Empirical Prediction of Pedestrian Comfort in Mobile Robot Pedestrian Encounters

Alireza Jafari; Hong-Son Nguyen; Yen-Chen Liu

cs.ROApr 15, 2026

Empirical Prediction of Pedestrian Comfort in Mobile Robot Pedestrian Encounters

Authors: Alireza Jafari, Hong-Son Nguyen, Yen-Chen Liu

Organizations: Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan

Abstract

Mobile robots joining public spaces like sidewalks must care for pedestrian comfort. Many studies consider pedestrians' objective safety, for example, by developing collision avoidance algorithms, but not enough studies take the pedestrian's subjective safety or comfort into consideration. Quantifying comfort is a major challenge that hinders mobile robots from understanding and responding to human emotions. We empirically look into the relationship between the mobile robot-pedestrian interaction kinematics and subjective comfort. We perform one-on-one experimental trials, each involving a mobile robot and a volunteer. Statistical analysis of pedestrians' reported comfort versus the kinematic variables shows moderate but significant correlations for most variables. Based on these empirical findings, we design three comfort estimators/predictors derived from the minimum distance, the minimum projected time-to-collision, and a composite estimator. The composite estimator employs all studied kinematic variables and reaches the highest prediction rate and classifying performance among the predictors. The composite predictor has an odds ratio of 3.67. In simple terms, when it identifies a pedestrian as comfortable, it is almost 4 times more likely that the pedestrian is comfortable rather than uncomfortable. The study provides a comfort quantifier for incorporating pedestrian feelings into path planners for more socially compliant robots.

Figures & tables

Panel of Figure 1 — Fig. 1: Spatial kinematic variables definitions. (a) The minimum of the relative Euclidean distance between the robot and the pedestrian during a trial, $D_{min}$ . (b) The perpendicular distance between the robot and the pedestrian at the passing moment, $D_{lat}$ . (c) The maximum curvature of the robot’s trajectory during a trial, $\rho$ . (d) the distance between the robot and the pedestrian at the moment of $T_{P}$ , $D_{T_{P}}$ .

Panel of Figure 2 — Fig. 2: (a) An Agilex Scout Mini is the mobile base. A Zedx depth camera detects the pedestrians. A 3D LiDAR measures the lateral distance. (b) The robot approaches the pedestrian head-on [ 23 ] and passes him in a trial. The supplementary video shows a sample experimental run.

Group	Trial 1	Trial 2	Trial 3	Trial 4	Trial 5	Slope	p–value
R14	4.25 (20%)	4.12 (17%)	4.06 (28%)	4.00 (26%)	3.81 (26%)	-0.10	0.18
R28	3.44 (30%)	3.38 (34%)	3.44 (32%)	3 62 (36%)	3.81 (29%)	+0.10	0.26
Total	3.84 (27%)	3.75 (27%)	3.75 (30%)	3.81 (31%)	3.81 (27%)	0.0	1.0

TABLE I: Comfort ratings across five consecutive trials averaged over the volunteers. Cells report the corresponding mean (absolute SD/mean

\times

100) for R14, R28, and the total.

Panel of Figure 4 — Fig. 3: Visual representation of the collected data and the kinematic variable trends after binning. The y–axis is the subjective comfort $S$ . The x–axis is (a) The robot speed $v$ . (b) The minimum distance $D_{min}$ . (c) The lateral distance $D_{lat}$ . (d) The maximum curvature $\rho$ . (e) The minimum PTTC $T_{p}$ (f) The distance at minimum PTTC $D_{T_{P}}$ .

