Abstract—A miniature tri-axial force sensor has been developed that complies with the requirements of integration into biomedical and robotic devices due to its size and accuracy. The sensor is a machined Titanium alloy body of the overall dimensions 8.6 × Ø3.4 mm with semi-conductor strain gauges embedded on it. The sensing beam’s size is 1 × 1 × 4.4 mm. We present here the design, calibration method and performance evaluation of our sensor. Properly calibrated, it can provide absolute resolution of 5 mN at 2 N full scale. The accuracy of the estimated angle of incidence is ± 1˚. The measured magnitude of the force is within the ± 4 % range of the actual one. At maximal load the accuracy of the shear angle is ± 1˚.

Index Terms- Force Sensor, Piezoresistive, Tri-Axial, Medical Robotics, Minimally Invasive Surgery

I. INTRODUCTION Multi-axial force sensors/torque sensors are often used for

feedback in surgery [1, 2]. Force information allows the surgeon to control the position of the surgical instrument and the magnitude and direction of the applied force.

Force feedback can be beneficial in minimally invasive surgery (MIS) which gains popularity because it reduces hospitalization time and post operative trauma. The cumbersome laparoscopic instruments, however, limit the surgeon’s ability to control the applied force. The absence of force feedback results in less precise tool navigation and higher risk of collateral damage during the intervention. The solution is embedding a multi-axial force sensor in the MIS tools and providing the surgeon force feedback.

Minimally invasive robotic surgery (MIRS) further increases MIS advantages by offering increased precision and reliability by extending the force sensitivity beyond the surgeon’s threshold of perception [3].

Our sensor can be installed at the tip of a robot and enable direct measurement of the contact force vector acting on the MIS/MIRS tool during tissue manipulation (See Fig. 1).

Recently, many 3D force sensors have been developed for MIS, however there is still a need for a solution that meets the size limitations, covers the critical force range and can be operated in surgical environment. Peirs et al. [4]

Manuscript received April 27, 2012. P. Baki is with the Computer Vision Laboratory, Department of

Information Technology and Electrical Engineering, ETH, Zurich, Switzerland (email: bakip@vision.ee.ethz.ch).

G. Székely is with the Computer Vision Laboratory, Department of Information Technology and Electrical Engineering, ETH, Zurich, Switzerland (email: szekely@vision.ee.ethz.ch).

G. Kósa is with the Robots and BioMedical MicroSystems (RBM2S) Laboratory, School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Israel (email: gkosa@post.tau.ac.il).

Fig. 1. Drawing of a miniature force sensor integrated in a minimal invasive biomedical device. Exploded (above) and assembled (below) views of the different assembly parts: miniature 3 DoF force sensor (1), Ø 0.5 mm fiberscope (2) going through the sensor, cover cap (3) screwed to the sensor’s upper part, an adapter to the (4) endoscope or a minimally invasive tool screwed to the lower part of the sensor and a miniature O ring (5) to seal the gap between the cap and the adapter.

performed in vivo experiments and showed that for MIS the needed force range is from 0 to 2.5 N with 10 mN resolution.

Beccai et al. [5] developed a silicon-based piezoresistive 3D (two force and one torque, or three force components) which they used for biomechanical measurements [6] and integrated into a minimally invasive surgical tool [7]. The resolution of the sensor is 3 mN for tangential loadings and 20 mN for normal loadings at full scale of 2 N. The sensor's size is 2.3 mm × 2.3 mm × 1.3 mm and it is assembled in a special packaging so the applied forces are transferred to the sensor body.

Seibold et al. [8] suggested a Stewart platform as a 6D sensor to be installed at the tip of a minimally invasive surgery tool. The sensor's size was Ø10 mm. Its accuracy was 300 mN at full scale of 3 N and showed about 10 % crosstalk. Puangmali et al. suggested a tri-axial optical fiber structure that was used to perform tissue palpation [9]. The sensor is composed of nonmetallic parts and therefore compatible with magnetic resonance imaging (MRI). The sensing principle is optical intensity modulation due to the movable reflector’s dislocation. The overall diameter of the sensor is 10 mm that makes it too big for MIS. The sensor’s resolution is 50 mN at full scale of 2 N. Peirs et al. [4] presented a tri-axial force sensor for MIRS. The introduced sensor is based on a flexible Titanium structure, the deformation is measured by three optical fibers. The sensor’s resolution is 10 mN at 2.5 N full scale, however, it has a

