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

This letter 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.

I. Introduction

For legged robots navigating challenging terrain, contact modeling for considering the interaction between the robot and terrain is crucial. The modeling is particularly critical on slippery terrain, where the robots encounter nonlinear and hybrid dynamics due to foot slippage. Recently, contact modelings using rigid body contact dynamics have gained attention in the field of legged robots [1], [2], [3], [4].