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, growing finger contact areas, and pointwise varying contact modes inside these areas. Consequently, contact constraints needed for deformable modeling are hardly established at the beginning of the grasping operation. This paper presents a grasping strategy that squeezes the object with two fingers under specified displacements rather than forces. A ‘stable’ squeeze minimizes the potential energy for the same amount of squeezing, while a ‘pure’ squeeze ensures that the object undergoes no rigid body motion as it deforms. Assuming linear elasticity, a finite element analysis guarantees equilibrium and the uniqueness of deformation during a squeeze action. An event-driven algorithm tracks the contact regions as well as the modes of contact in their interiors under Coulomb friction, which in turn serve as the needed constraints for deformation update. Grasp quality is characterized as the amount of work performed by the grasping fingers in resisting a known push by some adversary finger. Simulation and multiple experiments have been conducted to validate the results over solid and ring-like 2D objects.

A formal impulse-based analysis is presented for the collision of two rigid bodies at single contact point under Coulomb's friction in three dimensions (3D). The tangential impulse at the contact is known to be linear in the sliding velocity whose trajectory, parametrized with the normal impulse and referred to as the hodograph, is governed by a generally nonintegrable ordinary differential equation (ODE). Evolution of the hodograph is bounded by rays in several invariant directions of sliding in the contact plane. Exact lower and upper bounds are derived for the number of such invariant directions, utilizing the established positive definiteness of the matrix defining the governing ODE. If the hodograph reaches the origin, it either terminates (i.e., the contact sticks) or continues in a new direction (i.e., the contact resumes sliding) whose existence and uniqueness, only assumed in the literature, are proven. Closed-form integration of the ODE becomes possible as soon as the sliding velocity turns zero or takes on an invariant direction. Assuming Stronge's energy-based restitution, a complete algorithm is described to combine fast numerical integration (NI) with a case-by-case closed-form analysis. A number of solved collision instances are presented. It remains open whether the modeled impact process will always terminate under Coulomb's friction and Stronge's (or Poisson's) restitution hypothesis.

This paper describes a strategy for a robotic hand to pick up deformable 3D objects on a table. Inspired by human hand behavior, the robotic hand employs two rigid fingers to first squeeze such an object until it ''feels'' the object to be liftable. Such ''feeling'' is provided by a (virtual) liftability test that is repeatedly conducted during the squeeze. Passing of the test then triggers a lifting action. Throughout the manipulation the object's deformation and its state of contact with the fingers and the table are being tracked based on contact events. Deformable modeling uses the finite element method (FEM) while slip computation employs the homotopy continuation method to determine the contact displacements induced by finger movements. The experiment was conducted for everyday items ranging from vegetables to a toy. A simulation-based comparison between deformable grasping and rigid body grasping reveals why soft objects are easier to pick up than hard ones, and demonstrates how a rigid body grasping strategy may fail on soft objects in certain situations.

This work studies the dynamics of a 3D dimer bouncing upon a horizontal plate undergoing a vertical harmonic vibration. Despite complex interactions within the system due to impacts and friction, numerical simulation shows that, under certain conditions prescribed for the dynamics, the center of mass of the dimer, when projected onto a horizontal plane, will follow a circular orbit. The phenomenon is like a particle under Coulomb friction performing a ratchet motion that rotates around. Investigations further reveal that the dimer dynamics bear some typical characteristics of a nonlinear system, including sensitivity to the initial conditions and bifurcation behaviors related to the physical parameters of the dynamics. Our results indicate that the coefficient of restitution and the plate's vibration intensity play critical roles in exciting the circular orbit, while the dimer's geometry and the vibration frequency mainly influence the trajectory characteristics. These findings may help understand transport mechanisms underlying systems of granular matter with anisotropic particles.

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