# Cooperative vs. Teleoperation Control of the Steady Hand Eye Robot with
Adaptive Sclera Force Control: A Comparative Study

Mojtaba Esfandiari1, Ji Woong Kim1, Botao Zhao1, Golchehr Amirkhani1, Muhammad
Hadi1, Student, IEEE,
Peter Gehlbach2, Member, IEEE, Russell H. Taylor3, Life Fellow, IEEE, Iulian
Iordachita1, Senior Member, IEEE *This work is supported by the U.S. National
Institutes of Health under the grant numbers 2R01EB023943-04A1 and 1R01
EB025883-01A1, and partially by JHU internal funds.1 Mojtaba Esfandiari, Ji
Woong Kim, Botao Zhao, Golchehr Amirkhani, Muhammad Hadi, and Iulian
Iordachita are with the Department of Mechanical Engineering and also
Laboratory for Computational Sensing and Robotics at the Johns Hopkins
University, Baltimore, MD, 21218, USA (e-mail:
mesfand2,jkim447,bzhao17,gamirkh1, mhadi2, iordachita@jhu.edu). 2 Peter
Gehlbach is with the Wilmer Eye Institute, Johns Hopkins Hospital, Baltimore,
MD, 21287, USA. (e-mail<EMAIL_ADDRESS>3Russell H. Taylor is with the
Department of Computer Science and also the Laboratory for Computational
Sensing and Robotics at the Johns Hopkins University, Baltimore, MD, 21218,
USA<EMAIL_ADDRESS>
###### Abstract

A surgeon’s physiological hand tremor can significantly impact the outcome of
delicate and precise retinal surgery, such as retinal vein cannulation (RVC)
and epiretinal membrane peeling. Robot-assisted eye surgery technology
provides ophthalmologists with advanced capabilities such as hand tremor
cancellation, hand motion scaling, and safety constraints that enable them to
perform these otherwise challenging and high-risk surgeries with high
precision and safety. Steady-Hand Eye Robot (SHER) with cooperative control
mode can filter out surgeon’s hand tremor, yet another important safety
feature, that is, minimizing the contact force between the surgical instrument
and sclera surface for avoiding tissue damage cannot be met in this control
mode. Also, other capabilities, such as hand motion scaling and haptic
feedback, require a teleoperation control framework. In this work, for the
first time, we implemented a teleoperation control mode incorporated with an
adaptive sclera force control algorithm using a PHANTOM Omni haptic device and
a force-sensing surgical instrument equipped with Fiber Bragg Grating (FBG)
sensors attached to the SHER 2.1 end-effector. This adaptive sclera force
control algorithm allows the robot to dynamically minimize the tool-sclera
contact force. Moreover, for the first time, we compared the performance of
the proposed adaptive teleoperation mode with the cooperative mode by
conducting a vessel-following experiment inside an eye phantom under a
microscope.

##  I INTRODUCTION

Retinal vein occlusion (RVO) is the second most prevalent retinal vascular
disease. It occurs due to a retinal vein occlusion, leading to severe vision
loss. In 2015, an overall 28.06 million people worldwide (0.77$\%$ of people
aged 30-89 years) were affected by RVO, branch RVO (BRVO) (23.38 million), and
central RVO (CRVO) (4.67 million) [1]. There is no standard method for
directly treating RVO with surgery, as it requires consistently and safely
performing retinal vein cannulation (RVC). Due in part to human hand tremor
limits, this is not broadly possible without robotics-assisted surgical
systems. The diameter of the retinal veins is on the order of $150\pm 15\mu$m
[2], while, the root mean square (RMS) value of hand tremor of an ophthalmic
surgeon is reported as $182\mu$m [3], which is comparable to the vein
diameter. Therefore, performing freehand RVC is both challenging and
potentially unsafe using free-hand methods.

To address this issue, researchers developed several surgical robotic systems
such as the Steady Hand Eye Robot (SHER) [4], a hybrid parallel-serial micro-
manipulator [5], Preceyes [6], RVRMS [7], and others [8, 9, 10], trying to
mitigate (filter) physiological hand tremor and also to provide surgeons with
a higher level of skill and positioning accuracy.

