Imin Kao

Computing and controlling compliance of a robotic hand

The authors express the compliance of the grasp of a robotic hand as a function of grasp geometry, contact conditions between the fingers and the grasped object, and mechanical properties of the fingers. It is argued that the effects of structural compliance and small changes in the grasp geometry should be included in the computation. Factors are then examined that can lead a grasp to become unstable, independently of whether it satisfies force closure. Finally, the authors examine the reverse problem of how to specify servo gains at the joints of a robotic hand so as to achieve, as nearly as possible, a desired overall grasp compliance. It is shown that coupling between the joints of different fingers is useful in this context. >

Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers

In this paper, we develop the theoretical work on the properties and mapping of stiffness matrices between joint and Cartesian spaces of robotic hands and fingers, and propose the conservative congruence transformation (CCT). In this paper, we show that the conventional formulation between the joint and Cartesian spaces, K θ = J T θ K p J θ , first derived by Salisbury in 1980, is only valid at the unloaded equilibrium configuration. Once the grasping configuration is deviated from its unloaded configuration (for example, by the application of an external force), the conservative congruence transformation should be used. Theoretical development and numerical simulation are presented. The conservative congruence transformation accounts for the change in geometry via the differential Jacobian (Hessian matrix) of the robot manipulators when an external force is applied. The effect is captured in an effective stiffness matrix, K g , of the conservative congruence transformation. The results of this paper also indicate that the omission of the changes in Jacobian in the presence of external force would result in discrepancy of the work and lead to contradiction to the fundamental conservative properties of stiffness matrices. Through conservative congruence transformation, conservative and consistent physical properties of stiffness matrices can be preserved during mapping regardless of the usage of coordinate frames and the existence of external force.

Modeling of Contact Mechanics and Friction Limit Surfaces for Soft Fingers in Robotics, with Experimental Results:

A new theory in contact mechanics for modeling of soft fingers is proposed to define the relationship between the normal force and the radius of contact for soft fingers by considering general soft-finger materials, including linearly and nonlinearly elastic materials. The results show that the radius of contact is proportional to the normal force raised to the power of, which ranges from 0 to 1/3. This new theory subsumes the Hertzian contact model for linear elastic materials, where D 1/3. Experiments are conducted to validate the theory using artificial soft fingers made of various materials such as rubber and silicone. Results for human fingers are also compared. This theory provides a basis for numerically constructing friction limit surfaces. The numerical friction limit surface can be approximated by an ellipse, with the major and minor axes as the maximum friction force and the maximum moment with respect to the normal axis of contact, respectively. Combining the results of the contactmechanics model with the contact-pressure distribution, the normalized friction limit surface can be derived for anthropomorphic soft fingers. The results of the contact-mechanics model and the pressure distribution for soft fingers facilitate the construction of numerical friction limit surfaces, and will enable us to analyze and simulate contact behaviors of grasping and manipulation in robotics.

Quasistatic manipulation with compliance and sliding

We propose a method for modeling dextrous manipulation with sliding fingers. The approach combines compliance and friction limit surfaces. The method is useful for describing how a grasp will behave in the presence of external forces (e.g., when and how the fingertips will slide) and for planning how to control the fingers so that the grasped object will follow a desired trajectory. The sliding trajectories are characterized by a transient and steady-state solution. The underlying theory is first dis cussed and illustrated with several single-finger examples. Experimental results are also presented. The analysis is then extended to grasps with multiple sliding and nonslid ing fingers. The multifinger analysis is illustrated with an example of manipulating a card with two soft-contact fingers.

