When an object is held by a multi-fingered hand, the values of the contact forces can be multivalued. An objective function, when used in conjunction with the frictional and geometric constraints of the grasp, can however, give a unique set of finger force values. The selection of the objective function in determining the finger forces is dependent on the type of grasp required, the material properties of the object, and the limitations of the röbot fingers. In this paper several optimization functions are studied and their merits highlighted. The paper introduces a graphical representation of the finger force values and the objective functions that enable one to select and compare various grasping configurations. The impending motion of the object at different torque and finger force values are determined by observing the normalized coefficient of friction plots.

The purpose of this paper is in duplicate to present computer simulation results of concurrent grasp and object manipulation by a pair of three degrees of freedom (3-dof) robot fingers with rigid hemispherical finger-ends that induce rolling contacts with an object and propose a guidance of gain tuning. Although the existence of a class of sensory feedback signals that realize stable grasp and orientation control of the object concurrently has been shown theoretically, the problem of tuning of their feedback gains has not yet been solved. This paper proposes a guideline for tuning sensory feedback gains by deriving a relationship between the object mass and damping coefficients of finger motions through analyzing the overall fingers-object dynamics and taking into account the well-known force/velocity characteristics of human muscle in muscle physiology.

This paper is concerned with a stability theory of motion governed by Lagrange's equation for a pair of multi-degrees of freedom robot fingers with hemi-spherical finger ends grasping a rigid object under rolling contact constraints. When a pair of dual two d.o.f. fingers is used and motion of the overall fingers-object system is confined to a plane, it is shown that the total degree of freedom of the fingers-object system is redundant for realization of stable grasping though there arise four algebraic constraints. To resolve the redundancy problem without introducing any other extra and artificial performance index, a concept of stability of motion starting from a higher dimensional manifold to a lower-dimensional manifold, expressing a set of states of stable grasp with prescribed contact force, is introduced and thereby it is proved in a rigorous way that stable grasp in a dynamic sense is realized by a sensory feedback constructed by means of measurement data of finger joint angles and the rotational angle of the object. Further, it is shown that there exists an additional sensory feedback that realizes not only stable grasp but also orientation control of the object concurrently. Results of computer simulation based on Baumgarte's method are presented, which show the effectiveness of the proposed concept and analysis.

This paper analyses lumped-parameter dynamics of a pair of robot fingers with soft and deformable tips pinching a rigid object under the effect of a gravity force. The dynamics of the system in which area contacts between the finger-tips and the surfaces of the object arise are compared with those of a pair of rigid robot fingers with rigid contacts with an object, with or without effect of the gravity. It is then shown that there exists a sensory feedback from measurement of finger joint angles and the rotational angle of the object to command inputs to joint actuators, and this feedback connection from sensing to action realizes secure grasping of the object in a dynamic sense and regulation of the object posture. It is further shown that there are various types of other feedback connections from sensing to action, which can be used in combination of feedback signals for stable grasping and posture control of the object for realizing sophisticated object manipulation.