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Abstract
During retinal microsurgery, excessive interaction force between surgical instruments and intraocular tissue can cause serious accidents such as tissue injury, irreversible retinal damage, and even vision loss. It is essential to accurately sense the micro tool-tissue interaction force, especially for the Ophthalmic Microsurgery Robot. In this study, a fiber Bragg grating (FBG) three-dimensional (3-D) micro-force sensor for micro-forceps is proposed, which is integrated with the drive module as an end-effector and can be conveniently mounted onto the ophthalmic surgical robot. An innovative axial force sensitivity-enhancing structure is proposed based on the principles of flexure-hinge and flexible levers to overcome the low sensitivity of axial force measurement. A dual-grating temperature compensation method is adopted for axial force measurement, which considers the differential temperature sensitivity of the two FBGs. Three FBGs are arranged along the circumference of the guide tube in this study to measure transverse forces and compensate for effects caused by changes in temperature. The experimental results demonstrate that the micro-forceps designed in this study achieved a resolution of 0.13 mN for transverse force and 0.30 mN for axial force. The temperature compensation experiments show that the 3-D micro-force sensor can simultaneously compensate for temperature effects in axial and transverse force measurement.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The incidence rates of vision-related diseases, including retinal detachment, age-related macular degeneration, macular hole, vitreous hemorrhage, epiretinal membrane, and diabetic retinopathy, have been steadily increasing. The combined annual incidence rates of early and late age-related macular degeneration were 1.59 per 100 person-years [1]. Globally, there are approximately 537 million people with diabetes, and around one-third of them are at risk of developing diabetic retinopathy [2]. Patients with these diseases require immediate and essential retinal microsurgery to restore their vision effectively.
Typical retinal microsurgery tasks such as retinal vein cannulation, vitrectomy, and internal limiting membrane (ILM) peeling require accurate manipulation in the limited space inside the eye. Taking ILM peeling as an example, the procedure [3] can be divided into two main steps: first, the surgeon uses a sharp-tipped surgical instrument to create an initial flap on the ILM, which is only 0.5-2.5 µm thick. Then, the forceps are used to remove the desired membrane area. Although experienced clinicians have professional skills and capabilities only acquired through extensive training, performing these delicate operations during surgery remains challenging for them. The application of surgical robots is considered extremely promising to enhance the safety and stability of retinal microsurgery. Including teleoperated [4–8], cooperatively controlled [9–11], handheld [12], and so on, various surgical robots for retinal microsurgery have been investigated. To overcome the limitations of state-of-the-art designs related to the misalignment between the sclera incision and the remote center of motion, a 5-DOFs Robot with a novel double articulated parallelogram design has been proposed in our research group [13].
Research indicates that during retinal microsurgery, approximately 75% of manipulation events exerted forces below 7.5 mN, with only around 19% of these events being detectable [14]. Excessive interaction forces between surgical instruments and intraocular tissue during retinal microsurgery can result in severe accidents, including tissue injury, irreversible retinal damage, and vision loss. Accurately sensing the micro tool-tissue interaction force is essential for enhancing the safety and reliability of retinal microsurgery and preventing potential ocular damage caused by ophthalmic surgical robots. Various force sensors integrated into surgical instruments have been investigated for measuring the micro-force between the intraocular tissue and the surgical instrument. Fiber Bragg grating (FBG)-based force sensors have been widely preferred by researchers due to the unique benefits of FBGs, including high sensitivity, immunity to electromagnetic interference, compact dimensions, and the ability to measure multiple points simultaneously. A series of studies on the micro-force perception of ophthalmic instruments has been carried out at Johns Hopkins University, including the 1-axis force sensing prototype [15], the 2-DOF force sensing hook tool [16,17], the 2-DOF force sensing micro-forceps [18,19] and the 3-DOF force sensing instrument [20–22]. In these investigations, from one to three FBGs with a diameter of 80 µm were employed to measure forces for commonly used surgical instruments such as hooks and forceps. However, the root mean square (RMS) errors of axial forces can be as high as 1.68 mN, indicating the need for further improvement. Moreover, appropriate compensation methods need to be investigated to reduce force measurement errors induced by temperature fluctuations. Abushagur et al. [23,24] proposed a combination of tapered and normal FBGs for detecting surgical needle forces. Their study demonstrated that the tapered FBG could enhance axial force sensitivity and reduce the impact of transverse forces during tissue-needle interaction in vitreoretinal microsurgery. In the investigation, a tapered FBG with a minimum diameter of 40 µm was used, and the sensing point was suspended in the air. Thus, further improvement is needed to enhance the stability of the scheme. Zhang et al. [25] proposed an FBG configuration strategy where three FBGs are attached to the exterior of the tube shaft instead of being positioned at the center. This configuration enables the integration of 3-DOF force sensing into the retinal surgical microneedle, which also accommodates a hollow channel for the injection tube. However, the overall diameter of the microneedle is 0.9 mm, which exceeds the diameter of surgical instruments typically employed in ophthalmic microsurgery. Zhang et al. [26] presented an intraocular continuum manipulator that integrates three outer FBG strain sensors, enabling 3-DOF force sensing capabilities. However, the operative instrument of the manipulator is a surgical hook, which is incapable of performing ILM peeling. Micro-forceps are essential and indispensable tools in ILM peeling surgery [27]. Gonenc et al. [28,29] developed an electric micro-forceps with force-sensing capabilities and active tremor-canceling. However, it can only measure transverse forces. These studies confined the micro-force sensing unit to the body of small ophthalmic surgical instruments, thereby limiting the performance of force sensing in terms of sensitivity and range. Specifically, micro-forceps, which is an essential and commonly used surgical instrument, consist of a guide tube and forceps. In current 3-D micro-force measurement research for the micro-forceps, an FBG is embedded in the core of the forceps, resulting in low sensitivity for axial force measurement and the inability to perform temperature compensation directly.
