  Caging is a promising tool which allows a robot to manipulate an object
without directly reasoning about the contact dynamics involved. Furthermore,
caging also provides useful guarantees in terms of robustness to uncertainty,
and often serves as a way-point to a grasp. Unfortunately, previous work on
caging is often based on computational geometry or discrete topology tools,
causing restriction on gripper geometry, and difficulty on integration into
larger manipulation frameworks. In this paper, we develop a
convex-combinatorial model to characterize caging from an optimization
perspective. More specifically, we study the configuration space of the object,
where the fingers act as obstacles that enclose the configuration of the
object. The convex-combinatorial nature of this approach provides guarantees on
optimality, convergence and scalability, and its optimization nature makes it
adaptable for further applications on robot manipulation tasks.
