Dynamics and control of a set of dual fingers with soft tips

Abstract

This paper attempts firstly to derive a mathematical model of the dynamics of a set of dual fingers with soft and deformable tips which grasps and manipulates a rigid object with some dexterity. To gain a physical insight into the problem, consideration is restricted to the case that the motion of the whole system is confined to a horizontal plane. Secondly on the basis of the derived model it is shown that the rotation of the object can be indirectly controlled by the change of positions of the center points of both contact areas on the object. Then, each of the center points of contact areas can be positioned by inclining the last link of each corresponding finger against the object. It is further shown that, when both forces of pressing the object becomes almost equal, the equation of motion of the object in terms of rotational angles assumes the form of a harmonic oscillator with a forcing term, which can be regulated coordinately by the relative angle between the two last links contacting with the object. It is also shown that dynamics of this system satisfy passivity. Finally, design problems of control for dynamic stable grasping and enhancing dexterity in manipulating things are discussed on the basis of passivity analysis.