⚡ electrical engineering

Empirical Prediction of Pedestrian Comfort in Mobile Robot Pedestrian Encounters

This paper empirically investigates the relationship between mobile robot-pedestrian interaction kinematics and subjective comfort, demonstrating that a composite predictor utilizing multiple kinematic variables can effectively quantify pedestrian feelings to enable more socially compliant robot navigation.

Original authors: Alireza Jafari, Hong-Son Nguyen, Yen-Chen Liu

Published 2026-04-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alireza Jafari, Hong-Son Nguyen, Yen-Chen Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are walking down a busy sidewalk, minding your own business. Suddenly, a robot rolls up beside you. Do you feel safe? Do you feel like it's going to bump into you? Or do you feel a little anxious, wondering if it's going to cut you off?

This paper is about teaching robots to understand that feeling.

Most robots today are like very strict, nervous drivers. They only care about one thing: "Will I hit the person?" If the answer is "no," they are happy. But humans are more complex. We care about how the robot moves, not just if it hits us. A robot that zooms past you at high speed might not hit you, but it will make you jump. A robot that takes a weird, jerky turn might make you nervous even if it's far away.

The researchers wanted to figure out exactly what makes a pedestrian feel comfortable (or uncomfortable) when a robot is nearby, and then build a "comfort calculator" for the robot's brain.

The Experiment: The Robot Dance-Off

To figure this out, the team set up a hallway dance floor.

The Dancers: 32 volunteers and a small, wheeled robot (an Agilex Scout Mini).
The Move: The robot and the human would walk toward each other, pass by, and keep going.
The Twist: The robot didn't just walk at one speed. Sometimes it moved at a casual stroll (1.4 m/s), and other times it moved at a brisk, almost jogging pace (2.8 m/s).
The Scorecard: After every pass, the human had to rate how comfortable they felt on a scale of 1 to 5 (1 being "scary!" and 5 being "totally chill").

The Clues: What Makes Us Nervous?

The researchers looked at six different "clues" (kinematic variables) to see which ones made people feel safe or scared. Think of these as the ingredients in a recipe for anxiety:

How Close Did They Get? (Minimum Distance): The classic rule. The closer the robot gets, the more nervous we get.
How Fast Were They Going? (Speed): Faster robots made people more uncomfortable. It's like a car zooming past you on the sidewalk versus a slow walker.
How Far to the Side? (Lateral Distance): How much space did the robot leave on your left or right?
How Smooth Was the Turn? (Curvature): Did the robot turn like a graceful dancer, or did it jerk around like a robot with a broken leg?
Time to Crash? (Projected Time-to-Collision - PTTC): This is the most important clue. It's a "countdown." If the robot is moving fast and heading toward you, the "time to crash" is very low (like 0.5 seconds). If it's far away or slow, the countdown is high.
Distance at the "Countdown" Moment: How far away were you exactly when that countdown was at its lowest?

The Big Discovery:
While everyone assumed "distance" was the most important factor, the researchers found that Time-to-Collision (PTTC) was actually the strongest predictor of how people felt.

Analogy: Imagine a ball rolling toward you. If it's moving slowly, you have plenty of time to step aside, so you feel safe. If it's a bullet train, even if it's 10 meters away, your brain screams "DANGER!" because the time you have to react is almost zero. The robot's "countdown" matters more than just the raw distance.

The Solution: The "Comfort Calculator"

The researchers didn't just stop at finding the clues; they built three different "predictors" (algorithms) to guess how a human would feel in real-time.

The "Keep Your Distance" Predictor: This one only looks at how close the robot gets. It's the old-school method.
The "Time Is Money" Predictor: This one only looks at the Time-to-Collision (PTTC).
The "Super-Brain" Composite Predictor: This is the winner. It looks at all six clues at once. It's like a chef tasting a soup and checking the salt, the heat, the texture, and the smell all together, rather than just checking the salt.

The Results:
The "Super-Brain" predictor was the best.

When this predictor said, "Hey, this path is comfortable," it was right almost 4 times more often than if it just guessed randomly.
It was much better at spotting a comfortable path than the simple "distance-only" or "time-only" methods.

Why Does This Matter?

Right now, robots are like shy, awkward teenagers trying to navigate a party. They know not to bump into people, but they don't know how to be polite. They might stop abruptly or take a weird path that makes people feel uneasy.

This paper gives robots a new tool: Empathy.
By using this "Composite Predictor," future robots can plan their paths not just to avoid crashes, but to make humans feel safe and relaxed. They can choose the smoothest, most polite route, making our future interactions with robots in hospitals, airports, and on sidewalks feel natural and friendly, rather than scary and mechanical.

In a nutshell: We taught robots that it's not just about where they are, but how they get there. And the best way to measure that is by looking at how much time a human has to react, combined with a few other subtle cues.

1. Problem Statement

Mobile robots are increasingly entering public spaces (sidewalks, hospitals, airports), yet current path-planning algorithms prioritize objective safety (collision avoidance) over subjective safety (pedestrian comfort).

The Gap: While collision avoidance is well-studied, quantifying human emotions and anxiety to generate "socially compliant" paths remains a major challenge.
Limitations of Current Approaches: Most existing methods rely heavily on minimum distance (proxemics) and low-speed interactions. They often neglect other critical kinematic variables such as robot speed, lateral distance, trajectory curvature, and temporal metrics like Time-to-Collision (TTC).
Goal: To empirically quantify the relationship between robot-pedestrian interaction kinematics and subjective pedestrian comfort, and to develop predictive models that can be integrated into path planners.

