**Purpose**:
Robot assistance in membrane peeling may improve precision and dexterity or prevent complications by task automation. To design robotic devices, surgical instruments’ velocity, acceptable position/pose error, and load ability need to be precisely quantified.

**Methods**:
A fiber Bragg grating and inertial sensors are attached to forceps. Data collected from forceps and microscope images are used to quantify a surgeon's hand motion (tremor, velocity, posture perturbation) and operation force (voluntary and involuntary) in inner limiting membrane peeling. All peeling attempts are performed on rabbit eyes in vivo by expert surgeons.

**Results**:
The root mean square (RMS) of the tremor amplitude is 20.14 µm (transverse, *X*), 23.99 µm (transverse, *Y*), and 11.68 µm (axial, *Z*). The RMS posture perturbation is 0.43° (around *X*), 0.74° (around *Y*), and 0.46° (around *Z*). The RMS angular velocities are 1.74°/s (around *X*), 1.66°/s (around *Y*), and 1.46°/s (around *Z*), whereas the RMS velocities are 1.05 mm/s (transverse) and 1.44 mm/s (axial). The RMS force is 7.39 mN (voluntary force), 7.41 mN (operation force), and 0.5 mN (involuntary force).

**Conclusions**:
Hand motion and operation force are measured in membrane peeling. These parameters provide a potential baseline for determining a surgical robot's accuracy, velocity, and load capacity.

**Translational Relevance**:
Baseline data are obtained that can be used to guide ophthalmic robot design/evaluation.

^{1}Moreover, the outcome of ERM/ILM peeling is impacted by many factors, including but not limited to the absence of force sensing and the surgeon's physiological hand tremor, proficiency, and manipulative skills.

^{3}hand-held,

^{4}hands-on operated,

^{5}and untethered

^{6}robotic systems have been developed to enhance and expand the capabilities of surgeons. In robot-assisted ERM/ILM peeling, reasonable performance metrics are required to evaluate the robot's performance and facilitate controller design.

*z*(feed), rotation around axis

*z*(roll), rotation around axis

*y*(pitch), and rotation around axis

*x*(yaw). Performance metrics related to the movements include the range, velocity, and acceptable position/pose error. In addition, robot performance metrics also include the load capacity and acceptable force error.

^{4}The operation force has been used to determine the acceptable force error in the force control loop.

^{7}

^{8}Voluntary force and IF can provide baselines for the load capacity and acceptable force error.

^{9}measured the hand tremor amplitude and velocity during epiretinal membrane peeling. However, the test included only one sample. Researchers have also measured the force in peeling artificial models (rubber band,

^{10}polydimethylsiloxane

^{7}) and the ILM of chicken eggs.

^{7}

^{,}

^{11}For the operation force, the VF and IF were not distinguished. In addition, measurement results of the IF, posture perturbation, and angular velocity are still lacking. Therefore more in vivo tests are required to provide additional support.

^{4}and inertial sensors

^{14}are two standard methods of measuring hand motion. Optics can be highly precise but require multiple sightlines to the tracker targets and fail to measure posture. The limited sensing workspace and frequent sightline obstructions also limit the application of optics.

^{15}Inertial sensors require no sightlines and can measure posture, but inertial sensor accuracy is hampered by many factors, such as gyroscope drift, accelerometer noise, and accumulated error. Data fusion techniques and appropriate algorithms are required to calculate hand tremor.

^{14}

^{11}

*a*

_{1}′,

*a*

_{2}′,

*b*

_{1}′,

*b*

_{2}′ in Fig. 2(e)) can be obtained. By combining the coordinates obtained from video and posture of the forceps, the velocity of the forceps can be calculated. A detailed description of the algorithm is given in the next part. In this study, the video resolution and frame rates are 1920 × 1080 and 50 fps, respectively.

^{14}to calculate hand tremor. Here, we give a brief introduction.

*B*} and frame {

*S*} at the measurement origin of the IMU and the nontremulous position of the forceps tip, respectively. The orientation of {

*S*} is identical to {

*B*}. {

*W*} is the world coordinate system.

^{B}*and a drift-free estimation of the Euler angles (φ, θ, ψ). Angles φ, θ, ψ are defined as rotations about*

**A***X*,

_{B}*Y*, and

_{B}*Z*, respectively.

_{B}*A*) can be calculated as follows:

_{tip}*i*=

*X*,

_{B}*Y*,

_{B}*Z*;

_{B}*t*is the sampling time;

*k*is the current time step; and

*k*-1 is the previous time step.

^{S}

**A***) is estimated with the band-limited multiple Fourier linear combiner.*

_{tip}^{14}The position of the forceps tip due to tremor (

^{S}

**P***= [*

_{tip}*,*

^{S}P_{tip,x}*,*

^{S}P_{tip,y}*]*

^{S}P_{tip,z}^{T}) is calculated by double integration of

*A*. A detailed description of the tremor calculation algorithm, calibration procedure, and results can be found in our previous work.

_{tip}^{16}

*by multiplying the FBG wavelength shift Δ*

**F****S**with the calibration matrix (

**K**^{+}):

*= [*

**F***F*,

_{x}*F*]

_{y}^{T}, \(\Delta {\bf{S}} = {[ {\begin{array}{*{20}{c}} {\Delta {S_1}}&{\Delta {S_2}}&{\Delta {S_3}} \end{array}} ]^{\rm{T}}}\) and where Δ

*S*

_{1}, Δ

*S*

_{2}and Δ

*S*

_{3}are the wavelength shifts of FBG1, FBG2, and FBG3, respectively. The meaning of

*x*and

*y*are shown in Figure 2(d).

