/safe enough”), making it harder to detect algorithm-level differences.

Legible motion improved Human AA under distraction. Human AA residual variance increased from 0.041 (no-distraction) to 0.072 (distraction), reflecting more diverse walking under distraction. We also found that users walked with significantly lower acceleration next to SM, compared to the non-legible baseline NL (p<.05). This suggests that legible motion continued to promote smoother coordination, although this was not registered in users’ subjective ratings.

Coordination benefits of legible motion persisted under distraction. We repeated the exploratory analysis of Sec. 4.7 on the distraction data, and the Study 1 pattern held. Conflict-resolution time was longest under SM (2.35 s), shorter under DPL (1.78 s), and shortest under the non-legible baseline NL (0.81 s), with all pairwise differences significant (p<.01). Robot responsibility was higher under both legible algorithms (SM, R_{\text{robot}}=0.24; DPL, 0.23) than under NL (0.20; p<.01), although SM and DPL did not differ. These rankings reproduce Study 1, where the same strategies resolved conflicts earlier and took on more of the avoidance than NL. Crucially, these coordination benefits held even though subjective ratings showed no algorithm-level differences under distraction. Together with the lower Human AA for legible algorithms, this suggests that legible motion continued to shape how conflicts were resolved even when its effects were less apparent in participants’ subjective impressions.

Legible motion benefits were more pronounced for higher human walking speeds. The scatter plot in Fig. 6 illustrates the shift toward slower walking under distraction and the variation in the NL–SM Human AA difference across walking speeds in both attention conditions. Users walked significantly more slowly under distraction (p<.001). The acceleration difference was more often positive, suggesting that humans walked more unobstructed next to a legible robot, even in the distraction condition, with the effect more pronounced at higher speeds. We modeled speed as a continuous moderator with fixed effects of Algorithm, Distraction level, Speed, and their interactions, plus random intercepts for participants. The three-way interaction was not significant, but planned contrasts at the 25th, 50th, and 75th percentiles of pooled velocities showed stronger effects at higher speeds. Under distraction, SM consistently outperformed NL, with the gap widening as pace increased (\Delta=0.12,p=.020; \Delta=0.19,p<.001; \Delta=0.25,p=.001). In the no-distraction condition, effects were not significant at slower or medium speeds, likely because fewer participants walked at these levels, but became significant at faster speeds (\Delta=0.17,p=.001), though still smaller than under distraction (0.17 v s 0.25).

Summary. Our analysis suggests that legible motion can be effective under distraction in hallway navigation. Although the overall interaction for speed was not significant, planned contrasts showed a widening NL–SM gap at higher speeds, indicating that benefits became more pronounced under higher navigation demands. In particular, subjective ratings were less sensitive under distraction, as participants judged the robot more uniformly, but objective measures suggested that legible motion, particularly SM, led to smoother human motion. The persistence of these benefits motivates future work on exploring the implications of different \lambda values (eq. (5)) and the development of systems that automatically adapt \lambda to their surrounding context to strike efficient balance between functional and legible behavior.

6. Discussion

Across two studies, we approached the question of how should we adapt legible motion framework in SRN. Our findings indicate that the effectiveness of legible motion depends critically on how intent is represented and on the attentional state of human partners. Together, these results refine how legibility should be conceptualized and operationalized in social navigation settings. All algorithms were implemented within a common, carefully engineered model predictive control framework, so these comparisons isolate intent representation and adaptability while holding real-world navigation performance fixed. Below we discuss the implications of these findings for legible motion generation in hallway settings and design of social navigation systems, as well as limitations and directions for future work.

6.1. Intent representation shapes legible motion

A central insight from this work is that legibility in social robot navigation should not be treated as a straightforward extension of destination-based formulations developed for isolated, goal-directed tasks. In the hallway setting tested in Study 1, the destination-based formulation adopted in prior work (Kruse et al., 2012; Lichtenthäler and Kirsch, 2013; Taylor et al., 2022; Amirian et al., 2024; Dragan et al., 2013) was associated with higher reported workload and less smooth human motion, whereas the adaptive passing-side strategies supported smoother coordination and received higher competence ratings.

Our exploratory objective analysis reinforces this picture from a behavioral standpoint. Compared with goal-based legibility, passing-side strategies, and the adaptive variants in particular, enabled pedestrians to commit to a passing side earlier and led the robot to take on a larger share of the avoidance. Because these measures reflect how the encounter is jointly resolved rather than how it is perceived, their agreement with the subjective ratings indicates that interaction-level legibility shapes coordination behavior, not only impressions.

6.2. Adaptation strengthens legible motion

Beyond intent representation, our results highlight the importance of adaptability in legible motion. While static passing-side legibility improved objective smoothness relative to a non-legible baseline, its benefits were weaker and less consistently reflected in subjective measures compared to dynamically adaptive strategies. Open-ended responses suggest that fixed strategies were sometimes perceived as rigid or unresponsive, even when they avoided collision. In contrast, adaptive strategies continuously adjusted their expressed intent in response to human motion, reinforcing the reciprocal nature of navigation. This pattern highlights the value of using pedestrian motion to guide how the robot selects and updates its passing intent, strengthening the perceived benefits of clear passing-side signaling. These findings support treating pedestrians as interactive agents whose movements and emerging passing preferences inform the robot’s behavior throughout the encounter (Trautman et al., 2015; Mavrogiannis et al., 2022).

