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Hand synergies, or joint coordination patterns, have become an effective tool for achieving versatile robotic grasping with simple hands or planning algorithms. Here we propose a method to determine the hand synergies such that they can be physically implemented in an underactuated fashion. Given a kinematic hand model and a set of desired grasps, our algorithm optimizes a Mechanically Realizable Manifold designed to be achievable by a physical underactuation mechanism, enabling the resulting hand to achieve the desired grasps with few actuators. Furthermore, in contrast to existing methods for determining synergies which are only concerned with hand posture, our method explicitly optimizes the stability of the target grasps. We implement this method in the design of a three-finger single-actuator hand as an example, and evaluate its effectiveness numerically and experimentally.

This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a model must account for friction phenomena at each contact; the difficulty is that friction forces depend in non-linear fashion on contact behavior (stick or slip). We develop the first polynomialtime algorithm which either solves such complex equilibrium constraints for two-dimensional grasps, or otherwise concludes that no solution exists. To achieve this, we show that the number of possible "slip states" (where each contact is labeled as either sticking or slipping) that must be considered is polynomial (in fact quadratic) in the number of contacts, and not exponential as previously thought. Our algorithm captures passive response behaviors at each contact, while accounting for constraints on friction forces such as the maximum dissipation principle.

In this paper we focus on the following problem in multi-fingered robotic grasping: assuming that an external wrench is being applied to a grasped object, will the contact forces between the hand and the object, as well as the hand joints, respond in such a way as to preserve quasi-static equilibrium? In particular, we assume that there is no change in the joint torques being actively exerted by the motors; any change in contact forces and joint torques is due exclusively to passive effects arising in response to the external disturbance. Such passive effects include for example joints that are driven by highly geared motors (a common occurence in practice) and thus do not back drive in response to external torques. To account for nonlinear phenomena encountered in such cases, and which existing methods do not consider, we formulate the problem as a mixed integer program used in the inner loop of an iterative solver. We present evidence showing that this formulation captures important effects for assessing the stability of a grasp employing some of the most commonly used actuation mechanisms.Note to practitioners: Once a grasp of a given object has been chosen, our method has multiple possible applications. First, it can be used to determine how the choice of a pre-load (i.e. the torques applied to the joints as the grasp is created) affects the stability of the grasp. Second, once a pre-load has been chosen, our method can be used to determine which external disturbances can be resisted solely through passive effects, without further changes to the commands sent to the motors. We believe this approach is particularly relevant for the large family of grasping devices that are not equipped with tactile or proprioceptive sensors, and are thus unable to sense external disturbances or to control joint torques, but are still effective thanks to passive resistance effects.

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Passive reaction effects in grasp stability analysis occur when the contact forces and joint torques applied by a grasp change in response to external disturbances applied to the grasped object. For example, nonbackdrivable actuators (e.g. highly geared servos) will passively resist external disturbances without an actively applied command; for numerous robot hands using such motors, these effects can be highly beneficial as they increase grasp resistance without requiring active control. We introduce a grasp stability analysis method that can model these effects, and, for a given grasp, distinguish between disturbances that will be passively resisted and those that will not. We find that, in order to achieve this, the grasp model must include accurate energetic constraints. One way to achieve this is to consider the Maximum Dissipation Principle (MDP), a part of the Coulomb friction model that is rarely used in grasp stability analysis. However, the MDP constraints are non-convex, and difficult to solve efficiently. We thus introduce a convex relaxation method, along with an algorithm that successively refines this relaxation locally in order to obtain solutions to arbitrary accuracy efficiently. Our resulting algorithm can determine if a grasp is passively stable, solve for equilibrium contact forces and compute optimal actuator commands for stability. Its implementation is publicly available as part of the open-source GraspIt! simulator.