Development of a Soft-fingertip and Its Modeling ... - Semantic Scholar
Proceedings of the 2003 IEEE International Conference on Robotics & Automation Taipei, Taiwan, September 14-19, 2003
Development of a Soft-fingertip and Its Modeling Based on Force Distribution Kwi-Ho Park◦ , Byoung-Ho Kim† , and Shinichi Hirai◦ ◦
†
: Dept. of Robotics, Ritsumeikan Univ., Kusatsu, Shiga, Japan : JSPS Post-doc Fellow, Dept. of Robotics, Ritsumeikan Univ., Kusatsu, Shiga, Japan (E-mail: [email protected]) Abstract
In this paper, a hemisphere-shaped soft fingertip for soft fingers is developed and its modeling based on force distribution is presented. We first analyze the geometrical relation of the soft fingertip when it is deformed. Secondly, the force distribution of the soft fingertip is investigated by using a compressional strain mechanism. And then, we propose a nonlinear model of the soft fingertip which enables us to obtain the total contact force at the contact surface of each finger in manipulating tasks. Finally, the proposed force function is verified by experiment, where a tactile sensor is used to measure the contact force distribution in the contact surface and its total force. The developed soft fingertip and its force function can be usefully applied to soft-fingered manipulations. Keywords : development and modeling of a soft fingertip, force distribution, tactile sensor
1
Introduction
Many grasping and manipulation algorithms have been presented for manipulating of an object by multifingered hands [1]-[3]. Tactile sensor-based manipulation algorithms [4, 5] were developed to consider the reliable information about the grasp geometry including contact positions. By the way, the deformation effect of objects or soft fingertips is a common issue in general robotic applications. Recently, many researchers have been interested about the deformation of an object and/or a soft fingertip in multi-fingered manipulating tasks and thus, soft manipulations by multi-fingered hands have been considered as an active research field [6]-[9]. Also, it is well-known that the field of developing a soft finger and/or a soft fingertip is a fundamental area in soft manipulations.
0-7803-7736-2/03/$17.00 ©2003 IEEE
Related to the modeling of contact, compliant materials for robot fingers were tested [10]. Xydas et al. [11] presented a modeling of contact mechanics for soft fingers. Hiromitsu et al. [12] showed various type of contact shapes at the contact surface of a finger in a human grasping. From their observations of human grasping and contact mechanics, it is confirmed that when an object is being manipulated by a multifingered hand with soft fingertips, each fingertip force can be determined by considering the force distribution according to the deformation of soft fingertips. A strain-based silicone gel model was investigated [13]. For practical applications, however, those approaches are rather complex because their methodologies are based on a numerical algorithm. On the other hand, there are not so much researches related to develop a proper soft fingertip. The objective of this paper is to present a simple model of a soft fingertip for practical soft-fingered applications. We first develop a soft fingertip like human skin for soft-fingered manipulations and also present a simple model of the developed soft fingertip based on the force distribution at the contact surface. Through experimental works, we verify the proposed model of the developed soft fingertip, where a tactile sensor and a tactile sensor signal processing system are used to measure the contact force distribution in the contact surface and its total force.
2
Development of a Soft Fingertip
The object manipulating system by a human hand shown in Fig. 1 is one of typical soft-fingered manipulations. Usually, a human hand has many soft fingertips and thus it can be applied to various manipulating tasks. There are various type of contact shapes at the contact surface of a finger in a human
3169
grasping [12]. Generally, we can experience that the contact between the object and each fingertip of the object-hand system is made by a surface contact and also, soft fingertips are appropriately deformed during the manipulation process. In order to implement those soft-fingered manipulations, a proper soft fingertip is necessary.
Fig. 3. A simple one-dimensional contact and deformation.
Fig. 1. An object manipulating system by a human hand. For soft-fingered applications, we developed a hemisphere-shaped soft fingertip with radius of 0.01[m] as shown in Fig. 2, where a molding device is used to make our fingertip. The developed soft fingertip was made by using a Pringel compound of Exseal Co.(http://www.exseal.co.jp). The feature of our soft fingertip is similar to the skin of a human and thus, it can be applied to make a finger with soft fingertip.
