Understanding Slip Perception of Soft Fingertips by Modeling and Simulating Stick-Slip Phenomenon

Slip, especially incipient slip, is a complicated process for soft fingertips; and detection of this slip is important for stable manipulations by both human and robotic fingertips. Experimental research has attempted to explainthis phenomenon, but dynamic changes during this process could not be fully delineated. We propose here a dynamic model to investigate the sliding motion of soft fingertips on a plane with friction. The fingertip is comprised of a finite number of elastic, compressible and bendable cantilevers whose fr ee ends act as infinitesimal contact points. The contact surfac e is afterward meshed using a finite element method based on the coordinates of the contact points. By introducing Coulomb’ s law and contact compliance into each contact point, we were able to assess the frictional characteristics of the sliding motio ns of the fingertips. We also could successfully describe the dynamic ally localized displacements on the contact surface during stic k-slip transition, displacements that represent the sliding moti on of a soft fingertip. This model can be applied to different shape s of robotic fingertip, including the cylindrical and hemispherical models tested here. We also performed experiments to valida te the proposed simulation, including force/moment and vision setups. I. I NTRODUCTION Recent research in robotics has focused on the dexterous manipulation of objects using soft fingered robotic hands, e specially anthropomorphic hands. This type of research can b e categorized into two main groups. The first consists of studi es that focus on analyzing the contact mechanics between soft fingers and objects [1]. In the second, tactile sensing syste ms imitating those of humans, along with many types of sensors, have been developed to simulate human abilities in object grasping and dexterous handling [2]. Whereas the former studies consisted primarily of analysis of stable grasping or object postures controlled by soft fingertips during a pushi ng or rolling motion on the surface of objects; the latter studi es concentrated on the tactile texture perceptions of sensory fingertips, to increase efficiency during object manipulati on processes. Among the various movements of fingertips during object handling is slide/slip, which often occurs during co ntact and is considered important in dexterous manipulation [3]. For example, to assess the texture of an object’s surface, the fingertip needs to slide slightly on the surface to extrac t information about its roughness or friction. The sliding mo tion of an object between fingertips during grasping, or incipien t slip, is a crucial factor in stable object manipulation. How ever, while the latter studies have addressed all types of fingerti p motions, including pressing, rolling, and rubbing; the for mer studies have focused primarily on pure pushing and rolling movements, while ignoring slip or slide. The difficulties in modeling the sliding motion of fingertips comes from their compliance, their partial movements on contact surfaces, a nd the force/moment of friction. Kao and Cutkosky [4] have proposed a method that combines compliance and friction on a limited surface to compute the relative sliding motion between a grasped object and soft fingers. That article showe d concrete results in modeling contact and in approximation o f gross-motion planning. Fearing [5] introduced an algorith m for automatic stable grasping of polygonal objects by two fingers and a point contact with friction. Research has also addressed pushing operations using manipulators. Yoshika wa et al. [6] proposed a pushing method to identify the center of friction of an object with an unknown distribution of fricti on. In a similar method [7], relevant friction parameters were estimated by performing experimental pushes and observing the resultant motion. Nevertheless, most previous researc h has dealt only with quasi-static analysis, including gross sli ding, not on stick-slip phases (i.e. how and when it occurs), or par tial slip on the contact surface of a soft fingertip. In contrast, some contact models have been used in simulation, such as analytical ([8]) and conventional penalty methods ([9]) . Although the former methods result in a fast and accurate description of contact, they limit penetration between obj ects; in contrast, the latter methods can identify the contact are a, but can only use penetrative contacts. At the same time, the Fini te Element Analysis (FEA) model of a contacting soft fingertip was also developed. This method, however, is time-consumin g and usually solved in a static field ([10]). In contrast to the above approaches, Barbagli et al [11] attempted to determine the model that best fit the real rotational friction properti es of human fingertips and then extended the object/proxy algorit hm to simulate soft finger contact. In this paper, we have attempted to determine the frictional