To address the limitations above in measuring 3-D micro-force for micro-forceps, a novel FBG-based 3-D micro-force sensor with axial force sensitivity-enhancing is proposed in this study. This sensor is seamlessly integrated with the micro-forceps and the drive module, serving as an end-effector, and can be conveniently mounted onto the Ophthalmic Microsurgery Robot. This work presents a significant contribution by introducing an innovative sensitivity-enhancing structure with stereo flexure-hinge type levers. This structure effectively improves the sensitivity of axial force measurement while mitigating the transverse force crosstalk. Additionally, the designed sensing structure allows for easy separation from the micro-forceps, enabling reusability. Moreover, to address the impact of temperature fluctuations on axial force measurements using FBGs, a dual-grating temperature compensation method is adopted. This method accounts for the differential temperature sensitivity of the two FBGs, offering a reliable approach that does not solely rely on the wavelength shift difference between them.
2. Design of the 3-D micro-force sensor
2.1 Design requirements
To meet the 3-D micro-force measurement requirements of the Ophthalmic Microsurgery Robot when intraocular micro-forceps are used, specific design requirements for the micro-force sensors are presented in Table 1. The end-effector of the Ophthalmic Microsurgery Robot, developed by our research group [13], needs to achieve rotational motion. Therefore, the design of the sensor sensitivity-enhancing structure is constrained to fit within a cylindrical volume with a diameter of 32 mm. The commonly used 23 Ga intraocular micro-forceps with a maximum outer diameter of 0.6 mm is adopted. In intraocular microsurgery, the recommended safety-critical for the contact force between surgical instruments and intraocular tissue is approximately 7.5 mN [14]. Therefore, the desired force range is set larger than 10 mN with a force resolution of less than 1 mN, similar to the configuration utilized in previous work [21,25].
Table 1. Design specification of the proposed 3-D micro-force sensor
2.2 Design of the 3-D micro-force sensor
In this study, the 3-D micro-force sensor for micro-forceps was designed and integrated with the end-effector. The mechanical structure of the proposed 3-D micro-force sensor and the end-effector is illustrated in Fig. 1. The end-effector comprises the gear connecting it to the robot, the fixed support, the axial force sensitivity-enhancing structure, the micro-forceps, and the actuation mechanism of the micro-forceps.
Fig. 1. The 3-D micro-force sensor for micro-forceps. (a) The end-effector. (b) The detailed arrangement of the FBGs on the guide tube. (c) Cross-section view of the guide tube. (d) Right-side view of the end-effector. (e) The detailed arrangement of the FBGs on the axial force sensitivity-enhancing structure. (f) The axial force sensitivity-enhancing structure.
For the measurement of transverse forces, the structure and size of the guide tube are taken into account. The guide tube is characterized by a hollow cylindrical configuration, with a remarkably small outer diameter of only 0.6 mm. Consequently, the FBGs can only be arranged on the outer surface of the guide tube in the axial direction. To minimize the impact of the FBGs on the structural integrity and size of the guide tube, it’s preferable to minimize the number of FBGs used. The center wavelength shifts of the FBGs arranged on the outer surface of the guide tube are influenced by four factors, including temperature variations and three components of the external force. Conventional methods typically require the arrangement of at least four FBGs to achieve decoupling. However, by uniformly arranging the three FBGs along the circumference of the guide tube, it is possible to eliminate the effects of axial force and temperature, and decouple two components of the transverse force. Detailed explanations of this measurement principle are provided in section 2.3. Therefore, as shown in Fig. 1(b) and Fig. 1(c), three FBGs are arranged at 120° intervals along the circumference of the guide tube to detect the transverse forces.