The SHER is a 5-degree-of-freedom (DoF) robot manipulator that allows surgeons
to cooperatively manipulate a surgical instrument attached to its end-effector
towards a desired target (Fig. 1). Due to the high structural rigidity of the
robot, it removes surgeon hand tremors, but the small interaction force
present between the surgical instrument and the sclera entry port is
diminished during cooperative (admittance) control mode. Thus the contact
force exerted by the surgeon on the sclera surface can exceed a safe threshold
of 120 mN [11].

Figure 1: Vessel following experiment in an eye phantom with two different
control modes. The experiment setup includes the SHER 2.1, PHANTOM Omni, a
surgical microscope, an FBG interrogator, a force-sensing surgical instrument,
an eye phantom, and a light source.

To minimize the sclera force exerted on the needle, Ebrahimi et al. developed
adaptive force control algorithms, including adaptive norm control (ANC) and
adaptive component control (ACC), using a force-sensing instrument equipped
with fiber Bragg grating (FBG) to maintain the scleral forces below a safe
threshold [12, 13]. FBG sensors can be used for shape sensing [14] or force
sensing [15] in flexible needles or continuum robots. These concepts help to
dynamically enforce the remote center of motion (RCM) constraint on the
eyeball and reduce the risk of tearing the sclera during surgery. However,
this adaptive force control algorithm only works in the cooperative control
mode. Therefore the surgeon must still cooperate directly with the robot
handle. Incorporating such force control algorithms in a teleoperation
modality may provide surgeons with advanced capabilities and improve patient
safety [16, 17]. We calibrated an FBG-based force-sensing instrument based on
a method provided by [15] to estimate the tip force, the sclera force, and the
insertion depth by measuring the wavelength shifts of the FBG sensors. The
contributions of this paper are as follows:

  * •

We developed for the first time, to the best of our knowledge, a teleoperation
control mode with an adaptive sclera force control algorithm for retinal
surgery applications and implemented this adaptive teleoperation algorithm on
the SHER 2.1 system. This teleoperation control mode has several capabilities
including but not limited to 1- indirect manipulation of the robot using a
haptic interface, 2- scaling down the surgeon’s hand motion to increase
positioning accuracy, 3- reposition of hand frames to increase flexibility and
comfort, 4- dynamically maintaining the RCM constraint and minimizing the
tool-sclera interaction forces.

  * •

We compared, for the first time in robot-assisted retinal surgery
applications, the performance of the proposed teleoperation mode incorporated
with adaptive sclera force control with a cooperative mode equipped with the
same adaptive force control functionality. We conducted a vessel-following
experiment inside a plastic eye phantom under a surgical microscope to compare
the performance of the proposed adaptive teleoperation mode with the
cooperative mode.

Results are analyzed to study the pros and cons of the different control
modes.

The rest of this paper is organized as follows. Robot kinematics and control
algorithms are formulated in Section II. The experimental setup and experiment
procedure are explained in Section III. The experimental results are analyzed
in Section IV. Section V draws a discussion on the results and conclusion of
the paper.

##  II Robot Kinematics

Figure 2: (a) The Steady-Hand Eye Robot, (b) RCM constraint, tooltip
coordinate frame $\\{T\\}$, body coordinate frame $\\{B\\}$, and the spatial
coordinate frame $\\{S\\}$, (c) fiber Bragg gratings sensors attached across
the needle, (d) force-sensing instrument equipped with FBG sensors, and (e)
cross-section of the force-sensing needle equipped with three channels of
sensors [18].

The Steady-Hand Eye Robot is a 5-DoF robot manipulator, including three
translational and two rotational degrees of freedom. A surgical instrument,
e.g., a needle, can be attached to the robot end-effector. There is no roll
motion about the needle axis, however. The SHER motion is represented using
two coordinate frames: the spatial coordinate $\\{S\\}$, a fixed frame in
space located in the robot base, and the body coordinate $\\{B\\}$, which is
rigidly attached to the robot handle and moves with it. The tip coordinate
$\\{T\\}$ attached to the needle tip has the same orientation as coordinate
$\\{B\\}$ but with a constant shift along the negative $Z$ direction of
$\\{B\\}$ (Fig. 2).