Fig. 3 shows a contact status of a soft fingertip which is contacting into an object to the normal direction. Specially, let us consider a hemisphere-shaped soft fingertip with radius of a. Then, the following relation of a circle is satisfactory on the surface; x2 + z 2 = a2 .
(1)
The x-position of a point, Q, on the surface of the fingertip in the two-dimensional space is given by Qx = (a − d0 )tanθ
(2)
where d0 denotes the deformation length of the soft fingertip and θ implies a touching angle shown in Fig. 3. By combining (1) and (2), the z-position of the point Q can be represented as Qz = a2 − (a − d0 )2 tan2 θ. (3) Then, the z-directional length of QC is given by QC = Qz − (a − d0 ).
Fig. 2. A developed soft fingertip.
3
Geometrical Analysis of Soft Fingertips
When a soft fingertip is being contact into a rigid object, there exists some deformation. This section presents geometrical analysis of the deformation of soft fingertips. Particularly, we consider a typical onedimensional contact model of common manipulating tasks as shown in Fig. 3.
(4)
Physically, the length of QC implies the deformation at a point on the contact surface of the soft fingertip. Also, the maximum touching angle, θmax , can be determined by a2 − (a − d0 )2 −1 . (5) θmax = tan (a − d0 )2 Usually, the contacting area of a soft fingertip is dependently increased when the fingertip is being deformed. Specifically, when it is deformed as d0 as shown in Fig. 4, the radius of the contact surface observed at the contact point of C can be represented by
3170
r = (a − d0 )tanθ.
(6)
relation of a cylindrical particle of the soft fingertip. The stress, σ, pressed on the soft particle shown in Fig. 5 is defined as σ≡
F S
(9)
where F is the magnitude of the contact force that acts per contact area, S, of the particle.
Fig. 5. A cylindrical particle of a soft fingertip. When a small compressive contact force is applied to the soft particle, the length of the particle decreases, but the contact surface increases. From this physical phenomenon, the compressional strain, e, is defined as the fractional change in the length of the soft particle as follows: e≡ Fig. 4. The contacting area of a soft fingertip. Also, the small change of the radius, dr, is given by dr =
(a − d0 ) dθ, cos2 θ
(7)
Thus, the resultant area of the small increased contact surface due to the deformation, dS, can be obtained by dS
4
= rdrdϕ (a − d0 )2 sinθ = dθdϕ. cos3 θ
∆L L
(10)
where e is dimensionless and it is negative if the stress is due to compression such as many robotic grasping tasks(∆L < 0). Then, by using Young’s modulus(Y = σ/e) [14], the force relation acting on the soft particle is given by F =Y
∆L S. L
(11)
On the other hand, the pressure acting on a particle is defined as P ≡
(8)
F . S
(12)
By combining (11) and (12), the resultant force relation acting on a particle can be expressed as
Modeling of Soft Fingertip F = PS = Y
For soft-fingered object manipulations, this section presents a one-dimensional modeling of hemisphericalshaped soft fingertips as shown in Fig. 3. In this model, it is assumed that the shape of contact formed at the fingertip is symmetric to the normal axis of the fingertip. In order to obtain a proper model of a soft fingertip with hemispherical shape, we first analyze the force
∆L S. L
(13)
Note that the contact force at the surface of the soft particle depends on the pressure distribution of the soft particle, the length and its change of the soft particle, the area of contact surface, and the Young’s modulus of the soft particle. Then, we will model the soft fingertip of Fig. 3 as a set of infinite soft particles addressed in advance.
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(a) d0 =0.001[m]
(b) d0 =0.002[m]
Fig. 6. A model of a soft fingertip based on the force distribution. In this sense, the deformation of the fingertip can be modeled as a deformation set formed by the force distribution as shown in Fig. 6. Since the force of the fingertip is formed by the pressure, the pressure distribution for all particles will gives an idea to determine the total contacting force of the fingertip. Specifically, Figs. 7(a), (b), and (c) show theoretical pressure distribution patterns(P = Y ∆L L ) according to the deformation of 0.001[m], 0.002[m], and 0.003[m], respectively. As a result, by integrating the force distribution of the soft fingertip, the total contact force at the contact surface can be expressed as follows: 2π θmax P dS fc = 0
2π
0
= 0
= Y πd20
0
θmax
dL dS Y L (14)
where Y denotes the Young’s modulus of the fingertip
(c) d0 =0.003[m] Fig. 7. Pressure distribution patterns at each deformation of the soft fingertip. and it can be estimated by experiment. And length parameters of the soft fingertip according to the deformation are given by L = a2 − (a − d0 )2 tan2 θ (15) and dL =
a2 − (a − d0 )2 tan2 θ − (a − d0 ).
