pushing force ranging over 0.2kgf, error of position mea- surements is less ... per left:force, upper right:tangential component of spin torque, lower left:moment ...
Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems October 9 - 15, 2006, Beijing, China
Tactile Measurement of Local Contact Geometry Using Soft Fingertip with Force/Torque Sensor Kouji Murakami and Tsutomu Hasegawa Graduate School of Information Science and Electrical Engineering Kyushu University 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581 JAPAN {mkouji, hasegawa}@irvs.is.kyushu-u.ac.jp
Abstract— We propose a new method of tactile sensing for a fingertip of robotic hand based on the analysis of the mechanical constraints imposed to the contact between the fingertip and the contacting object. Using a simple fingertip with soft surface cover and a six-axis force/torque sensor, a new function is developed to measure direction of local geometry of a class of objects when the fingertip contacts with them. The developed function is useful not only to plan strategies for stable grasp and dexterous manipulation but also to recognize a geometrical shape of an object. Two necessary components, a six-axis force/torque sensor and a soft skin, are commercially available. They will neither restrict design of a robotic fingertip nor badly affect essential functions of stable grasping and manipulation. Index Terms— tactile sensing, soft fingertip, multifingered robotic hand
I. I NTRODUCTION A multi-fingered hand with soft fingertip has demonstrated higher dexterity in robotic manipulation than those hands with hard fingertip[1]. The improved dexterity owes mostly to deformation of the soft fingertip when it contacts with a manipulated object. For example, the change of contact area due to the deformation causes the change of the friction coefficient. Therefore slip control is possible with the soft fingertip by adequately adjusting contacting force. Another important feature of the soft fingertip is its capability of tactile sensing. This paper proposes a new idea of tactile sensing by the multi-fingered hand with soft fingertip. Concept of the soft contact model has been proposed and successfully used to analyze stability of contact in the context of multi-fingered robotic manipulation so far [2]. The soft contact of this model transmits three-dimensional force and one-dimensional spin torque around the surface normal of the contact. Many previous works with this model deal with rather simple situation of contact: point contact with planar surface assuming that the deformation of the soft material is negligibly small. However, the mechanical constraint of a contact differs significantly when the local geometry of the contacting part is complex and the deformation is large. We have analyzed the local geometry of the soft fingertip contact with a sharp linear wedge. Based on this analysis, we have already proposed a method of tactile sensing using a soft fingertip with six-axis force/torque sensor [3][4]:
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application to detecting transition of the fingertip contact between the edge and the planar surface, and to measuring the direction of the sharp edge being in contact with. Real objects to be manipulated may have various local geometry. This paper describes a new idea of formalizing a class of mechanical constraint of the soft contact. This class is characterized by the contact area having strip shape. Based on this formalization, a method of tactile measurement of contact geometry is proposed. Specific features of this method are summarized as followings. 1) The direction of various local geometry: a stick, a sharp wedge, a rounded wedge, a thin plate, a fringe of a cylinder and so on is measured while grasping the object stably and even statically without obstructing manipulation and grasping(Fig.1). 2) Required hardware elements are a fingertip covered with soft skin and a six-axis miniature force/torque sensor which is commercially available. 3) The direction of various local geometry is measured based solely on the fingertip sensor readings without relying on a geometric model of an object. 4) There is no constraint on the shape of the fingertip. The soft cover of the tip simultaneously enables adjusting the friction coefficient to augment capability of the finger [1].
Fig. 1.
Direction of a pen.
