Grasping deformable planar objects: Squeeze, stick/slip analysis, and energy-based optimalities

Robotic grasping of deformable objects is difficult and under-researched not simply due to the high computational cost of modeling. More fundamentally, several issues arise with the deformation of an object being grasped: a changing wrench space, (generally) growing finger contact areas, and pointwise varying contact modes inside these areas. Consequently, constraints needed for deformable modeling by the finite element method (FEM) are hardly established at the beginning of the action. This paper presents a grasping strategy that squeezes the object with two fingers under specified displacements rather than forces. Assuming linear elasticity, an FEM-based analysis ensures equilibrium and the uniqueness of deformation during the action. An event-driven algorithm tracks the contact regions as well as the modes of contact in their interiors, which in turn serve as the needed constraints for deformation update. The classes of “stable” and “pure” squeezes are introduced. Grasp quality is characterized by the amount of work done by the grasping fingers to resist a known disturbance by some adversary finger. An optimization algorithm is progressively developed for segment contacts under Coulomb friction. Simulation and multiple experiments have been conducted to validate the results over solid and ring-like 2D objects.