Variable	$\boldsymbol{dCor}$	Permutation p	Sample Size
Robot speed ( $v$ )	0.214	$<$ 0.001	158
Minimum distance ( $D_{min}$ )	0.219	$<$ 0.011	158
Lateral distance ( $D_{lat}$ )	0.167	0.132	145 a
Max. curvature ( $\rho$ )	0.107	0.732	158
Minimum PTTC ( $T_{p}$ )	0.269	0.002	158
Distance at min. $T_{p}$ ( $D_{T_{p}}$ )	0.196	0.033	158

TABLE II: Statistical comparison of the subjective comfort variation with the kinematic variables using distance correlation

dCor

and corresponding permutation p–value; the permutation iteration is 1000.

$\boldsymbol{\hat{S}_{d}\backslash S_{E}}$	0	1
0	35	48
1	15	47

TABLE III: Contingency table of

\hat{S}_{d}

S_{E}

$\boldsymbol{\hat{S}_{t}\backslash S_{E}}$	0	1
0	40	63
1	10	32

TABLE IV: Contingency table of

\hat{S}_{t}

S_{E}

Variable		$\boldsymbol{v}$	$\boldsymbol{D_{min}}$	$\boldsymbol{D_{lat}}$	$\boldsymbol{\rho}$	$\boldsymbol{T_{p}}$	$\boldsymbol{D_{T_{p}}}$
Weight		$\boldsymbol{w_{v}}$	$\boldsymbol{w_{d}}$	$\boldsymbol{w_{l}}$	$\boldsymbol{w_{r}}$	$\boldsymbol{w_{t}}$	$\boldsymbol{w_{p}}$
Bins	A	2	0	0	1	0	0
	B	0	1	0	0	0	1
	C	–	2	2	2	0	2
	D	–	2	1	0	2	2
	E	–	–	–	–	2	–

TABLE V: The assigned weights to each bin in Fig. 3 . The composite estimator combines all the variables across their internal bins.

Fig. 4: Comfort scores trend with the middle variable E.

$\boldsymbol{\hat{S}_{E}\backslash S_{E}}$	0	1
0	32	31
1	18	64

TABLE VI: Contingency table of

\hat{S}_{E}

S_{E}

Estimator	Accuracy	Precision	Recall	Specificity	$\boldsymbol{F}_{\textbf{1}}$
$\hat{S}_{E}$	0.662	0.674	0.781	0.508	0.723
$\hat{S}_{d}$	0.566	0.495	0.758	0.422	0.599
$\hat{S}_{t}$	0.497	0.337	0.762	0.388	0.467

TABLE VII: Estimator comparison using performance metrics for classification.

Human-Robot Interaction

Human-robot interaction studies how people and robots communicate, coordinate, and safely work or live together.

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Jul 20, 2026J/K move · Enter open · S save

Stability and Comfort in Mobile Robot-Pedestrian Interactions

Alireza Jafari, Hong-Son Nguyen, Yen-Chen Liu

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan

Robot Navigation Social Robot Navigation Human-Robot Interaction

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Mobile robots in public spaces must ensure pedestrians' comfort, and yet empirical studies of walkers' subjective safety are rare. Many classical navigation algorithms do not distinguish the walkers from dynamic obstacles and do not explicitly model subjective human factors. Moreover, most studies focus on holonomic mobile robots, whereas applications demand Nonholonomic Mobile Robots (NMR). This paper develops socially aware algorithms for NMRs, proves the stability, verifies the performance experimentally, and statistically analyzes the reported comfort. We design a framework for NMRs using Social Force Model (SFM) and the projected Time-to-collision Social Force Model (TSFM). We formalize the NMR-pedestrians' and NMR-obstacles' interactions and prove the system's stability, assuming boundedly nonpassive pedestrians. Simulations calibrate the models by maximizing a hybrid cost function of comfort and speed. Pedestrian-robot interaction experiments compare SFM and TSFM to two remote-controlled baselines and collect walkers' reported comfort. Statistical tools analyze survey results collected during the experiments. Benchmarking the algorithms against previous studies highlights the proposed methods' advantage with respect to the studied metrics. Overall, the models are stable and improve pedestrian comfort when an NMR navigates through a pedestrian crowd.

Abstract

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