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tactile sensor for robotic applications
Sensors and Actuators A 175 (2012) 60–72
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Force/tactile sensor for robotic applications G. De Maria, C. Natale, S. Pirozzi ∗ Dipartimento di Ingegneria dell’Informazione, Seconda Università degli Studi di Napoli, 81031 Aversa, Italy
a r t i c l e
i n f o
Article history: Received 26 July 2011 Received in revised form 19 December 2011 Accepted 20 December 2011 Available online 28 December 2011 Keywords: Force/torque sensor Tactile sensor Robotics Optoelectronics
a b s t r a c t The paper describes the detailed design and the prototype characterization of a novel tactile sensor1 for robotic applications. The sensor is based on a two-layer structure, i.e. a printed circuit board with optoelectronic components below a deformable silicon layer with a suitably designed geometry. The mechanical structure of the sensor has been optimized in terms of geometry and material physical properties to provide the sensor with different capabilities. The first capability is to work as a six-axis force/torque sensor; additionally, the sensor can be used as a tactile sensor providing a spatially distributed information exploited to estimate the geometry of the contact with a stiff external object. An analytical physical model and a complete experimental characterization of the sensor are presented. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Since the early days of robotics, researchers have recognized that equipping a robot with many sensors is a way to confer them autonomy sufficient to perform tasks in unstructured environments. This sensory system should provide information to the robot about physical properties of different nature. Among these properties, when manipulation tasks are considered, the sense of touch is of paramount importance. Tactile sense is used by humans to grasp and manipulate objects avoiding slippage, or to blindly operate in an dynamic environment. An artificial tactile sensor, by mimicking the human touch, should possess the capability to measure both dynamic and geometric quantities, i.e. contact forces and torques as well as spatial and geometrical information about the contacting surfaces. Each of these may be measured either as an average quantity for some part of the robot or as a spatially resolved, distributed quantity across a contact area [1]. A definition of tactile sensor is given by Lee and Nichols [2]: a device or system that can measure a given property of an object or contact event through physical contact between the sensor and the object. The one above is probably the best, and at the same time the broadest definition of a tactile sensor. Most of the tactile sensors already developed are constituted by an array of sensing elements, called taxels,2 integrated into the
∗ Corresponding author. E-mail address: [email protected] (S. Pirozzi). 1 Euopean patent pending, Application no. EP11425148.1. 2 The word taxel derives from the union of the words “tactile element”. 0924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2011.12.042
fingertips of a manipulator end effector. Already in 1982 Harmon [3], defined a first set of tactile sensor design parameters, making a list which is still widely used by researchers today. These features are absolutely general and application dependent, thus not definitive. Other very important design parameters may be found in [4], which is more focused on the feature of an entire sensing skin and on the integration of such a skin on a complex manipulator structure. A recent and comprehensive review on features that tactile sensors should possess and technologies used to realize them can be found in [5]. Very few commercial devices are currently available, even tough many technologies have been proposed in the scientific literature to build tactile sensors. This is mainly due to high manufacturing complexity and cost. In particular, prototypes of tactile sensors that use the following different technologies can be found: resistive [6–11], piezoelectric [12,13], capacitive [14,15], magnetic [16,17] and optoelectronic [17–21]. With reference to the optoelectronic technology, that exploits the electromagnetic properties of light, more details are described in the following since the prototype presented in this paper is based on this technology. Widely used sensors are based on Fibre Bragg Gratings (FBG). Typical examples are the two sensors discussed in [18], which exploit the relationship between the variations of the FBG wavelength and the external force applied to the FBG. The sensors based on optical fibres are expensive and difficult to integrate into complex robotic structures (e.g. anthropomorphic hands, robotic arms) because of the bending losses that occur in the fibres routing. Other sensors are based on scattering by small or big particles (compared to the wavelength used) and make use of highly scattering materials such as foams. An example of how foams can be used for tactile sensing technology can be found in [19], where the urethane foam
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Fig. 2. Sketch of the working principle.
Fig. 1. Structure of the force/tactile sensor.
presents a cavity, whose dimensions vary according to the external force applied. When the cavity is compressed, the scattered energy density varies, and by detecting this variation, it is possible to reconstruct the external force magnitude. The main drawback of this sensor type is related to the stochastic nature of the scattering phenomenon [22], therefore the measurement process is characterized by a lack of repeatability. The prototypes proposed in [20,21] use CCD cameras to measure tactile images. These solutions involve large volumes, weights and costs that complicate the integration into robotic hands. In [17] a sensor prototype with two different measuring systems is presented. One of these uses an LED and four phototransistors to measure the deformation in the centre of an elastic dome and then these deformation measurements are
experimentally related to the external vertical force applied to the dome. In the proposed configuration, the sensor works as a simple force sensor with a soft interface. The force/tactile sensor proposed in this paper exploits the thorough study based on Finite Element (FE) modelling conducted in [23] where the working principle has been presented for the first time. There, only a simplified prototype with limited sensing capabilities was tested with the aim of showing only the feasibility of the approach, while the main focus was on the mechanical characterization and optimization of the device. The sensor is based on the use of optoelectronic technologies and it aims to overcome most of the problems encountered in the works cited above, mainly: difficulty of the integration into small spaces, high costs, repeatability and complex conditioning electronics. The sensor has different capabilities, i.e. it can measure the six components of the force and torque vectors applied to it,
Fig. 3. Some pictures of the sensor prototype: (a) electronic layer, (b) bottom view of deformable layer, (c) top view of assembled sensor, and (d) bottom view of assembled sensor.
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Fig. 6. Calibration system as force/torque sensor.
16 x Fig. 4. A 3D sketch of the reference axes with respect to sensor taxels.
and it can be used as a tactile sensor providing a spatial and geometrical information about the contact with a stiff external object. In fact, an approximated analytical model of the physical contact is derived, that is usefully exploited to extract information on the contact geometry from the sensor signals. Experimental characterization results are presented to both validate the model and to show how the sensor, with a proper algorithm, can be used to provide a complete characterization of the contact between the sensor and a stiff external object. 2. Sensor concept To realize all the sensor capabilities as stated in the introduction, a deformable elastic layer is positioned above a matrix of sensible points (the taxels) so as to transduce the force and torque vectors into deformations which are then measured by the sensible 0.2
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points as explained in the following subsection. Furthermore, the signals provided by the taxels, which are spatially distributed below the deformable layer, constitute a spatially distributed information that will also allow to estimate the size and orientation of the contact surface between the external surface of the sensor and the objects in contact with it. The contemporary knowledge of all this information is essential for a use of the sensor in robotic applications where objects of different size and dimension have to be manipulated by robotic hands. 2.1. Working principle The proposed tactile sensor is based on the use of LED–phototransistor couples and a deformable elastic layer positioned above the optoelectronics devices (see Fig. 1). The optoelectronic components are organized in a matrix structure. For each couple, the LED illuminates the reflecting surface which coincides with the bottom facet of the deformable layer. Practically, the deformable layer transduces an external force and/or torque into a deformation of its bottom facet through its stiffness. An external force applied to the deformable layer produces local variations of the bottom surface of the elastic material and the couples of optical devices measure the deformations in a discrete number of points. In particular, these deformations produce a variation of the reflected light intensity and, accordingly, of the photo-current flowing into the photo-detector. The deformations can be positive or negative, i.e. the photo-current can locally increase or decrease (see Fig. 2), depending on amplitudes of tangential and normal force components, as well as on torque components. FE analysis, which has been carried out in [23], demonstrated that the latter relationship can be used to actually reconstruct the external force and/or torque components by measuring the elastic layer deformations in a discrete number of points. The paper cited above reports an experimentally identified model of the material used to realize the elastic layer, and then adopted in a FE analysis aimed at optimizing the shape of the deformable layer in order to obtain a satisfactory sensitivity for both normal and tangential components of the contact force vector. 2.2. Sensor prototype
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The realization of the sensor prototype (see Fig. 3(c)) took into account the results of the FE analysis to manufacture the deformable layer and some observations to select the optoelectronic components.
