Force Sensing and Feedback System Based on Novel Triaxial Force Capacitive Sensor for Minimally Invasive Surgical Robot

Minimally invasive surgery has attracted great attention due to small trauma, light pain, and quick recovery. Currently, most minimally invasive surgical robots lack the ability to force sense, resulting in high risks. Herein, a novel minimally invasive surgical force sensing and feedback system for minimally invasive surgical robot is proposed based on a flexible triaxial force capacitive sensor array. The capacitive force sensors utilize a microstructure electrode and orthogonal triangular pyramid microstructure to tackle the trade‐off between high sensitivity and wide‐detection range, showing 0–3 N detection range for normal force and high sensitivity of 69.19% N−1. Furthermore, the triaxial capacitive force sensors are integrated into the end‐effector of the minimally invasive surgical robot to form the minimally invasive surgical force sensing system. The system can show real‐time position of gripping or touching action, and the magnitude of triaxial force on the display surface. Importantly, the sensing force can further control the movement of the clamp, thus forming a novel force sensing and feedback system. The force sensing and feedback system of this minimally invasive surgical robot lays the foundation for its application in minimally invasive surgery andis expected to improve the safety and success of robotic‐assisted minimally invasive surgery.


Introduction
Compared with traditional surgery, minimally invasive surgery has significant advantages, such as less trauma, fewer complications, faster recovery, and lower cost. [1,2]Currently, minimally invasive surgical robots have been maturely applied in the fields of surgery, internal medicine, and orthopedics.[8] Essentially, a promising minimally invasive surgical force sensing system was an integration system of the accurate force sensing units, fast signals processing, and effective master from control.It is noted that the force sensing units not only need to sense the 1D normal force, but also the triaxial force to meet the need of different operation detection in the surgery.Moreover, the triaxial force sensor requires high sensitivity to achieve a good accuracy of sensing and feedback.Meanwhile, the triaxial force sensor also should possess a wide detection range to adapt to the complex workplaces and meet the various operating demands.Thus, the construction of high-performance force sensor was a key factor to resolve the lacking of force sensing of minimally invasive surgical robot.
Triaxial force sensors have been widely used in pathology detection, [9][10][11] robotic grasping, [12,13] angle measurement, [14][15][16][17] and robot-assisted surgery scenarios. [18]The triaxial force sensors have been prepared based on different sensing mechanisms, mainly including of piezoelectric, [19] piezoresistive, [20,21] and capacitive. [22,23]Piezoresistive strain gauge triaxial force sensors have been widely studied due to good stability and sensitivity. [24,25]However, the limitations of rigid silicon and complicated fabrication process hinder its application in largearea production and curved surface.Piezoelectric sensors can realize dynamic force detection by piezoelectric effect from the dielectric layer between the sensor electrodes. [26,27]However, this kind of sensor is unable to detect static force.Capacitive sensors have received more and more attention due to higher sensitivity, adjustability, and good dynamic response.Thus, the reported triaxial force sensors are mostly based on the capacitive sensing mechanism. [28,29]Huang et al. reported a triaxial force capacitive sensor based on striation effect theory, showing wide-detection range of 0-10 N, but the maximum sensitivity of the sensor was only 0.0095 N −1 . [30]Nagatomo and Miki prepared a triaxial force sensor using liquid metal as a 3D electrode and applied it to endoscopic palpation.The force detection range of the sensor possessed 0-5 N detection range, while its maximum sensitivity was only 0.7% N −1 . [31]Although the above sensors showed a large pressure detection range, the low sensitivity still limited their application in the accurate sensing.Meanwhile, various strategies were applied to enhance the sensitivity to broaden its application.Liu et al. used PDMS micropillar as a dielectric layer to improve the sensor performance.The optimized sensor showed maximum sensitivity of 237.48% N −1 , but its maximum detection pressure was only 0.15 N. [32] Similar to single sensors, the triaxial force sensors based on the four pressure arrays still had the trade-off between high sensitivity and wide-detection range, thus limiting the detection accuracy and range.In addition, the reported literatures about triaxial force sensors mainly focused on the fabrication process, rarely realized the integrated system, especially forming the force sensing and feedback system.Therefore, the construction of force sensing and feedback system based on high-performance flexible triaxial force sensors is still urgent in the field of minimally invasive surgical robot.
In this paper, a minimally invasive surgical force sensing and feedback system based on a novel flexible triaxial force capacitive sensor is proposed to detect the force of grip in minimally invasive surgical robot.[35] Owing to the synergistic effect of the microstructure electrodes and dielectric layer, the pressure sensor possesses high sensitivity, superior widedetection range, and good stability.Furthermore, the triaxial capacitive force sensor based on four sensor arrays can sensitively detect normal force of 0-3 N with a high sensitivity of 69.19% N −1 and tangential forces of 0-0.5 N s, showing comparable performance to the literature. [36]The sensor can accommodate a large degree of curved surfaces, and its performance remains essentially unchanged.Importantly, the minimally invasive surgical force sensing system is formed by integrating the flexible triaxial force capacitive sensor into the end-effector of the minimally invasive surgical robot.The system can detect the magnitude of the triaxial force and real-time position of the gripping or touching action by performing actions such as grasping and touching on the bionic tissue.