II. R ELATED WORKS Several works have been reported so far on the tactile recognition of geometric shape and pose of an object. Fearing[5] measured pose of a stick using tactile image. The pose is measured as direction of the longitudinal principal axis of ellipse appeared in the tactile image when
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the object is pushed against the sensor. Shimojo et al. [6] transformed tactile image into video signal and obtained the contour using vision processing. These methods assumes that the global tactile image of the object is obtained from widely distributed tactile sensing elements. However, actual implementation of tactile sensing elements on whole surface of the multi-fingered robotic hand is few due to the cost and difficulties of wiring. Gifu Hand[7] has been exceptionally covered with a film sheet of distributed tactile sensor as an attempt. The sensor was not completely fitted with the finger shape. Thus tactile sensing with distributed sensor elements can not yet be used with the multi-fingered robotic hand. Visual and tactile sensor fusion is proposed to measure pose of an object being manipulated by a multi-finger system[8] [9]. For realtime and accurate measurement, the template matching is used in the vision information process with the geometric model of the object. To improve the accuracy of pose measurement of an object, Ishikawa et al. [10] has proposed a method of planning surface position of the object to be touched by tactile sensor complementarily used with vision sensor. All the tactile sensing mentioned above is based on the object model given in advance. In contrast to these, a method of recognizing geometric shape of a polyhedron has been proposed using position and surface normal of the multiple contact points measured by active point-to-point contact with a fingertip[11]. However, this method relied on the assumption that the fingertip will not contact the polyhedron on its edge. Recently new fingertip sensors have been proposed utilizing distributed multiple receptor elements buried in a soft skin[12][13]. Measurement of force, friction coefficient, difference of the textural surface structure of object, and discrimination of contacting material are experimentally achieved directly by low level signal processing. However, the dexterous manipulation has not yet achieved using those sensors. Wiring of receptor elements and the durability of soft tissue are still open problem for the practical usage of those sensors. In contrast, the fingertip and tactile sensing method described in this paper is free from the problems mentioned above. Geometric information thus obtained will be effectively used to estimate pose of the grasped object with the model matching. In addition, it will be used to recognize geometric shape of the object. This paper describes the principle of measuring direction of various local geometry of an object, and experimental results using a multi-fingered hand.
penetrates the soft fingertip. Contact imposes itself as a filter for force/moment. Shallow penetration allows fewer constraints for moment in the contact; hence, a normal soft finger imparts three-axis of force and one-axis of moment. In contrast to this, a deep penetrated wedge imparts force/moment in all six directions. Two different cases of transmission of moment at the soft contact with deep penetration are shown in Figs.2 and 3. Contact by large planar surface without limitation of area transmits three dimensional forces and all three dimensional moments(Fig.2). This case is called the planar contact. On the other side, contact with limited strip area caused by local geometry of an object transmits three dimensional forces and mainly two dimensional moments: the one around the surface normal and another around one tangential axis perpendicular to the longitudinal principal axis of the strip area of contact (Fig.3). This case is called the line contact. For example, the transmissible moment at the soft fingertip contacting a stick-like object with deep penetration is decomposed into two components : the one which is parallel to surface normal of the fingertip at the contact, and another one which is perpendicular to both the surface normal and the direction of the stick itself (Fig.4). The latter is obtained from the spin torque measured at the fingertip link by subtracting the former. In this paper we call the latter the tangential component of the spin torque. Then the direction of the wedge is finally obtained as vector product of the tangential component of the spin torque and the surface normal of the fingertip. Salisbury[14] has analyzed the mechanical constraints at the planar contact and the line contact between a rigid planar surface and a rigid body. He also proposed tactile sensing of contact points and direction of line contact using a planar sensor having 6 axes force/torque measurement devise. In contrast to his work, there is no constraint on sensor shape in our method. Therefore, we can choose a hemispherical fingertip which enables dexterous precision manipulation without loosing the tactile sensing capability.
Fig. 2.
Contact with large planar surface.
III. C ONTACT OF SOFT FINGERTIP WITH AN OBJECT A. Principle of measurment Mechanical constraint of a soft fingertip contacting with an object differs depending on two major factors. The first one is the geometric property of the contacting part of the object: a stick, a sharp wedge, a rounded wedge, a thin plate, a fringe of a cylinder and so on. The second factor is how deeply the contact part of the object
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Fig. 3.
Contact with limited strip area.
position measurement when applied to non-planar contact with larger deformation by grasping force. To eliminate such error, we measure the position of the contact point at the beginning of the grasping process where the grasping force is not yet large. Assuming that the position of the contact point on the fingertip surface does not move, it is used for measuring the direction of wedge. IV. E XPERIMENT Fig. 4.
Geometric relationship at contact.