The sliding of robot fingers under combined torsion and shear loading

The authors are concerned with finding the magnitudes of applied moment and force which will cause a robot finger to slip on the surface of a grasped object. Friction and contact models used in previous grasp analyses are reviewed, and an improved model which includes torsion-shear interaction is described. Experimental measurements of the initiation of sliding as a function of loading are reported. These measurements suggest that a simple linear function of torsion and shear magnitudes will adequately predict the onset of the slip in many tasks. The use of this function is illustrated in two measures of slip susceptibility for grasp planning.<<ETX>>

Stiffness and contact mechanics for soft fingers in grasping and manipulation

In this paper, nonlinear stiffness of contact for soft fingers, commonly used in robotic grasping and manipulation, under a normal load is studied. Building upon previous research results of soft-finger contact expressed in the power-law equation, the equation for the nonlinear stiffness of soft contact was derived. This new theory relates the approach displacement (or the vertical depression) of soft fingertips with respect to the normal force applied. The nonlinear contact stiffness is found to be the product of an exponent and the ratio of the normal force versus approach displacement. Stiffness relationship of Hertzian contact for linear elastic materials is shown to be a special case of the general theory presented in this paper. Experimental results are used to validate the theoretical analysis. In addition, potential applications to fixturing are discussed.

Robotic stiffness control and calibration as applied to human grasping tasks

In this paper, we study stiffness analysis as applied to human grasping. Grasp stiffness has been demonstrated to be useful for modeling and controlling robotic manipulators. The computation of general linear R/sup 3/spl times/3/ stiffness matrices for grasping, which can be decomposed into symmetric (conservative) and asymmetric (nonconservative) components, offers physical insights for stiffness control in robotics as well as human grasping. Methods of stiffness calibration, using least-squares best fits with and without symmetry constraints, are presented and applied to the force and displacement data obtained from grasping tasks to study human grasping behaviors. The results of this study show that a linear relationship between force and displacement is capable of capturing the characteristics of the experimental data of human grasps for which displacements are small (on the order of one to seven mm). Different measures, proposed and developed in the robotics literature, are employed to predict the behavior of human grasps in reacting to externally applied loads.

Grasping, manipulation, and control with tactile sensing

Preliminary experiments are presented concerning the use of tactile sensing to enhance the flexibility and robustness of robotic manipulation. A simple two-fingered manipulator with very clean dynamics has been constructed to focus on tactile and force sensing in manipulation. Manipulation is characterized by constantly changing mechanical systems, as fingers make or break contact or start to roll or slide on the surface of a grasped object. It is important to detect these changes since control schemes must change to match the varying task requirements. Following the human model, it is shown that dynamic tactile sensors can reliably detect the changing contact conditions. In a simple grasp-lift-replace task, use of these sensors enables the manipulator to cope with uncertainty in object location and task forces.<<ETX>>

Study of soft-finger contact mechanics using finite elements analysis and experiments

Nonlinear finite element analysis is employed to study the soft-finger contact mechanics. Two fingertips of the same material but with different sizes are analyzed. The results are compared with experiments to support the power-law theory proposed by Xydas and Kao (1999). The material properties used in the FEM analysis are based upon uniaxial compression experiments conducted using the actual fingertip material. The coefficient of friction is also experimentally determined and applied in the simulation. Comparisons of numerical as well as experimental radii of contact are offered in conjunction with the power-law theory for soft fingers. The pressure distribution profile at the contact zone, obtained from the finite elements analysis, is plotted and the order of the generalized pressure distribution profile is calculated. Finally, the influence of friction over the contact area is investigated using FEM analysis.

A review of modeling of soft-contact fingers and stiffness control for dextrous manipulation in robotics

Dextrous manipulation involves a variety of subjects in robotics, including kinematics, rolling and sliding, contact mechanics, grasping planning and optimization, dynamics, and control. It is generally postulated in the literature that contacts in all grasping and manipulation are point contacts or soft contacts. The former can be modeled as either a frictionless point contact or a frictional point contact; the latter, although being a more practical model, has not been commonly utilized. In this paper, the recent progress in the modeling of dextrous manipulation utilizing soft contacts and stiffness control is presented. The result augments the well-known Hertzian contact model from linear elastic contacts to soft contacts. In addition, the conservative congruence transformation for stiffness control in robotics, that are often used in dextrous grasping and manipulation, is presented.