Design of the Minimally Invasive Surgical Robot
The minimally invasive surgical robot mainly consists of a flexible triaxial force capacitive sensor, signal acquisition circuit, dis-play interface, and operating master hand as shown in Figure 1.The flexible triaxial force capacitive sensor was used to detect the force when gripping or touching the tissue.The gripper and contact bar are used as experimental objects.In the data processing, the function fitting was used to directly output force value combining collecting data and setting parameters.Combining with the display, the triaxial force can be uploaded to the PC via serial communication for real-time display.Finally, the sensing force can be provided to the operation system to assist in the operation and improves the sense of presence.
The flexible triaxial force capacitive sensor was used as minimally invasive surgical force sensing units.The typical triaxial force capacitive sensor is mainly composed of four sensor arrays.When triaxial force is applied to the sensors in each direction, the four sensor units will identify and detect the triaxial force by displaying different capacitance value for the different directions of forces.In this work, a novel structure of flexible capacitive pressure sensor is proposed to solve the trade-off between high sensitivity and wide pressure detection range, inserting the microstructure electrode to enhance the sensitivity and using the microstructures orthogonally to improve the pressure detection range.The scheme of the fabrication process is shown in Figure 2. The sensor mainly consists of a bump, a triangular pyramid polydimethylsiloxane (PDMS) microstructure, a magnetron sputtered triangular pyramid microstructure electrode, a printed electrode with a triangular pyramid PDMS microstructure, and a flexible polyethylene terephthalate (PET) substrate.The triangular pyramid PDMS microstructure and the triangular pyramid microstructure electrode of the sensor are packaged in an orthogonal form.The 2 × 2 array of printed electrodes was used as the upper electrodes to form the four sensor arrays.The magnetron sputtering electrode was utilized as the bottom electrode.The size of the microstructure electrode was 6 mm × 6 mm, and the unit size of the printed electrode array was 2 mm × 2 mm.The dimensions of the triangular pyramid microstructure were designed to have a bottom edge length of 12.8 μm, a height of 10 μm.This above size design was according to literature and the simulated results. [35]