###  II-A Kinematics of the SHER

In this section, the forward kinematics of the SHER are developed using the
homogeneous representation $g_{SB}:\Theta\rightarrow SE(3)$ which maps the
robot joints variables $\Theta\in\mathbb{R}^{5}$ to the robot end-effector
coordinate, where $g_{SB}\in\mathbb{R}^{4\times 4}$ represents the
configuration of body coordinate $B$ relative to the spatial coordinate $S$
and is a matrix in the special Euclidean group $SE(3)$. To compute the forward
kinematics, we will use the product of the exponential formula [19] as follows

$g_{SB}(\Theta)=e^{\hat{\xi}_{1}\theta_{1}}...e^{\hat{\xi}_{5}\theta_{5}}g_{SB}(0)$
(1)

in which $\hat{\xi}_{i}\in se(3)$ denotes the $i^{th}$ twist, $\theta_{i}$ is
the $i^{th}$ element of the joints variable vector $\Theta$, and
$g_{SB}(0)\in\mathbb{R}^{4\times 4}$ represents the configuration of $B$
relative to $S$ when the robot is at its home position $(\Theta=\textbf{0})$.

The twist $\hat{\xi}_{i}$ for the first three prismatic joints ($i=1,2,3$) and
for the last two rotational joints ($i=4,5$) is defined as follows [19]

$\hat{\xi}_{i}=\begin{cases}\quad\begin{bmatrix}0_{3\times 3}&v_{i}\\\
0_{3\times 1}&0\\\ \end{bmatrix},\quad\quad\quad\quad\textrm{for}\quad
i=1,2,3\vspace{0.2cm}\\\
\quad\begin{bmatrix}\hat{\omega}_{i}&-\omega_{i}\times q_{i}\\\ 0_{3\times
1}&0\\\ \end{bmatrix},\quad\textrm{for}\quad i=4,5\end{cases}$ (2)

in which $v_{i}$ denotes the unit vector along the positive direction of the
$i^{th}$ prismatic joint and $\omega_{i}$ is the unit vector along the
positive direction of the rotation axis (counterclockwise) of the $i^{th}$
rotational joint, both expressed in the $S$ coordinate when the robot is at
home position. $q_{i}$ is an arbitrary point on the corresponding rotation
axis. The twist coordinate $\xi_{i}=(v_{i},\omega_{i})\in\mathbb{R}^{6}$
corresponding to the twist $\hat{\xi}_{i}$ can be computed as
$\xi_{i}=(\hat{\xi}_{i})^{\vee}$ where $\vee$ is the vee operator[19].

Using (1) and (2), the robot joint velocity vector
$\dot{\Theta}\in\mathbb{R}^{5}$ can be mapped to the robot end-effector
velocity vector $V_{SB}^{b}\in\mathbb{R}^{6}$ (the superscript $b$ means that
velocity of the body coordinate $B$ relative to the spatial coordinate $S$ is
expressed in the body coordinate $\\{B\\}$) as follows

$V_{SB}^{b}=J_{SB}(\Theta)\dot{\Theta}$ (3)

where the robot Jacobian $J_{SB}\in\mathbb{R}^{6\times 5}$ is computed as

$\displaystyle J_{SB}(\Theta)$
$\displaystyle=\begin{bmatrix}\xi_{1}^{\dagger}&...&\xi_{5}^{\dagger}\end{bmatrix},$
(4) $\displaystyle\xi_{i}^{\dagger}$
$\displaystyle=Ad^{-1}_{e^{\hat{\xi}_{i}\theta_{i}}...e^{\hat{\xi}_{5}\theta_{5}}g_{SB}(0)}\xi_{i}$

and $Ad_{g}:\mathbb{R}^{6}\rightarrow\mathbb{R}^{6}$ is the adjoint
transformation associated with a rigid body transformation $g=(p,R)\in SE(3)$
defined as [19]

$Ad_{g}=\begin{bmatrix}R&\hat{p}R\\\ 0&R\end{bmatrix}_{6\times 6}.$ (5)

