  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.