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Concerning the deformable layer of the realized prototype, it is made of black silicone in order to avoid cross-talk problems between taxels and ambient light disturbances, since the black colour guarantees the maximum absorption for every wavelengths. Only the surface which faces each devices pair is white to increase the sensor sensitivity (see Fig. 3(b)), ensuring the maximum reflection for every wavelengths. According to the FE analysis results, the aspect ratio of the black walls between taxels has been selected in order to reduce the horizontal deformations with respect to the vertical ones. In particular, for the presented prototype, the thickness of the black walls is 1 mm, while the extension of the white reflecting surfaces is 1.6 mm, which results in a total size for the
deformable layer of 11.4 mm × 11.4 mm. The height of the reflecting surfaces from the base of the deformable layer, in order to respect the necessary aspect ratio, is 1.5 mm. The top of the deformable layer is a section of a sphere with a radius of 11.4 mm. With the silicone choice modelled above, according to the numerical simulations, the expected measurement range of the sensor prototype is [0,4] N. The maximum force level can be adapted by changing the hardness of the deformable layer. The maximum measurable force is limited by the maximum vertical deformation of the reflecting surface of each taxel, so the former can be changed by acting on the deformable layer geometry. A linear relation between the Shore hardness and the logarithmic of Young’s modulus has been derived
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Analog-to-Digital converter chip (code AD7490, see Fig. 3(d)). The voltage supply for all components is 3.3 V. Each LED is used with a forward current less than 5 mA, with a maximum power consumption less than 200 mW for the whole sensor. This low power consumption and the local digitalization, together with its compact size (see pictures in Fig. 3), make this sensor particularly suitable to integrate into anthropomorphic robotic hands.
3. Prototype characterization as force/torque sensor
Fig. 8. Pictures of testing objects: (a) a standard bottle and (b) a classic can.
in [24] for elastomeric materials. Using this relation, the maximum predictable force level, with the current geometry, goes from 2 N to 40 N by changing the hardness of the deformable layer from 4 A to 60 A. Recalling the theory on LEDs and photodetectors radiation pattern [25], it is possible to consider the photocurrent (and thus the received radiant flux by the photodetector) proportional to the radiant intensity pattern of the LED and responsivity pattern of the photodetector, evaluated at the emitting and receiving angle respectively. Moreover the photocurrent is also inversely proportional to the squared distance between the two devices and the reflecting surface. As a consequence, the optoelectronic components should have very large viewing angles in order to minimize the effects of LED radiation pattern and photodetector responsivity pattern on the photocurrent and to leave only the dependence with the distance. Considering these aspects, the realized prototype uses optoelectronic components manufactured by OSRAM (see Fig. 3(a)). The LED (code SFH480) is an infrared emitter with a typical peak wavelength of 880 nm, while the detector is a silicon NPN phototransistor (code SFH3010) with a maximum peak sensitivity at 860 nm wavelength. Both the components have a viewing angle of ±80◦ . The conditioning electronics is only constituted by simple resistors without amplification and/or filtering stages. As a consequence, the collector current of the phototransistors, depending on the received light intensity, is easily translated into a voltage signal via a suitable resistor and then directly digitalized with an
The objective of this section is to show all the potentiality of the presented prototype sensor and a calibration procedure necessary to use it as a six-axes force/torque sensor. The characterization of the sensor has been made in the hypothesis that the contact surface can be approximated by a plane with an high stiffness with respect to the deformable layer. The hypothesis that the contact surface is a plane can be considered verified each time the external object has a curvature radius larger than that of the deformable layer. This condition is true for a large number of objects used in everyday manipulation and grasping tasks. Taking into account the hardness of the silicone, estimated in [23], used to realize the presented prototype, also the hypothesis of the high stiffness for the contact surface can be considered true for most of the daily use objects. Fig. 4 shows a sketch of the sensor, where the position of each cell with respect to the reference axes is indicated. The position of the kth taxel can be identified with the (xk , yk ) coordinates of the centre position of the taxel. At rest position, for each taxel, a certain amount of light emitted by the LED is reflected from the white surface and reaches the phototransistor, generating an initial voltage value on the collector. When an external force and/or torque is applied to the sensor, the distance of the reflecting surface of each cell from the corresponding LED/phototransistor couple on the electronic layer can be subjected to a positive or a negative variation. These distance variations imply changes of the reflected light and, accordingly, of the voltages measured on the phototransistor collector. Denoting with vk the voltage variation of the kth taxel, vk > 0 denotes an increasing distance (and then a decreasing photocurrect), while vk < 0 denotes a decreasing distance (and then an increasing photocurrect) between the reflecting surface and the electronic layer (obviously vk = 0 denotes no variation). Fig. 5 reports typical values of a voltage vk , for the realized prototype. To calibrate the prototype for use as a six-axes force/torque sensor, the proposed approach is based on the use of a neural network to interpolate a number of data sufficient to model the relationship between the applied forces and torques and the phototransistors measurements. The sensor has been mounted on a six-axes load cell used as reference sensor. The model used is the FTD-Nano-17 manufactured by ATI, with a measurement range equal to ±12 N and ±17 N for horizontal and vertical force components, respectively, while the measurement range for all torque components is equal to ±120 Nmm. The reference axes, reported in Fig. 4, are located on the plane that separates the prototype from the reference sensor. Fig. 6 shows the calibration system used to collect data for neural network training. An operator carried out various experiments, using a stiff plane, applying different external forces and torques and simultaneously acquiring all the voltage variations on the phototransistors and all the forces and torques components measured by the reference load cell. These data, acquired at a sample rate of 100 Hz, have been organized in a training set and a validation set to be used as input data (voltage variations) and target data (forces and torques components) of the neural network. A testing set has been prepared using data from experiments other than those used to collect the training and the validation sets, in order to assess the trained network.
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A standard two-layer feed-forward neural network fNN , trained with the Levenberg–Marquardt method, has been used to fit training data H = fNN (V ),
(1) ]T
where H = [Fx Fy Fz Tx Ty Tz is the output vector, Fi and Ti with i = x, y, z are force and torque components with respect to the reference axes and V = [v1 v2 . . . v16 ]T is the input vector containing the voltage variations of the taxels. The network is constituted by 24 neurons for the hidden layer and 6 neurons for the output layer. The trained network testing results are reported in Fig. 7(a) for the force components and in Fig. 7(b) for the torques.
The estimation is good for all force and torque components, especially when force and torque values are high enough. In fact, in the performance analysis it must be also taken into account that the training data are very noisy when the measured values are small compared to the full scale of the reference sensor. In different experiments the trained neural network has been tested with objects that have a finite curvature radius. In particular, Fig. 8 shows a standard bottle and a classic can used to collect additional testing data. Figs. 9 and 10 show the real and the estimated forces and torques for the bottle and the can, respectively. The estimation is accurate also in these cases, obviously with a minimal reduction in
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performance when the curvature radius of the contact surface decreases. It is important to underline that these performances have to be evaluated along with the fact that compared to commercially available sensors, the proposed one is more compact, low cost, low power consumption, provided with a digital interface, and the deformable layer guarantees good adaptability and stability during grasping and manipulation application.
e.g. complex robotic manipulation tasks, the availability to the control system of an estimate of contact plane position and orientation together with the interaction forces exchanged by the sensor and the external object are fundamental to successfully execute the task. To obtain this information from the sensor, an approximated physical model is first derived and validated to describe the contact between a stiff surface and the deformable layer.
