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Floor Friction Assessment from Robot Tire-Surface Interaction

Kulbhushan Komarraju, Nathaniel Pearson, Yu Gu, Jason Gross

arXiv:2610.33735v1cs.RO

TL;DR

Wheel slip can undermine wheel-odometry dead reckoning, while floor friction is rarely known in real deployments. This study compares independently estimated body velocity with wheel odometry on five surfaces, finding surface-dependent delay trends and 97.1% balanced classification accuracy from spectral features.

  • Problem

    Wheel slip can bias wheel odometry and degrade dead reckoning, while floor coefficient of friction is rarely known in real deployments and can vary over time and space.

    Source: §I · p. 1

  • Method

    A skid-steer robot traversed multiple surfaces under slip-inducing commands, and body-to-wheel velocity mismatch was analyzed by magnitude, response delay, and frequency-domain features.

    Source: §I · p. 1

  • Results

    97.1% balanced classification accuracy was achieved by spectral features under recording-level cross-validation, with consistent surface-dependent response-delay trends.

    Source: §I · p. 1

  • Takeaways & Limitations

    Wheel-to-body velocity mismatch magnitude and frequency characteristics contain useful information about tire-surface interactions and could support surface recognition and slip-aware odometry weighting.

    Source: §I · p. 1, §VI · p. 9

    Response delays rank wheel-to-body response rather than surface friction directly, and differing command waveforms across experiments limit direct friction comparison.

    Source: C. Wheel-to-Body Velocity Response Delay · p. 9

Abstract

from arXiv · show

Floor traction influences wheel-slip behavior, dead-reckoning accuracy, and the navigation performance of wheeled mobile robots that rely on wheel odometry. As these robots become increasingly common in GNSS-denied indoor environments, including automated manufacturing and retail facilities, their onboard measurements could also be used to characterize floor conditions and improve localization. In this study, a skid-steer robot was driven over five floor surfaces with distinct traction characteristics using commanded velocity profiles designed to induce wheel slip through repeated acceleration and direction reversal. Differences between the body velocity estimated from inertial sensing and the velocity obtained from wheel odometry were evaluated using the integrated relative-velocity error, phase-derived wheel-to-body response delay, and velocity-reversal response delay. Welch power spectral density analysis was additionally applied to characterize the frequency distribution of the velocity mismatch during positive and negative acceleration. Band-integrated spectral power, spectral centroid, and spectral decay rate were extracted from each recording and evaluated using linear discriminant analysis and multiclass classification. The response-delay measurements produced consistent surface-dependent trends, with the longest delays observed on soap and the shortest delays observed on carpet. The spectral features also provided clear separation among the tested surfaces, achieving a balanced classification accuracy of 97.1% under recording-level cross-validation. These results demonstrate that both the magnitude and frequency domain characteristics of wheel-to-body velocity mismatch contain useful information about tire-surface interactions. Such information could support surface recognition and the development of slip-aware wheel-odometry weighting within robot state-estimation frameworks.

I. INTRODUCTION

Wheel slip on traction-dependent indoor floors can bias dead reckoning and degrade state estimates, motivating inference of traction from robot motion. The paper proposes comparing body and wheel velocities and reports surface-dependent signatures, while situating this approach alongside other robotic friction-estimation methods.

I. INTRODUCTION

  • Wheel slip depends on tire-floor traction and can bias wheel odometry, causing dead-reckoning drift and degraded state estimates, especially during skid-steer turns.Turning inherently induces lateral and longitudinal slip in skid-steer robots.Source: §I · p. 1
  • Online traction inference is proposed as a way to incorporate floor information into state estimation for slip-aware dead reckoning and more reliable motion prediction.Floor coefficient of friction is rarely known in real deployments and can vary across space and time.Source: §I · p. 1
  • The proposed method compares IMU- and exteroceptive-estimated body velocity with wheel-odometry velocity, analyzing mismatch magnitude, response delays, and frequency signatures.Motion capture serves as a proxy for deployable exteroceptive odometry in this preliminary assessment.Source: §I · p. 1
  • Across five indoor surfaces, slip behavior separated clearly, the simple slip metric correlated strongly with ground-truth friction, and spectral features achieved 97.1% balanced classification accuracy.The phase-derived and velocity-reversal response delays also showed consistent surface-dependent trends.Source: §I · p. 1

