Passive Reaction Analysis for Grasp Stability

In this paper, we focus on the following problem in multifingered 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 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 occurrence in practice) and thus do not back drive in response to external torques. To account for nonlinear 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. Note to Practitioners -Once a grasp of a given object has been chosen, our method has multiple possible applications. First, it can be used to determine how the choice of a preload (i.e., the torques applied to the joints as the grasp is created) affects the stability of the grasp. Second, once a preload has been chosen, our method can be used to determine which external disturbances can be resisted solely through passive effects, without further changes to the commands sent to the motors. We believe this approach is particularly relevant for the large family of grasping devices that are not equipped with tactile or proprioceptive sensors, and are thus unable to sense external disturbances or to control joint torques, but are still effective thanks to passive resistance effects.