4. Prototype characterization as tactile sensor 4.1. Sensor model As said, the proposed prototype can be also used as tactile sensor, estimating not only force and torque components as described in Section 3, but also the contact geometry. In some applications,
In the model description, the deformable layer is considered as an elastic homogeneous hemisphere of known radius R and the
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Fig. 11. Geometric characteristics of the contact model.
external object as a stiff plane. The reference frame is considered having the origin in the centre of the sphere and the x and y axes aligned with those defined in Fig. 4. Fig. 11 shows a generic contact where the stiff external object deforms the elastic hemisphere until, at equilibrium, the contact plane coincides with the plane 2 . Then consider the plane 1 , parallel to the plane 2 and tangent to the hemisphere at the point P. Assume that during the deformation the contact plane moves, from the limit position 1 (corresponding to no deformation) to the 2 position, due to the concentrated force F. The full characterization of the contact geometry means to estimate the position and orientation of the plane 2 and the direction of the force F with respect to 2 . In particular, the plane 2 can be uniquely defined by and angles and by its distance TO from the origin of the reference frame. Considering the axial symmetry of the deformable layer, the angle can be directly estimated from the measured Fx and Fy components, reducing the three-dimensional problem in a two-dimensional one in the zp-plane, where the p axis is defined by the direction of the vector (Fx , Fy , 0) with magnitude Fp =
beam compression z depends only on force vertical component Fz , while the bending p depends only on force horizontal component Fp . Assuming a linear elastic response of the material, the relationships among the variables above are Fz =
ES z h
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Fx2 + Fy2 . Thus it is
= atan2(Fy , Fx ),
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where atan2(b, a) is the argument of the complex number a + ib. The projection of the contact area on the xy-plane is an ellipse. At equilibrium, the external force is balanced by the elastic reaction force of the deformable layer. Differently from [26], where the elastic body is approximated with an infinite set of elementary beams, in the proposed model, the deformable layer is approximated with a single elastic beam with elliptical cross section S with a size that depends on the angle and on the normal displacement dn = PT of the object. The height h of the elastic beam at rest is set equal to the height zP of the tangent point P, i.e. when there is no deformation, and it depends on the angle . According to the force F direction, the elastic beam can be subjected in the zp-plane to a pure compression, a pure bending or a combination of both. In particular, the
Fig. 12. Mechanical system for contact geometry characterization.
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where E is the material Young modulus and I is the area moment of inertia of the beam. Note that in Eqs. (3) and (4) the shear stress effect has been neglected. Considering the intersection point H between the plane 2 and the force F direction, it is convenient to introduce the tangential displacement dt = p/cos . Also note that TA =
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As expected, the force components are related to the contact geometry, uniquely defined by the dn , dt and variables. 4.2. Experimental validation of the model The model (11) and (12) has been derived assuming a linear elastic response of the material and that the hemisphere is homogeneous. These two conditions are not fully satisfied by the deformable layer of the presented prototype because of the wells above the taxels and because of the material nonlinear characteristic. In order to compensate for these discrepancies between the
assumptions of the model and the actual prototype, for the proposed sensor the following gray-box model is considered
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4.3. Relationship between the tactile image and the external force Note that the force F direction in Fig. 11, from the contact geometry point of view, is related only to the position of point H, for a fixed contact plane. As a consequence, being F related to the vk taxel voltage variations, as described in Section 3, it is possible to relate point H coordinates directly to the vk voltage variations. The set of voltage variations represents a tactile image that, for example, could be used to estimate a pressure map using an appropriate reference sensor. Whereas, in this paper, the information contained in the tactile image is used to estimate the coordinates of the point H in the xy-plane, i.e. the coordinate couple (xH , yH ). Rather than using a black-box approach, a model that requires a reduced number of measurements is proposed. The model is based on a centroidlike approach, in which the taxels that present negative voltage variations are properly weighted as
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(16)
The weights ˛k and ˇk can be estimated with a minimum of 16 measurements. In general, it is better to use a larger number of measurements and to derive the least squares solution with a pseudo-inversion operation. Using the mechanical structure in Fig. 12 a set of 40 measurements for the (xH , yH ) coordinates and the tactile images (the 16 voltage variations vk ) have been collected to estimate the weights ˛k and ˇk . Then the model (15) has been tested with different measurements and the results are reported in Fig. 15. The maximum estimation error is less than 0.5 mm for xH and less than 0.6 mm for yH . 4.4. Estimation of the contact geometry This section is aimed at showing how the capability of the sensor to reconstruct the force components and the gray-box structure of the model (13) and (14) can be exploited to estimate the contact geometry. The idea is that from the knowledge of the Fz and Fp force
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allows to obtain a good matching between the gray-box model and the experimental measurements, as shown below. Forces with different directions and magnitudes have been applied to the prototype sensor using different plane contacts, whose positions and orientations have been fixed with the mechanical structure shown in Fig. 12. In particular, the goniometer has been used to fix the angle values, while the micrometric stage to fix the dn and dt deformations values. In a first set of experiments, the , dn and dt values, measured with the mechanical structure, have been collected and used to estimate the parameters ki . Since Eqs. (13) and (14) are linear in the ki , a Least-Square (LS) approach has been used to obtain the values k1 = 1.3095, k2 = 0.2533, k3 = 3.4644, k4 = − 3.3025 and k5 = 0.9248. Data from a second set of experiments have been collected to test the model performance. Fig. 13 compares the reconstructed Fz and Fp with the force values measured by the reference sensor. The error is less than 0.15N for the vertical force component and less than 0.08N for the horizontal force component. The same procedure can be applied using the force components samples measured by the proposed prototype with the neural network (1). The comparison between measured and modelled force components is presented in Fig. 14. For this case the reconstruction error is only slightly worse than the previous case, due to the additional error introduced by the neural network.
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values, calculated with the neural network (1) and by inverting the model (13) and (14), the variables , dn and dt , that determine the contact geometry, can be estimated. Evidently, the two model equations are not sufficient to achieve the desired objective. In order to fully estimate the contact geometry variables a third equation is needed. With reference to Fig. 11, with simple geometrical considerations, the following relation is obtained pH = R sin − dt cos ,
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can be computed using Eq. (15). Thus, taking where pH = Eqs. (13) and (14) together with Eq. (17), a set of three equation is obtained with the three unknowns , dn and dt . This nonlinear system can be numerically solved to obtain the desired information about the contact geometry. First of all, in order to verify the effectiveness of the approach, the procedure has been tested with experimental input data collected from the reference sensor (regarding Fz and Fp ) and from the mechanical structure shown in Fig. 12 (regarding pH ). The results of the , dn and dt variables estimation are reported in Fig. 16, where the high accuracy obtained in the contact geometry reconstruction is evident. In particular, the maximum error is less than 0.2◦ for , less than 100 m for dn and less then 20 m for dt . Afterwards, the proposed procedure has been tested also with force data
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Fig. 18. Scheme of all the capabilities of the sensor.
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computed by the neural network (1) and with (xH , yH ) values calculated with Eq. (15). The results are shown in Fig. 17. In this case, the maximum error is less than 2◦ for , less than 200 m for dn and less then 60 m for dt , due to errors in the estimation of the force components and of the (xH , yH ) coordinates. In conclusion, all the capabilities of the proposed force/tactile sensor are summarized in the block diagram shown in Fig. 18. The sensor output signals, i.e. the vk voltage variations are used as inputs of the neural network, trained as described in Section 3, to estimate force and torque components W. The same signals are also used as inputs of the centroid-like model, identified as described in Section 4.3, to estimate, in conjunction with the estimated forces, the contact geometry variables, according to the procedure described in Section 4.4.
