A Novel Flexible Centralized Force Sensor Based on Tri‐Axis Force Refactoring Method for Arbitrary Force Components Measurement

Flexible force sensors have been widely applied in robotics for object exploring, remote controlling, and human–machine interactions. The tri‐axis force sensors for accurate measurement of normal and shear forces are generally in urgent demand. Most tri‐axis force sensors rely on signal analyzation between multiple elements to achieve force components, which may need numerous leading wires and limit the force angular sensing performance. Herein, a novel flexible centralized force sensor is developed based on a novel tri‐axis force refactoring method. Normal force is detected by the central parallel‐plates capacitor, and both the angle and amplitude of shear force can be extracted through the resistance changes. The normal force performance is characterized with a sensitivity of 0.057 N−1 and a detection range of 0–12 N, and the effective detection range of shear force is about 0.5–0.67 N. The minimum distinguished shear angle difference is about 7.3°, which can be further improved by increasing the sensing material's resistivity. Then, robotic grasping tests are performed and show that the sensor can accurately measure the normal and shear forces and applied shear force angle, which indicates its promising applications in potential robotic manipulation and interactions.


Introduction
Tactile perception is one of the most significant sensing capacities for humans to collect surrounding information, which assists in exploring object properties and interacting with ambient environment. [1,2]ith rapid progress of interactive technologies, it is in urgent demand to develop intelligent robotics that has tactile sensing capacities similar to human beings. [3]raditional tactile sensors encapsulated by rigid materials such as metals are too rigid to be covered onto curved surface of robotic bodies, which renders a great challenge to develop suitable tactile sensors.Flexible tactile sensor fabricated using soft materials can detect multiple haptic stimuli, such as pressure, strain, temperature, vibration, and so on. [4]It has been proved to be a satisfactory candidate for robotics to do human-like perceptions, the advanced applications have been reported in wearable devices, [5] health monitoring, [6] remote controlling, [7] robotic manipulations, [8,9] and virtual reality (VR) interactions. [10,11]mong multiple tactile stimuli, force or pressure is one of the most significant and commonly utilized mechanical information in robotic sensing, [12] which can not only provide visualized tactile feedback in human-machine interaction (HMI) tasks but also assist in extracting object properties, such as shape, rigidity and weight. [13]Several mechanisms have been reported for force sensing, including piezoresistive, capacitive, piezoelectric, triboelectric, magnetic, optical, and so on. [14]Among them, piezoresistive and capacitive force sensors generally have simple structural design and readout circuits, both the sensitivity and detection range have great scalability, which renders these sensors wide applications. [15]17][18] However, most of them just focus on mapping the force applied position or measuring the amplitude of normal force.The tri-axis force sensor that can simultaneously measure the normal and shear force components in various axis still needs to be investigated.
The tri-axis force sensors can enrich the sensing force information achieved by robotics, which is extremely significant for some specific applications.When the normal force is integrated with shear force components, a more stable grasping and manipulation can be achieved by slippage detecting, [19] and some object properties, especially friction coefficient and surface texture, can be easily extracted. [20,21]For decades, researchers have been working on the structural design of multiaxis force sensors.The combined structure with four sensing elements distributed in a 2 Â 2 array is the most commonly used structure for tri-axis force sensors. [22,23]The sensors using this structure can simultaneously measure the response and calculate the signal differences between various elements, which can be further converted to tri-axis components of arbitrary force.[26][27][28][29][30] Zhang et al. have reported a capacitive tri-axis force sensor with microstructures for invasive surgical applications. [31]And the tri-axis force sensor reported by Won et al. can even measure temperature and bending angle. [32]Besides, Chen et al. [33] have reported another combined structure using three piezoresistive sensing elements, which has similar sensing principle to the four elements' sensor using differential signals, and the capacitive sensor based on this threeelements structure has also been reported by Gu et al. [34] Except for this commonly used multielements distributed structure, other structures for tri-axis force sensing have also been reported, [35][36][37][38] and some of them can even detect the force moment. [39]However, almost all the tri-axis force sensor relies on signal analysis from multiple elements, which needs numerous leading wires and a complicated measuring circuit when used in a distributed array.Besides, the angular sensing performance of the combined structure sensor is less satisfactory.The shear angular resolution is the minimum angle that cause a distinguishable change of the measured signal.The smaller this angle is, the higher precision of the shear force can be achieved, which may further determine a more accurate resultant force.Most sensors just distinguish a shear force angle difference of 90°or 45°, [40][41][42] with a few sensors report an angular difference less than 30°. [33,43]If the shear force angle changes a small value, the signal differences calculated through different elements may seem similar to each other, which makes it confused to reconstruct a resultant force. [44]Therefore, it's necessary to simplify the structural design and improve the angular sensing performance of tri-axis force sensors.
We have developed a flexible centralized sensor inspired by the resistive potentiometer, and a novel tri-axis force refactoring method is proposed for accurate measurement of arbitrary force components in robotic manipulation tasks.The tri-axis force sensor has a multilayer structure with only three leading wires, and the bump electrode can simultaneously form resistive and capacitive circuits with the surrounding structures.Normal force is detected by the central parallel-plates capacitor, and both the angle and amplitude of shear force can be extracted through the resistance changes.All of the materials applied are highly flexible, which can be easily fabricated by casting and screenprinting techniques.This sensor has a normal force sensitivity of 0.057 N À1 with a maximum detection range of 12 N, and further characterization tests indicate desired repeatability and dynamic performance of normal force sensing.The resistance decreases nonlinearly with the amplitude of shear force, and the effective detection range of shear force is 0.5-0.67N.This sensor can minimally distinguish a shear angle difference of 7.3°, and this value can be further improved by improving the material resistivity.All of the force components measurement tests show little influence on each other.Finally, the sensor is mounted on a robotic manipulator to conduct grasping task, and both normal and shear force can be measured accurately, which indicates its promising application in robotic manipulation in the future.

