Abstract
Introduction
Robot technology is a significant step in the development of the world today. Robots need a variety of sensors to coordinate the activities to complete the task, obtaining the perception of the external environment. 1 The sensors include visual sensors, pressure sensors, proximity sensors, tactile sensors, and so on. 2 However, the tactile sensor of a robot is the key to judging whether a robot can accomplish a variety of complicated tasks. Therefore, it is necessary to install physical sensors on robot hands. Generally speaking, the more sensitive the tactile sensor is, the more accurate the perception of the environment is.
Nowadays, most tactile sensors used on flexible robot hands are capacitance 3,4 and resistive. 5 –7 However, the capacitance tactile sensor is hard to measure the variety of pressing force, so it can only be used in some applications where the accuracy is not very high. As a device to measure the interaction parameters between the sensor surface and the external object, the flexible tactile sensor contains many flexible tactile units. Each flexible tactile unit can obtain information from the external environment. Therefore, it can measure the pressure and multipoint distribution of the external environment, which helps the robot’s fingers to detect the shape of the object. But how to increase the sensitivity of the flexible tactile sensors? One method is to use an elastic material as the conductive layer. 8 So when the elastic material is compressed, the piezoelectric properties of the sensor are changed. Fujimoto et al. 9 used a piece of artificial finger skin installed on the surface of the robot hand to realize static friction sense. This skin is under higher sensitivity and softer than other materials. Another way to improve the sensitivity is to use piezoelectric composite as the intermediate dielectric layer, 10 Gereon Buscher et al. 11 present a novel, soft, and tactile skin. However, it is complicated to measure the value of touching force. It is a known fact that the insensitivity of the sensor can lead to problems such as catching the wrong object or insufficient grip. Hence, in this article, we develop a resistive flexible tactile sensor covered the curved fingertip surface of the robot hand. Moreover, through analyzing the relationship between gripping force and resistive voltage, a four-finger grasp control system was designed.
A lot of different tactile sensors have been applied in a dextrous robot hand, 12,13 Meanwhile, some researchers in the literature study the effects of different piezoelectric composites on flexible tactile sensors. For example, Stefano Stassi et al. 14 study the sensitivity characteristic of tactile sensors using unusual materials, filler orientation, and different composition ratios. They proposed that the greatest limitation of the piezoelectric materials is still the hysteresis of the sensor output, which reduces repeatability and sensitivity. But in practical applications, we also need precise control of the gripping force to avoid objects from falling off the robot’s fingers. Cheng-Hsin Chuang et al. 15 designed a new type of piezoelectric sensor that can detect sliding and contact forces. Their experimental results show that the range of contact force of flexible tactile sensor is 0.1–10 N. However, their control system is more complicated than others, and there is no specific example applied to the robot hand. Jong-Ho Kim et al. 16 also designed a sensor comprising100 micro-force sensors, with each size measuring only 10 mm and having three components force. But it is difficult to find the error when one of the sensors fails. Besides, it is necessary to realize a control system to detect the size of the force to grasp accuracy. Mengqian Tian et al. 17 Introduced a soft robot hand using a pneumatic control. The robot finger is driven by a flexible actuator made of a highly elastomeric material, and it can grasp only 0.55 kg of weight. Kento Mori et al. 18 proposed a new method that uses an electro-conjugate fluid under high direct current voltage, which can produce a power flow to control the robot’s hand. But this technology is not perfect enough to monitor fluid change accurately. Bianca S. Homberg et al. 19 designed a soft hand combined system which grasps and identifies objects based on internal state measurements; it realizes and autonomously performs grasps. It uses the camera and a clustering algorithm to detect the location of the object.
A few other flexible pressure sensors are reported in the literature. Núñez et al. 20,21 present a transparent tactile e-skin based on a single-layer graphene, coplanar interdigitate capacitive (IDC) electrodes. They proposed a bold innovation that a flexible tactile skin used a photovoltaic cell as a building block for energy-autonomous. They tested the tactile skin was installed on a robot hand, to grabbing of soft objects in application capabilities. Further, there are some new approaches to robot fingers. For example, Ntagios et al. 22 present an innovative way to design different complex shapes using three-dimensional (3-D) printing technology, such as robot finger with embedded tactile sensors. Compared to traditional non-embedded sensors robot skin, it has advantages to overcome wiring complexity. Nassar et al. 23 also did a similar study. But they proposed a new manufacturing method to obtain an intelligent sensing flexible structure with printed strain sensors and interconnected to obtain embedded electronic components. They embedded electronic components in the flexible 3-D printed structure.
In this article, an 8 × 8 flexible tactile sensors array based on a resistance sensing mechanism was designed. The finger we designed is sealed, so the internal pressure will change when pressing. And then we discussed the relationship between force and voltage and internal pressure. Subsequently, the tactile signal control system for analyzing the dynamic characteristics of the sensor is described. Moreover, a robot control system was designed and applied on a robot finger to realize the function of the grasped object. The structure of the article is as follows. In the “Design of the finger” section, the tactile sensor and robot finger designing will be described, and some characteristics of the tactile sensor are presented in the “Dynamic characteristics analysis and discussion” section; preliminary practical experiment will be presented in the “Robot tactile sensor finger grasp experiment” section.
Design of the finger
Design and manufacture of the flexible tactile unit
Generally speaking, the more the free electrons in a conductor, the better its conductivity will be. We use silica gel to make main components of flexible tactile sensor unit because it has good stretchability and stability. The conductive silica gel is generally prepared by mixing and dispersing a conductive powder such as metal or carbon black in a silica gel material, and the conductive rubber changes its own resistance value under the action of an external force. So we can use this feature to make flexible tactile sensors. We can determine whether there is pressure based on the resistance change of the conductive silica gel. Several kinds of silica gel and conductive carbon black that are common in the market were selected before manufacturing. Several types of silica gel are GD401 (Chengdu Chenguang Technology Trading Co., Ltd (China). It can be vulcanized into an elastomer after exposure to air, which is extremely convenient to use. Silicone rubber can work at −60°C to +200°C for a long time, has excellent electrical insulation properties and chemical stability, water resistance, weathering resistance, good adhesion to a variety of metal and nonmetallic materials (E640; Shenzhen Hongye Technology Co., Ltd, China). The E640 silicone rubber has a transparent appearance and is mixed with a solvent of A and B. The tensile strength is about 6.2 MPa, and it takes about 20–40 min to become solid (XC-107; Jinan Xingchi Chemical Products Co., Ltd, China). This product has excellent insulation, low volatility (<2.0%), and high viscosity (>7000 MPa·s), RTV-704 (Liyang Kangda Chemical Co., Ltd, China). It has high tensile strength (>0.8 MPa), high surface resistivity (>1.0 × 1014), high temperature resistance, and so on. Conductive carbon black chose superconducting carbon black bp2000 (US CABOT Co., Ltd, Boston, Massachusetts, USA). Its appearance is mainly black powder, and the specific surface area is 1500 m2/g.
We added 10% mass of conductive carbon black to these different types of silicone rubber and then added 5 ml of 95% absolute alcohol, stirring for 10 min, making evenly dispersed, reducing agglomeration, as shown in Figure 1. After 12 h of placement, we measured the resistance value of each type using a multimeter. The resistance value of GD401-type conductive silicone is 7.2 kΩ. However, the conductive silicones of type XC-107 and RTV-704 are insulated and have no electrical conductivity. Compared to the others, the E640-type conductive silicone has a resistance of 230 K. However, when a force is pressed on the surface of the conductive silica gel, the resistance value is in a state of abrupt change. So in this article, the next experiment is to select GD401 silica gel for experiments and discussion.

