Mobility of bodies in contact. I. A 2nd-order mobility index formultiple-finger grasps

Using a configuration-space approach, the paper develops a 2nd-order mobility theory for rigid bodies in contact. A major component of this theory is a coordinate invariant 2nd-order mobility index for a body, B, in frictionless contact with finger bodies A1,...A k. The index is an integer that captures the inherent mobility of B in an equilibrium grasp due to second order, or surface curvature, effects. It differentiates between grasps which are deemed equivalent by classical 1st-order theories, but are physically different. We further show that 2nd-order effects can be used to lower the effective mobility of a grasped object, and discuss implications of this result for achieving new lower bounds on the number of contacting finger bodies needed to immobilize an object. Physical interpretation and stability analysis of 2nd-order effects are taken up in the companion pape

Mobility of bodies in contact. II. How forces are generated bycurvature effects

For part I, see ibid., p.696-708. The paper considers how forces are produced by compliance and surface curvature effects in systems where an object a is kinematically immobilized to second-order by finger bodies Al,...,Ak. A class of configuration-space based elastic deformation models is introduced. Using these elastic deformation models, it is shown that any object which is kinematically immobilized to first or second-order is also dynamically locally asymptotically stable with respect to perturbations. Moreover, it is shown that for preloaded grasps kinematic immobility implies that the stiffness matrix of the grasp is positive definite. The stability result provides physical justification for using second-order effects for purposes of immobilization in practical applications. Simulations illustrate the concepts

The Stability of Heavy Objects with Multiple Contacts

In both robot grasping and robot locomotion, we wish to hold objects stably in the presence of gravity. We present a derivation of second-order stability conditions for a supported heavy object, employing the tool of Stratified Morse theory. We then apply these general results to the case of objects in the plane

New bounds on the number of frictionless fingers required to immobilize 2D objects

This paper develops new lower bounds on the number of frictionless fingers or fixtures which are required to immobilize planar objects. We study in detail the case of objects with smooth boundaries and polygonal objects. Analogous results for the case of piecewise smooth objects follow directly from the analysis presented herein. These results have obvious applications to fixture planning and grasp planning, as we show that it is possible to immobilize objects with fewer fingers than was previously thought possible

New bounds on the number of frictionless fingers required to immobilize 2D objects

This paper develops new lower bounds on the number of frictionless fingers or fixtures which are required to immobilize planar objects. We study in detail the case of objects with smooth boundaries and polygonal objects. Analogous results for the case of piecewise smooth objects follow directly from the analysis presented herein. These results have obvious applications to fixture planning and grasp planning, as we show that it is possible to immobilize objects with fewer fingers than was previously thought possible

A stiffness-based quality measure for compliant grasps and fixtures

This paper presents a systematic approach to quantifying the effectiveness of compliant grasps and fixtures of an object. The approach is physically motivated and applies to the grasping of two- and three-dimensional objects by any number of fingers. The approach is based on a characterization of the frame-invariant features of a grasp or fixture stiffness matrix. In particular, we define a set of frame-invariant characteristic stiffness parameters, and provide physical and geometric interpretation for these parameters. Using a physically meaningful scheme to make the rotational and translational stiffness parameters comparable, we define a frame-invariant quality measure, which we call the stiffness quality measure. An example of a frictional grasp illustrates the effectiveness of the quality measure. We then consider the optimal grasping of frictionless polygonal objects by three and four fingers. Such frictionless grasps are useful in high-load fixturing applications, and their relative simplicity allows an efficient computation of the globally optimal finger arrangement. We compute the optimal finger arrangement in several examples, and use these examples to discuss properties that characterize the stiffness quality measure

Gross motion analysis of fingertip-based within-hand manipulation

Fingertip-based within-hand manipulation, also called precision manipulation, refers to the repositioning of a grasped object within the workspace of a multi-fingered robot hand without breaking or changing the contact type between each fingertip and the object. Given a robot hand architecture and a set of assumed contact models, this paper presents a method to perform a gross motion analysis of its precision manipulation capabilities, regardless of the particularities of the object being manipulated. In particular, the technique allows the composition of the displacement manifold of the grasped object relative to the palm of the robot hand to be determined as well as the displacements that can be controlled—useful for high-level design and classification of hand function. The effects of a fingertip contacting a body in this analysis are modeled as kinematic chains composed of passive and resistant revolute joints; what permits the introduction of a general framework for the definition and classification of non-frictional and frictional contact types. Examples of the application of the proposed method in several architectures of multi-fingered hands with different contact assumptions are discussed; they illustrate how inappropriate contact conditions may lead to uncontrollable displacements of the grasped object

A survey of dextrous manipulation

technical reportThe development of mechanical end effectors capable of dextrous manipulation is a rapidly growing and quite successful field of research. It has in some sense put the focus on control issues, in particular, how to control these remarkably humanlike manipulators to perform the deft movement that we take for granted in the human hand. The kinematic and control issues surrounding manipulation research are clouded by more basic concerns such as: what is the goal of a manipulation system, is the anthropomorphic or functional design methodology appropriate, and to what degree does the control of the manipulator depend on other sensory systems. This paper examines the potential of creating a general purpose, anthropomorphically motivated, dextrous manipulation system. The discussion will focus on features of the human hand that permit its general usefulness as a manipulator. A survey of machinery designed to emulate these capabilities is presented. Finally, the tasks of grasping and manipulation are examined from the control standpoint to suggest a control paradigm which is descriptive, yet flexible and computationally efficient1