(16)
From (14), it is pointed out that the fingertip force is proportional to the square of the deformation of the soft fingertip. Next, in order to verify the proposed force relation given by (14), we performed experimental works by using the experimental setup shown in Fig. 8. The
3172
height gauge in Fig. 8 is to measure of the deformation of the fingertip and the tactile sensor system shown in Fig. 9 enables us to measure the contact force distribution in the contact surface and its total force. In this experiment, we used a tactile sensor(ISCAN10×10) and a tactile sensor system of Nitta Ltd.(http://www.nitta.co.jp).
In many soft-fingered practical applications, the control performance of a given task may be dependently determined as this value. Recently, we have developed a two-fingered hand with soft fingertips as shown in Fig. 12. In future, the developed soft fingertip and its modeling will be applied to soft-fingered manipulations using the developed hand.
(a) d0 =0.001[m] Fig. 8. Experimental setup.
PCI/ISA I/F Board
PCI/ISA Slot PC
Sensor Connector Tactile Sensor
(b) d0 =0.002[m] Fig. 9. A tactile sensor system. By measuring the contact force distribution according to the deformation of the fingertip, we evaluated the elasticity parameter(Y ) of the developed soft fingertip. The contact force distribution is obtained by integrating the pressure distribution in the contact surface. Through the experiment, we have obtained pressure distribution patterns of using the tactile sensor. Figs. 10(a), (b), and (c) show experimental pressure distribution patterns according to the deformation of 0.001[m], 0.002[m], and 0.003[m], respectively. By using (14) and those pressure distributions, we can finally obtain the total contact force as the deformation. Fig. 11 shows both experimental force profile of the soft fingertip and theoretical force profile according to the deformation. From the experimental evaluation, the elastic modulus, Y , is estimated as 0.25[MN/m2 ]. Physically, if the value of Y is more smaller, the compliance of a soft fingertip is more larger. Thus, the elasticity of our soft fingertip is more soft than a common rubber of 7[MN/m2 ] [14].
(c) d0 =0.003[m] Fig. 10. Pressure distribution patterns(unit: Kpa) of the tactile sensor for each deformation, where the dotted circle implies the pressed contact surface.
5
Concluding Remarks
In this paper, a hemisphere-shaped soft fingertip for soft fingers was developed and a nonlinear force
3173
References [1] A. B. A. Cole, J. E. Hauser, and S. S. Sastry, “Kinematics and control of multifingered hands with rolling contact,” IEEE Trans. on Automatic Control, Vol. 34, No. 4, pp. 398-404, 1989. [2] H. Maekawa, K. Tanie, and K. Komoria, “Dynamic grasping force control using tactile feedback for grasp of multifingered hand,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 2462-2469, 1996.
Fig. 11. Force profiles of the developed soft fingertip: experimental and theoretical results.
[3] X. -Z. Zheng, R. Nakashima, and T. Yoshikawa, “On dynamic control of finger sliding and object motion in manipulation with multifingered hands,” IEEE Trans. on Robotics and Automation, Vol. 16, No. 5, pp. 469481, 2000. [4] H. Maekawa, K. Tanie, K. Komoria, and M. Kaneko, “Development of a finger-shaped tactile sensor and its evaluation by active touch,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 1327-1334, 1992. [5] G. Kinoshita, Y. Kurimoto, H. Osumi, and K. Umeda, “Dynamic contact sensing of soft planar fingers with tactile sensors,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 565-570, 2001. [6] S. Arimoto, P. A. N. Nguyen, H. -Y. Han, and Z. Doulgeri, “Dynamics and control of a set of dual fingers with soft tips,” Robotica, Vol. 18, pp. 71-80, 2000. [7] T. Yoshikawa and T. Watanabe, “Dynamic control of soft-finger hands for povoting an object in contact with the envoronment,” IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 324-329, 2000.
