A polyhedral bound on the indeterminate contact forces in 2D fixturing and grasping arrangements

This paper considers 2D contact arrangements where several bodies grasp, fixture, or support an object via frictional point contacts. Within a strictly rigid body modelling paradigm, when an external wrench (i.e. force and torque) acts on the object, the reaction forces at the contacts are indeterminate and span an unbounded linear space. This paper analyzes the contact forces within a quasi-rigid body framework that keeps the desirable geometric properties of rigid body modelling, while also includes more realistic physical effects. Using two principles governing the mechanics of quasi-rigid contacts, we show that for any given external wrench acting on the object, the contact forces lie in a bounded polyhedral set. The polyhedral bound depends on the external wrench, the grasp's geometry, and the preload forces. But it does not depend on any detailed knowledge of the contact mechanics parameters. The bound is useful for "robust" grasp and fixture synthesis. Given a collection of external wrenches that may act on an object, the grasp's geometry and preload forces can be chosen such that all of these external wrenches would be automatically supported by the contacts

Grasping With Mechanical Intelligence

Many robotic hands have been designed and a number have been built. Because of the difficulty of controlling and using complex hands, which usually have nine or more degrees of freedom, the simple one- or two-degree-of-freedom gripper is still the most common robotic end effector. This thesis presents a new category of device: a medium-complexity end effector. With three to five degrees of freedom, such a tool is much easier to control and use, as well as more economical, compact and lightweight than complex hands. In order to increase the versatility, it was necessary to identify grasping primitives and to implement them in the mechanism. In addition, power and enveloping grasps are stressed over fingertip and precision grasps. The design is based upon analysis of object apprehension types, requisite characteristics for active sensing, and a determination of necessary environmental interactions. Contained in this thesis are the general concepts necessary to the design of a medium-complexity end effector, an analysis of typica.1 performance, and a computer simulation of a grasp planning algorithm specific to this type of mechanism. Finally, some details concerning the UPenn Hand - a tool designed for the research laboratory - are presented

Contact Force Analysis in Static Two-fingered Robot Grasping

[[abstract]]Static grasping of a spherical object by two robot fingers is studied in this paper. The fingers may be rigid bodies or elastic beams, they may grasp the body with various orientation angles, and the tightening displacements may be linear or angular. Closed-form solutions for normal and tangential contact forces due to tightening displacements are obtained by solving compatibility equations, force-displacement relations based on Hertz contact theory, and equations of equilibrium. Solutions show that relations between contact forces and tightening displacements depend upon the orientation of the fingers, the elastic constants of the materials, and area moments of inertia of the beams.[[sponsorship]]American Society of Mechanical Engineers[[notice]]補正完成[[incitationindex]]EI[[conferencetype]]國際[[conferencedate]]20130804~20130807[[booktype]]電子版[[iscallforpapers]]Y[[conferencelocation]]Portland, Oregon, US

Mechanics of Hybrid Active/Passive-Closure Grasps

In this paper, we discuss the directions of active and passive force closures in hybrid active/passive-closure grasps. We show the directions are orthogonal to each other. We also discuss the magnitudes of the internal forces in the manipulation of the object. In hybrid active/passive-closure grasps, there exist two kinds of magnitudes of internal forces. One is the magnitude of internal forces, which changes if the object moves and the geometry of the fingers changes. The other is the one which don’t change even when the object moves. We derive these two magnitudes

A Contact Stress Model for Determining Forces in an Equilibrium Grasp

Most available methods that predict the forces necessary to grasp an arbitrary object treat the object and the fingers as rigid bodies and the finger/object interface as a point contact with Coulomb friction. For statically indeterminate grasps, therefore, while it is possible to find grasps that are stable, there is no unique determination of the actual forces at the contact points and equilibrium grasps are determined as many-parameter families of solutions. Also, these models sometimes lead to phenomenologically incorrect results which, while satisfactory from a purely mathematical viewpoint, are counterintuitive and not likely to be realized in practice. The model developed here utilizes a contact-stress analysis of an arbitrarily shaped object in a multi-fingered grasp. The fingers and the object are all treated as elastic bodies and the region of contact is modeled as a deformable surface patch. The relationship between the friction and normal forces is now nonlocal and nonlinear in nature and departs from the Coulomb approximation. The nature of the constraints arising out of conditions for compatibility and static equilibrium motivated the formulation of the model as a non-linear constrained minimization problem. The total potential energy of the system is minimized, subject to the nonlinear, equality and inequality constraints on the system, using the Schittkowski algorithm. The model is able to predict the magnitude of the inwardly directed normal forces, and both the magnitude and direction of the tangential (friction) forces at each finger/object interface for grasped objects in static equilibrium. Examples in two and three dimensions are presented along with application of the model to the grasp transfer maneuver