Miniature Tri-Axial Force Sensor for Feedback in Minimally Invasive Surgery

Péter Baki, Gábor Székely, Gábor Kósa

3

1 2

5

4

diameter of 5 mm which is too big for e.g. intra-vascular applications. Weizhong et al. [10] introduced a tri-axial tactile force sensor based on piezoresistive principle. The MEMS structure showed very high sensitivity in low force range (3 µN), however can measure only up to1 mN, far too small for the typical force range of MIS (it is about 2 N, [4]). The sensing element’s size is 4 mm × 4 mm × 0.4 mm. Hu et al. [11] developed a 3D tactile sensor for MIS inspired by the principle of hair cells. The silicon sensor is based on the piezoresistive principle, the high aspect ratio provides increased shear sensitivity. 4 sensors form a 2 × 2 array, each sensor has a size of Ø390 µm × 470 µm. As the full scale of this sensor is in the mN range, it can only be considered for microsurgical applications.

In comparison to the sensors above our sensor presents a robust structure, miniature size, high accuracy and proven ability in measuring forces in 3D. The Ti structure reduces the temperature sensitivity which is further reduced by signal processing. The sensor has a through work channel of Ø 0.8 mm which enables wiring and tools to go through the sensor.

In this paper we focus on the design and calibration of a novel multi-axis force sensor for MIS. Our sensor provides force data that are comparable to the commercially available ones in terms of full range and resolution (see Table I). We developed a multiple degrees of freedom device that meets the size requirements of MIS and the structure makes it possible to further decrease the size without affecting the sensor’s performance. The sensing element is a monolithic Ti alloy beam which is advantageous in magnetic environments.

TABLE I

SENSOR SPECIFICATION

ATI Nano 17 Our sensor

Full Scale 12 N 2N Resolution 3.125mN 5mN Bandwidth >1kHz >1kHz Size Degrees of Freedom

14.5×Ø17 mm 6

8.6×Ø3.4 mm 3

This paper is structured as follows. Section II describes

the sensor model, the sensing principle, the mechanical and electrical properties as well as the basics of the signal conditioning circuit. Section III gives a brief introduction of the calibration setup and further considerations concerning the sensor’s evaluation are discussed. Section IV offers insight to the applied calibration algorithms and the achieved results. In section V a short conclusion summarizes our work and details possibilities for further improvements.

II. MODEL AND DESIGN

A. Sensor Model Our sensor design is based on a hollow beam that converts

the applied force to mechanical strain. The sensing element can be modeled as an Euler–Bernoulli beam. The interacting

A B C

Fig. 2. Mechanical drawing of the force sensor (A). Image of the monolithic Ti sensor beam (B) and the gauged force sensor (C). forces create bending in the shear directions and axial displacement (compression) in the normal direction .

Using the assumptions of the Euler-Bernoulli beam theory [12], we find the theoretical sensitivity of the sensor. The sensitivity due to bending is

xi

sgfsgiFt FYDBH

HLLLGSx

)316()2(48

43)(

π−+−

= (1)

and

yi

sgfsgiFt FYDHB

HLLLGSy

)316()2(48

43)(

π−+−

= . (2)

The sensitivity due to the application of an axial force is:

Zi

Ft FYDBH

GN)4/( 2

)(

π−= . (3)

where sgiL is the lowest point of the strain gauge (see Fig. 2 A), L is the length of the beam, sgfL is the highest point of the strain gauge, H is length of the beam’s face normal in Y, B is the length of the beam’s face normal in X direction, iD is the diameter of the inner hole, GF is the gauge factor and Y is the Young modulus of elasticity. The ratio between )(tSx (or )(tSy assuming a square beam cross section) and )(tN indicates the anisotropic nature of the sensitivity because of the beam like structure:

44

22

)(

)(

316)2)(4/4(12

i

sgfsgii

t

t

DHLLLDHH

NSxr

ππ

−+−−

== . (4)

For example, for the current design (L=4.4 mm; sgiL =1.7 mm; sgfL =1.9 mm; H=B=1 mm; iD =0.8 mm; Y=113.8 GPa) the sensitivity in the X and Z directions is:

2.10]67.17,180[],[ )()( =⇒= rNSx tt . (5) Omitting the inner through hole, iD =0 will result in:

6.15]8.8,137[],[ )()( =⇒= rNSx tt . (6) Consequently in addition to system integration advantages (channel leading to parts in front of the force sensor) the through hole increases the absolute sensitivity and its isotropy in the sensor.