^{17}is applied to the operation force

*to extract the involuntary force*

**F**

**F***. The voluntary force*

_{inv}

**F***is calculated by*

_{vol}

**F***=*

_{vol}*−*

**F**

**F***. The cutoff frequency is set as 2 Hz.*

_{inv}^{8}Following the calibration procedure,

^{18}the relative error and RMSE of the FBG sensors are 0.6% and 0.3 mN, respectively.

_{dis}, θ

_{dis}, ψ

_{dis}) can be obtained by applying a sharp high-pass filter

^{17}on the measured Euler angles (φ, θ, ψ). The cutoff frequency of the sharp high-pass filter is 2 Hz because the bandwidth of human eye-hand feedback usually spans from 0.5 Hz to 2 Hz.

^{8}Posture changes occurring above 2 Hz can be regarded as posture perturbation.

*a*

_{1},

*a*

_{2},

*b*

_{1},

*b*

_{2}) on the forceps:

*a*

_{1}is the tip of the forceps,

*a*

_{2}is the incision point, and

*b*

_{1}and

*b*

_{2}are the side points of the steel tube of the forceps. In addition,

*a*

_{1}′,

*a*

_{2}′,

*b*

_{1}′,

*b*

_{2}′ are the projections of the abovementioned points on the record image. The length of vector

**b**_{1}′

**b**_{2}′ is equal to the diameter of the steel tube

*d*.

*C*} and axial coordinate {

*A*}. Axes

*Z*,

_{C}*Z*and

_{A}*Z*are identical.

_{W}*C*}, the coordinates of

*a*

_{1}′ and

*a*

_{2}′ can be defined as

**a**_{1}′ = [

*a*

_{1}

*,*

_{x}*a*

_{1}

*, 0]*

_{y}^{T}and

**a**_{2}′ = [

*a*

_{2}

*,*

_{x}*a*

_{2}

*, 0]*

_{y}^{T}, respectively. Then, we can obtain the tip velocity

*v*as follows:

_{tip}*A*}, vector

**a**_{1}′

**a**_{2}′ = [0, 0,

*γl*

_{axial}]

^{T},

*l*

_{axial}= ||

**a**_{1}′ -

**a**_{2}′||. The length of

**a**_{1}

**a**_{2}can be derived as follows:

**a**_{1}

**a**_{2}is the real length on the forceps and

*γl*

_{axial}is the projection on the image.

*v*by differentiating the length of

_{axial}

**a**_{1}

**a**_{2}over time. After calibration, the relative error is approximately 3.4%. A detailed description of the calibration process can be found in Supplemental Material S1.

*X*of each eye. After all tests, we obtain multiple sets of RMS, SD, and MAX tremor along

_{S}*X*. The obtained ranges of RMS, SD, and MAX are 16.29 µm to 25.60 µm, 15.76 µm to 22.33 µm, and 101.8 µm to 152.4 µm, respectively. Therefore, in Table 2, the RMS, SD, and MAX of

_{S}*(expert 1) are written as “16.29–25.60,” “15.76–22.33,” and “101.8–152.4”, respectively. The rest are similar. The statistical results of each eye can be found in Supplemental Material S2.*

^{S}P_{tip,x}*v*and

_{tip}*v*are 1.05 ± 0.52 mm/s and 1.14 ± 0.66 mm/s, respectively. The mean MAX values of

_{axial}*v*and

_{tip}*v*are 1.91 mm/s and 2.06 mm/s, respectively. For different surgeons, the

_{axial}*P*values of

*v*and

_{tip}*v*are 0.22 and 0.28, respectively.

_{axial}*Xs*: 24 µm;

*Ys*: 22; µm

*Zs*: 20 µm),

^{9}as measured with inertial sensors in vitreoretinal microsurgery.

^{1}). We attribute this difference partly to the difference in the velocity measurement method. The sampling frequency of cameras is smaller than that of inertial sensors, and we do not need to use integration/filtering algorithms. The surgeons’ habits also contribute to this difference. Compared with retinal microsurgery,

^{1}surgeons tend to operate faster during in vivo tests.

^{7}) measured by the FBG sensors. This might be caused by two reasons: (1) the membrane of rabbits is more fragile than that of chicken eggs, and (2) compared with ex vivo tests, surgeons tend to operate more cautiously during in vivo tests.

^{5}

^{,}

^{19}

^{,}

^{20}In addition, in the real world, the ground truth (intended motion) is unknown. The abovementioned two facts indicate that it is nearly impossible to capture the full position error and accuracy. Therefore, we regard the derived metrics as “potential baseline” or “acceptable lower performance limits” rather than “strict accuracy requirements.” A robot that meets all derived metrics should have similar abilities to expert surgeons. This lays a foundation for robot-assisted ILM peeling.

*Xs*), 23.99 µm (

*Ys*), and 11.68 µm (

*Zs*). If the positioning error of the robot is smaller than the mentioned hand tremor, we can conclude the robot moves more stably than the expert surgeons’ hand. Therefore the robot can potentially be used in ILM peeling since expert surgeons can complete ILM peeling.

^{21}

^{,}

^{22}the number is still small. The following two aspects could compensate for this shortcoming: (1) The surgeons could complete multiple peeling attempts on each eye. Therefore multiple datasets could be obtained from each eye. (2) None of the evaluation results reached statistical significance because the

*P*value ranged from 0.22 to 0.95. Therefore the dataset number (approximately 40 peeling attempts) is larger than the number of eyes.

**Y. Zheng**, None;

**X. Yang**, None;

**B. Mo**, None;

**Y. Qi**, None;

**Y. Yang**, None;

**C. Lin**, None;

**S. Han**, None;

**N. Wang**, None;

**C. Guang**, None;

**W. Liu**, None

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