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

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