[11]
[12]
[13] [14]
[15]
[16] [17]
5. Conclusions The paper described the detailed design and the experimental characterization of a novel tactile sensor for robotic applications based on optoelectronic technology. The sensor mechanical structure has been designed so as to allow the device to work as a six-axis force/torque sensor. An analytical physical model has been derived to let the sensor act as a tactile sensor for estimation of the geometry of the contact with a stiff external object. A complete calibration procedure has been presented and the algorithms necessary to exploit all the sensor capabilities have been provided and experimentally tested, demonstrating the effectiveness of the whole sensor system. The new sensor has been shown to be capable of measuring not only force components (up to 3.5 N) but also torque components (up to 10 Nmm). Moreover, the reconstruction of the contact geometry is very accurate, obtaining a maximum error less than 0.2◦ for the orientation angles of the contact plane and less than 100 m for the radial deformation of the sensor. Further developments are expected in view of the integration of the sensor into the fingertips of a robotic hand and its use in real-time feedback control systems.
[18] [19]
[20]
[21]
[22] [23]
[24]
[25] [26]
biomechanical applications, Sensors and Actuators A: Physical 120 (2) (2005) 370–382. Y. Yamada, M.R. Cutkosky, Tactile sensor with 3-axis force and vibration sensing functions and its application to detect rotational slip, in: Proceedings of IEEE International Conference on Robotic and Automation, USA, 1994, pp. 3550–3557. K. Motoo, F. Arai, T. Fukuda, Piezoelectric vibration-type tactile sensor using elasticity and viscosity change of structure, IEEE Sensors Journal 7 (7) (2007) 1044–1051. G.M. Krishna, K. Rajanna, Tactile sensor based on piezoelectric resonance, IEEE Sensors Journal 4 (5) (2004) 691–697. T. Salo, T. Vancura, H. Baltes, Cmos-sealed membrane capacitors for medical tactile sensors, Journal of Micromechanics and Microengineering 16 (4) (2006) 769–778. J.L. Novak, Initial design and analysis of a capacitive sensor for shear and normal force measurement, in: Proceedings of IEEE International Conference on Robotic and Automation, USA, 1989, pp. 137–145. Z. Chi, K. Shida, A new multifunctional tactile sensor for three-dimensional force measurement, Sensors and Actuators A: Physical 111 (2-3) (2004) 172–179. E. Torres-Jara, I. Vasilescu, R. Coral, A soft touch: compliant tactile sensors for sensitive manipulation, in: CSAIL Technical Report MIT-CSAIL-TR-2006-014, 2006. J.S. Heo, J.H. Chung, J.J. Lee, Tactile sensor arrays using fiber Bragg grating sensors, Sensors and Actuators A: Physical 126 (2) (2006) 312–327. G. Hellard, R.A. Russell, A robust, sensitive and economical tactile sensor for a robotic manipulator, in: Proceedings of Australasian Conference on Robotics and Automation, Auckland, 2002, pp. 100–104. K. Kamiyama, K. Vlack, T. Mizota, H. Kajimoto, N. Kawakami, S. Tachi, Visionbased sensor for real-time measuring of surface traction fields, IEEE Computer Graphics and Applications 25 (1) (2005) 68–75. M. Ohka, Y. Mitsuya, Y. Matsunaga, S. Takeuchi, Sensing chracteristics of an optical three-axis tactile sensor under combined loading, Robotica 22 (2004) 213–221. A. Ishimaru, Wave Propagation and Scattering in Random Media, 1st edition, Academic Press, NY, USA, 1978. A. D’Amore, G. De Maria, L. Grassia, C. Natale, S. Pirozzi, Silicone-rubber-based tactile sensors for the measurement of normal and tangential components of the contact force, Journal of Applied Polymer Science 122 (6) (2011) 3758–3770. H. Qi, K. Joyce, M.C. Boyce, Durometer hardness and the stress–strain behavior of elastomeric materials, Rubber Chemistry and Technology 76 (2003) 419–435. S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, 1st edition, Prentice Hall, NJ, USA, 2001. T. Inoue, S. Hirai, Mechanics and Control of Soft-fingered Manipulation, 1st edition, Springer-Verlag, London, UK, 2009.
Biographies Acknowledgements The research leading to these results has been partly funded by the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant agreement no. 216239 (DEXMART project) and partly by the Italian Ministry of University and Scientific Research (PRIN 2009) under the national project ROCOCO. References [1] B. Siciliano, O. Khatib, Springer Handbook of Robotics, 1st edition, SpringerVerlag, Berlin, D, 2008. [2] M.H. Lee, H.R. Nicholls, Review article tactile sensing for mechatronics – a state of the art survey, Mechatronics 9 (1999) 1–31. [3] L.D. Harmon, Automated tactile sensing, The International Journal of Robotics Research 1 (2) (1982) 3–32. [4] Y. Ohmura, Y. Kuniyoshi, A. Nagakubo, Conformable and scalable tactile sensor skin for curved surfaces, in: Proceedings of IEEE International Conference on Robotics and Automation, USA, 2006, pp. 1348–1353. [5] R.S. Dahiya, G. Metta, M. Valle, G. Sandini, Tactile sensing – from humans to humanoids, IEEE Transactions on Robotics 26 (1) (2010) 1–20. [6] K.N. Tarchanidis, J.N. Lygouras, Data glove with a force sensor, IEEE Transactions on Instrumentations and Measurement 52 (3) (2003) 984–989. [7] E.S. Hwang, J.H. Seo, Y.J. Kim, A polymer-based flexible tactile sensor for both normal and shear load detections and its application for robotics, IEEE/ASME Journal of Microelectromechanical Systems 16 (3) (2007) 556–563. [8] M. Shimojo, A. Namiki, M. Ishikawa, R. Makino, K. Mabuchi, A tactile sensor sheet using pressure conductive rubber with electrical-wires stitched method, IEEE Sensors Journal 4 (5) (2004) 589–596. [9] A. Wisitsoraat, V. Patthanasetakul, T. Lomas, A. Tuantranont, Low cost thin film based piezoresistive mems tactile sensor, Sensors and Actuators A: Physical 139 (1–2) (2007) 17–22. [10] L. Beccai, S. Roccella, A. Arena, F. Valvo, P. Valdastri, A. Menciassi, M.C. Carrozza, P. Dario, Design and fabrication of a hybrid silicon three-axial force sensor for
Giuseppe De Maria was born in Napoli, Italy, on December 1948. In 1973 he received the Laurea degree in Electronic Engineering from the University of Naples. He was associate professor of Automatic Control at the University of Naples “Federico II”. Since 1992 he is full professor of Automatic Control at the Faculty of Engineering of the Second University of Naples. His research interests include robust control, control of mechanical systems, industrial and advanced robotics, control of aerospace and aeronautical systems, active noise and vibration control of flexible structures. Now his research interests are focused on the control of smart materials, in particular piezoceramics, magnetostrictive, with the aim to realize artificial muscles. Concerning this field of research he is responsible of National and European research contracts. He is work-package leader of the DEMART project in the 7th Framework Programme of European Community. Ciro Natale received the Laurea degree and the Research Doctorate degree in Electronic Engineering from the University of Naples in 1995 and 2000, respectively. From 2000 to 2004 he has been Research Associate at the Second University of Naples, where he currently holds the position of Associate Professor of Robotics. From November 1998 to April 1999 he was a Visiting Scholar at the German Aerospace centre in Oberpfaffenhofen, Germany. His research interests on robotics include modelling and control of industrial manipulators, force and visual control, cooperative robots. In the aeronautics application sector, his research activities are focused on modelling and control of flexible structures, active noise and vibration control, identification and control of smart materials. He has published more than 70 journal and conference papers as well as authored and co-authored monographs on robotics and control of flexible structures. He currently serves as Associate Editor of the IEEE Trans. on Control Systems Technology. Salvatore Pirozzi was born in Napoli, Italy, on April 21st, 1977. He received the Laurea and the Research Doctorate degree in Electronic Engineering from the Second University of Naples, Aversa, Italy, in 2001 and 2004, respectively. From 2008 he is a Assistant Professor at the Second University of Naples. His research interests include modelling and control of smart actuators for advanced feedback control systems and design of innovative sensors for robotics applications, as well as identification and control of vibrating systems. He published more than 30 international journal and conference papers and he is co-author of the book “Active Control of Flexible Structures”, published by Springer.