Object Manipulation under Hybrid Active/Passive Closure

In this paper, we discuss the manipulation of an object under hybrid active/passive closure. We show the orthogonality between the directions of active and passive force closures for general grasping systems. Based on the orthogonality, we decompose the dynamics of grasping system into the "active part" and the "passive part". By using the decomposition, we show that the grasped object can be manipulated only by considering the dynamics of the active part. We also consider how to determine the desired internal forces in order to satisfy frictional constraints during the manipulation. In order to verify the validity of our approach, some simulation results are shown

Grasp Stability Analysis with Passive Reactions

Despite decades of research robotic manipulation systems outside of highly-structured industrial applications are still far from ubiquitous. Perhaps particularly curious is the fact that there appears to be a large divide between the theoretical grasp modeling literature and the practical manipulation community. Specifically, it appears that the most successful approaches to tasks such as pick-and-place or grasping in clutter are those that have opted for simple grippers or even suction systems instead of dexterous multi-fingered platforms. We argue that the reason for the success of these simple manipulation systemsis what we call passive stability: passive phenomena due to nonbackdrivable joints or underactuation allow for robust grasping without complex sensor feedback or controller design. While these effects are being leveraged to great effect, it appears the practical manipulation community lacks the tools to analyze them. In fact, we argue that the traditional grasp modeling theory assumes a complexity that most robotic hands do not possess and is therefore of limited applicability to the robotic hands commonly used today. We discuss these limitations of the existing grasp modeling literature and setout to develop our own tools for the analysis of passive effects in robotic grasping. We show that problems of this kind are difficult to solve due to the non-convexity of the Maximum Dissipation Principle (MDP), which is part of the Coulomb friction law. We show that for planar grasps the MDP can be decomposed into a number of piecewise convex problems, which can be solved for efficiently. Despite decades of research robotic manipulation systems outside of highlystructured industrial applications are still far from ubiquitous. Perhaps particularly curious is the fact that there appears to be a large divide between the theoretical grasp modeling literature and the practical manipulation community. Specifically, it appears that the most successful approaches to tasks such as pick-and-place or grasping in clutter are those that have opted for simple grippers or even suction systems instead of dexterous multi-fingered platforms. We argue that the reason for the success of these simple manipulation systemsis what we call passive stability: passive phenomena due to nonbackdrivable joints or underactuation allow for robust grasping without complex sensor feedback or controller design. While these effects are being leveraged to great effect, it appears the practical manipulation community lacks the tools to analyze them. In fact, we argue that the traditional grasp modeling theory assumes a complexity that most robotic hands do not possess and is therefore of limited applicability to the robotic hands commonly used today. We discuss these limitations of the existing grasp modeling literature and setout to develop our own tools for the analysis of passive effects in robotic grasping. We show that problems of this kind are difficult to solve due to the non-convexity of the Maximum Dissipation Principle (MDP), which is part of the Coulomb friction law. We show that for planar grasps the MDP can be decomposed into a number of piecewise convex problems, which can be solved for efficiently. We show that the number of these piecewise convex problems is quadratic in the number of contacts and develop a polynomial time algorithm for their enumeration. Thus, we present the first polynomial runtime algorithm for the determination of passive stability of planar grasps. For the spacial case we present the first grasp model that captures passive effects due to nonbackdrivable actuators and underactuation. Formulating the grasp model as a Mixed Integer Program we illustrate that a consequence of omitting the maximum dissipation principle from this formulation is the introduction of solutions that violate energy conservation laws and are thus unphysical. We propose a physically motivated iterative scheme to mitigate this effect and thus provide the first algorithm that allows for the determination of passive stability for spacial grasps with both fully actuated and underactuated robotic hands. We verify the accuracy of our predictions with experimental data and illustrate practical applications of our algorithm. We build upon this work and describe a convex relaxation of the Coulombfriction law and a successive hierarchical tightening approach that allows us to find solutions to the exact problem including the maximum dissipation principle. It is the first grasp stability method that allows for the efficient solution of the passive stability problem to arbitrary accuracy. The generality of our grasp model allows us to solve a wide variety of problems such as the computation of optimal actuator commands. This makes our framework a valuable tool for practical manipulation applications. Our work is relevant beyond robotic manipulation as it applies to the stability of any assembly of rigid bodies with frictional contacts, unilateral constraints and externally applied wrenches. Finally, we argue that with the advent of data-driven methods as well as theemergence of a new generation of highly sensorized hands there are opportunities for the application of the traditional grasp modeling theory to fields such as robotic in-hand manipulation through model-free reinforcement learning. We present a method that applies traditional grasp models to maintain quasi-static stability throughout a nominally model-free reinforcement learning task. We suggest that such methods can potentially reduce the sample complexity of reinforcement learning for in-hand manipulation.We show that the number of these piecewise convex problems is quadratic in the number of contacts and develop a polynomial time algorithm for their enumeration. Thus, we present the first polynomial runtime algorithm for the determination of passive stability of planar grasps