Conductive silica gel with a mass fraction of 10%.
In the literature, many of the sensors are designed as triangles. 24 However, the flexible tactile sensor was designed is an 8 × 8 array of 2 mm thickness and can be divided into a small touch unit. This sensor will deal with the problems caused by the different shapes of the robot hand. In this article, some springy touch cells are utilized to form a flexible tactile sensor placed in the main contact points. The tactile sensor consists of the top layer, sensor layer, and the bottom layer, as shown in Figure 2. But the top surface of the sensor layer has horizontal conductive lines and the bottom has vertical conductive lines. The top layer is flexible silicone and is used to protect the inside of the sensor. Tactile sensor is embedded in the sensor layer. Between the horizontal conductive lines and vertical conductive lines is the flexible sensor unit. It insulates with silicone rubber by eliminating the internal interference of sensor units effectively. The top and bottom of the tactile sensor is also insulated with silicone rubber for protecting the sensor units. In addition, each sensor can be split into several sensing units, with diameter only 4 mm. Therefore, when our finger shape changes, each unit of the sensor can still measure the contact force. The bottom is a silicone rubber layer for protecting sensor layers from external non-insulators contact. And it also increases the friction and adhesion between the sensor and the finger surface. Without this layer, the sensor will touch the surface of the finger directly, which may reduce the sensitivity and accuracy of the sensor. As shown in Figure 3, when the finger touches the sensing unit, the shape of the sensor changes and indirectly affects the resistance characteristics of the sensor (listed below). The sensor layer is compressed, and the distance between the conductive particles becomes small. Therefore, the conductive particles are more easily contacted, so the resistance value of the conductive silica gel is reduced. Reading stable resistance or voltage value through signal acquisition system. Following will be explained in detail.