Sensor Structure Design
The resistive potentiometer can change the activated length of the resistor by adjusting the position of the contact spot between the electric brush and resistor, which can further adjust some electrical output. [45]Inspired by this principle, we propose a flexible sensor using only one centralized structure for tri-axis force sensing, as illustrated in Figure 1.The tri-axis sensor has a circular shape with a diameter of 10 mm, which is appropriate for placing on the robotic fingertip for tri-axis force sensing (Figure 1a).As illustrated in Figure 1b, this sensor mainly has a structure of four layers: top bump, top functional layer, middle circular support, and bottom functional layer.The top bump is designed to be a circular truncated cone with a height of 2.0 mm, which serves as a loading-carrying structure and transmits external force, especially shear loads to the underlying layers.The top functional layer consists of a flexible substrate, a circular bump resistor, and two electrodes.The circular resistor is 0.8 mm in height with a gap of approximately 15°.One electrode connects with one end of the circular resistor to measure the resistance, and another electrode goes through the gap and connects with the circular region in the middle to measure the capacitance.All these structures are fixed on a flexible substrate layer.Similar to the top one, the bottom functional layer has a flexible substrate and a bump electrode with a height of 0.8 mm in the center, which serves as the electrode for both the resistive and capacitive circuits.Finally, a flexible circular ring with a height of 1.4 mm connects both the top and bottom functional layers, which serves as a support to external forces and enables corresponding movement to the top structures.
Figure S1, Supporting Information, shows the cross-sectional view of the assembled sensor.When assembled, an initial gap of 0.2 mm in radius direction exists between the top circular resistor and the bottom bump electrode, and both of them have a cavity of 0.6 mm in the vertical direction.All of the substrate or basal materials are soft polymer materials, and the effective modulus of the sensor is also calibrated to be less than 1.05 MPa (Figure S2, Supporting Information), which renders this sensor highly flexible when subject to external forces.In addition, the bottom bump electrode can not only form a pair of capacitive parallel plates with the top capacitive electrode but also be reused to constitute an initially disconnected resistive circuit with the circular resistor on top.The whole sensing unit has only three leading wires, which is compact and wire saving in distributed matrix when compared with tri-axis force sensors with other structures (Table S1, Supporting Information).And it may contribute to the design of simple measuring circuit for tri-axis force sensors in the future.