B. Sensor Design In order to make the calibration easier, a monolithic

structure has been designed that consists of a base, the sensing beam itself and a threaded tip which serves fixing purposes (see Fig. 2 B). The metal part has been fabricated by wire electrical discharge machining (EDM). The beam has the size of 1 mm × 1 mm × 4.4 mm and there is a concentric Ø0.8 mm hole along its symmetry axis. FEM analysis showed that the sensor body can endure 10 N load. The force range is scalable by modifying the geometrical parameters. Semiconductor strain gauges manufactured by Micron Instruments Ltd. are used to convert the mechanical strain to electrically measurable signal which is resistance change due to piezoresistive effect. We chose this type of gauges because of their high gauge factor, small size and high linearity over a wide strain range. According to the manufacturer, the SS-027-013-500P gauge has resistance of 540 ± 50 Ω and a gauge factor of 155 ± 10. The thermal coefficient of the gauge factor is -0.324 1/C˚, whereas of the resistance is 0.432 1/C˚ at room temperature. The gauges are operating in three Wheatstone bridges so the sensitivity of an overall bridge is higher than of the single elements. The bridges are driven by DC voltage. The strain gauges are temperature compensated by the gauging company. In order to reduce the influence of temperature we used Ti6Al4V alloy which has a fairly low thermal expansion coefficient, 8.6 μStrain/C˚. Furthermore, this material is biocompatible and widely used in biomedical devices. Even though EDM and the assembly of strain gauges are costly technologies the fabrication expenses can be decreased significantly by automation of the assembly and large scale production. Our estimate is that the cost of the sensor could be reduced to a couple of hundred US dollars.

C. Electrical Design The shear forces (Fx and Fy) are measured by two half

Wheatstone bridges (Sx and Sy respectively) which are completed externally by additional resistors to form full bridges. Since the bending moment increases linearly from the tip to the base, the strain gauges are exposed to uneven strain distribution. In practice it means the strain’s average over the surface that is covered by the gauge. The strain gauges are placed close to the base where the bending strain is maximal (see Fig. 3). Both pairs of gauges are assembled on the sensing part in a way that the corresponding gauges are put on opposite sides of the beam. Therefore, the two shear base directions can be determined. Each half bridge contains two vertically fixed gauges which ensures that axial displacement has no effect on the shear force measurement.

The normal force Fz is converted into axial displacement and measured by a full bridge, N, which is positioned at the half height of the beam. The bridge consists of 4 strain gauges, two of them are in horizontal whereas the other two are in vertical orientation. We are interested in measuring the compressive strain, but experimental results revealed that this structure shows sensitivity in case of bending as well. We corrected this crosstalk by the signal processing as detailed later.

Fig.3. Strain gauges on the Euler-Bernoulli beam. The normal force component is measured by a full Wheatstone bridge (N), whereas the shear half bridges (Sx and Sy) are completed externally.

A piezoresistive strain gauge bridge produces an output voltage in the range of 100 mV. Such a low voltage cannot be sent directly to an AD stage, thus signal conditioning is required. We have developed a circuit that is responsible for the signal conditioning, data acquisition and communication. There are three input channels for the two bending and the axial displacement measurements. The analog input stage of each channel is an AD8221 precision instrumentation amplifier with high common-mode rejection ratio. No analog filter is used in the system. As the axial displacement sensitivity is significantly lower than in the shear directions, different gains have been applied to them: 150 for the normal and 25 for the shear channels. The amplified signal is then sent to the AT90USB1287 microcontroller’s integrated AD channels where the data conversion takes place at 10 bits. The acquired data is sent to the computer via RS232 serial port. The first natural frequency of the beam is 32.847 kHz and the maximal obtainable refresh rate for all the three channels is over 1kHz.

A LabVIEW virtual instrument displays the data and stores them in a file. The recorded data are then post-processed in Matlab. A primary focus of interest for us was to find a method allowing transforming the sensor’s raw signals to 3D force data, which are actually acting on the sensor. Once the corresponding calibration is performed, the signal processing can be carried out in real-time by the microcontroller.