###  II-B Cooperative Control of the SHER

The cooperative control mode of the SHER is based on an admittance control
method that lets the surgeons intuitively maneuver the robot end-effector
toward a desired target. To do this, the user hand force/torque exerted on the
robot handle $F_{h}^{b}\in\mathbb{R}^{6}$ is measured by a six DoF force
sensor (Nano17, ATI Industrial Automation, NC, USA), Fig. 1, and used in the
admittance control law to generate a desired end-effector velocity in the
robot body coordinate $V_{d}^{b}\in\mathbb{R}^{6}$ as follows

$V_{d}^{b}=\mathbb{K}F_{h}^{b}$ (6)

$\mathbb{K}\in\mathbb{R}^{6\times 6}$ is a diagonal matrix with constant
diagonal elements as the admittance gains. Having $V_{d}^{b}$, the desired
joints’ angular velocity vector $\dot{\Theta}_{d}\in\mathbb{R}^{5}$ can then
be calculated as

$\dot{\Theta}_{d}=J_{SB}^{\dagger}(\Theta)V_{d}^{b}$ (7)

and be passed to the SHER’s low-level controller to generate the desired
motion. $J_{SB}^{\dagger}$ is the Jacobian pseudo inverse [20] and is
calculated as

$J^{\dagger}_{SB}=J^{T}_{SB}(J_{SB}J^{T}_{SB})^{-1}.$ (8)

###  II-C Adaptive Force Control of the SHER

In this control algorithm, if each of the measured sclera force components,
$F_{sx}$ and $F_{sy}$, exceed the specified safety threshold, $T_{s}$, the
robot is controlled toward a safe sclera force trajectory [21]. By estimating
the sclera tissue stiffness, $\alpha_{i}$ $(i=x$ or $y)$, the desired sclera
force trajectory, $f_{dx}$ and $f_{dy}$, can be obtained using (9) and (10),
respectively:

$\displaystyle f_{dx}=\frac{T_{s}sign(F_{sx})}{2}(e^{(t-t_{x})}+1),$ (9)
$\displaystyle f_{dy}=\frac{T_{s}sign(F_{sy})}{2}(e^{(t-t_{y})}+1),$ (10)

where $t_{i}$ is the time when $F_{si}$ exceeds the safety threshold.

The desired linear velocity of the end-effector along the $x$ and $y$
directions in the body frame $\\{B\\}$ can be determined using (11) and (12):

$\displaystyle\dot{X}^{b}_{des_{i}}(t)=\alpha_{i}\dot{f}_{di}(t)-K_{fi}\Delta{f}_{i}(t),\quad
i=\\{x,y\\},$ (11)
$\displaystyle\dot{\alpha}_{i}=-\Gamma_{i}\dot{f}_{di}(t)\Delta{f}_{i}(t),\quad
i=\\{x,y\\}$ (12)

where $\Delta{f}_{i}=F_{si}-f_{di}$ is the sclera force error, and
$\Gamma_{i}$ and $K_{fi}$ are constant gains for adaptation law and the force
tracking error, respectively. $\alpha_{i}$ is the estimated tissue compliance,
and $\dot{f}_{di}$ is the derivative of $f_{di}$ which is derived using (9)
and (10). The desired end-effector velocity components in the $x$ and $y$
directions, using (11) and (12), are considered the desired robot end-effector
velocity. This adaptive sclera force control algorithm applies to both
cooperative and teleoperation control modalities. Therefore, the other
elements of the robot end-effector velocity will be calculated by abiding by
the user’s interaction forces in the cooperative control mode, and by the
PHANTOM Omni’s end-effector velocity (mapped to the SHER body coordinate
$\\{B\\}$) in the teleoperation control mode.

Figure 3: Block diagram of the proposed teleoperation control architecture
with adaptive sclera force control algorithm.

