  In this paper we focus on the following problem in multi-fingered robotic
grasping: assuming that an external wrench is being applied to a grasped
object, will the contact forces between the hand and the object, as well as the
hand joints, respond in such a way as to preserve quasi-static equilibrium? In
particular, we assume that there is no change in the joint torques being
actively exerted by the motors; any change in contact forces and joint torques
is due exclusively to passive effects arising in response to the external
disturbance. Such passive effects include for example joints that are driven by
highly geared motors (a common occurence in practice) and thus do not back
drive in response to external torques. To account for non- linear phenomena
encountered in such cases, and which existing methods do not consider, we
formulate the problem as a mixed integer program used in the inner loop of an
iterative solver. We present evidence showing that this formulation captures
important effects for assessing the stability of a grasp employing some of the
most commonly used actuation mechanisms.