Fig. 12. A developed two-fingered hand with soft fingertips. function of a soft fingertip according to the deformation was modeled by considering the force distribution in the contact surface. Through experimental evaluations, the proposed force function was verified, where a tactile sensor and a tactile sensor signal processing system were used to measure the contact force distribution in the contact surface and its total force. The proposed force function for soft fingertips enables us to obtain the total contact force at the contact surface of a finger in object manipulating tasks. Specifically, our model was considered in the one-dimensional contact of a finger. Additional work is to extend our approach to the two- and three-dimensional modelings of soft fingertips and also apply the developed soft fingertip to real soft-fingered applications.
Acknowledgments This work was supported by the research fund of Japan Society for the Promotion of Science.
[8] T. Wada, S. Hirai, S. Kawamura, and N. Namiji, “Robust manipulation of deformable objects by a simple PID feedback,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 85-90, 2001. [9] O. B. Bayazit, J. -M. Lien, and N. M. Amato, “Probabilistic roadmap motion planning for deformable objects,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 2126-2133, 2002. [10] M. R. Cutkosky, J. M. Jordan, and P. K. Wright, “Skin materials for robotic fingers,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 1649-1654, 1987. [11] N. Xydas and I. Kao, “Modeling of contact mechanics and friction limit surfaces for soft fingers in robotics, with experimental results,” Int. Jour. of Robotics Research, Vol. 18, No. 8, pp. 941-950, 1999. [12] S. Hiromitsu and T. Maeno, “Stick/slip distribution on the fingerpad and response of tactile receptors when human grasp an object,” Jour. of the Robotics Society of Japan, Vol. 68-c, No. 667, pp. 202-207, 2002. [13] Y. Satoh, F. Wakui, K. Sogabe, and N. Shimizu, “Steady-state response of silicon β gel and a mass system,” Dynamics and Design Conf. of Japan, pp. 647652, 2000. [14] P. M. Fishbane, S. Gasiorowicz, and S. T. Thornton, Physics for scientist and engineers, Prentice Hall, Englewood Cliffs, New Jersey, 1993.
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Development of a Soft-fingertip and Its Modeling Based on Force Distribution Kwi-Ho Park◦ , Byoung-Ho Kim† , and Shinichi Hirai◦ ◦
†
: Dept. of Robotics, Ritsumeikan Univ., Kusatsu, Shiga, Japan : JSPS Post-doc Fellow, Dept. of Robotics, Ritsumeikan Univ., Kusatsu, Shiga, Japan (E-mail: [email protected]) Abstract
In this paper, a hemisphere-shaped soft fingertip for soft fingers is developed and its modeling based on force distribution is presented. We first analyze the geometrical relation of the soft fingertip when it is deformed. Secondly, the force distribution of the soft fingertip is investigated by using a compressional strain mechanism. And then, we propose a nonlinear model of the soft fingertip which enables us to obtain the total contact force at the contact surface of each finger in manipulating tasks. Finally, the proposed force function is verified by experiment, where a tactile sensor is used to measure the contact force distribution in the contact surface and its total force. The developed soft fingertip and its force function can be usefully applied to soft-fingered manipulations. Keywords : development and modeling of a soft fingertip, force distribution, tactile sensor
1
Introduction
Many grasping and manipulation algorithms have been presented for manipulating of an object by multifingered hands [1]-[3]. Tactile sensor-based manipulation algorithms [4, 5] were developed to consider the reliable information about the grasp geometry including contact positions. By the way, the deformation effect of objects or soft fingertips is a common issue in general robotic applications. Recently, many researchers have been interested about the deformation of an object and/or a soft fingertip in multi-fingered manipulating tasks and thus, soft manipulations by multi-fingered hands have been considered as an active research field [6]-[9]. Also, it is well-known that the field of developing a soft finger and/or a soft fingertip is a fundamental area in soft manipulations.