A. Friction Estimation using Robots

  • Prior robotic friction estimation includes tactile slip-onset methods, legged-robot contact and terrain inference, and wheel-slip models, but much WMR work targets outdoor, deformable-terrain, or control settings.The paper focuses instead on traction-aware indoor navigation across common building materials.Source: A. Friction Estimation using Robots · p. 2

B. Sensor Fusion for Slip Estimation

Reliable slip inference requires body velocity estimated independently of wheel measurements. The paper fuses inertial and motion-capture data in a factor graph, then compares body and wheel velocities to characterize traction-related slip.

B. Sensor Fusion for Slip Estimation

  • Fusing IMU measurements with exteroceptive measurements can reduce the drift, noise, and bias associated with relying on a single source for state estimation.The resulting state estimates can be compared with wheel odometry to infer traction-related slip.Source: B. Sensor Fusion for Slip Estimation · p. 2

C. Slip-Based Friction Inference for Skid-Steer Robots

  • For skid-steer robots, tire-floor interaction affects body motion, making wheel-to-body velocity mismatch a compact descriptor of floor slipperiness.Turning and aggressive maneuvers induce lateral and longitudinal slip.Source: C. Slip-Based Friction Inference for… · p. 2

A. Robotic System Overview

  • The study estimates body velocity by fusing motion-capture and IMU measurements, then compares it with wheel odometry to quantify relative motion across surfaces.Motion capture is used as a validation proxy for more deployable visual or LiDAR odometry in this preliminary study.Source: A. Robotic System Overview · pp. 2–3

B. Factor-Graph State Estimation

  • The factor graph represents pose, velocity, and IMU biases as states linked by measurement constraints; its updates combine IMU preintegration with motion-capture pose and velocity measurements.Motion-capture and IMU data are fused using an ISAM2 factor graph framework.Source: Figure 2 · p. 3, B. Factor-Graph State Estimation · p. 3

1) IMU Preintegration:

The estimator pre-integrates high-frequency IMU measurements to form motion constraints for robot-state estimation.

1) IMU Preintegration:

  • High-frequency IMU measurements are pre-integrated using the standard pre-integrated IMU model.The measurements comprise accelerometer and gyroscope signals.Source: 1) IMU Preintegration · p. 3
  • The IMU input uIMU denotes tri-axial accelerometer and gyroscope measurements.Source: 1) IMU Preintegration · p. 3
  • Preintegration accumulates motion constraints at 125 Hz for incorporating body acceleration and angular velocity into kinematic estimates.Source: 1) IMU Preintegration · p. 3

2) Mocap Pose and Velocity Update:

Motion-capture pose and velocity measurements update the factor-graph estimate, while wheel-to-body velocity mismatch provides the slip measure. The method aligns odometry timestamps to the nearest factor-graph estimate.

2) Mocap Pose and Velocity Update:

  • Motion-capture pose updates receive higher weight than velocity updates because pose estimates are relatively accurate while differentiated velocity estimates are often noisy.At 192 Hz, motion capture provides world-frame pose and velocity priors that correct drift in uncorrected body-frame inertial navigation.Source: 2) Mocap Pose and Velocity Update · p. 4

C. Robot Wheel Slip Estimation

  • Each odometry timestamp is associated with the nearest factor-graph estimate because the two sources are sampled at different frequencies.Source: C. Robot Wheel Slip Estimation · p. 4
  • The slip velocity is the mismatch between longitudinal wheel velocity and body velocity, with body velocity computed from factor-graph velocity using estimated yaw.This quantity estimates mismatch between ideal pure-rolling wheel kinematics and true body motion.Source: C. Robot Wheel Slip Estimation · p. 4

D. Signal Conditioning and Slip Quantification

The section quantifies slip magnitude with segment-wise unsigned AUC, then analyzes relative-velocity spectra and derives recording-level features for surface classification.

