  Passive reaction effects in grasp stability analysis occur when the contact
forces and joint torques applied by a grasp change in response to external
disturbances applied to the grasped object. For example, nonbackdrivable
actuators (e.g. highly geared servos) will passively resist external
disturbances without an actively applied command; for numerous robot hands
using such motors, these effects can be highly beneficial as they increase
grasp resistance without requiring active control. We introduce a grasp
stability analysis method that can model these effects, and, for a given grasp,
distinguish between disturbances that will be passively resisted and those that
will not. We find that, in order to achieve this, the grasp model must include
accurate energetic constraints. One way to achieve this is to consider the
Maximum Dissipation Principle (MDP), a part of the Coulomb friction model that
is rarely used in grasp stability analysis. However, the MDP constraints are
non-convex, and difficult to solve efficiently. We thus introduce a convex
relaxation method, along with an algorithm that successively refines this
relaxation locally in order to obtain solutions to arbitrary accuracy
efficiently. Our resulting algorithm can determine if a grasp is passively
stable, solve for equilibrium contact forces and compute optimal actuator
commands for stability. Its implementation is publicly available as part of the
open-source GraspIt! simulator.