Performance Characterization of the Flexible Triaxial Force Capacitive Sensor
The flexible triaxial force capacitive sensor is based on four sensor units.The sensor unit is firstly investigated since the unit sensor is key factor to affect the performance of the triaxial force capacitive sensor.Similar to the reported literatures, [37][38][39][40][41][42][43][44][45][46][47] the performance of the capacitive sensor obviously depends on the morphology of microelectrodes and dielectric layer.The sensor unit is prepared based on the three spacing microstructures of 10, 20, and 30 μm, which size is set to 1 cm × 1 cm without the bump.As shown in Figure S1 of the Supporting Information, the prepared microstructures have distinct triangular pyramid shapes.Moreover, the sensitivity and detection range obviously depend on spacing microstructure size (Figure S2, Supporting Information).The sensor with a spacing of 20 μm triangular pyramid microstructure shows excellent performance.In the small pressure (0-6 kPa), the sensitivity of the sensor improves as the microstructures spacing increases.The sensitivity  of the sensor with the microstructure spacing of 30 μm is 0.23245 kPa −1 , while the sensors based on the microstructure spacing of 20 and 10 μm show 0.13674 and 0.08392 kPa −1 .With the increase of pressure, the capacitance value changes slowly and the sensitivity decreases.Moreover, the sensitivity of the spacing in larger pressure shows different changeable tendency.The sensitivity decreases with the increase of the microstructure spacing.
In b the pressure range of 6.4-30 kPa, the sensitivity of the sensor with microstructure spacing of 30 μm is only 0.01096 kPa −1 , while the sensitivity of the sensor with microstructure spacing of 20 μm increases to 0.01838 kPa −1 in the pressure range of 8-30 kPa, and the sensitivity of the sensor with microstructure spacing of 10 μm is 0.02063 kPa −1 in the pressure range of 7.56-30 kPa. [48]Thus, a pressure sensor based on a triangular pyramid microstructure with a spacing of 20 μm is used in the following section.
The performance of the flexible triaxial force capacitive sensor is then investigated.The relative capacitance change of the sensor varies greatly in the pressure range of 0-3 N and has an obvious response to pressure (Figure 3a).The sensor showed the stable response to pressure from 0.02 N to 3 N in each cyclic pressure (Figure 3b).The relative capacitance change rate under same pressure is almost unchanged.The results confirm that the sensor has excellent dynamic stability and ability of sensing small pressure.The relative capacitance change rate is essentially constant when loading and unloading pressure in the pressure range of 0-1 N, 2 N, and 3 N (Figure 3c; Figure S3, Supporting Information).The hysteresis value is only 0.02, 0.025, and 0.056, indicating an excellent stability.The relative capacitance change rate remains almost the same after cycling the dynamic pressure 1000 times at 0.5 N, which also confirmed its excellent stability (Figure 3d).In addition, the sensor also shows good flexibility.As shown in Figure 3e, there is no significant change in the initial capacitance value of the sensor arrays for different curvature radii (radii of 10, 15, 20, 25, and 30 mm), indicating excellent bending performance and verifying the potential application on curved surfaces.
Except high sensitivity, wide-detection and high stability, the sensor also shows fast response ability.During the fast loadingunloading pressure process, the response time and recovery time of the sensor are 162 and 324 ms, respectively (Figure S3, Supporting Information), demonstrating fast response speed and recovery speed.At the same time, the sensor has excellent dynamic resolution.As shown in Figure S4 of the Supporting Information, the relative capacitance changes significantly at different pressures loading force from 0.04 N to 3 N, proving excellent resolution in the pressure range of 0-3 N.For the triaxial force, the repeatability of the sensor is also another important parameter.Herein, the same normal load of 0-3 N is applied to five different sensing units.The relative capacitance change rate error is only 6% (Figure S5, Supporting Information), indicating the feasibility and repeatability of the sensor preparation process.The unit sensor of the flexible triaxial force capacitive sensor has excellent low hysteresis of 0.056.These above results confirm that the sensor shows stable dynamic response, and excellent stability, demonstrating its promising application in minimally invasive surgery.