III. CALIBRATION PROCESS AND SETUP In order to gain actual 3D force data, the sensor had to be

calibrated. An external force vector was applied on our sensor from various directions and we compared the readout of the 3 bridges to the force measured by the ATI Nano 17. We intend to mount the force sensor at the tip of a catheter or another medical tool. The sensor’s location and size enables modeling the contact interaction of the tool with the tissue as a point force acting on the axes of the sensor. This assumption allows us to neglect the torque applied on the sensor. As the length of the beam is relatively short, this approach is capable of characterizing the sensor. We have introduced a model in which the sensor tip is the origin and all the interacting forces have radial direction (see Fig. 4).

Fig. 4. Physical model of the measurements: the applied force is defined by its shear angle (Φ), angle of incidence (θ) and force magnitude. Three independent degrees of freedom have been selected in order to implement the aforementioned calibration model: the shear angle Φ, the angle of incidence θ and the translation in radial direction F . The latter one is a 1 DoF movement and the applied force is measured by a standard force sensor that is in interaction with our sensor. This way, in a given solid angle domain, arbitrary shear angle - angle of incidence combinations [θ, Φ] can be set up and the interacting force’s magnitude is also known. After making recordings from defined directions one can find the relationship between the sensor’s recorded data and the given angular setup.

We have built a calibrating setup so that the necessary measurements can be done in a repeatable and precise manner (see Fig. 5). The design consists of aluminum parts in order to provide a rigid structure which serves as a frame for our experiments. One rotational degree of freedom is implemented by a disc on which the sensor is assembled. By rotating this element the shear angle can be set to the desired

Fig. 5. Calibrating mechanism presenting 4 degrees of freedom: two rotational and two translational. The red arrow corresponds to the angle of incidence (θ), the yellow to the shear angle (Φ) and the blue to the sliding movement. There is a fourth translational DoF (green) which ensures that the interaction point is on the Nano 17’s symmetry axis.

value. The angle of incidence is adjustable by tilting the base of the disc. The third, translational degree of freedom is implemented by a slide. There is an ATI Nano17 6 DoF force sensor assembled on the moving part so the interacting force is always directed toward it. As the slide with the Nano17 has only one DoF and the interaction point is intersected by the Nano17’s length axis no shear forces or torques occur. For this reason, the normal force component of the ATI sensor is identical to the absolute force that is applied on our sensor's tip. In order to achieve isotropic load we fixed a hemisphere shaped metal cap on the thread. In our experience the cap does not introduce additional stress on the column. Even in case if no cap, the occurring torque is not significant owing to the short sensing beam.

IV. CALIBRATION RESULTS The following analysis investigates the possibilities of

assessing the applied 3D force based on the sensor’s data. The primary goal of this step is to reveal the cross-dependencies in our sensor’s raw data and to find a model which makes it possible to calculate the actual forces with satisfying accuracy. All the experiments were performed using the calibration device described in section III. Fig. 6 shows the bridge outputs in a fixed orientation as functions of the applied force. One can see that a 1 DoF force interaction results in a linear force trajectory. Therefore, recording the outputs with the same constant load we can determine the sensitivity in a given direction. The initial experiments showed that there is no observable drift of the signals. The peak-to-peak noise of 15 mV is canceled by digital filtering of the oversampled signals.

We use the slide’s own weight of 2.62 N as a constant load for the calibration experiments. During the experiment continuous recordings are made at different shear directions while θ ranges from 0 to 30° in 5° steps measured from the sensor’s orthogonal direction (see Fig. 7). Taking the average of the values measured at constant load we got static points in the parameter space of the raw signals. One can see in Fig. 8 that at different shear angle setups the recorded points at the orthogonal direction deviate from the origin (Sx, Sy=0).

Fig. 6. Typical force trajectories of the amplified bridge signals. Constant force direction results in linear curves.

Slide

Nano17

RotationAxis Φ

RotationAxis θ

Tri-Axial Force Sensor

Fig. 7. Bridge sensitivities as a function of the angle of incidence. The measurements presented are: X shear force (blue circle); Y shear force (red square) and Z axial force (black triangle).

Fig. 8. Recorded points in the shear plane. The measurements were made in 8 shear directions with the angle of incidence ranging from 0˚ to 30˚ with 5˚ steps (black circles). One can see that the closer the points are to the normal direction the more significant the shear angle error is.

