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Anatomy of Uncertainty: Expressive Descriptors of Robotic Manipulator Motion for Non-verbal Communication in Human-Robot Collaboration

This paper presents a mathematical framework that maps robotic perceptual uncertainty to expressive motion states using Laban Movement Analysis and kinematic descriptors, validated by a human-subject study showing that participants can reliably interpret robot confidence, curiosity, hesitance, and fear through non-verbal movement cues.

Original authors: Ridhima Bector, Souravik Dutta, Poornima Ramachandran, Ree Yan Yeoh, Jui Hien Tan, Domenico Campolo, Bernhard Johannes Schmitt

Published 2026-07-16

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CC BY 4.0

Original authors: Ridhima Bector, Souravik Dutta, Poornima Ramachandran, Ree Yan Yeoh, Jui Hien Tan, Domenico Campolo, Bernhard Johannes Schmitt

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 a world where robots aren't just silent, clanking machines, but partners who can "speak" without saying a word. This is the realm of Human-Robot Collaboration, a branch of science dedicated to getting humans and machines to work together safely and smoothly. For this to happen, a robot needs more than just a list of instructions; it needs to show us what it's thinking. Just like a human might pause before crossing a busy street or lean in curiously to inspect a strange object, a robot needs to communicate its internal state. Two key ideas make this possible: Perceptual Uncertainty, which is simply a robot's feeling of "I'm not 100% sure what's happening right now," and Non-verbal Communication, the art of using body language (or in this case, arm movements) to share that feeling. Why does this matter? Because if a robot acts like it knows exactly what to do when it's actually confused, it might make a dangerous mistake. But if it can show us it's "thinking" or "worried," we humans can step in, slow down, or help out, making teamwork much safer and more natural.

This paper, titled "Anatomy of Uncertainty," dives deep into how a robot's arm can act out its confusion, curiosity, or confidence. The researchers, working with robotic arms, asked a big question: Can we teach a robot to use its movements to tell us, "I'm unsure about this object," or "I'm scared I might drop it"? To answer this, they didn't just guess; they built a mathematical "anatomy" of robot feelings. They borrowed a system called Laban Movement Analysis, which is like a dictionary for human dance and movement, breaking actions down into qualities like "strong vs. light" or "fast vs. slow." They mapped these dance moves onto two invisible axes: Commitment (how much the robot wants to go toward the goal) and Vigilance (how much it's looking around and checking for trouble).

By mixing these two axes, the team created a "state space" where different robot moods live. For example, high commitment and low vigilance equals Confidence (zooming straight to the target). High vigilance with low commitment equals Fear (backing away while shaking). They identified five basic "motion primitives"—the building blocks of robot movement: Approach (moving forward), Pause (stopping to think), Retreat (moving back), Exploration (looking around), and Oscillation (shivering). They then turned these into 11 specific, measurable numbers, like how fast the arm accelerates, how many times it stops, how far it backs up, and how much it tilts or shakes.

To see if this "robot body language" actually works, the researchers created videos of a robot arm performing four different "moods": Confident, Curious, Hesitant, and Fearful. They showed these videos to 55 human participants and asked them to guess what the robot was feeling. The results were clear: people could reliably tell the difference. When the robot moved fast with few stops, people saw Confidence. When it moved slowly, looked around, and tilted its "head," people saw Curiosity. When it stopped often, backed away, and moved slowly, people saw Hesitation. And when it backed away quickly with lots of pauses and shaking, people saw Fear.

The study didn't just stop at identifying the moods; it also tested how changing specific numbers changed the "intensity" of the feeling. They found that making the robot pause for shorter times and move faster made it look more confident. Conversely, making it pause longer, back away further, and shake more made it look more fearful or hesitant. However, they also discovered that not every movement mattered equally. Changing how fast the robot tilted or how hard it shook didn't always make the feeling stronger or weaker in a way people could easily spot. This suggests that for a robot to communicate uncertainty effectively, it needs to get the big picture right—combining speed, stopping, and direction—rather than just tweaking tiny details.

Ultimately, this paper suggests that we can give robots a "vocabulary" of movement to express their uncertainty. While the current study used pre-made videos designed by humans, the authors propose that in the future, robots could use this same "anatomy" to automatically calculate how they should move based on their own sensors. If a robot's camera gets blurry, it could automatically decide to "hesitate" and "look around" instead of blindly grabbing an object, letting the human partner know exactly what's going on inside the machine's brain.

Technical Summary: Anatomy of Uncertainty

Problem Statement

Robots operating in human-robot collaboration (HRC) environments frequently encounter perceptual uncertainty due to sensor noise, occlusion, ambiguous observations, and imperfect models. While classical decision-making frameworks address this internally through belief states, a critical gap exists in non-verbal communication: humans cannot infer whether a robot is confidently resolved, gathering information, or unable to determine an action if the robot executes all tasks with identical motion profiles. Existing methods for expressive robot motion often map movement qualities to discrete emotions or goals but lack a unified mathematical account of how perceptual uncertainty should be decomposed into behavioral processes. Furthermore, there is insufficient literature identifying a sufficient set of measurable motion parameters that can systematically express different uncertainty-related states (e.g., confidence vs. fear) and their intensities.