0-7803-7736-2/03/$17.00 ©2003 IEEE
Related to the modeling of contact, compliant materials for robot fingers were tested [10]. Xydas et al. [11] presented a modeling of contact mechanics for soft fingers. Hiromitsu et al. [12] showed various type of contact shapes at the contact surface of a finger in a human grasping. From their observations of human grasping and contact mechanics, it is confirmed that when an object is being manipulated by a multifingered hand with soft fingertips, each fingertip force can be determined by considering the force distribution according to the deformation of soft fingertips. A strain-based silicone gel model was investigated [13]. For practical applications, however, those approaches are rather complex because their methodologies are based on a numerical algorithm. On the other hand, there are not so much researches related to develop a proper soft fingertip. The objective of this paper is to present a simple model of a soft fingertip for practical soft-fingered applications. We first develop a soft fingertip like human skin for soft-fingered manipulations and also present a simple model of the developed soft fingertip based on the force distribution at the contact surface. Through experimental works, we verify the proposed model of the developed soft fingertip, where a tactile sensor and a tactile sensor signal processing system are used to measure the contact force distribution in the contact surface and its total force.
2
Development of a Soft Fingertip
The object manipulating system by a human hand shown in Fig. 1 is one of typical soft-fingered manipulations. Usually, a human hand has many soft fingertips and thus it can be applied to various manipulating tasks. There are various type of contact shapes at the contact surface of a finger in a human
3169
grasping [12]. Generally, we can experience that the contact between the object and each fingertip of the object-hand system is made by a surface contact and also, soft fingertips are appropriately deformed during the manipulation process. In order to implement those soft-fingered manipulations, a proper soft fingertip is necessary.
Fig. 3. A simple one-dimensional contact and deformation.
Fig. 1. An object manipulating system by a human hand. For soft-fingered applications, we developed a hemisphere-shaped soft fingertip with radius of 0.01[m] as shown in Fig. 2, where a molding device is used to make our fingertip. The developed soft fingertip was made by using a Pringel compound of Exseal Co.(http://www.exseal.co.jp). The feature of our soft fingertip is similar to the skin of a human and thus, it can be applied to make a finger with soft fingertip.
Fig. 3 shows a contact status of a soft fingertip which is contacting into an object to the normal direction. Specially, let us consider a hemisphere-shaped soft fingertip with radius of a. Then, the following relation of a circle is satisfactory on the surface; x2 + z 2 = a2 .
(1)
The x-position of a point, Q, on the surface of the fingertip in the two-dimensional space is given by Qx = (a − d0 )tanθ
(2)
where d0 denotes the deformation length of the soft fingertip and θ implies a touching angle shown in Fig. 3. By combining (1) and (2), the z-position of the point Q can be represented as Qz = a2 − (a − d0 )2 tan2 θ. (3) Then, the z-directional length of QC is given by QC = Qz − (a − d0 ).
Fig. 2. A developed soft fingertip.
3
Geometrical Analysis of Soft Fingertips
When a soft fingertip is being contact into a rigid object, there exists some deformation. This section presents geometrical analysis of the deformation of soft fingertips. Particularly, we consider a typical onedimensional contact model of common manipulating tasks as shown in Fig. 3.
(4)
Physically, the length of QC implies the deformation at a point on the contact surface of the soft fingertip. Also, the maximum touching angle, θmax , can be determined by a2 − (a − d0 )2 −1 . (5) θmax = tan (a − d0 )2 Usually, the contacting area of a soft fingertip is dependently increased when the fingertip is being deformed. Specifically, when it is deformed as d0 as shown in Fig. 4, the radius of the contact surface observed at the contact point of C can be represented by
3170
r = (a − d0 )tanθ.
(6)
relation of a cylindrical particle of the soft fingertip. The stress, σ, pressed on the soft particle shown in Fig. 5 is defined as σ≡
F S
(9)
where F is the magnitude of the contact force that acts per contact area, S, of the particle.