An innovative axial force sensitivity-enhancing structure based on straight-beam type flexure-hinge and flexible levers is designed to measure the axial force. As illustrated in Fig. 1(d) and Fig. 1(e), two FBGs are arranged at symmetrical positions on the upper and lower surfaces of the beam structure, respectively. This arrangement facilitates the measurement of axial forces and enables temperature compensation. The axial force sensitivity-enhancing structure is depicted in Fig. 1(f). The structure consists of three force amplification flexible levers distributed at 120° angles, forming a 3-D configuration that amplifies axial forces and reduces transverse force crosstalk. The three flexible levers amplify the input axial force by acting on the beam, causing strain, which is then transmitted to the FBGs.
2.3 Measurement principle
To sense the 3-D micro-force applied to the micro-forceps, FBG sensors are adopted and arranged based on the structure of the micro-forceps. The elastic strain and the temperature fluctuations are the most critical factors that affect the central wavelength shift of FBGs. The linear relationship between central wavelength shift and these two factors can be written as
- 1) Transverse Force Calculation: One end of the guide tube is fixed, and the other is subjected to the transverse force transmitted through the jaws. The elastic strain on the surface of the guide tube caused by the micro-force is transferred to the three FBG sensors and leads to the central wavelength shift of the FBGs. Considering the influence of ambient temperature fluctuations, the central wavelength shift of each FBG sensor can be expressed as$$\Delta {\lambda _i} = C_i^{{F_x}}{F_x} + C_i^{{F_y}}{F_y} + C_i^{{F_z}}{F_z} + {C^{\Delta T}}\Delta T,i = 1,2,3,$$where $C_i^{F_x}, C_i^{F_y}, C_i^{F_z}$, and CΔT are the constants associated with the Fx, Fy, Fz, and ΔT, respectively. The material characteristics of optical fibers and the bonding condition at the guide tube for each fiber are mostly similar. Therefore, it’s persuasive to assume that the temperature constant CΔT is the same for each FBG sensor. When three FBG sensors are arranged at 120° intervals along the circumference of the guide tube, the neutral plane of the guide tube caused by the transverse force passes through the center of the guide tube. The sum of the distance from the center of the guide tube to the center of each FBG on the compression side is equal to the sum of the distance from the center of the guide tube to the center of each FBG on the compression side. Consequently, the tensile strain and the compressive strain induced by the transverse force on the three FBGs are equal. In other words, the average central wavelength shift caused by the transverse force Fx and Fy can be eliminated [16,21]. Therefore, the common mode (Δλmean) only related to the axial force Fz and ambient temperature change ΔT can be written as follows:
By subtracting the common mode from the central wavelength shift, the remaining differential mode of each FBG sensor can be expressed as follows:
$$\Delta \lambda _i^{diff} = \Delta {\lambda _i} - \Delta {\lambda _{mean}} = C_i^{{F_x}}{F_x} + C_i^{{F_y}}{F_y},i = 1,2,3.$$From Eq. (4), a linear relationship between transverse force and the remaining differential mode of each FBG sensor can be observed. So transverse force can be calculated as follows:
where Ctr is a 2 × 3 coefficient matrix, which can be found through calibration experiments. - 2) Axial Force Calculation: The axial force sensitivity-enhancing structure is designed to be sensitive only to axial force and not transverse force. The axial force from the jaws is transferred to the axial force sensitivity-enhancing structure resulting in the elastic strain on the upper and lower surfaces of the beam. The elastic strain is transferred to the optical fibers arranged on the beam’s upper and lower surfaces leading to the central wavelength shift of FBG sensors. According to the deformation law of the beam with one end fixed and one end simply supported, the central wavelength shift of FBG sensors can be expressed as follows:
Due to the arrangement of the FBGs on the upper and lower surfaces of the beam, it is difficult to ensure consistency during optical fiber bonding, which can result in inconsistent force sensitivity coefficients and temperature sensitivity coefficients for the two FBGs. Owing to the arrangement of the two sensing points, the axial force can be directly solved as follows:
3. Optimization and simulation
3.1 Optimization of the axial force sensitivity-enhancing structure
To improve the axial sensitivity of the micro-force sensor, the key parameters of the axial force sensitivity-enhancing structure were optimized based on finite element simulation using Ansys Workbench (ANSYS, Inc., Pennsylvania, US). The detailed parameters are shown in Fig. 2. The strain in the axial force sensitivity-enhancing structure generated by the input force can be transferred to the optical fiber, causing the central wavelength shift of the FBG sensors. Therefore, the maximum strain in the optical fiber glued on the upper surface of the beam is selected as the objective function of optimization when the external axial force is set as 7.5 mN. The corresponding variation ranges and constraints of the key parameters for the axial sensitizing structure have been set properly, as shown in Table 2. The material utilized for fabricating the sensing structure through 3-D printing is 4600 type (WeNext Technology Co., Ltd., Shenzhen, China). Young’s modulus and Poisson’s ratio of the material are set as 0.41 and 2.51 GPa, respectively. The physical parameters of the other components, including the optical fiber, the glue, and the micro-forceps, are shown in Table 3.