Tri-Axis Force Sensing Principle
In contrast to traditional tri-axis force sensors with multiple elements, this sensor can directly measure tri-axis force components with fewer sensing units and leading wires, and tri-axis force sensing principle is illustrated in Figure 2. As shown in Figure 2a, an arbitrary force can be decomposed into three constituents, that is normal force F N , shear force F S , and direction angle of shear force θ.The shear force angle θ explains the direction of the applied force in the horizontal plane.In our work, this angle is defined as the included angle between the shear force FS and the positive y axis.This decomposing method aims to detect the shear force angle directly, which may contribute to improving its measuring performances.If multiple stimuli from different directions are applied to the sensor simultaneously, we first compose them into a resultant force and analyze its force components.First, the bump electrode and top capacitive electrode can form a parallel-plate capacitor, and the measured capacitance C can be expressed as where ε 0 is the vacuum permittivity; ε r is the relative permittivity of dielectric layer; A is the overlapping area; and d is the distance between electrodes.When the sensor is compressed by a normal force (Figure 2b), the circular support buckles obviously and the top layer moves lower, which decreases the parallel-plate distance and increases the measured capacitance.
Besides, the bump electrode can be reused with the circular resistor on top to form an initially disconnected resistive circuit.Figure 2c provides the sectional view of these two structures when the sensor is subjected to a shear force.The bump electrode is fixed on the bottom substrate without movement, and the circular resistor on top shifts horizontally due to the shear force, which forms a mechanical contact and establishes a resistive measuring circuit.A part of the circular resistor enters into the circuit, and the measured resistance R can be expressed as Where R in is the intrinsic resistance of the part entering into the circuit; R cont. is the contact resistance; and R elec. is the electrode resistance.
The enlarged view in Figure 2c shows that the actually connected part is not a simple line contact but an area contact.First, R in consists of two parts namely R in1 and R in2 , which can be expressed as R in1 = ρL 1 /A 1 and R in2 = ρL 2 /A 2 , respectively, where ρ is the material intrinsic resistivity, L is the activated length, and A is the sectional area.Since L 1 is much larger than L 2 , while A 1 is much smaller than A 2 , R in2 can be neglected when compared with R in1 .Thus, the intrinsic resistance R in can be approximately expressed as where θ is the shear force angle; r is the radius of the circular resistor; and l is the half-length of the contacted area.
Besides, the contact resistance R cont. is composed of the tunneling resistance and constriction resistance.Since the conductive fillers' content of the composite material has greatly exceeded the percolation threshold, the tunneling effect is not obvious.Thus, R cont. is mainly influenced by constriction resistance, which is expressed as R cont.= Kρ/2l, where K is the sensor constant, ρ and l have been explained previously. [46]In addition, the intrinsic resistivity of the electrode material is extremely low, the electrode resistance R elec.can be neglected.Thus, the measured resistance R can be approximately expressed as Similar to a resistive potentiometer, R increases with the activated length of the circular resistor, which is proportional to the shear force angle θ.Noticed that R is inversely proportional to the contact length l, which is easily extended by a large shear force.Figure 2d gives the schematic view of the resistance change during a shear loading process.Initially, R cannot be measured since the bump electrode and circular resistor is isolated from each other.When these two structures first connect with each other due to a shear force F S , the conductive path is established but the measured resistance is too large and unstable due to a small l.We measure the resistance variation by the time and wait it reduces to a relatively stable and distinguishable value.Then, the average level of the first few values of the measured resistance is calculated as R 0 to preliminarily represent the shear force angle, and the relative reduction value of the resistance due to the increasing F S can be regarded as ΔR to calibrate the shear force amplitude.Since the measured capacitance C can represent the normal force, this sensor is able to detect arbitrary forces.

