Contact Space Computation of Two-Finger Gravity Based Caging Grasps Security Measure

Gravity based caging describes robotic grasps where the robot hand forms a basket-shape supporting an object against gravity. Basket grasps allow secure object transport with simple hands that use a small number of fingers. A basket grasp can be described in the grasped object configuration space as a cavity formed by the supporting finger c-obstacles and the grasped object gravitational energy. A puncture point exists from which the object c-space trajectory escapes out of the cavity with minimal increase in its gravitational energy, which defines the basket grasp depth. This letter describes an algorithm that computes the depth of basket grasps formed by two-finger robotic hands in 2-D gravitational environments. In the basket depth problem, contact space parametrizes all single and two-finger contacts on the supported object boundary as well as the object orientation on the supporting fingers. Starting from a candidate basket grasp, the algorithm incrementally constructs and searches a basket graph embedded in the low-dimensional contact space. The graph edges represent physical movements of the object in contact with the supporting fingers and the object's minimal-height escape path on the graph determines the basket grasp security measure. The algorithm is fully implemented and demonstrated on representative examples ranging from simplified to realistic objects.