Form-closure caging grasps of polygons with a parallel-jaw gripper

Parallel-jaw gripper finds wide applications in various industrial sectors. In this paper, we mainly focus on the problem of form closure caging grasps of polygons with a parallel-jaw gripper equipped with four fingers. The form closure caging grasp is helpful for the fingers placements and contact region selections of a pneumatic gripper, as it is less sensitive to fingers misplacements. We firstly prove that there is always a path from a cage to a form closure grasp of the object that never breaks the cage, as long as the attractive region constructed in the configuration space has a local minimum. If such a minimum cannot be found, we further adjust the fingers arrangements to produce the form closure grasp. Meanwhile, we also develop an algorithm to compute the initial cage of the form closure grasp. Simulations of the grasping process witness the effectiveness of the above analysis results.