The principle of triaxial force detection based on four pressure sensor arrays is shown in Figure S6 of the Supporting Information.The test platform for the flexible triaxial force capacitive sensor is shown in Figure S7 of the Supporting Information.The triaxial force capacitive sensor includes four sensing units, which are named C1, C2, C3, and C4.The triaxial force is defined as F Z , F X , and F Y .The structure and signal processing system are shown in Figure 4a,b.The capacitance values of the sensor arrays (C1, C2, C3, C4) increase rapidly when the normal force increases from 0 N to 1 N.When the normal force is more than 1 N, the increase tendency of the capacitance values of the sensor arrays (C1, C2, C3, C4) becomes slowly.As we know, the microstructure and the bump are squeezed more difficult in the large pressure compared to that in small pressure.According to the fitted results, the sensor shows 69.19% N −1 in 0-1 N and 13.93% N −1 in 1-3 N(Figure 4c), respectively.Moreover, the response curves of the sensor arrays (C1, C2, C3, C4) to the pressure of 0-3 N show good consistency, further indicating excellent uniformity.It is noted that the obtained sensor performance is better than that of the reported literatures. [22,29,30,32,49,50]The high sensitivity in 0-1 N demonstrates that the sensor can measure a gentle touch and small contact force.The sensitivity in 1-3 N makes it possible to measure larger contact force.The capability of measuring both small and large forces makes it to be suitable for robotics and prosthetic hand applications.Furthermore, the tangential forces in the x-axis and y-axis directions are tested and calibrated.The tangential force in the x-axis causes a capacitance increase for C3 and C4, while resulting in a capacitance decrease for C1 and C2 (Figure 4d).The capacitance values of C1 and C4 decrease and those of C2 and C3 increase when the tangential force is applied on the y-axis (Figure 4e).The sensitivity to x-axis shear force is calculated as 53.91%N −1 + 28.56% N −1 )/2 = 41.23%N −1 (0.04123% mN −1 , Figure 4d).Similarly, the sensitivity to the y-axis shear force is calculated as 41.59% N −1 (0.04159% mN −1 , Figure 4e), which shows similar value with the sensitivity to the x-axis shear force (0.04123% mN −1 ), further indicating the excellent uniformity and stability.
According  [50] ⎧ ⎪ ⎨ ⎪ ⎩ In the above equations, d 1 , d 2 , d 3 , and d 4 are calculated as where C 1,2,3,4 are the initial capacitance values of sensor arrays (C1, C2, C3, C4), while C i,j,k,l correspond to the capacitance values of sensor arrays when they are subjected to load.The three spacing parameters d X , d Y , and d Z and the triaxial forces F X , F Y , and F Z are linearly fitted.The relationship between the triaxial force applied to the sensor and the spacing parameters is shown in Figure 5a-c.Based on the above calibration results, the triaxial force and spacing parameters are fitted.The R 2 of linear fitted curve is more than 0.99, indicating high degree of overlap between the fitted curve and the actual measured value (Figure 5df).Thus, the triaxial force output can be realized in practical application according to the fitted functional relationship.
In addition, the tangential forces in the x-and y-axis directions are calibrated for only one direction when calibrating the sensor for triaxial force.In the function fitting, the test direction is defined as the positive direction (d X > 0, d Y > 0).The sensor is subjected to a force opposite to the test direction in practical According to the above fitting results, the sensor can show the value of force in-time when the force in different directions is loaded on the sensor.
To clearly clarify the interference of multiaxial force in the calculation process, the matrix calculation is also used to consider the interference of multiaxial force in the calculation process.The calibration data of the reference sensor is solved by matrix calculation and function fitting, respectively.The matrix calculated process is provided in the Supporting Information.And the comparing results of matrix calculation and function fitting are shown in Table S1 of the Supporting Information.It was seen that the result of function fitting is close to the experiment of matrix calculation, further confirming that the proposed method of calculation of triaxial force is very effective.Thus, this paper adopted the function fitting method to calibrate the sensor data and measure the 3D force.
The triaxial force sensor is compared with various types of 3D force sensors researched by various teams at home and abroad, and the performance comparison is summarized in Table S2 of the Supporting Information.It can be found that the sensor designed in this paper has improved in sensitivity, pressure detection range, and normal force resolution under the limited sensor size.And the comprehensive performance obtained in various aspects is better or at least comparable to that reported in the literatures [1,25,27,33,[51][52][53][54][55] These above results prove that the obtained sensor can sense the normal and shear forces can meet the need of the minimally invasive surgical force sensing system such as minimally invasive surgical robots for digestive endoscopy.