Sensor Fabrication Process
To fabricate the tri-axis force sensor, it is significant to prepare the materials of various structures, especially the circular resistor.All of the materials applied in the sensor fabrication process are rubber-based materials or polymer nanocomposites.The top bump, circular support, and substrate layers are made by the polydimethylsiloxane (PDMS) base resin and curing agent with a mass ratio of 10:1, which provides excellent flexibility and desirable structural deformation.Both the materials of electrodes and circular resistor are conductive nanocomposite with a substrate of silicone rubber (SR), which are prepared using a mechanical blending method.The former material is mainly composed of Ag nanoflakes (AgNFs) and nano-SiO 2 with a corresponding amount of dispersant mixed in SR, and the latter material has conductive fillers of graphene nanoplates (GNPs), AgNFs, and some dispersing agents.The electrode material is highly conductive since the mass ratio of SR, AgNFs, and nano-SiO 2 is 1:2:0.1.The addition of nano-SiO 2 can increase Young's modulus of the bump electrode, which prevents large deformation when applied by shear force. [47]Besides, the SR/GNPs/AgNFs composite with a mass ratio of 1:0.05:0.8 has acceptable resistivity, which can provide great linearity of the measured resistance to detect shear force angle.
Based on the designed structure, the tri-axis force sensor can be fabricated through a four-step process, as shown in Figure 3. First, in Figure 3ai-iv, the SR/GNPs/AgNFs composite resistor, isolating layer (SR), SR/AgNFs/SiO 2 electrode, and PDMS substrate are successively fabricated through casting and screenprinting technology, which forms the top functional layer.Second, both the top bump and circular support are fabricated by casting PDMS into the stainless steel mold (Figure 3av).Then, the bottom functional layer composed of the bump electrode and PDMS substrate can be fabricated using a similar method, as illustrated in Figure 3avi-viii.Finally, all these layers are assembled with an adhesion agent of SR (Figure 3b), and an optical view of the encapsulated tri-axis force sensor is shown in Figure 3c.Although the height of this sensor is a little thick (approximately 4 mm), it is still suitable to act as a sensing unit to be integrated on the robotic fingertip for complicated manipulation tasks.It is easy to see the initial cavity between the functional structures in the sensor due to great transparency of PDMS.In addition, the electrode leading wires have a line space of 1 mm, which is extracted to be compatible with flexible printed circuit (FPC) connectors.
After fabrication, the morphologies of the composite sensing materials are first investigated through a scanning electron microscope (SEM), as shown in Figure S3, Supporting Information.Despite a high content of nanofillers, both the composite of SR/GNPs/AgNFs (Figure S3a, Supporting Information) and SR/AgNFs/SiO2 (Figure S3b, Supporting Information) are tightly bonded with the PDMS substrate without obvious delamination boundaries.Figure S3c,e, Supporting Information, shows the morphologies of the SR/GNPs/AgNFs composite at the initial state and compressed state, respectively, and Figure S3d,f, Supporting Information, gives the enlarged view.There exists numerous nanofillers that uniformly disperse in the SR substrate, and the nanofillers' amount have exceeded the percolation threshold, which provides abundant conductive paths.There are also some micro-pores between the conductive nanofillers.When the material is compressed, the amount of the micro-pores shows a neglected reduction, which indicates that the measured resistance is less influenced by the external forces.
In addition, the sensor deformation under external forces is also investigated, as shown in Figure S4, Supporting Information.Figure S4a,c, Supporting Information, gives the optical sectional view of the sensor without external forces, respectively.When the sensor is applied by normal force, the top bump is curved and the whole sensor is compressed, which reduces the distance between the capacitive electrode plates and causes an apparent increase in the measured capacitance (Figure S4b, Supporting Information).Besides, a shear force can tilt the circular support and force the top functional layers to shift horizontally.Thus, a resistive circuit is established due to the contact between the circular resistor and the bottom bump electrode (Figure S4d, Supporting Information), which assists in detecting both the angle and amplitude of the shear force.