Fig. 2. The optimization parameters of the axial force sensitivity-enhancing structure. (a) The front view of the axial force sensitivity-enhancing structure. (b) The top view of the axial force sensitivity-enhancing structure.
Table 2. The Variation Ranges and Constraints of Optimization Parameters
Table 3. Physical Parameters of the Components
The direct optimization module in ANSYS workbench software is used to optimize the design parameters of the axial force sensitivity-enhancing structure. In order to obtain a more reliable solution for the optimal design parameters, three built-in optimization methods in the direct optimization module, including multi-objective genetic algorithm (MOGA), nonlinear programming by quadratic Lagrangian (NLPQL), and mixed integer sequential quadratic programming (MISQP) are adopted and compared with each other. NLPQL and MISQP are gradient-based optimization methods for a single objective multi-variate optimization, whereas MOGA is population-based method for multi-objective global optimization. NLPQL works well for medium size and well-scaled problems [30]. Because NLPQL is a local single-objective optimization method, it’s sensitive to the starting point [31]. A good starting point can offer a better optimal design. The starting point of the final optimization process is determined manually based on preliminary optimization results using these three methods. The parameters after optimization are shown in Table 4. Among the three adopted methods, the NLPQL optimization method yields the most maximum strain. Therefore, the corresponding optimized parameters are selected as optimal values for utilization. The simulation results depicted in Fig. 3 compare the maximum strain of FBG 4 and FBG 5 before and after optimizing the axial force sensitivity-enhancing structure. After optimization, the maximum strain of FBG 4 and FBG 5 increased by 129% and 146%, respectively. These results clearly demonstrate the necessity and effectiveness of simulation optimization in enhancing the sensor's sensitivity.
Fig. 3. The maximum strain of FBGs before and after optimization of the axial force sensitivity-enhancing structure.
Table 4. The Optimal Design Parameters
The mechanical strength of the axial force sensitivity-enhancing structure is evaluated through simulation before and after optimization. The external forces are set to 7.5 mN and 25 mN. Both tension and compression directions are included in the simulation. The maximum normal stress of the entire structure under each external force is obtained. The results in Table 5 indicate that the maximum normal stress of the structure increases after optimization compared to the pre-optimized state, but it remains significantly below the material's tensile strength of 38 MPa [32]. Therefore, the mechanical strength of the optimized structure greatly fulfills the application requirements.
Table 5. The Maximum Normal Stress of The Axial Force Sensitivity-enhancing Structure
3.2 Simulation of the proposed sensor performance
The sensitivity of the micro-force sensor relies on the length L and initial position S of the FBG. Hence, a finite element simulation is conducted to determine the optimal length and initial position of the FBG under static load. Due to the symmetric positioning of the two fibers on the axial force sensitivity-enhancing structure and the cyclic symmetry of the three optical fibers on the guide tube, only one fiber from each component is selected for simulation and analysis. In Fig. 4(a), the observation objects are chosen as optical fiber 4 on the upper surface of the axial force sensitivity-enhancing structure and the optical fiber 1 glued on the guide tube. To avoid the influence of scleral interaction forces, the FBGs on the guide tube are positioned at a distance of 24 mm from the tip of the forceps, considering the eyeball diameter of approximately 24 mm. For the simulation of axial force sensitivity, a load force of 7.5 mN is applied along the z-axis at the jaw's tip. Similarly, for transverse force sensitivity, a load force of 7.5 mN is applied along the y-axis. Figure 4(b) demonstrates the relationship between the average strain and the length of the FBG. Both optical fiber 1 and 4 exhibit a decreasing trend in average strain with increasing FBG length. To optimize the sensor's sensitivity, it is recommended to select the minimum length for the FBG. Consequently, a length of 3 mm is chosen for the FBG in conjunction with the FBG inscription technique. Figure 4(c) illustrates the relationship between the average strain and the initial position of the FBGs. Both optical fibers displayed a parabolic pattern, indicating an initial increase followed by a subsequent decrease in average strain with varying initial positions. Therefore, FBG 1 and FBG 4 are positioned at 3.5 mm and 2 mm, respectively, corresponding to their respective maximum average strain values.