B. Formalization We now formalize how to measure the direction of various local geometry of an object being grasped by the fingertip covered with soft skin and equipped with sixaxis force/torque sensor. We assume that geometric shape information of the fingertip is known and that position of contact point on the fingertip and a surface normal are measurable. Let f , m, r, q be force, moment, position of contact point, spin torque at the contact point on the fingertip, respectively. Every vector is expressed in the force sensor coordinate system. Force f and moment m exerted by the fingertip are measured by the six-axis force/torque sensor. The position r of contact point on the fingertip is measured by implementing Bicchi’s method[15] which needs a geometrical shape of the fingertip and output signals of the six-axis force/torque sensor. The spin torque q is obtained from the balance equation of force and moment as: m = q + r×f
(1)
By removing the partial spin torque around the surface normal at r from q, we define h as Eq.(3). Vector h indicates the tangential component of the spin torque which is defined in the previous subsection. We can detect the direction of the wedge as outer product of vector n and vector h. n =
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We conducted experiments to measure the direction of various local geometry of an object being grasped by two fingers while changing a geometrical shape of a grasped object and grasp configuration. Experiment setups is shown in Fig.5. The developed soft fingertips are connected to upper link of each finger of a 4-jointed 2-fingered robotic hand. The geometrical shape of a grasped object is unknown to the system. The sequence of the experiment is as followings. 1) Two fingers are set open to grasp. Then an object is put into the open space and is kept still. 2) Each finger moves to close the hand from initial position aiming at the position of another fingertip respectively. 3) When the fingertip contacts the object, a position of contact on the fingertip is measured. 4) In order to keep stable grasp, each fingertip exerts constant inner grasping force toward another contact point respectively. The direction of the wedge is measured at the end of this motion. It should be noted that the proposed tactile sensing is implemented in such a simple and ordinary grasping strategy. The magnitude of pushing force at the contact has to be larger than a certain threshold value for precise measurement of the position of contact point by Bicchi’s method. We have already investigated the specific threshold with regard to the developed fingertip(Fig.7). With the pushing force ranging over 0.2kgf , error of position measurements is less than 0.5mm. Therefore, we decide that the magnitude of grasping force is approximately 0.5kgf in this experiment for the precise measurement of contact position and sufficient wedging into soft skin.
(3)
where is the gradient operator, S(r) is the function describes the surface of the fingertip. C. Implementation When the fingertip contacts with a planar surface, the position of contact point on a fingertip is obtained from measured force/moment using a six-axis sensor together with geometric shape information of the fingertip. We are using a method proposed by Bicchi[15] for this position measurement. However, this method assumes the spin torque only around the surface normal at the contact point. This is not true in contact with a real object like a stick. Consequently the method suffers larger error in contact
Fig. 5.
Experimental setups.
In the experiment, the fingertip tries to contact an object with four different directions, -45, 0, 45, and 90 degrees respectively with respect to the fingertip coordinate system shown in Fig.6. The fingertip coordinate system
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Measured direction of a stick-like object.
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A. Structure of Soft Fingertip
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We have developed a robotic fingertip with soft skin[1]. Fig.7 shows the inner structure and its appearance. The fingertip is composed of an inner shell, a hard nail and a soft skin. The inner shell and the hard nail are made of aluminum. The inner shell is a cylinder with a hemisphere on its top. Its radius is 11mm. The soft skin is made of silicone rubber covering the inner shell. The skin has constant thickness. The thickness of the skin is 5mm. The inner shell is fixed to six-axis force/torque sensor which is then connected to the upper link of a finger. The exerted force/moment to the fingertip is measured by the force/torque sensor.
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Soft fingertip with nail.
B. Contact with a sharp-cut cross section of a thin plate The shape of the contact area of the soft fingertip with a sharp-cut cross section of a thin plate is a long strip clipped by the edge of the plate. The direction of the contacting plate is defined by the longitudinal principal axis of the area of contact. The right fingertip in Fig.5 contacts with the plate 4 times each with different directions. The thickness of the plate is 1mm. The results of tactile measurement using right finger in fig.5 are shown in Figs. 8 through 11. Two charts in the left side of each figure show output of the force sensor: force and moment respectively. Two charts in the right show the magnitude of the tangential component of spin torque at the contact and the measured direction of the plate respectively. Force and moment are
with respect to the hand coordinate system attached at the center of the palm. The direction of the plate is with respect to the fingertip coordinate system respectively. Horizontal axis of each chart shows the elapsed time. The fingers begin grasping motion at the time 0. The fingertips contact with the plate at around 2 seconds. And then grasping force is increased. The stable grasp is accomplished at around 4 s. The servo cycle of the finger control is 20ms. Sensing is made in the same cycle time. When the fingertip contacts the plate with -45, 0, and 45 degree respectively, the direction of the plate is successfully measured. On the other hand, the direction of the plate is not measured accurately when the fingertip contacts with the plate with 90 degree. The result of this experiment is explained as followings. In our setups of experiment shown in Fig.5, all joint axes of the fingers are in parallel with y-axis of the hand coordinate system and the gravitational force is in -z direction. The direction of the plate is in parallel with y-axis when the fingertip contacts it with the direction of 90 degrees. To measure this direction, spin torque component in x-z plane
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on the plate. The magnitude of pusing force is 0.5Kgf. The length of each cross section of the plate is sufficiently long compared with the size of the soft fingertip. Fig.13 shows the result of experiment.