characteristics of a 3-D soft fingertip during unilateral sl iding motion relative to an object. We have proposed a method to model vertical and horizontal deformations of the soft fingertip during sliding by introducing virtual cantilever s. Moreover, we have modeled the contact surface by employing the FEA method, along with Coulomb’s frictional law. This can significantly reduce calculation time, while still assu ring he dynamic behavior of the system during stick-slip transi tion. Non-contact cantilevers Contact cantilevers Contact surface Contact cantilevers (a) Modeled fingertip (b) Meshed contact surface Tp Pi k Pj P Fig. 1. Model of a sliding soft fingertip with virtual cantile v rs and meshed contact surface. Results from simulation and experimental validation can th eoretically explain, for the first time, localized movements on the contact surface during the stick-slip phase, as determi n d experimentally. II. PROPOSEDHYBRID MODELING OF A HEMISPHERICAL SOFT FINGERTIP Many shapes are used to form robotic soft fingertips. We have categorized them into two main groups with respect to grasped objects with rigid flat facets. The first generates uniform distribution of normal stress, such as square and rectangular fingertips. The second is characterized by the n onuniform distribution of contact force, including cylindri cal, hemispherical, and human-like fingertips. Both groups are distinguished by rigid fingertips in compliant contact, fea turing a pre-slide stage and characteristics of hysteresis. Mo re particularly with the second group, the pre-slide generate s localized displacements on the contact surface, which are important in incipient slip detection ([20]). A dynamic mod el with the appearance of friction is required to represent the se phenomena and characteristics of soft fingertips. We have developed a model, which, with some simplifications, can be employed to investigate slip motions of soft fingertips of different shapes, especially during stick-slip transitio n. Since this model focuses onwhat happenson the entirecontact surface, we have combined discrete and FEA methods to model a general 3-D soft fingertip. By so doing, the calculati on times will be reduced considerably, while still assuring th e correctness of the model. Assume that a three dimensional (3-D) soft fingertip with an arbitrary but continuous outer surface is pushed vertica lly with a specific contact penetration by a normal force Fn on a rigid flat plane, and slides horizontally with an external fo rce Ft (Fig. 1(a)). Inoue ([1]) proposed a soft fingertip model comprised of an infinite number of vertical elastic virtual springs that could be used to investigate the deformation of the fingertip during pushing or rolling motion on an object. This model, however, was not sufficient to demonstrate slidi ng motion with the appearance of frictional force. Therefore, instead of virtual springs, we have proposed a model, in which the soft fingertip is comprised of a finite number of virtual elastic cantilevers that are compressible, tensil , and bendable (Fig. 1(b)). This model can represent the diverse deformations of a soft fingertip during a sliding motion, in which the fingertip is pushed and slid at the same time. These cantilevers are fixed on the flat surface of the fingertip, with their free ends on its outer surface. Each cantilever has a uniform circular cross sectional area, whereas the lengths of the cantilevers differ depending on their coordinates with in the fingertip. When the fingertip is pushed, some cantilevers will make contact with the object, causing the deformations of these cantilevers. Based on geometrical distributions, we were able to calculate the deformation of each contacting cantilever, which have non-uniform distribution on the con tact surface. Afterwards, we meshed the 2-D contact surface usin g the Voight model to describe the elastic and viscous propert ies of the contact surface ([12]) on the O −XY coordinates. Each node was equivalent to the free end of a contacting cantileve r. Each element is a triangle Tp with three nodes referred as Pi, Pj , andPk in a counterclockwise direction. Fig. 1(c) illustrates a possible mesh of the contact surface. For the sake of simplicity, we made three assumptions: 1) When a cantilever is bent, its deformation is significant only at the free end. 2) Interactions between continuous cantilevers only occur between their free ends on the contact surface. 3) Only cantilevers whose free ends are acting on the contact surface are considered (dark colored cantilevers in Fig. 1(b)). Cantilevers outside the contact surface are deemed irrelevant to the sliding motion of the fingertip (light colored cantilevers in Fig. 1(b)). As a result, when the fingertip is pushed and slid, its deforma tion will be represented by deformations of all contacting c antilevers. Moreover, external forces acting on each node on t he contact surface can be assessed by calculating the compress ing and bending forces of the corresponding can