Bionic Tissue Simulation Test Based on Designed Force Sensing System
To investigate its applications in detection of force of the tissue during the minimally invasive surgery, the triaxial force sensor is integrated into the gripper and contact bar in the end-effector of the minimally invasive robot.A series of gripping and touching bionic tissues are performed to simulate the practical application of minimally invasive surgery.The triaxial force sensor is first integrated on the gripper controlled by the Phantom Omni operating master hand to grip simulated biomimetic tissue.The photograph of the minimally invasive surgical robot integrated with triaxial forces sensors was shown in Figure S8 of the Supporting Information.When the gripper slowly grips the bionic tissue, the normal force F Z increases slowly, and the tangential forces F X and F Y remain unchanged.The normal force F Z remains constant when the gripper moves to a certain position and holds.After slowly releasing the gripper, the normal force F Z slowly decreases and returns to the initial state (Figure 6a).As shown in Figure 6b, the gripper grips the bionic tissue at a certain position and tugs in the x-axis direction while maintaining the clamped state.The force F X increases, while the normal force F Z slightly decreases.The tangential force F Y remains unchanged when the gripper drags in the x-axis direction.After the gripper is released quickly, the normal force F Z and the tangential force F X rapidly decrease to zero.Similarly, the gripper tugs the bionic tissue in the y-axis direction while maintaining gripping after gripping the bionic tissue at a certain position.The tangential force F Y increases, while the normal force F Z slightly decreases and the tangential force F X remains constant.After the gripper is released quickly, the normal force F Z and the tangential force F Y rapidly decrease to zero (Figure 6c).The above sensing force process was clearly demonstrated in Video S1 of the Supporting Information.It is noted that the Phantom Omni operating master hand can feel force feedback from the front of the gripper when gripping the bionic tissue.The force feedback disappears when the gripper is released, as shown in Figure 6d and Video S2 (Supporting Information) shows that the system possesses the force feedback effects with the Phantom Omni operating master hand.The above gripping experiments verify that the triaxial force sensor can detect the magnitude of the triaxial force in real time while gripping the bionic tissue, offering the possibility of practical gripping for minimally invasive surgery.
Due to excellent flexibility, the sensor can be integrated into the curved contact bar to detect contacting force when touching simulated biomimetic tissue.These actions can simulate the magnitude of the triaxial force of the contact bar in touching the bionic tissue surface in minimally invasive surgery.When the contact bar touches the surface of the bionic tissue in the positive direction, the normal force F Z increases rapidly, and the tangen-tial forces F X and F Y remain unchanged.The normal force F Z remains stable and constant when the contact bar is held at a certain position.When the contact bar is removed from the surface of the bionic tissue, the normal force F Z rapidly decreases to zero when the sensor returns to the initial state (Figure 7a).As shown in Figure 7b, the tangential force F X increases, while the normal force F Z decreases and tangential force F Y remains unchanged when the contact bar moves in the x-axis direction after compressing the bionic tissue at a certain position.The normal force F Z and tangential force F X decrease rapidly to zero after the contact bar is removed from the surface of the bionic tissue.Similarly, the tangential force F Y increases.The normal force F Z decreases, and the tangential force F X remains unchanged when the contact bar moves in the y-axis direction on the surface of the bionic tissue while maintaining compression.The normal force F Z and the tangential force F Y rapidly decrease to zero after the contact bar is removed from the surface of the bionic tissue (Figure 7c).Video S3 of the Supporting Information obviously shows the whole force sensing process.The above touch experiments verify that the sensor can detect the magnitude of the triaxial force in real time when touching the bionic tissue, which offers the possibility of practical touch for minimally invasive surgery.
To verify potential application on the curved surface, the sensor is wrapped around the contact bar to touch the bionic tissue.As the contact bar slides toward the surface of the bionic tissue in any direction, the triaxial force changes simultaneously (Figure S9a, Supporting Information).When the contact bar is removed from the surface of the bionic tissue, the triaxial force instantaneously decreases to zero (Figure S9b, Supporting Information).In addition, a real-time demo interface is developed by Unity, which includes real-time images of the minimally invasive surgical end-effector and the magnitude of triaxial force.When the normal force detected by the sensor is greater than 2 N, the system will send an alarm signal to remind the doctor of the safety of the operation.Video S4 of the Supporting Information also elucidates the above process.These results all confirm the effective application in the minimally invasive surgical force sensing system.