2. Methodology

A. Experimental Setup

Platform: An Agilex Scout Mini mobile robot equipped with Mecanum wheels (configured as a nonholonomic differential-drive robot), a Zedx depth camera, 3D LiDAR, and an Nvidia Jetson AGX Orin.
Environment: A 3.2-meter-wide hallway.
Participants: 32 volunteers (22 males, 10 females; ages 23–41).
Procedure:
- Participants walked casually toward the robot.
- The robot approached head-on, passed the pedestrian, and returned to the center.
- Speed Conditions: Two constant speeds were tested: 1.4 m/s (R14) and 2.8 m/s (R28). Higher speeds were chosen to reduce randomness in human danger interpretation.
- Data Collection: Each participant completed 5 trials. Total valid trials: 158 (after discarding data with sensor failures).
- Feedback: Participants rated their comfort on a 1–5 Likert scale (1 = most dangerous, 5 = most comfortable) after each trial.

B. Kinematic Variables Studied

The study analyzed six specific kinematic variables extracted from the robot's trajectory and relative motion:

Robot Speed ( $v$ ): Constant speed during the trial.
Minimum Distance ( $D_{min}$ ): The closest Euclidean distance between the robot and pedestrian.
Lateral Distance ( $D_{lat}$ ): The perpendicular distance at the moment of passing.
Maximum Curvature ( $\rho$ ): The sharpest turn in the robot's trajectory ( $\rho = 1/r$ ).
Minimum Projected Time-to-Collision ( $T_p$ ): The lowest value of PTTC during the interaction.
Distance at Minimum PTTC ( $D_{TP}$ ): The distance between the robot and pedestrian at the exact moment $T_p$ occurs.

C. Statistical Analysis

Correlation: Used Distance Correlation (dCor) with permutation testing (1000 iterations) to detect non-linear and non-monotonic relationships without assuming normality.
Predictor Design: Created three binary classifiers (Comfort = 1 if rating $\ge$ $\geq$ 4, else 0) based on:
1. Minimum Distance Predictor ( $\hat{S}_d$ ): Thresholded at $D_{min} \ge 1.0$ m.
2. PTTC Predictor ( $\hat{S}_t$ ): Thresholded at $T_p \ge 0.7$ s.
3. Composite Predictor ( $\hat{S}_E$ ): A weighted sum of bins from all six variables.

3. Key Results

A. Correlation Analysis

Statistical analysis revealed the strength of the relationship between kinematic variables and subjective comfort:

Strongest Correlation: Minimum PTTC ( $T_p$ ) ($dCor = 0.269, p=0.002$). Longer time-to-collision correlates strongly with higher comfort.
Strong Correlations: Robot Speed ( $v$ ) and Minimum Distance ( $D_{min}$ ) ( $dCor \approx 0.21$ ). Higher speeds and closer distances reduce comfort.
Moderate/Significant: Distance at Min PTTC ( $D_{TP}$ ) ($dCor = 0.196, p=0.033$).
Weak/Insignificant: Lateral Distance ( $D_{lat}$ ) and Maximum Curvature ( $\rho$ ). While visual trends suggested an "inverted U" shape (optimal values exist), statistical significance was low, likely due to sample size or experimental constraints.

B. Predictor Performance

The study compared the three estimators using Accuracy, Precision, Recall, Specificity, and F1 Score.

Metric	Composite ( $\hat{S}_E$ )	Min Distance ( $\hat{S}_d$ )	Min PTTC ( $\hat{S}_t$ )
Accuracy	0.662	0.566	0.497
Precision	0.674	0.495	0.337
Recall	0.781	0.758	0.762
Specificity	0.508	0.422	0.388
F1 Score	0.723	0.599	0.467
Odds Ratio	3.67	2.28	2.03

Key Finding: The Composite Predictor significantly outperformed single-variable predictors.
Odds Ratio Interpretation: When the composite predictor identifies a pedestrian as "comfortable," there is a 3.67 times higher odds that the pedestrian is actually comfortable compared to when the predictor does not flag them. This is nearly double the performance of the standard minimum distance metric.

4. Key Contributions

Empirical Kinematic Analysis: The paper provides a comprehensive statistical evaluation of six kinematic variables, moving beyond the traditional reliance on minimum distance alone. It highlights PTTC as the most critical temporal indicator of comfort.
Novel Composite Estimator: Development of a multi-variable comfort predictor that combines spatial, temporal, and behavioral metrics. This model achieves the highest F1 score (0.723) and Odds Ratio (3.67).
Quantification Framework: Offers a concrete method to convert subjective human feelings into a quantifiable metric that can be directly integrated into robot cost functions for path planning (e.g., in Reinforcement Learning).

5. Significance and Future Work

Social Compliance: This research enables mobile robots to move not just safely, but comfortably, reducing anxiety and improving social acceptance in public spaces.
Algorithmic Integration: Path planners can now use the composite estimator as a reward function, penalizing trajectories that result in low comfort scores even if they are collision-free.
Limitations & Future Directions:
- Limitations: Small sample size, potential volunteer bias (positive attitude toward robots), reliance on manual binning, and the use of a remote-controlled robot rather than a fully autonomous one.
- Future Work: Extending the model to diverse environments and demographics, integrating the predictor into fully autonomous path-planning frameworks, and utilizing machine learning on large-scale trajectory datasets to automate the derivation of comfort predictors.

Conclusion: The study demonstrates that while minimum distance is a necessary factor, it is insufficient for predicting pedestrian comfort. A composite approach incorporating Projected Time-to-Collision (PTTC) and other kinematic variables provides a significantly more accurate and socially compliant metric for mobile robot navigation.