Exploded view of the resistance tactile sensing array.

Shape change of applied force.
Figure 4 shows an 8 × 8 array sensor with an overall dimension of 2.4 × 2.4 in (6 × 6 cm2). One of its eight pins is connected to a filter-rectifier circuit; the other eight ports are attached to the data processing circuit. The unstable power supply clutter is filtered out when the 5 V power supply passes through the filter circuit, and then the sensor array is powered. Then the analog-to-digital converter (ADC) reads the sensor’s data continuously. The sensor’s data are abruptly changed once the sensor is pressed, and the control system triggers the interrupt for further subsequent operations, for example, grabbing an object or moving to other places. The specific circuit design will be described in detail in the following sections.

The 8 × 8 array of flexible tactile sensor.
Structural design of flexible fingers
At present, most flexible manipulators are driven by motors, gas–liquid, and functional material. However, it is difficult to grasp objects for poor flexibility. Flexible tactile fingers described in this article are controlled by pneumatic and electric controls. Each finger is very flexible because of two main flexible joints. The molds for making fingers are designed with 3-D modeling software (SolidWorks (version SolidWorks2016)), printed, and shaped by 3-D printing technology (polylactic acid material). The molds are filled with silicone (GD401), and the fingers are formed after the silicone solidifies. There is an air pump at the bottom of the finger to prevent the finger from bending when grasping objects, and the movement of the finger is controlled by the motor. As we can see in Figure 6(a), the structure of the finger can be divided into three parts (finger body, the tactile sensor, and protect layer). The finger body was made of a stretchy material that increased flexibility without reducing strength. Different from the finger of other research studies in the literature, 25,26 our fingers can grasp the maximum weight of around 10 N. This will be seen in the subsequent experiment. Also, the size of the fingers is almost the same as the human. 27 We also designed several different bending angles on the simulation software to analyze the maximum force for grasping objects (Figure 5).

Different angles for force diagram.

(a) Flexible finger structure. (b) Force analysis of flexible finger. (c) Cutaway view of the finger placement sensor.
We analyzed the different bending angles of the fingers using ANSYS (version 18.1) simulation software. From Figure 5(a) to (i), the degree of the finger is increased from 133° to 141°. Then the maximum stress on each finger surface is calculated. From 133° to 138°, the stress on the finger is always increased shown in Table 1. However, when the angle is increased, the stress on the finger is decreased. This is because the direction of the force of the finger is perpendicular to the surface of the finger before increasing angle to 138°. After that, the stress on the finger is dispersed by other planes, so the vertical pressure is reduced.
Relationship between finger touch force and bending angle.
So the bending angle designed is 138° which is the most stressed. The diameter
The flexible tactile sensor unit is composed of elastic conductive silicone rubber. The resistance of the silicone rubber changed when the conductive silicone rubber is influenced by the external force. This characteristic is the force sensitivity of the conductive rubber. However, different mass of carbon black in conductive silica affects the force-sensitive characteristics. We tested the piezoresistive properties of different four carbon blacks with a mass fraction of 10% (shown in Figure 7) by increasing the force of 5 g each time and keeping the stabilization time for 1 min. The first is bp2000 carbon black. The second is ultrafine nickel-clad copper powder. The third is N293 carbon black. And the fourth is 15,000 mesh high-conductivity carbon black. As can be seen from Figure 7, compared with several other materials, bp2000-type carbon black shows better stability. This is mainly due to the inherent high conductivity of bp2000 and the influence of its particle chain and network easy to cooperate. Conductive silica gel has obtained good electrical conductivity after forming conductive channels. At this time, the increase of force has little effect on the resistance of the rubber.

Effect of carbon black mass fraction of 11% on piezoresistive properties.
So we performed a mass fraction experiment on bp2000 filled carbon black. As shown in Figure 8, increase from 4% to 15%, observe the resistance of the filled carbon black. The carbon content of 8% is the most suitable. When the carbon content in the silicone is less than 8%, the conductive silicone is insulation. When the carbon content reaches about 8%, the resistance rapidly drops, and at this time, a small amount of carbon is added, and the conductivity of the material is remarkably enhanced. If the carbon content is further increased, the electrical conductivity will be stabilized in a small range, as shown in Figure 8. Besides, to reduce the hardness of the silicone, 95% anhydrous ethanol was chosen as the diluent of the conductive composite material for its volatility.