Fig. 3 shows a schematic of the proposed teleoperation control mode featuring
an adaptive sclera force control algorithm. This architecture comprises three
main components: a high-level controller, a mid-level optimizer with joint
constraints, and a low-level joint velocity controller (Galil). The high-level
controller consists of two key elements: an adaptive sclera force controller
that takes input from the sclera force components $F_{sx}$ and $F_{sy}$
measured in the body coordinate system ${B}$ by the force-sensing instrument,
which, generates the desired adaptive end-effector velocity in the SHER body
coordinate as $\dot{X}_{A}^{b}$ ($=\dot{X}^{b}_{des}$ in (11)), along with a
kinematic controller that maps the end-effector velocity of the Omni, denoted
as $\dot{X}_{o}$, to the SHER body coordinate as $\dot{X}_{o}^{b}$. The
control policy chooses between $\dot{X}_{A}^{b}$ and $\dot{X}_{o}^{b}$
depending on the magnitude of the sclera force. It then generates the desired
end-effector velocity in both the SHER body coordinate ($\dot{X}_{des}^{b}$)
and the SHER spatial coordinate ($\dot{X}_{des}^{s}$). The mid-level optimizer
calculates the optimal desired joint rates, denoted as $\dot{q}_{des}$, for
the SHER while considering its joint limit constraints. Lastly, the low-level
Galil joint velocity controller produces the necessary control commands to
achieve the desired joint velocities. Other signals include $\dot{q}_{real}$
(absolute joint velocities of SHER), $\dot{X}_{real}^{s}$ (actual end-effector
velocity in the spatial coordinate of SHER), and $f_{dx}$ and $f_{dy}$
(desired sclera force components in the body coordinate ${B}$).

##  III Experiments

###  III-A Experimental Setup

Due to the recommendation of our clinical lead, we decided to conduct a
”vessel-following” experiment [22], which is a typical task in retinal
surgery, for validation experiments and to compare the performance of four
different control modes: cooperative mode (without enforcing adaptive sclera
force control), adaptive cooperative mode (with enforcing adaptive sclera
force control), teleoperation mode, and adaptive teleoperation mode. The setup
is prepared to measure and record the SHER’s kinematic information, the
interaction force between the user’s hand and the SHER handle, and the tool-
sclera interaction force. The experimental setup includes the SHER 2.1, a
PHANTOM Omni robot (SensAble Technologies Inc., MA, USA), an ATI force sensor
(Nano17, ATI Industrial Automation, NC, USA), a force-sensing tool with nine
FBG sensors (Technica Optical Components, China), an FBG interrogator
(HYPERION si155, Luna), an eye phantom, a surgical microscope (Zeiss, OPMI),
and an LED dual-light illuminator as shown in Fig.1. All devices were
connected to a main computer using a TCP-IP connection. The PHANTOM Omni is
used as a joystick controller to teleoperate the SHER 2.1. and a 6-DoF ATI
Nano 17 force sensor is embedded with the SHER’s end-effector to measure the
hand-tool interaction forces and torques from all three Cartesian coordinates.
An FBG force-sensing tool [23] is used for measuring the sclera force applied
to the eye phantom by the surgical instrument. The tool shaft has three FBG
fibers arranged at 120-degree intervals around it. A total number of nine FBG
sensors are contained in the three fibers as shown in Fig. 2e-d. The FBG
interrogator receives those optical signals from the FBG sensors and converts
them into force readings. The eye phantom is an anatomical eye model that
imitates critical features of a natural human eye. This experiment is
performed under an LED dual-light illuminator to get a high-contrast view from
the microscope during the manipulation.

###  III-B Experimental Procedure

To perform the vessel-following experiment, the user is asked to follow a set
of specific procedures [22] and track a colored trajectory on the retinal
surface of an eye phantom simulating retinal veins, for each of the four
different control modes: cooperative, adaptive cooperative, teleoperation, and
adaptive teleoperation modes. The vessels’ pattern includes four different
colors: red (R), green (G), blue (B), and yellow (Y). The experiment includes
5 sets of tests, and each includes 5 trials, a total of 25 trials for each
control mode. Each trial is conducted by tracking in random order, the RGBY
colors. All tests are performed under a microscope using an illuminator for
best visualization. During the cooperative control mode, the user directly
manipulates the SHER’s tool handle, whereas, during the teleoperation mode,
the user indirectly manipulates the SHER using the PHANTOM Omni. In all
control modes, the user manipulates the force-sensing tool with the dominant
hand and holds a secondary tool with the non-dominant hand to re-orient the
eye phantom under the microscope. Of note, it is typical to perform retinal
surgery bimanually. All the kinematic and force data measured from the robot
and the force-sensing tool are collected in a .csv file and analyzed in
MATLAB.