Fig. 4. The influence of position and length on the average strain of FBGs. (a) The distribution of the optical fibers. (b) The relationship between the average strain and the length of the FBG. (c) The relationship between the average strain and the initial position of the FBG.
The sensitivity and cross-sensitivity characteristics of the 3-D micro-force sensor are analyzed through static simulations based on finite elements. Figure 5(a) shows that both FBG 4 and 5 achieve an axial force-induced sensitivity of 0.5 pm/mN within the load range of [0, 25 mN]. In contrast, the transverse force-induced sensitivity of FBG 4 and 5 is below 0.004 pm/mN. The corresponding crosstalk interference is determined to be 0.8%. As illustrated in Fig. 5(b), the maximum transverse and axial force-induced sensitivity of the three FBGs arranged on the guide tube are 9.32 pm/mN and 9.2 × 10−5 pm/mN, respectively. The corresponding crosstalk is nearly zero. The FBGs on the axial force sensitivity-enhancing structure exhibit high sensitivity to axial forces but low sensitivity to transverse forces. Conversely, the FBGs on the guide tube demonstrate the opposite characteristics. Therefore, the proposed 3-D micro-force detection scheme based on FBGs is considered feasible.
Fig. 5. The relationship between the external force and the average strain of the FBGs: (a) arranged on the axial force sensitivity-enhancing structure, (b) arranged on the guide tube.
Modal analysis and harmonic response analysis are carried out to analyze the dynamic characteristics of the proposed axial sensitivity-enhancing structure. It can be seen from Fig. 6(a) and Fig. 6(b) that the first two vibration modes of axial sensitivity-enhancing structure are the vibration of the forceps along the x and y directions, respectively, with an almost similar resonant frequency of 53 Hz. During the harmonic response analysis, simulations are conducted with an excitation frequency set at 100 Hz and an incremental interval of 1 Hz. The applied load along the z direction is 25 mN. As shown in Fig. 6(c), the maximum amplitude of the response is only 4 × 10−3 mm in the three directions at the frequency of 53 Hz. Thus, the operational bandwidth of the axial sensitivity-enhancing structure proposed in this investigation can be designated as 0-35 Hz. The upper limit is selected as two-thirds of the first-order resonance frequency based on established engineering practices. In practical ophthalmic microsurgery, the frequency of the force applied to the forceps is notably low and falls entirely within the prescribed operating bandwidth.
Fig. 6. The dynamic characteristics analysis of axial sensitivity-enhancing structure. (a) The first-order modal. (b) The second-order modal. (c) Harmonic response.
4. Experimental study
4.1 Fabrication and assembly
The major components of the proposed end-effector are manufactured using 3-D printing technology. Subsequently, the FBGs are glued to the axial force sensitivity-enhancing structure and the guide tube using medical-grade adhesive Loctite 4013 (Henkel, CT, USA). Since the FBG interrogator (FBG-scan 904, FBGS, GER) utilized in the study has a maximum channel capacity of only four, both FBGs with a length of 5 mm, positioned on the axial force sensitivity-enhancing structure, are inscribed on a single optical fiber. A novel spiral wrapping method is employed to arrange and secure the fiber onto the axial force sensitivity-enhancing structure, mitigating the impact of bending loss in the optical fiber on the demodulation of the FBG's central wavelength. The minimum radius of curvature for the entire curved fiber segment exceeds 7.5 mm, adhering to the minimum bending radius requirement for the specific fiber (Jinan Dahui Photoelectric Technology Co., Ltd, CHN) utilized in this investigation. Consequently, the two FBGs can work properly simultaneously. The initial position of the FBGs is selected at 2 mm according to the simulation results mentioned above. To improve the sensitivity of the axial force sensitivity-enhancing structure, the coating layer at the grating region of the fiber is removed. The fiber-bonded axial force sensitivity-enhancing structure is allowed an undisturbed period of 24 hours to facilitate the complete polymerization of the applied instant adhesive. A layer of Polydimethylsiloxane (SYLGARD 184, Dow Corning Co., Ltd, USA) is coated on the surface of the grating region to increase protection and avoid the fracture of the FBG. The fabricated axial force sensitivity-enhancing structure with the integrated FBGs is shown in Fig. 7(a). To guarantee that the fibers positioned on the guide tube are uniformly spaced at 120° intervals around the circumference, a positional fixture is devised and subsequently produced using 3-D printing technology. As depicted in Fig. 7(b), the guide tube and three optical fibers are threaded through the orifice of the positional fixture. The axial positions of the guide tube and fibers are meticulously adjusted to ensure uniformity before being affixed together using instant adhesive. Following complete curing of the adhesive, the positional fixture is removed. As illustrated in Fig. 7(c), the axial force sensitivity-enhancing structure, guide tube, forceps, actuation mechanism, and other associated components are ultimately integrated to form the end-effector of the Ophthalmic Microsurgery Robot, enabling precise 3-D micro-force measurements.