Conclusions
In summary, an innovative force sensing and feedback system based on novel flexible triaxial force capacitive sensor is proposed to minimally invasive surgical robot.The capacitive force sensors mainly consist of a triangular pyramid microstructure electrode and an orthogonal triangular pyramid microstructure insulating layer to solve the trade-off between high sensitivity and wide-detection range, showing 0-3 N detection range for normal force and high sensitivity of 69.19% N −1 .Furthermore, the triaxial capacitive force sensors are integrated into the end-effector of the minimally invasive surgical robot to form the minimally invasive surgical force sensing system.The system can show realtime the position of gripping or touching action, and the magnitude of triaxial force on display surface.Importantly, the sensing force can further control the movement of clamp, thus forming a novel force sensing and feedback system.The obtained novel minimally invasive surgical force sensing system based on a flexible triaxial force capacitive sensor has laid the foundation for its application in minimally invasive surgery.

Experimental Section
Fabrication of the Sensor: The fabrication process of the flexible triaxial force capacitive sensor was as followed.A silicon mold with a triangular pyramid microstructure was fabricated by standard photolithography and wet etching processes.The surface of the silicon mold was treated with trimethylchlorosilane for hydrophobicity to reduce adhesion.The 2 × 2 printed electrode array was designed by CAD and prepared by a screenprinting process.The printed electrode array was obtained by printing conductive silver paste on 38-μm-thick PET and then heated at 80 °C for 2 h to improve conductivity and adhesion.PDMS with a 5:1 ratio of primary agent to curing agent was spin-coated onto the silicon mold at 2000 rpm for 40 s.Then, the printed electrode was covered on the surface and heated at 90 °C for 3 h, and the silicon mold was detached to obtain the printed electrode containing the triangular pyramid PDMS microstructure.Similarly, PDMS with a 5:1 ratio of primary agent to curing agent was spincoated onto the silicone mold at 3500 rpm for 40 s.The surface of the silicon mold was covered with 125-μm-thick PET and heated at 90 °C for 3 h.Then, the PET was peeled off from the silicon mold to obtain the PET containing the triangular pyramid PDMS microstructure, and finally the Cr/Cu microstructure electrode was prepared by magnetron sputtering on the above triangular pyramid PDMS microstructure.
The bump mold was prepared by electrical discharge machining, and the bump was obtained by pouring PDMS with a 5:1 ratio of primary agent to curing agent into the bump mold and curing PDMS by heating at 90 °C for 5 h.The length and width of the bump are 6 mm and the height is 1 mm.The printed electrode array with triangular pyramid PDMS microstructure and Cr/Cu microstructure electrode are packaged top and bottom in microstructure orthogonality.And the bump was attached to the printed electrode layer to complete the preparation of the flexible triaxial force capacitive sensor.
Integration of Force Sensing System: The flexible triaxial force capacitive sensor was integrated into the gripper of the end of the minimally invasive surgical actuator to detect triaxial force during gripping the bionic tissue.The gripper was fixed on a rail that was lifted and lowered by motor control.And clamping and relaxation of the gripper was controlled by the Phantom Omni operating master hand.The force sensed by the sensors on the clamp gripper can be fed back to the physician through the Phantom Omni TOUCH operating master hand to determine the tightness of the gripper.The flexible triaxial force capacitive sensor was also integrated into the contact bar to detect the touching force of bionic tissue.The contact bar was prepared by 3D printing.The simulated bionic tissue was touched at different dimensions to assess the magnitude of the triaxial force after integrating the flexible triaxial force capacitive sensor.
Characterizations and Measurements: The Z-axis displacement stage and the Mark-10 force gauge were used to load pressure to the flexible triaxial force capacitive sensor.A TH2838 LCR digital bridge was used to test the performance of the unit of the triaxial force capacitive sensor, and the test frequency was set to 1 MHz.The microstructure was characterized by field emission scanning electron microscopy (VEGA3 TESCAN) at a high voltage and magnification of 10 kV and 1200 times, respectively.
The six-axis force sensor ATI-Nano17 was used to calibrate the triaxial force capacitive sensor.The ATI-Nano17 and the triaxial force capacitive sensor were fixed on the 3D printed base by resin.To precisely control the magnitude and direction of the applied force, the test platform was fixed on an optical stage.The triaxial force was measured by changing different positions of the three-axis displacement stage.The test platform of the whole system was shown in Figure S7 of the Supporting Information.The signal of the sensor array was measured by a homemade capacitance measurement circuit, including a microcontroller Arduino, a single-blade double-throw switch SN74LVC1G3157, a capacitance digital conversion chip AD7746, and a display interface on the PC.To measure the capacitance of the sensor array, the single-blade double-throw switch SN74LVC1G3157 was used to select the different channels.The test end of AD7746 was connected to the four sensing units and the single knife double-throw switch SN74LVC1G3157.By controlling SN74LVC1G3157 on or off through Arduino, the four sensing units were measured in turn.And then the collected data were transferred to Arduino through an I 2 C communication protocol.Finally, the measurement data were transferred to the PC via serial communication, and the information of the triaxial force was displayed on the PC in real time.