Normal Force Characterization
The tri-axis force sensing performance of the fabricated force sensor is investigated on a customized characterization platform, as illustrated in Figure S5, Supporting Information.As shown in Figure S5a, Supporting Information, a high-precision 6-DoF loading cell is mounted on a Z-axis moving stage, and a rotation stage is mounted on the X-axis moving stage.When testing, a loading bar is adhered to the sensor, which is fixed on the center region of the rotation stage.The normal and shear forces are applied through the movement of the Z-axis and X-axis moving stages, respectively.And the shear force angle can be modulated by adjusting the rotation stage.Through the FPC connector, the tri-axis force sensor is connected into the detection circuit that illustrated in Figure S5b, Supporting Information, in which the resistance and capacitance signals are measured by the digital multimeter and capacitive printed circuit board (PCB).The detailed information is explained in the Experimental Section.
The normal force sensing performances of the sensor are thoroughly investigated, as illustrated in Figure 4.The calibrating results of the normal force sensitivity are shown in Figure 4a.The relative capacitance response increases linearly with the increasing force, and the normal force sensitivity is fitted as S 1 = 0.057 N À1 from 0 to 12 N without shear loading.The calibration results of normal force sensitivity under increasing shear loading is shown in Figure S6, Supporting Information.Since the radius of the top capacitive electrode is slightly smaller than that of the bottom one, the capacitor overlapping area of the electrodes is almost constant unless the sensor is applied by large shear loadings, which has already exceeded the effective sensing range of the shear force (0.5-0.67 N, Figure 5a).Thus, the normal force measurement shows great robustness to shear force.Despite no micro-patterned structures between the capacitive electrodes, the normal force sensing range can cover the daily manipulation tasks.
Stability tests using cyclic normal loading with different magnitudes and frequencies are then conducted, and the measured results are plotted in Figure 4b,c.First, 5 cycles of normal forces of 3, 5, and 7 N with a frequency of 0.1 Hz are sequentially applied to the sensor, and each loading maintains about 4.5 s.As shown in Figure 4b, the measured capacitance rises progressively according to the increasing force, and the peak value fluctuation during each set of cycles can be neglected, which indicates excellent amplitude stability of the force sensor.In addition, cyclic stability tests using normal forces with an incremental frequency of 0.5-4 Hz are also conducted.The peak value of the capacitive response remains almost unchanged regardless of the increasing force frequency, and the frequency detection range satisfies the needs of daily usage.
To further demonstrate the normal force repeatability of the sensor, a loading/unloading test of 300 cycles using a force of 5 N with frequency of 0.2 Hz is conducted (Figure 4d). Figure 4e gives the enlarged view of the repetitive changing signal, both the peak and original values of the measured capacitance remain unchanged, which indicates good repeatability of the normal force sensing.Finally, dynamic response performance is illustrated in Figure 4f.A square-wave force of approximately 5 N is applied to the sensor, and the loading process maintains about 5 s.During the load maintaining stage, the measured force shows a slight decline, which may be caused by the stress relaxation of the flexible structure, as shown in Figure S7, Supporting Information.Since the upward resilience of the circular support and the sinking of the central part cancel with each other, the average distance between the capacitive electrode plates almost remains stable.The measured capacitance shows rapid change with a response time of 100 ms and a recovery time of 250 ms.After unloading, the relative capacitive response shows a little increase of 0.02 due to the hysteresis of the flexible structure, which is negligible and can be recovered over time.