D. Signal Conditioning and Slip Quantification

  • Unsigned AUC is computed per up- or down-segment to measure cumulative slip magnitude independently of direction.Segment AUC values are averaged per surface category for comparison.Source: D. Signal Conditioning and Slip… · p. 4

E. Relative-Velocity Spectral Distribution

  • Welch PSDs characterize relative-velocity mismatch during positive- and negative-slope body-velocity segments resampled to a uniform time grid.Overlapping windowed periodograms are averaged, and a Hann window reduces spectral leakage.Source: E. Relative-Velocity Spectral… · p. 4
  • Three features are extracted separately by slope direction from run-level mean PSDs over 3.5–9.5 Hz, excluding recordings with fewer than four valid segments per direction.Spectra are normalized for shape comparison, frequency-filtered by segment resolution and Nyquist limits, and interpolated onto a common grid.Source: E. Relative-Velocity Spectral… · p. 4
  • Shrinkage LDA provides a descriptive two-axis projection, while class-balanced logistic regression is evaluated with recording-level leave-one-out cross-validation.Training-fold means and standard deviations are used to standardize both training and held-out recordings; performance is reported as balanced accuracy.Source: E. Relative-Velocity Spectral… · p. 5

F. Frequency-Domain Velocity Response Analysis

The analysis estimates wheel-to-body response delay at the primary command-reversal frequency and checks it against direct zero-crossing delays.

F. Frequency-Domain Velocity Response Analysis

  • The primary excitation frequency is derived from the median time between consecutive command reversals, with two reversals treated as one oscillation.Each complete recording is one independent observation, and median delay across valid reversals is used for surface comparisons.Source: F. Frequency-Domain Velocity Response… · p. 5
  • Odometry and body velocity are fit with sinusoidal least-squares models, and their Fourier components are evaluated at the exact reversal frequency rather than the nearest FFT bin.The model accounts for signal offset and slow linear drift.Source: F. Frequency-Domain Velocity Response… · p. 5
  • The body-to-odometry phase difference is converted to an equivalent catch-up delay; a positive delay means body velocity lags wheel odometry.A direct time-domain delay from interpolated odometry and body-velocity zero crossings provides a complementary measure.Source: F. Frequency-Domain Velocity Response… · p. 5

A. Hardware Platform

The experiments use a skid-steer robot with inertial, encoder, and motion-capture measurements to compare repeated reversal maneuvers across surfaces.

A. Hardware Platform

  • The 40.3 kg skid-steer robot uses an IMU at 125 Hz, wheel encoders at 20 Hz, and Vicon motion capture at 192 Hz for pose and velocity.The tires are rubber; the exact material is not specified in the passage.Source: A. Hardware Platform · pp. 5–6

B. Surface Conditions

  • The five tested surfaces span different friction conditions, with soap identified as the most slippery and carpet as the least slippery.Soap-oil and vinyl are named in the supplied surface descriptions.Source: B. Surface Conditions · p. 6

C. Testing Procedure

  • Each surface is tested with five independent trials of repeated forward–reverse maneuvers, switching direction every 2 s at maximum longitudinal speed to induce slip.Each reversal instantaneously switches the commanded velocity; the profile is shown in Fig. 3.Source: C. Testing Procedure · p. 6, Figure 3 · p. 6

D. Evaluation Metric

The evaluation uses duration-normalized unsigned AUC of relative velocity, and the results compare body-velocity estimates with wheel odometry across five surfaces. The largest mismatch occurred on soap, while carpet showed the closest velocity tracking.