Fig. 7. The fabrication and assembly of the end-effector of the Ophthalmic Microsurgery Robot. (a) The axial force sensitivity-enhancing structure. (b) The guide tube. (c) The end-effector.
4.2 Temperature coefficients calibration
Before assembling the end-effector, the temperature coefficients of the FBGs arranged on the axial force sensitivity-enhancing structure and the guide tube are calibrated. The experimental setup is shown in Fig. 8, where the low-temperature thermostat (NingBo ShuangJia Instrument Co., Ltd., CHN) is used to create a constant temperature environment in the bath with a temperature fluctuation of ±0.05 °C. Considering the operating conditions of the sensors, the temperature calibration range for the FBGs on the axial force sensitivity-enhancing structure is established as 24-32 °C, with a 2 °C interval. Similarly, the temperature calibration range for the FBGs arranged on the guide tube is determined to be 24-32 °C, also with a 2 °C interval. The axial force sensitivity-enhancing structure and the guide tube are placed in the low-temperature thermostat and fully submerged in water. Each temperature is maintained for 15 minutes. The calibration experiments are performed three times in total. The FBG interrogator is configured with a sampling rate of 100 Hz.
The relationship between the central wavelength shift of the FBGs on the axial force sensitivity-enhancing structure and the guide tube and the temperature are shown in Fig. 9(a) and Fig. 9(b), respectively. The temperature coefficients of FBG 4 and FBG 5 are 70.65 pm/°C and 81.99 pm/°C, respectively. The temperature coefficients of FBGs on the guide tube are 26.75 pm/°C, 27.99 pm/°C, and 24.23 pm/°C, respectively.
Fig. 9. The relationship between the central wavelength shifts of the FBGs and the temperature: (a) FBGs on the axial force sensitivity-enhancing structure, (b) FBGs on the guide tube.
4.3 Axial force calibration
The force sensitivity coefficients of the two FBGs arranged on the axial force sensitivity-enhancing structure vary due to subtle differences in fabrication processes, such as bonding location and adhesive layer thickness. To determine their force sensitivity coefficients, calibration experiments are conducted for both tension and compression scenarios. Figure 10(a) illustrates the experimental setup for the axial force calibration. The axial force sensitivity-enhancing structure is secured using a fixture, and loading forces are applied via 5 washers. Each washer provides approximately 4.68 mN of force, and its weight is measured using a scale (Dongguan Shengheng Electronics Co., Ltd., CHN) with an accuracy of 0.001 g. To apply negative z-axis force (compression force), the axial force sensitivity-enhancing structure is inverted as shown in Fig. 10(b), and the loading force is applied through a holder with washers. Conversely, as depicted in Fig. 10(c), positive z-axis force (tension force) is applied using a metallic hook. The experiments are conducted with the axial force sensitivity-enhancing structure covered by a plastic box to minimize the influence of temperature. Each calibration experiment is repeated 10 times for both tension and compression scenarios. The calibration experiments are conducted to get the force sensitivity coefficients of FBGs. The force sensitivity coefficients of FBGs reflect the ratios between the shift of the FBG center wavelength and the axial external force that causes this shift. When the axial force sensitivity-enhancing structure is inverted, its weight only changes the initial value of the FBG center wavelength, and doesn’t affect the FBG center wavelength shift. Thus, the structure's weight doesn’t affect the calibration results.
Fig. 10. Experimental setup for the axial force coefficients calibration. (a) The calibration system. (b) The loading of compression force. (c) The loading of tension force.
As shown in Fig. 11(a), the force sensitivity coefficients of FBG4 and FBG5 are -0.9297 pm/mN and 1.0925 pm/mN, respectively. By integrating the temperature sensitivity coefficients of the two FBGs with Eq. (7), the axial force coefficient matrix can be expressed as follows:
Fig. 11. The results of axial force coefficients calibration: (a) the relationship between the central wavelength shifts of the FBGs and actual forces, (b) estimated axial forces versus actual forces, and (c) residual errors.
Thus, the estimated axial forces are obtained by Eq. (8). As depicted in Fig. 11(b) and Fig. 11(c), the estimated axial force exhibits a high degree of concordance with the actual forces. The linearity error is 2.26%, with a maximum absolute residual error of 1.13 mN and a root mean square (RMS) error of 0.37 mN. The resolution of the FBG interrogator is 0.3 pm. Combined with the axial force coefficient matrix, the resolution of the axial force can be calculated as 0.30 mN.
