Simulation of grasping tasks using the nonsmooth generalized-alpha method

In robotics, a grasping task involves a mechanical interaction between a robotic arm, its end-effector and the object to be grasped. In this work, the robot and the end-effector are modelled as a multibody system composed of a set of bodies and kinematic joints, which interact with the object through unilateral contact conditions with friction. Therefore, the equations of motion include a set of nonlinear bilateral and unilateral constraints, which can become redundant depending on the contact status.

Previously, we have developed the nonsmooth generalized-alpha method for mechanical systems with frictionless contact conditions. The aim of the method is to combine the robustness of the nonsmooth contact dynamics method with a second-order generalized-alpha scheme in order to capture accurately dynamic and vibration phenomena. Also, all constraints can be enforced simultaneously at position and velocity levels provided the definition of a suitable constraint activation strategy in a Newton semi-smooth algorithm. This means that the non-penetrability condition is enforced exactly together with an impact law at velocity level.

In this talk, we discuss the applicability of this method to grasping problems with constraint redundancy and friction phenomena. The activation status is more complex in this case as (i) the Lagrange multipliers are not uniquely defined, (ii) the transitions between non-contact, sliding contact and sticking contact states have to be handled properly.