Passive Static Equilibrium with Frictional Contacts and Application to Grasp Stability Analysis

TL;DR

This paper introduces a polynomial-time algorithm for passive grasp stability analysis that accounts for frictional contact behaviors, enabling efficient and physically consistent equilibrium solutions in two-dimensional grasps.

Contribution

It presents the first polynomial-time method to solve complex frictional equilibrium constraints in 2D grasps, considering slip and stick states at contacts.

Findings

Algorithm efficiently determines equilibrium or infeasibility.

Number of slip states considered is polynomial in contact count.

Captures realistic frictional contact behaviors and constraints.

Abstract

This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a model must account for friction phenomena at each contact; the difficulty is that friction forces depend in non-linear fashion on contact behavior (stick or slip). We develop the first polynomial-time algorithm which either solves such complex equilibrium constraints for two-dimensional grasps, or otherwise concludes that no solution exists. To achieve this, we show that the number of possible `slip states' (where each contact is labeled as either sticking or slipping) that must be considered is polynomial (in fact quadratic) in the number of contacts, and not exponential as previously thought. Our algorithm captures passive response behaviors at each contact, while accounting for constraints on friction forces such as the maximum dissipation principle.