Contents lists available at SciVerse ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Force/tactile sensor for robotic applications G. De Maria, C. Natale, S. Pirozzi ∗ Dipartimento di Ingegneria dell’Informazione, Seconda Università degli Studi di Napoli, 81031 Aversa, Italy
a r t i c l e
i n f o
Article history: Received 26 July 2011 Received in revised form 19 December 2011 Accepted 20 December 2011 Available online 28 December 2011 Keywords: Force/torque sensor Tactile sensor Robotics Optoelectronics
a b s t r a c t The paper describes the detailed design and the prototype characterization of a novel tactile sensor1 for robotic applications. The sensor is based on a two-layer structure, i.e. a printed circuit board with optoelectronic components below a deformable silicon layer with a suitably designed geometry. The mechanical structure of the sensor has been optimized in terms of geometry and material physical properties to provide the sensor with different capabilities. The first capability is to work as a six-axis force/torque sensor; additionally, the sensor can be used as a tactile sensor providing a spatially distributed information exploited to estimate the geometry of the contact with a stiff external object. An analytical physical model and a complete experimental characterization of the sensor are presented. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Since the early days of robotics, researchers have recognized that equipping a robot with many sensors is a way to confer them autonomy sufficient to perform tasks in unstructured environments. This sensory system should provide information to the robot about physical properties of different nature. Among these properties, when manipulation tasks are considered, the sense of touch is of paramount importance. Tactile sense is used by humans to grasp and manipulate objects avoiding slippage, or to blindly operate in an dynamic environment. An artificial tactile sensor, by mimicking the human touch, should possess the capability to measure both dynamic and geometric quantities, i.e. contact forces and torques as well as spatial and geometrical information about the contacting surfaces. Each of these may be measured either as an average quantity for some part of the robot or as a spatially resolved, distributed quantity across a contact area [1]. A definition of tactile sensor is given by Lee and Nichols [2]: a device or system that can measure a given property of an object or contact event through physical contact between the sensor and the object. The one above is probably the best, and at the same time the broadest definition of a tactile sensor. Most of the tactile sensors already developed are constituted by an array of sensing elements, called taxels,2 integrated into the
∗ Corresponding author. E-mail address: [email protected] (S. Pirozzi). 1 Euopean patent pending, Application no. EP11425148.1. 2 The word taxel derives from the union of the words “tactile element”. 0924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2011.12.042
fingertips of a manipulator end effector. Already in 1982 Harmon [3], defined a first set of tactile sensor design parameters, making a list which is still widely used by researchers today. These features are absolutely general and application dependent, thus not definitive. Other very important design parameters may be found in [4], which is more focused on the feature of an entire sensing skin and on the integration of such a skin on a complex manipulator structure. A recent and comprehensive review on features that tactile sensors should possess and technologies used to realize them can be found in [5]. Very few commercial devices are currently available, even tough many technologies have been proposed in the scientific literature to build tactile sensors. This is mainly due to high manufacturing complexity and cost. In particular, prototypes of tactile sensors that use the following different technologies can be found: resistive [6–11], piezoelectric [12,13], capacitive [14,15], magnetic [16,17] and optoelectronic [17–21]. With reference to the optoelectronic technology, that exploits the electromagnetic properties of light, more details are described in the following since the prototype presented in this paper is based on this technology. Widely used sensors are based on Fibre Bragg Gratings (FBG). Typical examples are the two sensors discussed in [18], which exploit the relationship between the variations of the FBG wavelength and the external force applied to the FBG. The sensors based on optical fibres are expensive and difficult to integrate into complex robotic structures (e.g. anthropomorphic hands, robotic arms) because of the bending losses that occur in the fibres routing. Other sensors are based on scattering by small or big particles (compared to the wavelength used) and make use of highly scattering materials such as foams. An example of how foams can be used for tactile sensing technology can be found in [19], where the urethane foam
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Fig. 2. Sketch of the working principle.
Fig. 1. Structure of the force/tactile sensor.
presents a cavity, whose dimensions vary according to the external force applied. When the cavity is compressed, the scattered energy density varies, and by detecting this variation, it is possible to reconstruct the external force magnitude. The main drawback of this sensor type is related to the stochastic nature of the scattering phenomenon [22], therefore the measurement process is characterized by a lack of repeatability. The prototypes proposed in [20,21] use CCD cameras to measure tactile images. These solutions involve large volumes, weights and costs that complicate the integration into robotic hands. In [17] a sensor prototype with two different measuring systems is presented. One of these uses an LED and four phototransistors to measure the deformation in the centre of an elastic dome and then these deformation measurements are
experimentally related to the external vertical force applied to the dome. In the proposed configuration, the sensor works as a simple force sensor with a soft interface. The force/tactile sensor proposed in this paper exploits the thorough study based on Finite Element (FE) modelling conducted in [23] where the working principle has been presented for the first time. There, only a simplified prototype with limited sensing capabilities was tested with the aim of showing only the feasibility of the approach, while the main focus was on the mechanical characterization and optimization of the device. The sensor is based on the use of optoelectronic technologies and it aims to overcome most of the problems encountered in the works cited above, mainly: difficulty of the integration into small spaces, high costs, repeatability and complex conditioning electronics. The sensor has different capabilities, i.e. it can measure the six components of the force and torque vectors applied to it,
Fig. 3. Some pictures of the sensor prototype: (a) electronic layer, (b) bottom view of deformable layer, (c) top view of assembled sensor, and (d) bottom view of assembled sensor.
