We propose a polynomial force-motion model for planar sliding. The set of generalized friction loads is the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. Additionally, 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. Simulation and robotic experiments validate the accuracy and efficiency of our approach. We also show practical applications of our model including stable pushing of objects and free sliding dynamic simulations.

Regrasping is the process of adjusting the position and orientation of an object in one's hand. The study of robotic regrasping has generally been limited to use of theoretical analytical models and cases with little uncertainty. Analytical models and simulations have so far proven unable to capture the complexity of the real world. Empirical statistical models are more promising, but collecting good data is difficult. In this paper, we collect data from 3300 robot regrasps, and use this data to learn two probability functions: 1) The probability that the object is still in the robot's hand after a regrasp action; and 2) The probability distribution of the object pose after the regrasp given that the object is still grasped. Both of these functions are learned using kernel density estimation with a similarity metric over object pose. We show that our data-driven models achieve comparable accuracy to a geometric model and an off-the-shelf simulator in classification and prediction tasks, while also enabling us to predict probability distributions.

Pivoting is the rotation of an object between two fingers using gravity and inertial forces to impart angular momentum. We present an analysis of the mechanics of pivoting and a framework for planning and execution. Extrinsic dexterity was defined by Chavan-Dafle et al. [1] as the use of external forces, such as gravity and inertial forces in post grasp manipulation. We analyze one such regrasp termed “pivoting” by Rao et al. [2]. We find a grasp and arm trajectory which can rotate an object between stable poses, if any. We demonstrate an implementation of pivoting with an ABB industrial arm and a two fingered gripper.

“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 hand-scripted, 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.

This video presents the application of Extrinsic Dexterity to change the pose of an object in the hand, i.e., to regrasp the object.