Online Friction Coefficient Identification for Legged Robots on Slippery Terrain Using Smoothed Contact Gradients

TL;DR

The paper tackles online friction-coefficient identification for legged robots operating on slippery terrain by deriving analytic smoothed gradients of contact impulses with respect to the friction coefficient $μ$ and smoothing the tangential complementarity constraint using $ρ_{\mathrm{t}}$. It combines this with a confidence-score–based update rule and a data-rejection mechanism to ensure informative, robust online updates, solved via SQP Gauss-Newton on a discrete-time, contact-driven model. The authors validate on the KAIST HOUND quadruped, showing fast, consistent convergence under diverse initial conditions and terrain states, outperforming nonsmoothed gradients and randomized-smoothing baselines in computation time and stability. The approach enables reliable online friction estimation that can benefit model-based controllers that rely on accurate $μ$ for Coulomb-friction cones, particularly during transitions between slippery and nonslippery surfaces.

Abstract

This paper proposes an online friction coefficient identification framework for legged robots on slippery terrain. The approach formulates the optimization problem to minimize the sum of residuals between actual and predicted states parameterized by the friction coefficient in rigid body contact dynamics. Notably, the proposed framework leverages the analytic smoothed gradient of contact impulses, obtained by smoothing the complementarity condition of Coulomb friction, to solve the issue of non-informative gradients induced from the nonsmooth contact dynamics. Moreover, we introduce the rejection method to filter out data with high normal contact velocity following contact initiations during friction coefficient identification for legged robots. To validate the proposed framework, we conduct the experiments using a quadrupedal robot platform, KAIST HOUND, on slippery and nonslippery terrain. We observe that our framework achieves fast and consistent friction coefficient identification within various initial conditions.

Figures (9)

• Figure 1: We present an online friction coefficient identification framework using proprioceptive measurements for legged robots. \ref{['sub@fig:a']} With proposed smoothed gradients with respect to the friction coefficient, our framework can handle the issue of non-informative gradients caused by the nonsmooth contact dynamics in friction coefficient identification \ref{['sub@fig:b']} An illustration of constraint space for proposed gradients and nonsmooth gradients.
• Figure 2: An illustration of contact states covered in rigid-body contact dynamics, excluding an opening contact, and our proposed smoothed conditions. The proposed smoothing is applied to the complementarity condition of Coulomb friction in contact states. In the smoothed conditions, the red line represents the smoothed constraint, while the brown line depicts the nonsmoothed constraint.
• Figure 3: An overall proposed framework of the online friction coefficient identification for legged robots. Based on adaptive online system identification chen2022real using confidence score-based update, this work proposes analytic smoothed gradients with respect to friction coefficient and employs the rejection method. The rejection method calculates the rejection score based on the contact velocity in the normal direction and excludes the states where the rejection score exceeds a certain threshold. The processed data is utilized in the optimization problem, employing a hard contact model within the propagations of dynamics. When computing the gradient in the optimization problem, we specifically utilize the smoothed gradient of contact impulse with respect to the friction coefficient.
• Figure 4: The experimental results of friction coefficient identification show the effects of proposed smoothed gradients and rejection methods. Without smoothed gradients, non-informative gradients can impede friction coefficient identification. The rejection method allows for consistent friction coefficient identification, especially when the legged robot traverses nonslippery terrain. The purple area represents the slip states on the slippery terrains where the norm of tangential estimated foot velocity from the state estimator Joonha2023TRO exceeds 0.4 m/s.
• Figure 5: As depicted by a green dotted circle, the rejection method can effectively prevent undesired increases in the confidence score, especially on nonslippery terrain. Conversely, described by a red dotted circle, rejection scores do not significantly impede the increases in confidence scores when the robot slips on the slippery terrain.