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and it can be used as a tactile sensor providing a spatial and geometrical information about the contact with a stiff external object. In fact, an approximated analytical model of the physical contact is derived, that is usefully exploited to extract information on the contact geometry from the sensor signals. Experimental characterization results are presented to both validate the model and to show how the sensor, with a proper algorithm, can be used to provide a complete characterization of the contact between the sensor and a stiff external object. 2. Sensor concept To realize all the sensor capabilities as stated in the introduction, a deformable elastic layer is positioned above a matrix of sensible points (the taxels) so as to transduce the force and torque vectors into deformations which are then measured by the sensible 0.2
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points as explained in the following subsection. Furthermore, the signals provided by the taxels, which are spatially distributed below the deformable layer, constitute a spatially distributed information that will also allow to estimate the size and orientation of the contact surface between the external surface of the sensor and the objects in contact with it. The contemporary knowledge of all this information is essential for a use of the sensor in robotic applications where objects of different size and dimension have to be manipulated by robotic hands. 2.1. Working principle The proposed tactile sensor is based on the use of LED–phototransistor couples and a deformable elastic layer positioned above the optoelectronics devices (see Fig. 1). The optoelectronic components are organized in a matrix structure. For each couple, the LED illuminates the reflecting surface which coincides with the bottom facet of the deformable layer. Practically, the deformable layer transduces an external force and/or torque into a deformation of its bottom facet through its stiffness. An external force applied to the deformable layer produces local variations of the bottom surface of the elastic material and the couples of optical devices measure the deformations in a discrete number of points. In particular, these deformations produce a variation of the reflected light intensity and, accordingly, of the photo-current flowing into the photo-detector. The deformations can be positive or negative, i.e. the photo-current can locally increase or decrease (see Fig. 2), depending on amplitudes of tangential and normal force components, as well as on torque components. FE analysis, which has been carried out in [23], demonstrated that the latter relationship can be used to actually reconstruct the external force and/or torque components by measuring the elastic layer deformations in a discrete number of points. The paper cited above reports an experimentally identified model of the material used to realize the elastic layer, and then adopted in a FE analysis aimed at optimizing the shape of the deformable layer in order to obtain a satisfactory sensitivity for both normal and tangential components of the contact force vector. 2.2. Sensor prototype
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Concerning the deformable layer of the realized prototype, it is made of black silicone in order to avoid cross-talk problems between taxels and ambient light disturbances, since the black colour guarantees the maximum absorption for every wavelengths. Only the surface which faces each devices pair is white to increase the sensor sensitivity (see Fig. 3(b)), ensuring the maximum reflection for every wavelengths. According to the FE analysis results, the aspect ratio of the black walls between taxels has been selected in order to reduce the horizontal deformations with respect to the vertical ones. In particular, for the presented prototype, the thickness of the black walls is 1 mm, while the extension of the white reflecting surfaces is 1.6 mm, which results in a total size for the
deformable layer of 11.4 mm × 11.4 mm. The height of the reflecting surfaces from the base of the deformable layer, in order to respect the necessary aspect ratio, is 1.5 mm. The top of the deformable layer is a section of a sphere with a radius of 11.4 mm. With the silicone choice modelled above, according to the numerical simulations, the expected measurement range of the sensor prototype is [0,4] N. The maximum force level can be adapted by changing the hardness of the deformable layer. The maximum measurable force is limited by the maximum vertical deformation of the reflecting surface of each taxel, so the former can be changed by acting on the deformable layer geometry. A linear relation between the Shore hardness and the logarithmic of Young’s modulus has been derived
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Analog-to-Digital converter chip (code AD7490, see Fig. 3(d)). The voltage supply for all components is 3.3 V. Each LED is used with a forward current less than 5 mA, with a maximum power consumption less than 200 mW for the whole sensor. This low power consumption and the local digitalization, together with its compact size (see pictures in Fig. 3), make this sensor particularly suitable to integrate into anthropomorphic robotic hands.
3. Prototype characterization as force/torque sensor
Fig. 8. Pictures of testing objects: (a) a standard bottle and (b) a classic can.
in [24] for elastomeric materials. Using this relation, the maximum predictable force level, with the current geometry, goes from 2 N to 40 N by changing the hardness of the deformable layer from 4 A to 60 A. Recalling the theory on LEDs and photodetectors radiation pattern [25], it is possible to consider the photocurrent (and thus the received radiant flux by the photodetector) proportional to the radiant intensity pattern of the LED and responsivity pattern of the photodetector, evaluated at the emitting and receiving angle respectively. Moreover the photocurrent is also inversely proportional to the squared distance between the two devices and the reflecting surface. As a consequence, the optoelectronic components should have very large viewing angles in order to minimize the effects of LED radiation pattern and photodetector responsivity pattern on the photocurrent and to leave only the dependence with the distance. Considering these aspects, the realized prototype uses optoelectronic components manufactured by OSRAM (see Fig. 3(a)). The LED (code SFH480) is an infrared emitter with a typical peak wavelength of 880 nm, while the detector is a silicon NPN phototransistor (code SFH3010) with a maximum peak sensitivity at 860 nm wavelength. Both the components have a viewing angle of ±80◦ . The conditioning electronics is only constituted by simple resistors without amplification and/or filtering stages. As a consequence, the collector current of the phototransistors, depending on the received light intensity, is easily translated into a voltage signal via a suitable resistor and then directly digitalized with an
The objective of this section is to show all the potentiality of the presented prototype sensor and a calibration procedure necessary to use it as a six-axes force/torque sensor. The characterization of the sensor has been made in the hypothesis that the contact surface can be approximated by a plane with an high stiffness with respect to the deformable layer. The hypothesis that the contact surface is a plane can be considered verified each time the external object has a curvature radius larger than that of the deformable layer. This condition is true for a large number of objects used in everyday manipulation and grasping tasks. Taking into account the hardness of the silicone, estimated in [23], used to realize the presented prototype, also the hypothesis of the high stiffness for the contact surface can be considered true for most of the daily use objects. Fig. 4 shows a sketch of the sensor, where the position of each cell with respect to the reference axes is indicated. The position of the kth taxel can be identified with the (xk , yk ) coordinates of the centre position of the taxel. At rest position, for each taxel, a certain amount of light emitted by the LED is reflected from the white surface and reaches the phototransistor, generating an initial voltage value on the collector. When an external force and/or torque is applied to the sensor, the distance of the reflecting surface of each cell from the corresponding LED/phototransistor couple on the electronic layer can be subjected to a positive or a negative variation. These distance variations imply changes of the reflected light and, accordingly, of the voltages measured on the phototransistor collector. Denoting with vk the voltage variation of the kth taxel, vk > 0 denotes an increasing distance (and then a decreasing photocurrect), while vk < 0 denotes a decreasing distance (and then an increasing photocurrect) between the reflecting surface and the electronic layer (obviously vk = 0 denotes no variation). Fig. 5 reports typical values of a voltage vk , for the realized prototype. To calibrate the prototype for use as a six-axes force/torque sensor, the proposed approach is based on the use of a neural network to interpolate a number of data sufficient to model the relationship between the applied forces and torques and the phototransistors measurements. The sensor has been mounted on a six-axes load cell used as reference sensor. The model used is the FTD-Nano-17 manufactured by ATI, with a measurement range equal to ±12 N and ±17 N for horizontal and vertical force components, respectively, while the measurement range for all torque components is equal to ±120 Nmm. The reference axes, reported in Fig. 4, are located on the plane that separates the prototype from the reference sensor. Fig. 6 shows the calibration system used to collect data for neural network training. An operator carried out various experiments, using a stiff plane, applying different external forces and torques and simultaneously acquiring all the voltage variations on the phototransistors and all the forces and torques components measured by the reference load cell. These data, acquired at a sample rate of 100 Hz, have been organized in a training set and a validation set to be used as input data (voltage variations) and target data (forces and torques components) of the neural network. A testing set has been prepared using data from experiments other than those used to collect the training and the validation sets, in order to assess the trained network.
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A standard two-layer feed-forward neural network fNN , trained with the Levenberg–Marquardt method, has been used to fit training data H = fNN (V ),
(1) ]T
where H = [Fx Fy Fz Tx Ty Tz is the output vector, Fi and Ti with i = x, y, z are force and torque components with respect to the reference axes and V = [v1 v2 . . . v16 ]T is the input vector containing the voltage variations of the taxels. The network is constituted by 24 neurons for the hidden layer and 6 neurons for the output layer. The trained network testing results are reported in Fig. 7(a) for the force components and in Fig. 7(b) for the torques.
