Beyond Coulomb: Stochastic Friction Models for Practical Grasping and Manipulation (2023)

Reliable grasping and manipulation in daily tasks and unstructured environments require accurate contact modeling and grasp stability estimation. A key component is the coefficient of friction, which is variable and dependent on many factors. However, robotics applications often use Coulomb's model of friction, which ignores this variability and instead assumes that the coefficient of friction is a constant. In this work, we conducted sliding experiments with robot fingers and a robot hand, and show that rubber friction varies strongly with normal force <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F_{n}$</tex-math></inline-formula> and contact velocity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$v$</tex-math></inline-formula> , and includes a significant stochastic component. We present a framework for modeling the coefficient of friction <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> as a distribution rather than a constant, and show how this distribution can be narrowed when given a prior on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F_{n}$</tex-math></inline-formula> or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$v$</tex-math></inline-formula> . For a given distribution, the likelihood of slipping is a continuous function with respect to the tangential-to-normal force ratio, instead of a step function according to Coulomb's law. By modeling friction as a function of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F_{n}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$v$</tex-math></inline-formula> , we demonstrate that friction parameters can be estimated using regression models from a single sliding stroke of the fingertip against the object surface, and that strokes spanning a larger range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F_{n}$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$v$</tex-math></inline-formula> space provide better friction estimates. These results can be applied to grasp control to enable a quantitative trade-off between the likelihood of slipping vs. grasp force levels, and to sliding manipulation planning by elucidating the relationship between desired velocity and anticipated force levels. Application of this model to machine learning has the potential to enhance reinforcement learning and sim-to-real transfer by providing more accurate representations of frictional behavior.