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Fig. 11. Contact with the plate whose direction is 90 degree (upper left:force, upper right:tangential component of spin torque, lower left:moment, lower right:measured direction).
must be obtained. However, there is no joint actuator and external force which generates spin torque in x-z plane. Although small spin toque is actually measured in our experiment due to alignment error of the fingers and grasped object, it is not sufficient. This experiment explicitly shows that our method has measurable range of direction of the plate depending on the configuration of the contact with respect to finger axes and external forces. C. Contact with a sharp-cut cross section of a thick plate We have conducted the experiment using thicker plates similarly with sectionIV-B. When the thickness of a plate becomes smaller, the plate comes to be similar to an edge. When the thickness of the plate becomes larger, the plate comes to be similar to a flat surface. We investigated the influence of the thickness of plates on the precision of measurement of the direction of contact. We used six different plates whose thickness are 1, 2, 3, 4, 10, and 15 mm respectively (Fig.12). First, we measured the area of contact on the cross section of the plate using the soft fingertip painted with color ink. After pushing each plate against the soft fingertip, we measured colored area
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When the thickness of the plate becomes larger, the shape of the area of contact changes to a round from a stick, and the direction of the plate can not be defined uniquely. Accordingly we can not measure the direction of the plate. Because the mechanical constraint imposed to the soft fingertip by the thick plate becomes similar to a large flat surface. The results of tactile measurement using the right finger in Fig.5 are shown in Figs.14 through 17. Left chart shows the magnitude of tangential component of the spin torque. Right chart shows the measured direction of the plate. Horizontal axis of each chart shows the elapsed time. Since the result with 90 degrees is very noisy and inaccurate, we exclude it from the chart for the benefit of visibility. In the case that the thickness of the plate is 2mm, the direction of the plate is measured correctly. On the other hand, the error of the measurement is large when the fingertip contact with the plate whose thickness is larger than 3mm, due to the change of mechanical constraint at the contact. It is confirmed that we can measure the direction of the plate whose thickness is smaller than 2mm by using the soft fingertip. If we used larger soft fingertip, we would be able to measure the direction of the thicker plate. D. Contact with cylindrical surface Using cylinder as contacting object, experiments have been conducted. The shape of the area of contact is approximated by a longer rectangle whose longitudinal principal axis is in parallel with the axis of the cylinder. This direction of the longitudinal principal axis is measured as direction of the cylinder. Width of the area of contact increases according to increase of the radius of the cylinder. Consequently the mechanical constraint imposed to the soft
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fingertip by the thick cylinder becomes similar to a large flat surface. We investigated the influence of the length of diameter of cylinders on the precision of measurement of the direction of contact. We used three different cylinders whose diameters are 4, 6, 10, and 14 mm respectively (Fig.18). The results of tactile measurement using right finger in Fig.5 are shown in Figs.19 through 22. Left chart shows the magnitude of tangential component of the spin torque. Right chart shows the measured direction of cylinder. Horizontal axis of each chart shows the elapsed time. The error of the measurement is large when the fingertip contact with cylinder of larger diameter, due to the change of mechanical constraint at the contact. This result is interpreted in the same way as described in the previous section. It is confirmed that we can measure the direction of the
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cylinder whose diameter is smaller than 6mm by using the soft fingertip. If we used larger soft fingertip, we would be able to measure the direction of the thicker cylinder. E. Contact with fringe of circular bottom of a cylinder Direction of contacting fringe of a bottom of a cylinder is defined by tangential direction of the fringe at the contact. Using an experimental piece of a part of cylinder bottom as shown in Fig.23, the direction of the fringe has been measured. Diameter of the cylinder is 40mm. In the experiment, the fingertip is contact with the fringe of the cylinder bottom in three different directions, -45, 0, 45,
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and 90 degrees respectively with respect to the fingertip coordinate system. The results of tactile measurement using right finger in Fig.5 are shown in Fig.24. Left chart shows the magnitude of tangential component of the spin torque. Right chart shows the measured direction of the fringe of the cylinder bottom. Horizontal axis of each chart shows the elapsed time. The tangential direction has been successfully measured. measured direction
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Appearance of a bottom of a cylinder.