The estimation is good for all force and torque components, especially when force and torque values are high enough. In fact, in the performance analysis it must be also taken into account that the training data are very noisy when the measured values are small compared to the full scale of the reference sensor. In different experiments the trained neural network has been tested with objects that have a finite curvature radius. In particular, Fig. 8 shows a standard bottle and a classic can used to collect additional testing data. Figs. 9 and 10 show the real and the estimated forces and torques for the bottle and the can, respectively. The estimation is accurate also in these cases, obviously with a minimal reduction in
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performance when the curvature radius of the contact surface decreases. It is important to underline that these performances have to be evaluated along with the fact that compared to commercially available sensors, the proposed one is more compact, low cost, low power consumption, provided with a digital interface, and the deformable layer guarantees good adaptability and stability during grasping and manipulation application.
e.g. complex robotic manipulation tasks, the availability to the control system of an estimate of contact plane position and orientation together with the interaction forces exchanged by the sensor and the external object are fundamental to successfully execute the task. To obtain this information from the sensor, an approximated physical model is first derived and validated to describe the contact between a stiff surface and the deformable layer.
4. Prototype characterization as tactile sensor 4.1. Sensor model As said, the proposed prototype can be also used as tactile sensor, estimating not only force and torque components as described in Section 3, but also the contact geometry. In some applications,
In the model description, the deformable layer is considered as an elastic homogeneous hemisphere of known radius R and the
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Fig. 11. Geometric characteristics of the contact model.
external object as a stiff plane. The reference frame is considered having the origin in the centre of the sphere and the x and y axes aligned with those defined in Fig. 4. Fig. 11 shows a generic contact where the stiff external object deforms the elastic hemisphere until, at equilibrium, the contact plane coincides with the plane 2 . Then consider the plane 1 , parallel to the plane 2 and tangent to the hemisphere at the point P. Assume that during the deformation the contact plane moves, from the limit position 1 (corresponding to no deformation) to the 2 position, due to the concentrated force F. The full characterization of the contact geometry means to estimate the position and orientation of the plane 2 and the direction of the force F with respect to 2 . In particular, the plane 2 can be uniquely defined by and angles and by its distance TO from the origin of the reference frame. Considering the axial symmetry of the deformable layer, the angle can be directly estimated from the measured Fx and Fy components, reducing the three-dimensional problem in a two-dimensional one in the zp-plane, where the p axis is defined by the direction of the vector (Fx , Fy , 0) with magnitude Fp =
beam compression z depends only on force vertical component Fz , while the bending p depends only on force horizontal component Fp . Assuming a linear elastic response of the material, the relationships among the variables above are Fz =
ES z h
(3)
Fp =
3EI p, h3
(4)
Fx2 + Fy2 . Thus it is
= atan2(Fy , Fx ),
(2)
where atan2(b, a) is the argument of the complex number a + ib. The projection of the contact area on the xy-plane is an ellipse. At equilibrium, the external force is balanced by the elastic reaction force of the deformable layer. Differently from [26], where the elastic body is approximated with an infinite set of elementary beams, in the proposed model, the deformable layer is approximated with a single elastic beam with elliptical cross section S with a size that depends on the angle and on the normal displacement dn = PT of the object. The height h of the elastic beam at rest is set equal to the height zP of the tangent point P, i.e. when there is no deformation, and it depends on the angle . According to the force F direction, the elastic beam can be subjected in the zp-plane to a pure compression, a pure bending or a combination of both. In particular, the
Fig. 12. Mechanical system for contact geometry characterization.
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where E is the material Young modulus and I is the area moment of inertia of the beam. Note that in Eqs. (3) and (4) the shear stress effect has been neglected. Considering the intersection point H between the plane 2 and the force F direction, it is convenient to introduce the tangential displacement dt = p/cos . Also note that TA =
R2 − (R − dn )2 =
2Rdn − dn2 .
h = R cos S=
dn z = − dt sin cos
(6)
p = dt cos
(7)
(9)
Recalling that the area moment of inertia of a beam with elliptical cross section is I = (ab3 )/4, where a = TA and b = TA cos are the ellipse semi-major axis and the semi-minor axis respectively, it is possible to deduce
(5)
The use of dn and dt variables and Eq. (5) allow, with simple geometrical considerations, to obtain
(8)
(2Rdn − dn2 ) cos
I=
(2Rdn − dn2 )2 cos3 4
(10)
Substituting Eqs. (6)–(10) in Eqs. (3) and (4), the following model is obtained
Fz = 2E
dn2 − dn dt sin cos
E + R
dn2
dn3 dt sin − cos
(11)
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Fp =
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(12)
As expected, the force components are related to the contact geometry, uniquely defined by the dn , dt and variables. 4.2. Experimental validation of the model The model (11) and (12) has been derived assuming a linear elastic response of the material and that the hemisphere is homogeneous. These two conditions are not fully satisfied by the deformable layer of the presented prototype because of the wells above the taxels and because of the material nonlinear characteristic. In order to compensate for these discrepancies between the
assumptions of the model and the actual prototype, for the proposed sensor the following gray-box model is considered
Fz = k1
dn2 − dn dt sin cos
+ k2
dn2
dn3 dt sin − cos
Fp = k3 dn2 dt cos + k4 dn3 dt cos + k5 dn4 dt cos .
(13)
(14)
The model structure is the same of Eqs. (11) and (12), assuming ki , with i = 1, . . ., 5, constant parameters to identify. This choice allows to maintain the same explicit relationship between the force components and the variables that determine the contact geometry as the one derived in the analytical model, but, at the same time, it
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4.3. Relationship between the tactile image and the external force Note that the force F direction in Fig. 11, from the contact geometry point of view, is related only to the position of point H, for a fixed contact plane. As a consequence, being F related to the vk taxel voltage variations, as described in Section 3, it is possible to relate point H coordinates directly to the vk voltage variations. The set of voltage variations represents a tactile image that, for example, could be used to estimate a pressure map using an appropriate reference sensor. Whereas, in this paper, the information contained in the tactile image is used to estimate the coordinates of the point H in the xy-plane, i.e. the coordinate couple (xH , yH ). Rather than using a black-box approach, a model that requires a reduced number of measurements is proposed. The model is based on a centroidlike approach, in which the taxels that present negative voltage variations are properly weighted as
16
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˛ G(vk ) k=1 k
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k=1
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vk if vk ≤ 0 if vk > 0
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16
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G(vk )
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,
(15)
(16)
The weights ˛k and ˇk can be estimated with a minimum of 16 measurements. In general, it is better to use a larger number of measurements and to derive the least squares solution with a pseudo-inversion operation. Using the mechanical structure in Fig. 12 a set of 40 measurements for the (xH , yH ) coordinates and the tactile images (the 16 voltage variations vk ) have been collected to estimate the weights ˛k and ˇk . Then the model (15) has been tested with different measurements and the results are reported in Fig. 15. The maximum estimation error is less than 0.5 mm for xH and less than 0.6 mm for yH . 4.4. Estimation of the contact geometry This section is aimed at showing how the capability of the sensor to reconstruct the force components and the gray-box structure of the model (13) and (14) can be exploited to estimate the contact geometry. The idea is that from the knowledge of the Fz and Fp force
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allows to obtain a good matching between the gray-box model and the experimental measurements, as shown below. Forces with different directions and magnitudes have been applied to the prototype sensor using different plane contacts, whose positions and orientations have been fixed with the mechanical structure shown in Fig. 12. In particular, the goniometer has been used to fix the angle values, while the micrometric stage to fix the dn and dt deformations values. In a first set of experiments, the , dn and dt values, measured with the mechanical structure, have been collected and used to estimate the parameters ki . Since Eqs. (13) and (14) are linear in the ki , a Least-Square (LS) approach has been used to obtain the values k1 = 1.3095, k2 = 0.2533, k3 = 3.4644, k4 = − 3.3025 and k5 = 0.9248. Data from a second set of experiments have been collected to test the model performance. Fig. 13 compares the reconstructed Fz and Fp with the force values measured by the reference sensor. The error is less than 0.15N for the vertical force component and less than 0.08N for the horizontal force component. The same procedure can be applied using the force components samples measured by the proposed prototype with the neural network (1). The comparison between measured and modelled force components is presented in Fig. 14. For this case the reconstruction error is only slightly worse than the previous case, due to the additional error introduced by the neural network.
