Passive Static Equilibrium with Frictional Contacts and Application to Grasp Stability Analysis
This addresses grasp stability analysis for robotics, providing a computationally efficient method for physically consistent modeling, though it is incremental in improving algorithmic complexity.
The paper tackles the problem of passive grasp stability under external disturbances by accounting for friction at contacts, and develops the first polynomial-time algorithm that solves equilibrium constraints for 2D grasps or determines no solution exists, reducing the number of slip states considered from exponential to quadratic in contacts.
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.