4.4 Transverse force calibration
The experimental setup for the transverse force calibration is shown in Fig. 12(a). To achieve uniform calibration in spatial angles, two rotation stages (Beijing Yongyu Lihui Technology Co., Ltd., CHN) are used to adjust the angle of force application with an accuracy of 0.01°. As depicted in Fig. 12(b), in the right-handed coordinate system, rotation about the z-axis is defined as the angle α and rotation about the y-axis is defined as the angle β. The range of angle α is from 0° to 360° with an interval of 15°, and the range of angle β is from 0° to 90° with an interval of 15°. To apply the external force, five aluminum washers, identical to those used for calibrating the axial force, are utilized. Hence, the force F applied on the tip of the micro-forceps can be expressed as
Fig. 12. Experimental setup for the transverse force coefficients calibration. (a) The calibration system. (b) The distribution of angle α and angle β.
Utilizing the least squares method and Eq. (5) with the collected calibration data, the matrix coefficients for the transverse force can be obtained as follows:
As shown in Fig. 13(a) and Fig. 13(b), the estimated transverse forces are closely conforming with the actual forces, with corresponding linear errors of 1.6% and 1.9% for Fx and Fy, respectively. The maximum absolute residual errors are 0.77 mN and 0.95 mN for Fx and Fy, respectively. The corresponding RMS errors are 0.26 mN for Fx and 0.24 mN for Fy. As shown in Fig. 12(c) and Fig. 12(d), the residual errors of the estimated transverse forces for Fx and Fy both exhibit a certain rotational regularity, which is caused by the non-coincidence of the z-axis of the forceps with the rotating axis of the rotation stage. Obviously, this non-coincidence is due to the assembly error of the end-effector. The transverse force resolution is up to 0.13 mN, as calculated by combining the resolution of the FBG interrogator and the maximum coefficient in the decoupling matrix for the transverse forces.
Fig. 13. The relationship between calculated transverse force and actual force: (a) along the x-axial, (b) along the y-axial, (c) the residual error along the x-axial, and (d) the residual error along the y-axial.
4.5 Validation
According to the calculation method of axial force and transverse force mentioned above, this study adopts two different methods to compensate for the effect of temperature change on the wavelength drift of FBGs in axial force and transverse force measurements, respectively. In the temperature compensation verification experiments, four load conditions, including a no-load condition, are established using three washers. For each load condition, a rapid and significant change in the ambient temperature is achieved by bringing a hot water cup close to the sensor. The wavelength shifts of the FBGs are recorded for 60 seconds with a sampling frequency of 100 Hz. For the axial force measurement temperature compensation verification experiment, the load is applied in the z-direction. Regarding the transverse force, the load is applied in the y direction. As shown in Fig. 14(a), the green arrow indicates that the temperature changes when the hot water cup is brought close to the sensor, resulting in the center wavelengths of FBG 4 and FBG 5 on the axial sensitivity-enhancing structure changing by approximately 10 pm. However, after temperature compensation, the estimated axial force fluctuations remain within 1 mN under the four load conditions, demonstrating the effectiveness of temperature compensation for axial force measurement. As shown in Fig. 14 (b), the center wavelengths of FBG 1, FBG 2, and FBG 3 used for transverse force measurement exhibit noticeable changes under the influence of the sudden temperature change. After temperature compensation, the estimated force fluctuations remain within 0.3 mN, confirming the effectiveness of the temperature compensation. Thus, these two approaches are highly efficacious in compensating for the effect of temperature change in axial force and transverse force measurement.
Fig. 14. The influence of temperature fluctuations on the central wavelength shifts and the estimation of the forces. (a) The FBGs on the axial sensitizing structure. (b) The FBGs on the guide tube.
Validation experiments are conducted to confirm the performance of the proposed 3-D micro-force sensors for micro-forceps, using a two-stage rotation table identical to the one used in the transverse force calibration experiment. The magnitudes and angles of force application are different. Three washers, each imposing a force of approximately 6.37 mN, are utilized as loads. The angles α are systematically varied from 0° to 360° at 20° intervals, while the angles β are varied from 0° to 80° at 20° increments. The experiment is repeated four times, resulting in a total of 864 measurements acquired from 72 unique orientations. As illustrated in Fig. 15 (a) and Fig. 15(b), the estimated transverse forces exhibit a high degree of concordance with the actual forces, as evidenced by the corresponding linear errors of 2.10% and 2.60%, respectively. As depicted in Fig. 15(d) and Fig. 15(e), the maximum absolute residual errors for Fx and Fy are 1.06mN and 1.32mN, respectively. The RMS errors are 0.32 mN and 0.30 mN for Fx and Fy, respectively. As shown in Fig. 15(c), the estimated and actual axial forces are closely matched, with a linearity error of 4.32%. As illustrated in Fig. 15(f), the maximum absolute residual error and the RMS error are 2.46 mN and 0.92 mN, respectively. Compared to the previous similar study [25], the RMS error has decreased by 40.26%, and the maximum absolute residual error has decreased by 38.25%.