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values, calculated with the neural network (1) and by inverting the model (13) and (14), the variables , dn and dt , that determine the contact geometry, can be estimated. Evidently, the two model equations are not sufficient to achieve the desired objective. In order to fully estimate the contact geometry variables a third equation is needed. With reference to Fig. 11, with simple geometrical considerations, the following relation is obtained pH = R sin − dt cos ,
2 xH
2 + yH
(17)
can be computed using Eq. (15). Thus, taking where pH = Eqs. (13) and (14) together with Eq. (17), a set of three equation is obtained with the three unknowns , dn and dt . This nonlinear system can be numerically solved to obtain the desired information about the contact geometry. First of all, in order to verify the effectiveness of the approach, the procedure has been tested with experimental input data collected from the reference sensor (regarding Fz and Fp ) and from the mechanical structure shown in Fig. 12 (regarding pH ). The results of the , dn and dt variables estimation are reported in Fig. 16, where the high accuracy obtained in the contact geometry reconstruction is evident. In particular, the maximum error is less than 0.2◦ for , less than 100 m for dn and less then 20 m for dt . Afterwards, the proposed procedure has been tested also with force data
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Fig. 18. Scheme of all the capabilities of the sensor.
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computed by the neural network (1) and with (xH , yH ) values calculated with Eq. (15). The results are shown in Fig. 17. In this case, the maximum error is less than 2◦ for , less than 200 m for dn and less then 60 m for dt , due to errors in the estimation of the force components and of the (xH , yH ) coordinates. In conclusion, all the capabilities of the proposed force/tactile sensor are summarized in the block diagram shown in Fig. 18. The sensor output signals, i.e. the vk voltage variations are used as inputs of the neural network, trained as described in Section 3, to estimate force and torque components W. The same signals are also used as inputs of the centroid-like model, identified as described in Section 4.3, to estimate, in conjunction with the estimated forces, the contact geometry variables, according to the procedure described in Section 4.4.
[11]
[12]
[13] [14]
[15]
[16] [17]
5. Conclusions The paper described the detailed design and the experimental characterization of a novel tactile sensor for robotic applications based on optoelectronic technology. The sensor mechanical structure has been designed so as to allow the device to work as a six-axis force/torque sensor. An analytical physical model has been derived to let the sensor act as a tactile sensor for estimation of the geometry of the contact with a stiff external object. A complete calibration procedure has been presented and the algorithms necessary to exploit all the sensor capabilities have been provided and experimentally tested, demonstrating the effectiveness of the whole sensor system. The new sensor has been shown to be capable of measuring not only force components (up to 3.5 N) but also torque components (up to 10 Nmm). Moreover, the reconstruction of the contact geometry is very accurate, obtaining a maximum error less than 0.2◦ for the orientation angles of the contact plane and less than 100 m for the radial deformation of the sensor. Further developments are expected in view of the integration of the sensor into the fingertips of a robotic hand and its use in real-time feedback control systems.
[18] [19]
[20]
[21]
[22] [23]
[24]
[25] [26]
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Biographies Acknowledgements The research leading to these results has been partly funded by the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant agreement no. 216239 (DEXMART project) and partly by the Italian Ministry of University and Scientific Research (PRIN 2009) under the national project ROCOCO. References [1] B. Siciliano, O. Khatib, Springer Handbook of Robotics, 1st edition, SpringerVerlag, Berlin, D, 2008. [2] M.H. Lee, H.R. Nicholls, Review article tactile sensing for mechatronics – a state of the art survey, Mechatronics 9 (1999) 1–31. [3] L.D. Harmon, Automated tactile sensing, The International Journal of Robotics Research 1 (2) (1982) 3–32. [4] Y. Ohmura, Y. Kuniyoshi, A. Nagakubo, Conformable and scalable tactile sensor skin for curved surfaces, in: Proceedings of IEEE International Conference on Robotics and Automation, USA, 2006, pp. 1348–1353. [5] R.S. Dahiya, G. Metta, M. Valle, G. Sandini, Tactile sensing – from humans to humanoids, IEEE Transactions on Robotics 26 (1) (2010) 1–20. [6] K.N. Tarchanidis, J.N. Lygouras, Data glove with a force sensor, IEEE Transactions on Instrumentations and Measurement 52 (3) (2003) 984–989. [7] E.S. Hwang, J.H. Seo, Y.J. Kim, A polymer-based flexible tactile sensor for both normal and shear load detections and its application for robotics, IEEE/ASME Journal of Microelectromechanical Systems 16 (3) (2007) 556–563. [8] M. Shimojo, A. Namiki, M. Ishikawa, R. Makino, K. Mabuchi, A tactile sensor sheet using pressure conductive rubber with electrical-wires stitched method, IEEE Sensors Journal 4 (5) (2004) 589–596. [9] A. Wisitsoraat, V. Patthanasetakul, T. Lomas, A. Tuantranont, Low cost thin film based piezoresistive mems tactile sensor, Sensors and Actuators A: Physical 139 (1–2) (2007) 17–22. [10] L. Beccai, S. Roccella, A. Arena, F. Valvo, P. Valdastri, A. Menciassi, M.C. Carrozza, P. Dario, Design and fabrication of a hybrid silicon three-axial force sensor for
Giuseppe De Maria was born in Napoli, Italy, on December 1948. In 1973 he received the Laurea degree in Electronic Engineering from the University of Naples. He was associate professor of Automatic Control at the University of Naples “Federico II”. Since 1992 he is full professor of Automatic Control at the Faculty of Engineering of the Second University of Naples. His research interests include robust control, control of mechanical systems, industrial and advanced robotics, control of aerospace and aeronautical systems, active noise and vibration control of flexible structures. Now his research interests are focused on the control of smart materials, in particular piezoceramics, magnetostrictive, with the aim to realize artificial muscles. Concerning this field of research he is responsible of National and European research contracts. He is work-package leader of the DEMART project in the 7th Framework Programme of European Community. Ciro Natale received the Laurea degree and the Research Doctorate degree in Electronic Engineering from the University of Naples in 1995 and 2000, respectively. From 2000 to 2004 he has been Research Associate at the Second University of Naples, where he currently holds the position of Associate Professor of Robotics. From November 1998 to April 1999 he was a Visiting Scholar at the German Aerospace centre in Oberpfaffenhofen, Germany. His research interests on robotics include modelling and control of industrial manipulators, force and visual control, cooperative robots. In the aeronautics application sector, his research activities are focused on modelling and control of flexible structures, active noise and vibration control, identification and control of smart materials. He has published more than 70 journal and conference papers as well as authored and co-authored monographs on robotics and control of flexible structures. He currently serves as Associate Editor of the IEEE Trans. on Control Systems Technology. Salvatore Pirozzi was born in Napoli, Italy, on April 21st, 1977. He received the Laurea and the Research Doctorate degree in Electronic Engineering from the Second University of Naples, Aversa, Italy, in 2001 and 2004, respectively. From 2008 he is a Assistant Professor at the Second University of Naples. His research interests include modelling and control of smart actuators for advanced feedback control systems and design of innovative sensors for robotics applications, as well as identification and control of vibrating systems. He published more than 30 international journal and conference papers and he is co-author of the book “Active Control of Flexible Structures”, published by Springer.