Since these measurements were all made in the θ=0˚ direction with a constant load, the erroneously observed shear components around the origin are probably caused by the calibration mechanics mostly due to the slide’s imperfection. Since 3D force recording is extremely sensitive to any kind of deviation from the ideal conditions, we regard this phenomenon unavoidable. The experiments showed that the signal vector’s length is heavily dependent on its orientation. One would expect the recorded points to be on a spherical surface in the variable space [Sx, Sy, N] as the load is constant and only the direction varies. Fig. 9 demonstrates the angular dependency of the measured vector’s magnitude. Unlike the standard LLSE method, our approach takes this effect into consideration. In order to take into account the high certainty of signals Sx and Sy compared to N (caused by the sensitivity difference (4)) we converted the Cartesian coordinates into spherical ones:

= −

SxSy1tanφ , (7)

+= −

22

1tanSySx

Nθ , (8)

222 NSySxR ++= . (9)

This step is necessary in order to exploit the higher accuracy of Sx and Sy due the higher sensitivity of the sensor in the bending direction. In the original parameter space the magnitude sensitivity depends on all three parameters, whereas after the transformation it is only dependent on the angular components. As a result, the recorded static points span a surface that can be approximated by a 4th order, two variable polynomial (see Fig. 10):

( ) ji

i jijR aP φθφθ ∑∑

= =

=4

1

4

1, . (10)

Therefore, if the calculated angle of incidence and shear angle are known, the force magnitude can be determined:

( ) 17,~

NanoR

FP

RRφθ

= , (11)

where FNano17 is the force measured by the Nano 17 sensor. The angle of incidence which is obtained from the measurements, can be calculated in the same way:

( ) ji

i jijb φθφθθ ∑∑

= =

=4

1

4

1,~ . (12)

Knowing the calculated shear angle (7), the estimated force magnitude (11) and angle of incidence (12), the 3D force vector can be deduced using a spherical to Cartesian coordinate transformation:

Fig. 9. Illustration of the cross dependency between the output signals of the bridges. The sensitivity of the normal bridge varies in different shear directions.

Fig. 10. Recorded points and the estimated surface as a function of the calculated shear angle (Φ) and angle of incidence (θ). The force scaling factor represents the ratio between the calculated magnitude (R) and the actual force in a given direction.

)cos()~sin(~ φθRFx = , (13)

)sin()~sin(~ φθRFy = , (14)

)~cos(~ θRFz = . (15) The calibrated data are in accordance with the theoretical values as demonstrated in Fig. 11. The angle of incidence and the shear angle both can be determined with ±1˚ accuracy and the force magnitude is within the ± 4 % range as shown in Fig. 12.

Fig. 11. Illustration of the recorded points in the actual force space relative to the calibrating load (2.62 N). The red crosses are the target values and the black circles are the measured ones, respectively.

Fig. 12. Recorded points in 4 shear directions relative to the calibrating load.0˚ (red circle), 45˚ (blue square), 90˚ (black diamond), 135˚ (cyan triangle). As each measurement was carried out by applying constant load (2.62 N), the measured points are expected to be on the arc. The radial lines represent the angle of incidence in 5˚ steps.

V. CONCLUSION AND FUTURE WORKS A novel piezoresistive tri-axial force sensor has been

developed which can be manufactured by conventional fabricating technologies. The robust structure and the size of the sensor make it possible to integrate it into a catheter of the size of 11 Fr (3.67 mm).

In spite of its miniature size the sensor's measurement performance is comparable to large size, commercial multi-axial force sensors (e.g. ATI Nano 17). The introduced calibration method allowed achieving angular and magnitudinal accuracy, which makes it possible to use the 3D force sensor in any application in which both precision and small sensor size play a significant role.

We achieved an absolute resolution of 5 mN using a calibrating load of 2.62 N. After appropriate calibration the accuracy of both the angle of incidence and the shear angle is ± 1˚ and the magnitude of the force can be determined

with ± 4 % error. Integration of the sensor in minimally invasive surgical instruments is currently ongoing. Covering the sensor body with biocompatible silicone will prevent environmental impacts and make sterilization possible without influencing the performance of the sensor.

In the future we intend to further increase the sensor’s performance by redesigning the gauging in order to achieve isotropic sensitivity. We also intend to further reduce the size of the sensor. In addition we plan to improve the calibration setup in order to reduce measurement errors.

ACKNOWLEDGMENT This work was supported by the Swiss National Science

Foundation within the frames of the NCCR CO-ME project. We thank the Elizabeth and Nicholas Slezak Super Center for Cardiac Research and Medical Engineering for their generous support.

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