Elastic Model of a Deformable Fingertip

To date, much research has been done on the manipulation of objects by softfingered robotic hands. Most of these studies, particularly the earlier ones, focused only on contact mechanisms on various soft fingers. More recently, there has been an increase in the number of studies investigating the sensing mechanisms of the human hand and designing control systems in robotic applications to emulate the human capabilities that are applicable to robotic hands. Conventional studies, however, have not explicitly provided any analytical exploration of the simplicity in grasping and manipulating motions in terms of soft-fingered handling. It has therefore been very difficult to derive a fine elastic model of soft materials used in fingertips. Yokokohji et al. proposed a control scheme with visual sensors that can cancel the frictional twist/spin moment at the contact point of soft fingertips and achieved stable grasping by spherical soft fingertips [YSY99, YSY00]. Maekawa et al. developed a finger-shaped tactile sensor covered with a soft, thin material and proposed a control algorithm based on tactile feedback using a sensor that requires no information about the geometry of the grasped object [MKT92, MTK92]. They managed to control the position of an object along a desired trajectory. In these papers, point-contacts were used to represent the constraints of rolling contact in their theoretical models, although the fingertips were made from a soft material such as rubber. Arimoto et al. verified the passivity of equations of motion for a total handling system using a Lagrangian function incorporating the elastic potential energy due to the deformation of soft fingertips [ANH00] and compensated for the gravity effect in 3D space [ADN02]. An elastic force model was also derived for the elastic potential energy of a system in which, for simplicity, virtual linear springs were arranged in a radial pattern inside hemispherical soft fingertips. Doulgeri et al. discussed the problem of stable grasping with deformable fingertips on which rolling constraints were described as nonholo-