Figure 4: Example of sclera force components $F_{sx}$ and $F_{sy}$ and sclera
force norm $F_{s}$ for adaptive teleoperation control mode. The adaptive
sclera force controller is activated if $|F_{sx}|$ or $|F_{sy}|$ reaches a
threshold value of 100 mN. The goal of the adaptive force controller is to
maintain the sclera norm force $F_{s}$ below a safe threshold (120 mN) [11].

##  IV Experimental Results and Discussion

To the best of our knowledge, this is the first time a teleoperation control
mode incorporated with an adaptive sclera force control algorithm has been
implemented on a surgical robotic system, the SHER 2.1, for retinal surgery
applications. The primary comparison between the performance of the four
control modes is studied by considering several key factors that are of
notable importance in robot-assisted eye surgery, such as the tool-sclera
interaction force, which is essential for the safety of the patient, and the
human-robot interaction force (represented as the handle force) and the task
completion time, which relates to the surgeons’ comfort and intuition level.
Also, a higher completion time generally results in more operational costs in
an actual operating room.

Figure 5: Example of tooltip insertion depth during the vessel-following
experiment.

The user is asked to hold the needle tip as close as possible to the bottom of
the eye phantom and above the colored veins without touching them. Fig. 5
shows an example of the tooltip insertion depth. The average value of the
maximum insertion depth for all control modes is greater than 25 mm
demonstrating that the user performed the vessel-following with consistent
insertion depth and trajectory tracking for all four control modes. Of note,
the eye phantom used in this experience has a 32 mm diameter while the human
eye diameter is about 24 mm.

TABLE I: Mean and maximum sclera force, handle force/torque, and the
completion time for the four control modes during the vessel-following tests.
The values inside the parenthesis are the standard deviations.  TABLE II:
P-values of the results of Table I. The p-values are calculated using ttest2
method in MATLAB. Blue: the difference is significant, red: the difference is
not significant, black: the difference is not interpretable.

