Uniform vs. Lognormal Kinematics in Robots: Perceptual Preferences for Robotic Movements

Abstract: Collaborative robots or cobots interact with humans in a common work environment. In cobots, one under investigated but important issue is related to their movement and how it is perceived by humans. This paper tries to analyze whether humans prefer a robot moving in a human or in a robotic fashion. To this end, the present work lays out what differentiates the movement performed by an industrial robotic arm from that performed by a human one. The main difference lies in the fact that the robotic movement has a trapezoidal speed profile, while for the human arm, the speed profile is bell-shaped and during complex movements, it can be considered as a sum of superimposed bell-shaped movements. Based on the lognormality principle, a procedure was developed for a robotic arm to perform human-like movements. Both speed profiles were implemented in two industrial robots, namely, an ABB IRB 120 and a Universal Robot UR3. Three tests were used to study the subjects' preference when seeing both movements and another analyzed the same when interacting with the robot by touching its ends with their fingers.

• The paper shows that human subjects do not significantly prefer lognormal (human-like) profiles over uniform trapezoidal motions in collaborative settings.
• It presents a novel motion synthesis approach using the Sigma-Lognormal model coupled with forward and inverse kinematics to emulate human arm movements.
• Empirical evaluations across video, physical, and haptic studies confirm near-identical execution performance with negligible differences between the two kinematic profiles.

Perceptual Preferences for Robotic Movements: Uniform vs. Lognormal Kinematics

Overview

This paper addresses the perceptual implications of robotic movement kinematics, specifically investigating whether humans exhibit a preference for robotic (trapezoidal speed profile) or human-like (lognormal speed profile) movement in collaborative robot contexts. The research includes the development and synthesis of human-like motion for robotic arms based on the Sigma-Lognormal model and a comprehensive set of user studies quantifying preference and perceptual discrimination in HRI (human-robot interaction) settings.

Human vs. Robotic Kinematic Modeling

The human arm’s motion is characterized by redundancy in degrees of freedom and bell-shaped velocity profiles, explained by the kinematic theory of rapid movements and the Sigma-Lognormal model. Industrial robotic arms, modeled with fewer degrees of freedom, typically use trapezoidal velocity profiles—constant velocity segments with acceleration ramps at the beginning and end.

The authors formalize the equivalence between human and robotic joints and implement movement generation for both paradigms. Lognormal profiles are synthesized for robots via time-parameterized spatial trajectories and executed using forward/inverse kinematics, fixing terminal joint orientations to suppress reorientation confounds.

Movement Synthesis and Execution

Human-like (lognormal) and trapezoidal profiles are both implemented in ABB IRB120 and UR3 robotic arms. Trajectory planning for lognormal profiles leverages the cumulative density function of the lognormal, parameterized to match duration, scaling, and segment composition. Trapezoidal profiles are generated according to conventional practice, with modifiable acceleration constraints.

Empirical validation through high-frequency positional sensing verifies that the robots can accurately reproduce both profile types, yielding SNRs above 22, quantifying near-identical execution between programmed and actual velocity profiles.

Experimental Protocols and Results

Visual and Interactive Preference Assessments

Four studies are conducted:

1. Video-based discrimination and rating (n=1088): Participants watched videos of robot movements with both profiles, selecting the friendlier and rating perceived friendliness. No significant preference was found; both movement types scored similarly, with a slight, statistically insignificant preference for uniform (trapezoidal) profiles.
2. Abstract motion inference (n=369): Subjects watched animated dots tracing lognormal or trapezoidal trajectories and were asked to classify the origin (human or robotic) and select their preference. Identification accuracy hovered near chance (53–55%), with no clear profile preference.
3. Physical robot observation (UR3, n=61): Participants provided confidence ratings for collaboration with UR3 robot performing each profile. Uniform profiles were rated marginally higher (mean 3.7) than lognormal (mean 3.4), yet these differences did not achieve significance.
4. Haptic interaction study (ABB IRB120, n=118): Subjects were instructed to physically follow the end effector across programmed figures using both movement types. Preferences were split: ~42–44% preferred lognormal, ~33–44% uniform, and ~14–22% expressed no preference, with average friendliness/confidence ratings for both within 0.1–0.3 on a 5-point scale.

Strong Claims and Contradictions

The paper concludes that contrary to assumptions motivating human-like motion in HRI, there is no systematic perceptual or subjective preference for lognormal ('human') over trapezoidal ('robotic') speed profiles. In some instances, uniform/trapezoidal profiles were rated as slightly preferable, directly contradicting much of the anthropomorphism-focused literature.

Theoretical and Practical Implications

The results challenge the prevailing view that human-likeness in robot motion necessarily improves perceived friendliness, safety, or willingness to collaborate. The lack of strong preference or ability to differentiate between kinematics suggests that, at least for the speed profiles and movement scales tested, factors such as predictability, smoothness, and task context may override any anthropomorphic preference in velocity profiles.

For practical HRI design, this indicates that optimizing for anthropomorphic motion profiles may yield diminishing returns regarding subjective user experience and perceived safety or comfort, especially for industrial collaborative tasks.

Future Directions

The authors propose that further work should disambiguate the influence of contextual variables—speed, amplitude, movement complexity—on kinematic preference and test additional motion types beyond point-to-point translation. Investigating domain-specific interactions in service or social robots, and probing neural or implicit physiological responses, may reveal subtler perceptual or ergonomic consequences not captured in explicit ratings or simple discrimination tasks.

Conclusion

This study rigorously examines the hypothesis that humans prefer robots with human-like (lognormal) movement kinematics over traditional robotic (trapezoidal) movement. Across comprehensive observational, inferential, and interactive user studies, the data indicate no consistent preference and, in cases, a slight bias toward uniform (robotic) speed profiles. These findings imply that, for HRI applications involving collaborative or industrial robots, anthropomorphic velocity profiles are not inherently advantageous from a perceptual or interactional perspective, redirecting the focus of motion synthesis in physical HRI.