Figure 2 .
Figure 2. Fabrication process of the flexible triaxial force capacitive sensor.

Figure 3 .
Figure 3.The performance of the unit sensor.a) Pressure-relative capacitance change rate curve.b) Dynamic stability at a pressure of 0-3 N. c-e) Hysteresis curve, stability under 1000 cycles of loading and unloading pressure and stability at curvature radii of 10, 15, 20, 25, and 30 mm.

Figure 4 .
Figure 4. Schematic sensor structure and performance of the triaxial force sensor.a) The structure of flexible triaxial force capacitive sensor.b) Signal acquisition circuit.c-e) Triaxial force calibration of the sensor.
to the capacitance calculation formula (d = S/C ), the spacing parameters can be obtained.The spacings between the electrodes of the four sensing units C1, C2, C3, and C4 are defined as d 1 , d 2 , d 3 , and d 4 , where three spacing parameters d X , d Y , and d Z are defined in the triaxial force.The parameters d 1 , d 2 , d 3 , and d 4 of the four sensing sensors and the three spacing parameters d X , d Y , and d Z of the triaxial force are calculated as follows

Figure 5 .
Figure 5. Functional relationship between triaxial force and spacing parameters.a-c) Test results between triaxial force and spacing parameters.d-f) Function fitting between triaxial force and spacing parameters.

4 Z
applications (d X < 0, d Y < 0), then the functional relationship can be obtained by symmetry.By fitting the function of the three spacing parameters and the triaxial force, the functional relationship between d X , d Y , and d Z and F X , F Y , and F Z can be obtained as follows F Z = 0.303d Z + 19.478d 2 Z − 311.94d 3 Z + 2325.589d

Figure 6 .
Figure 6.Real-time triaxial force when gripping bionic tissue.a-c) F Z , F Z and F X , F Z , and F Y .d) The force feedback of the Phantom Omni operating master hand.

Figure 7 .
Figure 7. Real-time triaxial force when touching bionic tissue.a-c) F Z , F Z and F X , F Z , and F Y .