Fig. 5. A cylindrical particle of a soft fingertip. When a small compressive contact force is applied to the soft particle, the length of the particle decreases, but the contact surface increases. From this physical phenomenon, the compressional strain, e, is defined as the fractional change in the length of the soft particle as follows: e≡ Fig. 4. The contacting area of a soft fingertip. Also, the small change of the radius, dr, is given by dr =
(a − d0 ) dθ, cos2 θ
(7)
Thus, the resultant area of the small increased contact surface due to the deformation, dS, can be obtained by dS
4
= rdrdϕ (a − d0 )2 sinθ = dθdϕ. cos3 θ
∆L L
(10)
where e is dimensionless and it is negative if the stress is due to compression such as many robotic grasping tasks(∆L < 0). Then, by using Young’s modulus(Y = σ/e) [14], the force relation acting on the soft particle is given by F =Y
∆L S. L
(11)
On the other hand, the pressure acting on a particle is defined as P ≡
(8)
F . S
(12)
By combining (11) and (12), the resultant force relation acting on a particle can be expressed as
Modeling of Soft Fingertip F = PS = Y
For soft-fingered object manipulations, this section presents a one-dimensional modeling of hemisphericalshaped soft fingertips as shown in Fig. 3. In this model, it is assumed that the shape of contact formed at the fingertip is symmetric to the normal axis of the fingertip. In order to obtain a proper model of a soft fingertip with hemispherical shape, we first analyze the force
∆L S. L
(13)
Note that the contact force at the surface of the soft particle depends on the pressure distribution of the soft particle, the length and its change of the soft particle, the area of contact surface, and the Young’s modulus of the soft particle. Then, we will model the soft fingertip of Fig. 3 as a set of infinite soft particles addressed in advance.
3171
(a) d0 =0.001[m]
(b) d0 =0.002[m]
Fig. 6. A model of a soft fingertip based on the force distribution. In this sense, the deformation of the fingertip can be modeled as a deformation set formed by the force distribution as shown in Fig. 6. Since the force of the fingertip is formed by the pressure, the pressure distribution for all particles will gives an idea to determine the total contacting force of the fingertip. Specifically, Figs. 7(a), (b), and (c) show theoretical pressure distribution patterns(P = Y ∆L L ) according to the deformation of 0.001[m], 0.002[m], and 0.003[m], respectively. As a result, by integrating the force distribution of the soft fingertip, the total contact force at the contact surface can be expressed as follows: 2π θmax P dS fc = 0
2π
0
= 0
= Y πd20
0
θmax
dL dS Y L (14)
where Y denotes the Young’s modulus of the fingertip
(c) d0 =0.003[m] Fig. 7. Pressure distribution patterns at each deformation of the soft fingertip. and it can be estimated by experiment. And length parameters of the soft fingertip according to the deformation are given by L = a2 − (a − d0 )2 tan2 θ (15) and dL =
a2 − (a − d0 )2 tan2 θ − (a − d0 ).
(16)
From (14), it is pointed out that the fingertip force is proportional to the square of the deformation of the soft fingertip. Next, in order to verify the proposed force relation given by (14), we performed experimental works by using the experimental setup shown in Fig. 8. The
3172
height gauge in Fig. 8 is to measure of the deformation of the fingertip and the tactile sensor system shown in Fig. 9 enables us to measure the contact force distribution in the contact surface and its total force. In this experiment, we used a tactile sensor(ISCAN10×10) and a tactile sensor system of Nitta Ltd.(http://www.nitta.co.jp).
In many soft-fingered practical applications, the control performance of a given task may be dependently determined as this value. Recently, we have developed a two-fingered hand with soft fingertips as shown in Fig. 12. In future, the developed soft fingertip and its modeling will be applied to soft-fingered manipulations using the developed hand.
(a) d0 =0.001[m] Fig. 8. Experimental setup.
PCI/ISA I/F Board
PCI/ISA Slot PC
Sensor Connector Tactile Sensor
(b) d0 =0.002[m] Fig. 9. A tactile sensor system. By measuring the contact force distribution according to the deformation of the fingertip, we evaluated the elasticity parameter(Y ) of the developed soft fingertip. The contact force distribution is obtained by integrating the pressure distribution in the contact surface. Through the experiment, we have obtained pressure distribution patterns of using the tactile sensor. Figs. 10(a), (b), and (c) show experimental pressure distribution patterns according to the deformation of 0.001[m], 0.002[m], and 0.003[m], respectively. By using (14) and those pressure distributions, we can finally obtain the total contact force as the deformation. Fig. 11 shows both experimental force profile of the soft fingertip and theoretical force profile according to the deformation. From the experimental evaluation, the elastic modulus, Y , is estimated as 0.25[MN/m2 ]. Physically, if the value of Y is more smaller, the compliance of a soft fingertip is more larger. Thus, the elasticity of our soft fingertip is more soft than a common rubber of 7[MN/m2 ] [14].