The curve of resistivity and carbon content.
Dynamic characteristics analysis and discussion
To analyze the dynamic characteristics of the sensor, this article designs detection devices as shown in Figure 9. The system consists of a data acquisition module and a data processing module. The acquisition module is mainly sampling the data of the flexible tactile sensor unit, and the software is used to analyze and process data. The main control core of the hardware is STM32F103ZET6-type MCU, 28 the serial communication circuit, ADC sampling circuit, crystal oscillator circuit, 29,30 the voltage stabilizing the circuit, the filter circuit, and so on. After acquiring data through the sampling circuit, the ADC of MCU converts the data and transfers to a computer for analysis. The article considered embedding the control part of the finger. This will increase the weight and reduce the flexibility and softness of the finger. So the article is still designing off-chip control mode.

The diagram of system structure.
As we can see in Figure 9, the power module has a rectifier circuit and a filter circuit. The sampling circuit can get the changed value immediately when the resistance of the sensor changes. The sampling circuit is mainly composed of the amplifying circuit and triode. The analog data of the sampling circuit are transmitted to the AD module for digital conversion. The AD is a single-chip, single-supply, 12-bit precision, 65 MSPS high-speed ADC from Analog Devices, Inc. (ADI, Norwood, Massachusetts, USA) 31 with an on-chip integrated high-performance amplifier and the reference voltage source. Moreover, it has multistage differential pipeline architecture with built-in digital output error correction logic that provides 12-bit accuracy at rated data rates and guaranteed no missing codes over the entire operating temperature range. Next, the AD unit transmits digital data to MCU (shown in Figure 8) control using the serial peripheral interface (SPI). 32
To reduce the error caused by the communication delay between the tactile sensor and the MCU, SPI controller operating frequency should be set at the highest frequency (18 MHz). So it takes 443 ns to receive a byte of data. With the constant stress, conductive silicone will be deformed, and the resistance decreased with the increase of the force. And the phenomenon that the resistance values change continuously is called creep, which is also called hysteresis. The phenomenon of resistance creep is particularly evident in silicone rubber. The molecular chain of silicone rubber is flexible, and the main composition of carbon black is a rigid molecule. Under pressure, the carbon molecule is compressed, which leads to molecular recombination, and the conductivity of the molecule decreases. The resistance change rate of conductive silica materials depends mainly on the diameter of the conductive particles in the material, the distribution of particle size, the motion ability of the polymer chain, and the degree of interaction between the polymer and the conductive particles. Because of the creep of the silicone rubber material, the stress-sensitive conductive silicone and the strain of the conductive silicone are not consistent in time. This effect causes the sensor to have a certain hysteresis in the measurement. To enhance the accuracy of the measurement, four same tactile sensor units were selected, the force applied on each unit should be equal, and then the average value of the tactile sensor unit outputs should be taken as the output of the whole sensor. This article uses standard weight to load pressure onto the tactile sensor. And then we load force between in 0 N and 10 N at each point. To allow flexible silicone to fully recover elasticity, staying at intervals of 15 min when increasing 1 N.
What is more, after the hardware system collects data, we need to process the data in the software so that obtaining valid data each time. In practical applications, because of the external electromagnetic and noise interference, the acquired A/D raw data will inevitably produce erroneous data, so we will reject the wrong data. In this article, first, we get enough data, if all the data will be stable near a certain value, these data can be used, otherwise we will discard these data. Second, sorting these data, discard the smallest and largest data, and then take these average values. So the value calculated at this time is very accurate. The frequency of the CPU is 72 MHz, and the time to run an instruction is about 1 ns. So calculating these algorithms can take up to a few milliseconds at most. Following is our analysis of the dynamic characteristics of the sensor based on these data.
Creep characteristic curve of varying pressure and constant pressure curve of the sensor is shown in Figure 10(a) and (b), respectively. On the one hand, we can see that the resistance reduces sharply as the pressure increases from 0 N to 5 N, but the latter change is relatively flat. This phenomenon can be explained that the conductive particles in the electroconductive silicone are in a state of uneven dispersion when the electric resistance is subjected to the first pressurization. When the pressure is increased, the position between the particles changes, resulting in a shorter contact distance. So the conductive particles form a relatively stable conductive network. The conductivity tends to be stable at a macroscopic level. On the other hand, due to the particularity of the rubber material, the conductive silicone rubber has creep characteristic with time. In the linear region where the sample has piezoresistive properties, applying to the sample to obtain the creep characteristic phenomenon under different applied pressures. So we tested the resistance of changing at constant pressure with time. We select four tactile sensor units, measuring the resistance change with 300 s when loading 3 N and 5 N, respectively. By analyzing the data, we can conclude that under the action of constant pressure, the creep curve of the resistance is the same as the required time. There are two main reasons: firstly, the adjacent particles begin to contact to form a conductive channel, and the isolated conductive particles near the conductive chain participate in the conductive network, which makes the conductive network more perfect. Secondly, the silicone rubber matrix material generates creep, so that the isolated conductive particles at a long distance generated a long-term slip and attached to the conductive chain to form an additional conductive path. Creep time is related to the slip distance of conductive particles. However, under the action of constant pressure, due to the creep phenomenon of the matrix, the conductive network is destroyed, and the additional conductive channel formed by the lateral slip of the conductive particles cancels, and the creep time is approximated to a constant value. We can see from Figure 10(a) that creep characteristic of varying pressure of sensor was not obvious after 6 N pressure. Therefore, the gravity of the object grasped by the finger is preferably between 0 N and 6 N, and the sensor works at the best state. In other words, the sensor has high sensitivity. The constant pressure creep characteristics of the sensor are stable at 75 s. Therefore, when we use a flexible finger to move the object, the duration of the hold time is preferably 75 s, and the sensor can work at its best. In general, the flexible fingers will have high application value in future soft robots.

