  [...] We argue that the traditional grasp modeling theory assumes a
complexity that most robotic hands do not possess and is therefore of limited
applicability to the robotic hands commonly used today. We discuss these
limitations of the existing grasp modeling literature and set out to develop
our own tools for the analysis of passive effects in robotic grasping. We show
that problems of this kind are difficult to solve due to the non-convexity of
the Maximum Dissipation Principle (MDP), which is part of the Coulomb friction
law. We show that for planar grasps the MDP can be decomposed into a number of
piecewise convex problems, which can be solved for efficiently. [...] Thus, we
present the first polynomial runtime algorithm for the determination of passive
stability of planar grasps. For the spacial case we [...] describe a convex
relaxation of the Coulomb friction law and a successive hierarchical tightening
approach that allows us to find solutions to the exact problem including the
maximum dissipation principle. [...] The generality of our grasp model allows
us to solve a wide variety of problems such as the computation of optimal
actuator commands. This makes our framework a valuable tool for practical
manipulation applications. Our work is relevant beyond robotic manipulation as
it applies to the stability of any assembly of rigid bodies with frictional
contacts, unilateral constraints and externally applied wrenches. Finally, we
argue that with the advent of data-driven methods as well as the emergence of a
new generation of highly sensorized hands there are opportunities for the
application of the traditional grasp modeling theory to fields such as robotic
in-hand manipulation through model-free reinforcement learning. We present a
method that applies traditional grasp models to maintain quasi-static stability
throughout a nominally model-free reinforcement learning task. [...]