Fig. 15. The estimated forces versus actual forces for (a) Fx, (b) Fy, and (c) Fz, and the residual errors of (d) Fx, (e) Fy, and (f) Fz.
4.6 Discussion
The axial force sensitivity-enhancing structure designed in this study employs two FBGs. Temperature calibration experiments indicate that the temperature sensitivity coefficient values of the two FBGs are dissimilar, differing by 11.34 pm/°C. This difference is attributed to the inconsistent thickness of the applied instant adhesive layers and the fact that both gratings are situated on the same fiber, with dissimilar central wavelengths initially engraved. As a result of the significant differences in temperature sensitivity coefficients, the direct subtraction approach is avoided. Instead, the temperature compensation method presented in this study directly combines the central wavelength shifts equations of two FBGs, which is found to be effective. The temperature sensitivity coefficients of the FBGs arranged on the axial force sensitivity-enhancing structure and the guide tube are larger than the traditional FBGs. Because the thermal expansion coefficient of the main material of the FBG, silica dioxide, is smaller than that of the guide tube [33,34]. After removing the coating layer and bonding to the outer surface of the guide tube, the FBGs become more temperature-sensitive. The temperature sensitivity of the FBGs on the axial force sensitivity-enhancing structure is higher than that of the FBGs on the guide tube. It’s because the Polydimethylsiloxane with a large coefficient of thermal expansion [33] is used to encapsulate and protect FBGs on the axial force sensitivity-enhancing structure. Therefore, when applying protective coatings to FBGs, it may be advantageous to select other materials with smaller coefficients of thermal expansion.
In this study, the maximum absolute residual error of the force measurements obtained from the proposed sensor is larger than the force resolution, which is deemed acceptable. Because accuracy and resolution represent two distinct characteristics of the sensor. By comparing with previous relevant studies, this research has achieved improvements in accuracy of force measurement. In future studies, further improvements can be achieved by fabricating high-quality FBGs and refining the manufacturing process of the sensor.
This study focuses on developing a sensor for measuring 3-D forces between micro-forceps and intraocular tissues while neglecting the measurement of the interaction forces between the forceps and the sclera. Large interaction forces between the instrument and the sclera can cause ocular damage and delay the recovery of the eye. Therefore, our future research will further integrate the measurement of scleral forces into the designed 3-D micro-force sensor to enhance the safety of the Ophthalmic Microsurgery Robot.
5. Conclusions
In this study, a new FBG-based 3-D micro-force sensor for micro-forceps with axial force sensitivity-enhancing has been developed for the Ophthalmic Microsurgery Robot. An innovative structure was proposed by incorporating the principles of flexure-hinge and flexible lever mechanisms to address the challenge of low sensitivity in axial force measurement. The design parameters of the axial force sensitivity-enhancing structure were optimized using finite element simulation. This led to a 129% increase in strain values on the FBGs under equivalent external force. Furthermore, finite element simulation analysis revealed that the structure exhibited negligible crosstalk induced by transverse forces. Two FBGs were arranged into this structure, and a dual-grating temperature compensation method was adopted to compensate for the influence of temperature fluctuations on axial force measurement. For the transverse force measurement and its temperature compensation, three FBGs were arranged at 120° intervals along the circumference of the guide tube. The proposed sensor, the micro-forceps, and the actuation mechanism were integrated into an end-effector, enabling its use in the Ophthalmic Microsurgery Robot. Temperature coefficient calibration experiments for FBGs, as well as 3-D micro-force calibration experiments, were conducted. The results revealed that the sensor designed for micro-forceps achieved a resolution of 0.13 mN for transverse force and 0.30 mN for axial force. The temperature compensation verification experiment demonstrated the capability of the 3-D micro-force sensor to compensate for temperature effects on both axial and transverse forces simultaneously. The validation experiments for 3-D force measurement were conducted, which showed RMS errors of 0.32 mN, 0.30 mN, and 0.92 mN for Fx, Fy, and Fz, respectively, indicating that the sensor possesses high measurement accuracy. Overall, this work addresses the challenge of 3-D micro-force measurement in micro-forceps, laying the groundwork for future force feedback control in the Ophthalmic Microsurgery Robot.
Funding
Science and Technology Project of Xi’an, Shaanxi Province, China (No. 21RGZN0007).
Acknowledgments
We thank Professor Dongsheng Zhang and Professor Xiaojun Shi for the experimental equipment.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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