Shear Force Characterization
The shear force sensing performances are characterized through the testing platform, and the results are illustrated in Figure 5. Different from the characterization process of some traditional tri-axis force sensors, an initial normal loading is unnecessary due to the independent design of shear sensing structure.Figure 5a provides the measured resistance under shear force with different amplitudes, and the tests are conducted at a fixed angle of 90°.The resistance decreases with the increasing shear load as expected, and the sensitivity of shear force can be calibrated as 668 kΩ N À1 (0.5-0.55 N) and 7.1 kΩ N À1 (0.55-0.67 N).The larger sensitivity is mainly determined by the contact resistance due to small contact length, and the initial resistance plays a dominant role when the contact length is large enough, which contributes to a smaller sensitivity.Even though the measured sensitivity reduces, the resistance change value still maintains in a scale of kΩ, which can obviously distinguish the shear load as illustrated in the enlarged subplot in Figure 5a.This sensor can hardly detect shear force less than 0.50 N due to the initial cavity between the circular resistor and the bump electrode, which is mainly determined by the effective Young's modulus of the circular support as well as the width of the cavity.In addition, since both the circular resistor and bump electrode are flexible, the contact area will easily saturate without further variation under large shear load, and shear force more than 0.67 N can no longer provide obvious variation of the measured resistance.Thus, the effective sensing range of shear force is approximately 0.5-0.67N.Both the upper and lower limit of shear force sensing range are mainly limited by the fabrication technique and the materials, which can be further improved in future works.Noticed that the resistance is more unstable when the shear force is smaller (Equation ( 3)), it is significant to use (R 0 -ΔR) to correct the judgment of the shear force angle, which is completed by comparing the measured value with the resistance data base measured before.
To further demonstrate the shear force stability, cyclic loadings with different magnitudes are applied to the sensor, and the measured results are plotted in Figure 5b.The sensor is initially subjected to a shear force of 0.7 N at 180°, which is then sequentially reduced to 0.55, 0.58, and 0.62 N.Each force is repeatedly loaded with 3 cycles, and each loading maintains about 7.5 s.The measured resistance decreases when the shear force becomes larger.During each set of cycles, the peak value of the resistance almost remains identical, which indicates great amplitude stability of shear force sensing.Noticed that the measured resistance slightly declines during the load maintaining stage, which may result from the hysteresis of the conductive nanocomposites.Besides, a repeatability test of 300 cycles by changing the shear force from 0.7 to 0.62 N is conducted, and the measured result is plotted in Figure S8, Supporting Information.Both the peak and original values of the measured resistance slightly fluctuate over time, which is caused by the repeated construction of the resistive conductive path.The enlarged view shows that the resistive response seems unchanged during a set of cycles, which indicates acceptable repeatability of shear force sensing.
To investigate angle influences on the shear force sensing performance, resistance characterization tests under different angles of 90°, 180°, and 270°are conducted, as illustrated in Figure 5c.The measured resistance always shows a decreasing tendency to the increasing shear force regardless of the load angle, and the enlarged view proves that the resistance value increases with the angle, which has a longer length of the resistor connected into the measurement circuit as expected.When testing the shear force, the relative resistance change at different angles is similar, which indicates the angle-independent capacity of shear force sensing.Noticed that the force sensing range shows a little difference, which is caused by the various initial cavity due to assembly error.Furthermore, Figure 5d also provides the normal force influence on the shear force sensing.Various normal forces of 0, 1, and 3 N are applied to the sensor initially, and resistance changes under shear force load at an angle of 180°are recorded.Noticed that the effective sensing range of shear force has an offset when the normal force is applied.This is mainly caused by the rotation of the circular resistor when applied by normal force (Figure S7, Supporting Information), which requires a larger shear force to make a contact with the bump electrode.We have also eliminated the offset value and overlap these calibration curves, and the results are plotted in Figure S9, Supporting Information.The calibration curves almost overlap with each other, which indicates that normal force has little influence on the variation trend of shear force.In practical, we can investigate the relation between the normal force and the offset value of shear force sensing range.If the normal forces have been measured, we can calculate the error value and accordingly shift the calibration curve of the shear force.When the shear force reaches about 3-5 N, the rotating deformation may saturate (Figure S9b, Supporting Information), and the calibration curve of shear force will not need larger offset value to compensate the normal force influence.
Finally, the shear force angle with an incremental value of 15°i s characterized as shown in Figure 5e, and all the resistance is detected at a constant shear force of 0.7 N.This sensor can directly measure the shear force angle without signal difference computation.The measured resistance increases linearly with the shear force angle, and the angle sensitivity can be fitted as S θ = 4.81 Ω °À1 with R 2 to be 0.96.Noticed that the resistance error measured at different angle are varied around an average value of 35 Ω (Figure S10, Supporting Information), which corresponds to a shear angle resolution of 7.3°.This performance is regarded as competitive with some recently reported works, [27,44,48] and further improvement can be achieved by adjusting the material electrical resistivity, which is promising for shear angle measurement in robotic applications.However, a dead zone of approximately 15°also exists due to the designed gap of the circular resistor.Figure S11, Supporting Information, provides another structure design of the tri-axis sensor to prevent the dead zone of shear angle measurement.All the structural layers are almost identical to the previous one, except for the circular resistor, which is a full circle with two electrode wires leading out.The detailed sensing principle of this structure is demonstrated in Supporting Information.Although the dead zone of shear angle measurement can be eliminated, the resistance response is nonlinear, and it is complicated to simultaneously analyze two signals with more leading wires.The minimum discernibility of shear force is less satisfied, especially when the contact spot is close to the opposite of the leading wires.Thus, it is reasonable to sacrifice the full angle detection capacity to improve the sensing performance.
The performance comparison results between this sensor and other reported works are listed in Table S2, Supporting Information.For the normal force-sensing performances, the sensitivity value is not quite competitive, but it maintains linear within a large sensing range of 12 N, which is more advanced than some reported works and enough for practical application.For the shear force amplitude, the sensitivity is competitive, but the sensing range is unsatisfactory (0.5-0.67 N), which can be further enlarged by improving the manufacturing technique and materials.Besides, the shear force angle resolution is one of the innovations of this work (7.3°), and it has great novelty when compared with other reported works.

