Evaluating a grasp generated by a set of hand-object contact locations is a key component of many grasp planning algorithms. In this paper, we present a novel second-order cone program (SOCP) based optimization formulation for evaluating a grasps’ ability to apply wrenches to generate a linear motion along a given direction and/or an angular motion about the given direction. Our quality measure can be computed efficiently since the SOCP is a convex optimization problem, which can be solved optimally with interior point methods. A key feature of our approach is that we can consider the effect of contact wrenches from any contact of the object with the environment. This is different from the extant literature where only the effect of finger-object contacts is considered. Exploiting the environmental contact is useful in many manipulation scenarios either to enhance the dexterity of simple hands or improve the payload capability of the manipulator. In contrast to most existing approaches, our approach also takes into account the practical constraint that the maximum contact force that can be applied at a finger-object contact can be different for each contact. We can also include the effect of external forces like gravity, as well as the joint torque constraints of the fingers/manipulators. Furthermore, for a given motion path as a constant screw motion or a sequence of constant screw motions, we can discretize the path and compute a global grasp metric to accomplish the whole task with a chosen set of finger-object contact locations.

We present a principled method for motion prediction via dynamic simulation for rigid bodies in intermittent contact with each other where the contact is assumed to be a planar non-convex contact patch. The planar non-convex contact patch can either be a topologically connected set or disconnected set. Such algorithms are useful in planning and control for robotic manipulation. Most work in rigid body dynamic simulation assume that the contact between objects is a point contact, which may not be valid in many applications. In this paper, by using the convex hull of the contact patch, we build on our recent work on simulating rigid bodies with convex contact patches, for simulating motion of objects with planar non-convex contact patches. We formulate a discrete-time mixed complementarity problem where we solve the contact detection and integration of the equations of motion simultaneously. Thus, our method is a geometrically-implicit method and we prove that in our formulation, there is no artificial penetration between the contacting rigid bodies. We solve for the equivalent contact point (ECP) and contact impulse of each contact patch simultaneously along with the state, i.e., configuration and velocity of the objects. We provide empirical evidence to show that our method can seamlessly capture transition between different contact modes like patch contact to multiple or single point contact during simulation.