(c) d0 =0.003[m] Fig. 10. Pressure distribution patterns(unit: Kpa) of the tactile sensor for each deformation, where the dotted circle implies the pressed contact surface.
5
Concluding Remarks
In this paper, a hemisphere-shaped soft fingertip for soft fingers was developed and a nonlinear force
3173
References [1] A. B. A. Cole, J. E. Hauser, and S. S. Sastry, “Kinematics and control of multifingered hands with rolling contact,” IEEE Trans. on Automatic Control, Vol. 34, No. 4, pp. 398-404, 1989. [2] H. Maekawa, K. Tanie, and K. Komoria, “Dynamic grasping force control using tactile feedback for grasp of multifingered hand,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 2462-2469, 1996.
Fig. 11. Force profiles of the developed soft fingertip: experimental and theoretical results.
[3] X. -Z. Zheng, R. Nakashima, and T. Yoshikawa, “On dynamic control of finger sliding and object motion in manipulation with multifingered hands,” IEEE Trans. on Robotics and Automation, Vol. 16, No. 5, pp. 469481, 2000. [4] H. Maekawa, K. Tanie, K. Komoria, and M. Kaneko, “Development of a finger-shaped tactile sensor and its evaluation by active touch,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 1327-1334, 1992. [5] G. Kinoshita, Y. Kurimoto, H. Osumi, and K. Umeda, “Dynamic contact sensing of soft planar fingers with tactile sensors,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 565-570, 2001. [6] S. Arimoto, P. A. N. Nguyen, H. -Y. Han, and Z. Doulgeri, “Dynamics and control of a set of dual fingers with soft tips,” Robotica, Vol. 18, pp. 71-80, 2000. [7] T. Yoshikawa and T. Watanabe, “Dynamic control of soft-finger hands for povoting an object in contact with the envoronment,” IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 324-329, 2000.
Fig. 12. A developed two-fingered hand with soft fingertips. function of a soft fingertip according to the deformation was modeled by considering the force distribution in the contact surface. Through experimental evaluations, the proposed force function was verified, where a tactile sensor and a tactile sensor signal processing system were used to measure the contact force distribution in the contact surface and its total force. The proposed force function for soft fingertips enables us to obtain the total contact force at the contact surface of a finger in object manipulating tasks. Specifically, our model was considered in the one-dimensional contact of a finger. Additional work is to extend our approach to the two- and three-dimensional modelings of soft fingertips and also apply the developed soft fingertip to real soft-fingered applications.
Acknowledgments This work was supported by the research fund of Japan Society for the Promotion of Science.
[8] T. Wada, S. Hirai, S. Kawamura, and N. Namiji, “Robust manipulation of deformable objects by a simple PID feedback,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 85-90, 2001. [9] O. B. Bayazit, J. -M. Lien, and N. M. Amato, “Probabilistic roadmap motion planning for deformable objects,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 2126-2133, 2002. [10] M. R. Cutkosky, J. M. Jordan, and P. K. Wright, “Skin materials for robotic fingers,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 1649-1654, 1987. [11] N. Xydas and I. Kao, “Modeling of contact mechanics and friction limit surfaces for soft fingers in robotics, with experimental results,” Int. Jour. of Robotics Research, Vol. 18, No. 8, pp. 941-950, 1999. [12] S. Hiromitsu and T. Maeno, “Stick/slip distribution on the fingerpad and response of tactile receptors when human grasp an object,” Jour. of the Robotics Society of Japan, Vol. 68-c, No. 667, pp. 202-207, 2002. [13] Y. Satoh, F. Wakui, K. Sogabe, and N. Shimizu, “Steady-state response of silicon β gel and a mass system,” Dynamics and Design Conf. of Japan, pp. 647652, 2000. [14] P. M. Fishbane, S. Gasiorowicz, and S. T. Thornton, Physics for scientist and engineers, Prentice Hall, Englewood Cliffs, New Jersey, 1993.
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