Applications in Robotic Hand Grasping
In practical robotic grasping tasks, both the objects and robotic manipulators are subjected to arbitrary force.And simultaneous analysis of both normal and shear forces assists in extracting the objects' complicated information.To verify the tri-axis force detection capacity of the sensor, an object grasping test using a robotic manipulator is conducted, as shown in Figure 6.A pair of tri-axis force sensors are installed on a two-jaw manipulator to grasp an aluminum alloy block of 200 g, and the manipulator is mounted on a robotic arm (Figure 6a).When grasping the object, the sensors are not only subjected to normal forces caused by robotic clamping load but also applied by shear forces with a direction parallel to the gravity of the object.The normal force measurement can prevent object destruction and guarantee a stable grasping without slippage, and the shear force helps detect the object weight.In addition, since the direction of shear force is always parallel to the gravity, rotation of the robotic grasper in a vertical plane will cause a variation in shear force angle, which assists in inferring the grasped pose of the object.
Figure 6b provides the measured resistance and capacitance signal during the grasping test.The robotic manipulator rotates from 0°(vertical state) to 180°with an angle increment of 45°, and each position maintains about 15 s.First, the measured capacitance increases rapidly once the object is grasped, and the grasping force maintains about 8.5 N. No obvious fluctuation is observed during the rotating process, which also indicates that the normal force sensing is independent of shear load.The resistance signal also quickly drops to the initial value when lifting the object, and it rises incrementally with the rotation angle.During each rotating state, the resistance shows a fast increase at first several seconds and then declines to a stable value.That is because the movement of the robotic manipulators destructs the established conductive path and increases the contact resistance between the circular resistor and bump electrode.When the rotation stops, the falling trend of the object forms a stable conductive path again.The stable value of the measured resistance is almost consistent with the rotation angle, which demonstrates that this tri-axis force sensor can preliminarily tell the pose of the grasping object.
In addition, the tri-axis force sensor reported in this work has great advantage in the centralized structure as well as a high distinguishable shear angle difference, which can also be potentially utilized in some other applications.For instance, this sensor can be used as a controlling button for human-machine interface, which can provide complicated instructions based on input from multiple directions.In VR applications, this sensor can not only assist the game character to move in multiple directions not merely along the axis but also can simulate more complex grasping gestures based on the tri-axis force signal.And we believe that these potential applications can be easily achieved if the performance of this sensor is improved.

Conclusion
In summary, this work develops a flexible centralized tri-axis force sensor with multilayer and bump structures, which has only one sensing unit with three leading wires to measure tri-axis force components.A new tri-axis force refactoring method inspired by the resistive potentiometer is presented, and the bump electrode can simultaneously form resistive and capacitive circuits with the surrounding structures.Normal force is characterized by the central parallel-plates capacitor, and both the angle and amplitude of shear force can be extracted through the resistance changes.For normal force sensing, this sensor can reach a sensitivity of 0.057 N À1 with maximum detection range of about 12 N, and both the repeatability and dynamic performance are satisfactory.The resistance decreases nonlinearly with shear force amplitude with an effective detection range of about 0.5-0.67N, and the minimum distinguished shear angle difference is about 7.3°.All of the force components measurements show little influence on each other.Finally, the sensor is fixed on the working surface of a robotic manipulator, and both normal and shear force information can be measured accurately when grasping an object.The current limitation mainly focuses on how to improve the shear sensing performances, such as to expand the detection range of the shear force amplitude and reduce the minimum distinction limit of shear angle.And further research can be conducted in applying high-accuracy mechanical fabrication techniques or increasing the intrinsic resistivity of the material.In general, this sensor has simplified the structure and measuring circuit of the tri-axis force sensors, and the results of the grasping test indicate its promising application in robotic hand manipulation in the future.