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[6] M. Shimojo, M. Ishikawa, and K. Kanaya, “A Flexible High Resolution Tactile Imager with Video Signal Output” Proc.IEEE ICRA pp. 384-391 1991 [7] H. Kawasaki, T. Komatsu, and K. Uchiyama, “Dextrous Anthropomorphic Robot Hand with Distributed Tactile Sensor: Gifu Hand II” IEEE/ASME Trans. on Mechatronics, Vol.7, No.3, Sep 2002 [8] K. Honda, T. Hasegawa, T. Kiriki, and T. Matsuoka, “Real-Time Pose Estimation of an Object Manipulated by a Multi-Fingered Hand Using 3-D Stereo Vision and Tactile Sensing” Proc.IEEE/RSJ IROS, pp. 1814-1819 1998 [9] Y. Yokokohji, M. Sakamoto, and T. Yoshikawa, “Vision-Aided Object Manipulation by a Multifingered Hand with Soft Fingertips” Proc.IEEE ICRA pp. 3201-3208 1999 [10] T. Mukai and M. Ishikawa, “Vision and Touch Fusion System Using Active Sensing” JRSJ Vol.15, No.1, pp. 75-81 1997 [11] K. Nagata, T. Keino, and T. Omata, “Acquisition of an Object Model by Manipulation with a Multifingered Hand” Proc.IEEE/RSJ IROS pp. 1045-1051 1996 [12] Y. Mukaibo, H. Shirado, M. Konyo, and T. Maeno, “Development of a Texture Sensor Emulating the Tissue Structure and Perceptual Mechanism of Human Fingers” Proc. of IEEE ICRA, pp. 2576-2581, 2005 [13] Y. Tada, K. Hosoda, and M. Asada, “Learn to Grasp Utilizing Anthropomorphic Fingertips together with a Vision Sensor” Proc. of IEEE/RSJ IROS, pp. 486-491 2005 [14] Salisbury J. K., “Interpretation of contact geometries from force measurements”, Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 240-247, 1984 [15] A.Bicchi, “Intrinsic Contact Sensing for Soft fingers” Proc. of IEEE ICRA, pp. 968-973 1990
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Fig. 24. Direction of contacting fringe of a bottom of the cylinder (left:tangential component of spin torque, right:measured direction).
V. C ONCLUSION A new method of tactile sensing is proposed using soft fingertip equipped with six-axis force/torque sensor. Direction of local geometry of a class of objects has been successfully measured based on the analysis of the mechanical constraint of the soft fingertip in contact with a part of object with deep penetration. The method applies to measuring direction of various local geometry: a stick, a sharp wedge, a rounded wedge, a thin plate, a fringe of a cylinder and so on. Future work will include implementation of the method in the context of actual dexterous manipulation of real objects by multi-fingered robotic hand. R EFERENCES [1] Kouji Murakami and Tsutomu Hasegawa, Proc.IEEE ICRA, pp. 708713 2003 [2] Y. Li, I. Kao, “A Review of Modeling of Soft-Contact fingers and Stiffness Control for Dexterous Manipulation in Robotics”, Proc. ICRA, pp. 3055-3060 2001 [3] Kouji Murakami and Tsutomu Hasegawa, “A New Method of Tactile Sensing Using Fingertip with Soft Skin” Proc. of IEEE/RSJ IROS, pp. 535-pp.540 2003 [4] Kouji Murakami and Tsutomu Hasegawa, “Tactile Sensing of Edge Direction of an Object with a Soft Fingertip Contact” Proc.IEEE ICRA, pp. 2582-2588 2005 [5] R. S. Fearing, “Some Experiments with Tactile Sensing during Grasping” Proc. IEEE ICRA, pp. 1637-1643 1987
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