6.3. Impact of social norms

Our design partly disentangles legibility from adherence to social norms. Passing-side legibility (PL) signals a side clearly but assigns it at random, so its coordination gains over the non-legible (NL) and goal-based (GL) baselines stem from early signaling rather than just from choosing a norm-appropriate side. A passing-side analysis is consistent with this. A side convention was clearly at play (69% of encounters resolved to the same side, p<.001), but adherence to it did not track performance. Because GL and NL do not signal a side, it was set by the human, so they most often resolved on the conventional side (81% and 76%) yet were rated lowest. PL, in contrast, deviated from the convention most (51%) while still achieving better objective coordination than both baselines. However, the discomfort voiced with NL and GL, described as “almost always in my way” or taking “the same path I was moving,” may also reflect perceived obstruction, path overlap, or encroachment on personal space. These concerns intersect with legibility because early communication of the robot’s near-term motion can help pedestrians anticipate whether their path will be obstructed and where they can pass. For the adaptive strategies (DPL, SM) especially, legible signaling and socially appropriate accommodation remain intertwined by construction. More fundamentally, social norms such as personal-space expectations and passing-side conventions are intrinsic to social navigation and interact with legibility (Francis et al., 2025). In this setting, motion that clarifies the robot’s intent may also resolve path conflicts, reduce perceived collision risk, and accommodate the pedestrian’s preferred route, making their effects difficult to separate.

6.4. Benefits persist under divided attention

Study 2 examined how human attention modulates the impact of legible motion by introducing a realistic distraction task. Under distraction, subjective ratings of competence and discomfort became less sensitive to algorithmic differences, yet objective measures of coordination, such as Human AA, the time taken to resolve conflicts, and the robot’s share of the avoidance, continued to favor legible strategies over a non-legible baseline. This dissociation suggests that legible motion can influence interaction dynamics even when pedestrians are absorbed in secondary tasks. One interpretation is that under divided attention, pedestrians rely more heavily on peripheral, low-level motion cues than on explicit inference. In such cases, legibility might operate at a behavioral level, supporting smoother coordination without necessarily registering as a distinct qualitative experience. Exploratory analyses further indicate that the benefits of legible motion under distraction were more pronounced at typical and higher walking speeds, where coordination demands are greater. This contrast is especially relevant to legibility as a perceptual process. In Study 1, when navigation was the sole task, the adaptive strategies DPL and SM were rated more competent than NL, whereas Study 2 found no significant subjective differences between algorithms under distraction. Since pedestrians must perceive the robot’s motion to infer its intent, the subjective benefits of legibility may depend on attention to that motion, even as its effects on coordination persist.

6.5. Design implications

From a design perspective, our findings suggest that SRN systems may benefit from prioritizing interaction-level representations of intent over destination inference in constrained hallway-like environments, and from incorporating adaptive mechanisms that allow expressed intent to evolve during interaction. Treating human attention as an explicit contextual variable further underscores the importance of measuring and reasoning about distraction when designing navigation behaviors that balance efficiency with legibility. Importantly, all of these capabilities can be realized within the same control framework, making the balance between functional objectives and interaction-level legibility a directly tunable design parameter.

6.6. Limitations and future work

Our studies were conducted in a controlled laboratory hallway with scripted tasks and one-on-one encounters, ensuring precision and repeatability. Ongoing work involves transferring our system to a field deployment in our academic building to test more natural interactions with crowds. Although randomizing the passing side in PL partly separated intent signaling from adherence to the prevailing side convention, legibility and social norms remained inherently intertwined. Future studies could vary legibility formulations and norm compliance independently to examine their individual and combined effects. For safety and consistency, the robot operated at a fixed maximum speed of 0.33~\text{m/s} across all trials, corresponding to the manufacturer’s recommended limit. This choice aligns with prior indoor navigation studies in constrained spaces (Lu and Smart, 2013; Butler and Agah, 2001; Ginés et al., 2019; Kamezaki et al., 2020) and reflects realistic operating speeds of mobile robots deployed in environments such as offices, hospitals, and supermarkets. This likely enabled users to focus more attention on the distraction task without fear of collisions. Because speed was held fixed, our findings characterize legible motion at a single operating point. Future work involves the use of a faster robot, equipped with passive and active safety modules to be safer and more reliable around people.

A broader motivation for our work is to understand when a robot should prioritize legible signals. We approached this question focusing on distraction, suggesting that the benefits of legible motion may persist even when pedestrians are inattentive. Future work will focus on online estimation and adaptation of \lambda to dynamically balance efficiency and legibility. Finally, we will explore additional contextual factors including environmental complexity, physical effort, and task urgency.

7. Conclusion

This work examined how robot motion can convey intent during head-on hallway encounters. In Study 1, signaling a passing side reduced Human AA relative to the non-legible baseline, while the adaptive passing-side strategies also received higher competence ratings. The destination-based strategy elicited greater workload and Human AA than the adaptive strategies. In this setting, the robot’s near-term passing behavior was more useful for coordination than its final destination alone. Study 2 examined these strategies while pedestrians performed a distraction task. SM continued to reduce Human AA relative to NL, although subjective ratings did not significantly distinguish the algorithms under distraction. Together, the studies support designing social navigation around clear near-term motion and adaptation to pedestrian movement, and evaluating its effects through both human perceptions and observed coordination. Future studies should test other encounter geometries and passing norms while directly measuring how pedestrians infer robot intent.

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