Abstract-"In-hand manipulation" is the ability to reposition an object in the hand, for example when adjusting the grasp of a hammer before hammering a nail. The common approach to in-hand manipulation with robotic hands, known as dexterous manipulation [1], is to hold an object within the fingertips of the hand and wiggle the fingers, or walk them along the object's surface. Dexterous manipulation, however, is just one of the many techniques available to the robot. The robot can also roll the object in the hand by using gravity, or adjust the object's pose by pressing it against a surface, or if fast enough, it can even toss the object in the air and catch it in a different pose. All these techniques have one thing in common: they rely on resources extrinsic to the hand, either gravity, external contacts or dynamic arm motions. We refer to them as "extrinsic dexterity".In this paper we study extrinsic dexterity in the context of regrasp operations, for example when switching from a power to a precision grasp, and we demonstrate that even simple grippers are capable of ample in-hand manipulation. We develop twelve regrasp actions, all open-loop and handscripted, and evaluate their effectiveness with over 1200 trials of regrasps and sequences of regrasps, for three different objects (see video [2]). The long-term goal of this work is to develop a general repertoire of these behaviors, and to understand how such a repertoire might eventually constitute a general-purpose in-hand manipulation capability.

We propose a polynomial model for planar sliding mechanics. For the force-motion mapping, we treat the set of generalized friction loads as the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. The polynomial is confined to be convex even-degree homogeneous in order to obey the maximum work inequality, symmetry, shape invariance in scale, and fast invertibility. We present a simple and statistically efficient model identification procedure using a sum-of-squares convex relaxation. We then derive the kinematic contact model that resolves the contact modes and instantaneous object motion given a position controlled manipulator action. The inherently stochastic object-to-surface friction distributions are modeled by sampling polynomial parameters from distributions that preserve sum-of-squares convexity. Thanks to the model smoothness, the mechanics of patch contact is captured while being computationally efficient without mode selection at support points. Simulation and robotic experiments on pushing and grasping validate the accuracy and efficiency of our approach.

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Grasping an object is usually only an intermediate goal for a robotic manipulator. To finish the task, the robot needs to know where the object is in its hand and what action to execute. This paper presents a general statistical framework to address these problems. Given a novel object, the robot learns a statistical model of grasp state conditioned on sensor values. The robot also builds a statistical model of the requirements of the task in terms of grasp state accuracy. Both of these models are constructed by offline experiments. The online process then grasps objects and chooses actions to maximize likelihood of success. This paper describes the framework in detail, and demonstrates its effectiveness experimentally in placing, dropping, and insertion tasks. To construct statistical models, the robot performed over 8000 grasp trials, and over 1000 trials each of placing, dropping and insertion.