Characteristic curve (a) of force from 0 N to 10 N and (b) under constant force.
In addition, we also test pressing experiment for the above four points separately, as shown in Figure 11. We pushed four points in a period. The value drops suddenly when pressed, and then rising slowly and trending to stable. So this also checks the above experimental results. The spacing between particles sharply decreases when pressed, and thus electrical conductivity and resistance increase when the value drops. At the same time, the data are usually stable while the creep phenomenon was generating. Besides, a conductive network comprising conductive particles and matrix material makes friction during motion. So this friction is the main reason for creep phenomenon in composite materials. From the above analysis, it is known that the creep phenomenon of conductive composites is inevitable.

Four tactile sensor unit force tests.
Robot tactile sensor finger grasp experiment
In this article, the tactile sensors can be integrated into the finger inside and gets adapted to perceive the size of the force. When grasping the object, tactile sensors of the fingertip detect a change in voltage through the ADC module. The varying voltage was captured by the I/O interrupt, and then the program can process the data and control the action of the actuator to grab or release. Meanwhile, the air pressure module detects the pressure of the finger cavity changed when flexible fingers are squeezed. Then the control system inflates the finger to increase the grasping force by turning on the pump.
As shown in Figure 12, the device is composed of four flexible touch fingers. Figure 12(a) and (b) is the minimum and maximum angles of the mechanism, respectively. The grasping of the mechanism is controlled by the motor, and the tactile sensor embedding in the finger is to feed back the pressure value by force.

Robot flexible touch finger (a) close state and (b) open state.
As shown in Figure 13, some experiments were performed to test the performance of the soft hand, the objects used in the experiments include orange (Figure 13(a)), apple (Figure 13(b)), bottle (Figure 13(c)), tissue (Figure 13(d)), USB flash disk (Figure 13(e)), and mouse (Figure 13(f)). For some soft objects (as Figure 13(c)) and tiny objects (as Figure 13(e)), the fingers can grasp easily. Consequently, this flexible touch finger will be applied in a multipoint control robot hand in the future.

Soft robot hand grasping objects of different shapes: (a) orange, (b) apple, (c) bottle, (d) tissue, (e) USB flash disk, and (f) mouse.
Conclusion
In this article, a resistive sensor array for flexible touch fingers was designed and fabricated. Optimal features of our tactile sensors can be split into individual touch units, embedding the finger inside. We also analyzed the creep and hysteresis characteristics of tactile sensors. Finally, we also demonstrated an experiment for the application of robotic grasp object, showing the finger’s flexibility and sensitivity. For the flexible robot fingers, the effective measuring force ranges from 0 N to 10 N. The experiment shows that the flexible touch finger has the control system integrated into the dexterous robot hand, and it can lay a good foundation for the touch skin of imitating the human hand in the future. In the future study, the tactile sensor unit needs to improve the accuracy and range, and the flexible touch finger will realize full flexibility distortion and perception, achieving multi-touch.
