A Convex-Combinatorial Model for Planar Caging

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. However, caging is traditionally difficult to integrate as part of larger manipulation frameworks, where caging is not the goal but an intermediate condition. In this paper, we develop a convex-combinatorial model to characterize caging from an optimization perspective. More specifically, we derive a set of sufficient constraints to enclose the configuration of the object in a compact-connected component of its free-space. The convex-combinatorial nature of this approach provides guarantees on optimality and convergence, and its optimization nature makes it versatile for further applications on robot manipulation tasks. To the best of our knowledge, this is the first optimization-based approach to formulate the caging condition.