D. Evaluation Metric

  • Mean segment-wise unsigned AUC of relative velocity is normalized by trial duration; larger values indicate more cumulative slip and lower friction.Source: D. Evaluation Metric · p. 6

V. RESULTS

  • Figures 4–6 compare factor-graph and wheel-odometry velocities and relative-velocity profiles for concrete, vinyl, and melamine board.Source: §V · p. 6, Figure 4 · p. 6, Figure 5 · p. 6
  • Carpet showed the least sliding and steepest relative-velocity rise and fall, while soap had the largest velocity mismatch among the five surfaces.The soap mixture produced more slip than the other surfaces; on carpet, estimated body velocity nearly overlapped wheel velocity.Source: §V · p. 7, Figure 7 · p. 7, Figure 8 · p. 7

A. Spectral analysis results

Across five surfaces, velocity-mismatch magnitude, spectral shape, and response timing varied with surface. The delay measures agreed on Soap as longest and Carpet as shortest, while the spectral features and AUC analysis also distinguished surfaces.

B. AUC analysis

  • Soap had the highest median AUC and Carpet the lowest; the inferred slip ordering aligned with the tribometer CoF ordering from Carpet highest to Soap lowest.The reported slip ordering was Soap, Concrete, Board, Vinyl, then Carpet; Vinyl, Board, Concrete, and Soap had decreasing CoF after Carpet.Source: B. AUC analysis · p. 7, Table I · p. 7, Figure 11 · p. 9

A. Spectral analysis results

  • Normalized mismatch power concentrated at low frequencies; Concrete and Board decayed fastest, Soap was broader and flatter, and Vinyl and Carpet were intermediate across slope directions.The normalized spectrum describes the frequency distribution of mismatch power, not its total magnitude or a friction ranking.Source: A. Spectral analysis results · p. 7, Figure 9 · p. 8

B. AUC analysis

  • R2 = 0.978 for the first-order fit shows a strong negative linear correlation between median AUC and tribometer SCoF across the tested surfaces.The model relates the average median AUC values from up and down segments to measured static friction.Source: B. AUC analysis · p. 7, Figure 12 · p. 9

C. Wheel-to-Body Velocity Response Delay

  • Soap had the longest and Carpet the shortest delays under both phase-derived and direct-reversal measures.Phase-derived medians were 0.349 s for Soap and 0.031 s for Carpet; direct-reversal medians were 0.494 s for Soap and 0.025 s for Carpet. Board, Concrete, and Vinyl phase-derived medians were 0.157 s, 0.120 s, and 0.116 s; direct-reversal medians were 0.265 s, 0.215 s, and 0.197 s, respectively.Source: C. Wheel-to-Body Velocity Response Delay · p. 9
  • Delay measurements do not strongly separate Concrete from Vinyl, while Board’s second-largest delays do not imply the second-largest AUC-based mismatch.The Board timing component may include vehicle inertia, controller response, signal filtering, or sensor synchronization.Source: C. Wheel-to-Body Velocity Response Delay · p. 9
  • The measured delays rank response timing, not friction; direct friction comparisons require identical command waveforms and sensor-processing conditions across surfaces.The command-reversal frequencies were not identical across all surface experiments.Source: C. Wheel-to-Body Velocity Response Delay · p. 9

VI. CONCLUSION AND FUTURE WORK

The paper compares measures of wheel-to-body velocity mismatch to examine their relation to tire-floor friction. It suggests traction assessment and surface identification as potential uses, with extensions to additional sensing and state-estimation applications.

VI. CONCLUSION AND FUTURE WORK

  • The developed techniques examine how the magnitude and timing of wheel-to-body velocity mismatch relate to measured tire-floor friction.Source: §VI · p. 9
  • The method could be extended by replacing motion-capture updates with visual or LiDAR-based odometry and by incorporating lateral slip.The authors describe lateral-slip inclusion as a way to enable richer tire-surface characterization.Source: §VI · p. 9
  • Integrating slip estimation and surface characterization into state estimation could potentially improve robot localization accuracy and control.Source: §VI · p. 9
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