Planar sliding with dry friction Part 1. Limit surface and moment function

By S. Goyal, Andy Ruina, J. Papadopoulos. 1991

Abstract We present two geometric descriptions of the net frictional force and moment between a rigid body and a planar surface on which it slides. The limit surface, from classical plasticity theory, is the surface in load space which bounds the set of all possible frictional forces and moments that can be sustained by the frictional interface. Zhukovskii's moment function (N.E. Zhukovskii, Collected Works, Vol. 1, Gostekhizdat, Moscow, 1948, pp. 339–354) is the net frictional moment about the body's instantaneous center of rotation as a function of its location. Both of these descriptions implicitly contain the full relation between slip motion and frictional load. While Zhukovskii's moment function applies only to ordinary isotropic Coulomb friction, the limit surface applies to a wider class of friction laws that includes, for example, contact mediated by massless rigid wheels. Both the limit surface and the moment function can be used to deduce results concerning the motion of sliding rigid bodies.

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Citations in the corpus

Learning Synergies Between Pushing and Grasping with Self-Supervised Deep Reinforcement Learning (2018, neutral): “based [1], [2], [3] or data-driven [4], [5], [6] approaches.”
More than a million ways to be pushed. A high-fidelity experimental dataset of planar pushing (2016, background): “These are usually based on Coulomb’s friction law, often rewritten as the maximumpower inequality [16].”
A convex polynomial force-motion model for planar sliding: Identification and application (2016, background): “[10] who found that all possible generalized friction loads during sliding form a limit surface (LS) constructed from the Minkowsky sum of limit curves at individual support points.”
Three-dimensional limit analysis of rigid blocks assemblages. Part I: Torsion failure on frictional interfaces and limit analysis formulation (2005, background): “In fact, only the work of Goyal et al. (1991) was found in the literature.”
A Planning Framework for Non-Prehensile Manipulation under Clutter and Uncertainty (2012, unknown): “Goyal et al. (1991)”
Learning Visual Affordances for Robotic Manipulation (2019, background): “The literature in this area is vast, emerging early from classical solutions that explicitly model the dynamics of pushing with frictional forces [70, 35].”
Policy transfer via modularity (2017, background): “This study showed that most of the models that are normally used for estimating friction, such as the principle of maximum-power inequality [6] and the ellipsoidal approximation of a limit surface [8], do not always hold in”
Dynamic in-hand sliding manipulation (2015, background): “[9] describe the concept of a limit surface as a two-dimensional surface in a local three-dimensional forcemoment space.”
Mechanics, Planning, and Control for Tapping (1998, methodology): “Our analysis of the mechanics of a sliding object is built upon the work of Voyenli and Eriksen [20] who studied the motion of sliding disks and rings and the work of Goyal et al.([8] and [9]) who formulated a limit surface representation of the relationship between net frictional force and torque a”
Realtime State Estimation with Tactile and Visual Sensing. Application to Planar Manipulation (2017, methodology): “It is based on the Limit Surface (LS) [18] for force-motion mapping, and an ellipsoid approximation of LS [19] for fast computation.”
Policy transfer via modularity and reward guiding (2017, background): “However, pushing is a challenging task for robots due to frictional forces that are difﬁcult to model [6], [7], [8], [9].”