Experimental Section
Preparation of the Materials: For the substrate material, mixed the PDMS (Sylgard 184, Corning Co., Ltd.) base resin and curing agent with a mass ratio of 10:1.The mixture was blended for 3 min and degassed it for 2 min in a planetary mixer (AR 100, Thinky Corporation) to get the uncured PDMS for further fabrication.During the nanocomposite preparation, SR (GD401, Zhonghao Chenguang Research Ins.) was selected as the polymer substrate, tetrahydrofuran (THF, Sinopharm Chemical Reagent Co., Ltd) was selected as a solvent, and polyvinylpyrrolidone (PVP, Sigma-Aldrich Trading Co. Ltd.) and hyperbranched dispersant (7455H, Guangzhou Silok Polymer Co., Ltd.) were chosen as the dispersant to prevent agglomeration of the nanofillers.For the electrode material, the SR, silver nanoflakes (AgNFs, Nanjing XFNANO Materials Tech Co., Ltd.), Figure 6.Grasping applications of a robotic manipulator: a) Object grasping test using a robotic manipulator with tri-axis force sensors mounted on the working surface; b) various rotation states of robotic grasper and their corresponding sensor signals.
Fabrication Process of Tri-Axis Force Sensor: The whole sensor fabrication process mainly consisted of four steps.Step 1: fabricated the top functional layer.Filled the SR/GNPs/AgNFs composite material into the stainless steel mold and heated at 80 °C for 2 h to cure it.Screen printed a 100 μm layer of SR and heated at 80 °C for 1 h.Screen printed 200 layer of SR/AgNFs/SiO2 electrode and heated at 80 °C for 1 h.Spin-coated a 300 μm layer of PDMS substrate and heated at 80 °C for 1 h.Peeled off the top functional layer after curing, and dipped it into the L-ascorbic acid (LAA) solution at 80 °C for 1 h to reduce the oxidized AgNFs.Step 2: fabricated the bottom functional layer.Filled the SR/AgNFs/SiO2 composite material into the stainless steel mold, and screen printed a 200 μm layer of SR/AgNFs/SiO2 electrode and subsequently heated at 80 °C for 2 h.Spincoated a 300 μm layer of PDMS substrate and heated at 80 °C for 1 h.Peeled off the bottom functional layer after cured and dipped it into the LAA solution at 80 °C for 1 h to reduce the oxidized AgNFs.Step 3: fabricated the top bump and circular support.Filled the PDMS into the stainless steel mold, and heated at 80 °C for 2 h.Peeled off the top bump and circular support after being cured.Step 4: sensor assembly.All the layers were put into an assembly mold, and an adhesion agent of SR was used to stick different layers.An initial normal force was applied on the top bump and heated at 80 °C for 2 h.Thus, a flexible tri-axis force sensor was obtained.
Optical Characterization of the Material and Sensor: The morphologies and connection of the two nanocomposites were obtained by a SEM (SU-3500, HITACHI Ltd.).The sensor cross-sectional deformation was observed by a laser confocal microscope (LSCM, OLS 4100, Olympus).
Tri-Axis Force Characterization Platform and Measurement Circuit: Forces applied to the sensor were characterized by a high-precision 6-DoF load cell (Mini 40, ATI Industrial Automation), which can measure a normal force of 240 N with a resolution of 0.02 N, and it can also measure a shear force of 80 N with a resolution of 0.01 N. The load cell was fixed on a Z-axis high-resolution linear moving stage (UTS100, Newport) with a minimum displacement of 300 nm.The tri-axis force sensor was mounted on a manual rotation platform (PT R60, PDV) to change the shear force direction, which can adjust the angle from 0 to 360°with an angle resolution of 55 00 .And the rotation stage was mounted on another high-resolution linear moving stage for X-axis movement.The normal and shear forces can be applied by adjusting the Z-axis and X-axis moving stages, respectively.The resistance was measured by a digital multimeter (34465A, Keysight), and the capacitance was recorded by a PCB using a capacitance-digital converter (CDC, AD7153).

Figure 1 .
Figure 1.Schematic view of tri-axis force sensor: a) The assembled tri-axis sensor attached to a robotic hand; b) explosive view of the sensor.

Figure 2 .
Figure 2. Sensing principle of the tri-axis force sensor: a) Arbitrary force being decoupled into three force components; b) sectional view of the sensor subjected to normal force; c) sectional view of the sensor subjected to shear force, the enlarged diagram shows the resistance composition; d) resistance changes during shear loading.

Figure 3 .
Figure 3. Schematic view of the sensor fabrication process: a) Fabrication process of different parts.b) Assembly of different parts.c) Optical image of the fabricated sensor.

Figure 4 .
Figure 4.The normal force characterization results of the sensor: a) Characterization of normal force sensitivity; b) stability loading test using cyclic normal forces with incremental amplitudes; c) stability loading test using cyclic normal forces with incremental frequencies; d) repeatability loading test of 300 cycles; e) enlarged view of the capacitive response during repeatability test; f ) dynamic loading tests.

Figure 5 .
Figure 5.The shear force characterization results of the sensor: a) Characterization of shear force sensitivity at the angle of 90°; b) stability loading test using cyclic shear forces with incremental amplitudes; c) angle influences on the shear force sensing performance; d) normal force influences on the shear force sensing performance; e) characterization of shear angle sensitivity.