Methodology

The authors propose a mathematical framework that translates perceptual uncertainty into robotic manipulator motion using Laban Movement Analysis (LMA) as a qualitative interpretive foundation.

1. Behavioral Modeling (Commitment-Vigilance State Space)
The core of the framework is a 2D latent behavioral model mapping four LMA Effort factors (Weight, Time, Space, Flow) onto two orthogonal dimensions:

Commitment ( $C$ ): Represents the degree of motor investment toward a task goal (approach vs. withdrawal). Derived from Weight and Time factors.
Vigilance ( $V$ ): Represents the allocation of motion to monitoring, checking, and information gathering. Derived from Space and Flow factors.

This $C-V$ space defines five canonical behavioral states associated with increasing perceptual uncertainty:

Confidence: High Commitment, Low Vigilance (Direct, fast approach).
Curiosity: High Commitment, High Vigilance (Approach with scanning/exploration).
Hesitance: Low/Negative Commitment, Low Vigilance (Oscillation between approach and withdrawal).
Fear: Low/Negative Commitment, High Vigilance (Retreat with defensive monitoring).
Inactivity: Low/Negative Commitment, Low Vigilance (Complete disengagement).

2. Motion Primitives and Expressive Descriptors
To operationalize these states, the authors define five elemental motion primitives: Approach, Pause, Retreat, Exploration, and Oscillation. These are parameterized by 11 computable expressive descriptors derived from kinematic and geometric data:

Kinematic/Temporal: Approach acceleration, Pause count, Pause duration, Retreat count, Retreat distance, Retreat acceleration.
Geometric/Orientation: Horizontal gaze angle, Vertical gaze angle, Tilt angle, Tilt velocity.
Micro-movement: Shiver amplitude (high-frequency oscillation).

These descriptors allow the translation of the abstract $C-V$ state into specific, measurable end-effector trajectories.

Key Contributions

The paper makes three primary contributions:

An Anatomical Behavioral Model: A mathematical projection of LMA Effort factors onto a Commitment-Vigilance state space, organizing uncertainty-related states (confidence, curiosity, hesitance, fear, inactivity) based on task-directed engagement and uncertainty-management behavior.
A Set of Motion Primitives and Descriptors: A translation of the behavioral model into manipulator trajectories using five primitives parameterized by 11 specific kinematic and geometric descriptors, providing a reusable set for generating and measuring uncertainty-related behaviors.
Human-Perception Validation: A video-based human-subject study evaluating whether these descriptor-parameterized trajectories successfully communicate distinct behavioral states and whether systematic changes in individual descriptors modulate perceived expressive intensity.

Experimental Results

An IRB-approved online study with 55 valid participants evaluated four base trajectories (Confident, Curious, Hesitant, Fearful) and their variations.

Recognition of States (H1): Participants reliably identified the intended behavioral states at rates significantly above chance ( $p < .001$ ). Post-hoc analysis confirmed a single dominant behavioral state for each trajectory (e.g., the "Hesitant" trajectory was predominantly identified as such, with no competing categories reaching significance).
Modulation of Intensity (H2): Systematic changes in specific descriptors significantly altered the perceived intensity of the states:
- Confidence: Increased by shorter pauses and higher approach acceleration.
- Curiosity: Increased by greater tilt amplitude, larger horizontal/vertical gaze angles, and faster approach acceleration.
- Hesitance: Increased by longer pauses, greater retreat distance/count, and slower approach acceleration.
- Fear: Increased by longer pauses, higher pause/retreat counts, and slower approach acceleration.
Non-Dominant Descriptors: Certain parameters, such as shiver amplitude (for fear), retreat acceleration (for fear/hesitance), and tilt velocity (for curiosity), did not produce clear perceptual differentiation when manipulated in isolation, suggesting they may require joint modulation or larger variations to be effective.

Significance and Claims

The paper claims to establish a perceptually grounded basis for encoding robot uncertainty in motion. It demonstrates that perceptual uncertainty is not represented by a single kinematic cue but emerges from coordinated variations in task commitment and information-seeking behavior. The results support the use of structured combinations of approach, interruption, exploration, and withdrawal to convey internal states to human collaborators.

The authors modestly note limitations: the current descriptor values and trajectories were designed manually rather than autonomously computed from real-time perception, and the study relied on video-based evaluation rather than closed-loop interaction. Consequently, the framework currently serves as a motion-design methodology rather than a fully autonomous control system. Future work is proposed to integrate these descriptors with Dynamic Movement Primitives (DMPs) to enable autonomous trajectory generation conditioned on a robot's estimated perceptual uncertainty, safety constraints, and task requirements.