Table I summarizes six key evaluation metrics based on experimental data from
25 trials for each control mode: mean sclera force, maximum sclera force, mean
handle force, mean handle torque, mean completion time, and percentage of the
aggregate completion times in which the recorded sclera force was above the
safety threshold of 120 mN, across all 25 trials. Fig. 4 shows an example of
the sclera force magnitude in one of the adaptive teleoperation trials.
Similar behavior is observed in the adaptive cooperative mode. Once each of
the sclera force components, $F_{sx}$ and $F_{sy}$, exceeds the adaptive
threshold of 100 mN, the adaptive force control algorithm gets activated
trying to reduce the sclera force magnitude along a desired exponential
trajectory to maintain the sclera force below a safe threshold of 120 mN. This
safety feature is missing in the cooperative and teleoperation modes and the
sclera force may exceed the 120 mN threshold by a significant amount which
could be dangerous for the patient. Fig. 6 shows the mean tool-sclera
interaction forces for 25 trials for the two adaptive control modes. The mean
sclera force for the adaptive cooperative and adaptive teleoperation modes are
$35.93\pm 8.72$ mN and $41.52\pm 13.40$ mN, respectively, which are lower than
their non-adaptive counterparts. This value for the teleoperation modes is
higher than that of the cooperative modes (Table I). Also, the maximum sclera
force for the adaptive cooperative and adaptive teleoperation modes are
$247.98\pm 26.06$ mN and $274.99\pm 46.10$ mN, respectively, whereas these
values for the cooperative and teleoperation modes are $637.83\pm 105.18$ mN
and $442.66\pm 87.37$ mN. This demonstrates that the adaptive sclera force
control significantly reduced the force applied to the sclera in both
cooperative and teleoperation modes. As for the handle force/torque, there is
no direct contact between the SHER handle and the user in the teleoperation
modes, and the handle force/torque in the teleoperation modes is just the
reflection of the sclera force on the handle coordinate which is a very small
force compared to that of the cooperative modes (Table I). As mentioned,
another important metric that shows the surgeon’s comfort during interaction
with the robot is the mean task completion time. The mean completion time for
the teleoperation and adaptive teleoperation modes is $44.04\pm 6.43$ s and
$45.74\pm 11.69$ s while these values for the cooperative and adaptive
cooperative modes are $34.82\pm 2.87$ s and $37.08\pm 10.95$ s, respectively,
which shows that the cooperative modes are a bit faster than the teleoperation
modes. Moreover, for both adaptive cooperative and adaptive teleoperation the
percentage of the completion time in which the sclera force is greater than
120 mN is about 30% less than the cooperative and teleoperation modes,
respectively (Table I). The corresponding p-values of the results of Table I
are provided in Table II. For example, Table II indicates that the p-value for
the mean sclera force between the teleoperation and adaptive teleoperation
modes is 0.03279 ($<$0.05) which demonstrates that based on the experimental
results the difference between the two control modes is statistically
significant. This proves that the adaptive teleoperation mode compared to the
teleoperation mode (non-adaptive) can significantly improve patients’ safety
in terms of mean sclera force being exerted on the eye. However, this
difference between the adaptive cooperative and adaptive teleoperation is not
statistically significant (since p-value = 0.08 $>$ 0.05), which means that
these two modes have similar performance in terms of mean sclera force.
Similarly, the difference between the cooperative and adaptive cooperative in
terms of the maximum sclera force is statistically significant (p-value =
0.0305) while the difference between the cooperative and teleoperation is not
significant (p-value = 0.2826). In terms of the mean completion time, there is
no significant difference between the cooperative and adaptive cooperative
modes (p-value = 0.3199) whereas, the difference between each cooperative mode
and each teleoperation mode is significant (at the p-values $<$ 0.05 level).
Of note, these results are collected by a single expert user and cannot be
extrapolated to non-expert users (users who are not at their learning curve
plateau [24]). To the best of our knowledge, the comparison provided above
between the cooperative and the teleoperation modes equipped with an adaptive
sclera force control algorithm is drawn for the first time in robot-assisted
retinal surgery applications.

(a)

(b)

Figure 6: Average of the tool-sclera interaction forces for 25 trials for each
of the two different control modes: (a) adaptive cooperative and (b) adaptive
teleoperation.

##  V Conclusion and Future Work

In this work, we implemented, for the first time in robot-assisted retinal
surgery applications, a novel adaptive sclera force control algorithm in a
teleoperation control modality for SHER 2.1 using an FBG-based force-sensing
surgical instrument. The performance of this adaptive teleoperation control
mode is compared with three previously developed control modes, namely, the
cooperative, the teleoperation, and the adaptive cooperative modes in a
vessel-following experiment inside an eye phantom. These experiments are
conducted unilaterally, and the secondary tool used for rotating the eye
phantom has no force-sensing capability. The performance of all four control
modes is compared based on several relevant metrics related to the safety of
the surgery, and the comfort of the surgeon. These results are reported in
Table I. They show that both the adaptive cooperative and the adaptive
teleoperation modes outperform the cooperative and the teleoperation modes
(non-adaptive modes) in terms of the mean and maximum sclera force and the
percentage of time at which the sclera force is over 120 mN. The task
completion time is shorter for the cooperative modes due to the direct
manipulation; however, the teleoperation mode provides additional capabilities
such as motion scaling and repositioning that could potentially improve the
manipulability and positioning precision. For future work, we aim to provide a
bilateral teleoperation framework in which two robots, namely SHER 2.0 and
SHER 2.1, are both equipped with a force-sensing instrument with adaptive
sclera force control capability which improves the safety of the tool-sclera
interaction force for the secondary tool as well. Moreover, model predictive
control [25], [26, 27] and haptic force feedback may be added to the
teleoperation mode such that the sclera force is reflected by the haptic
device and perceived by the surgeon.

##  VI Acknowledgment

The authors appreciate Anton Deguet for his technical help in software
development.

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