Motion Compensation and Adaptive Force Control via iOCT–FBG Sensor Fusion for Robotic Subretinal Injection

Abstract

Subretinal injection is a highly delicate procedure that demands micron-level precision to avoid irreversible retinal damage. Current robotic systems achieve accurate positioning but remain limited by retinal motion and the lack of tip-force feedback. We present the first adaptive tip-force compensation framework for robotic subretinal injection, fusing intraoperative optical coherence tomography (iOCT) vision with fiber Bragg grating (FBG) force sensing. Our architecture integrates a finite-state machine (FSM) for surgical phase coordination, a Long Short-Term Memory (LSTM) enhanced residual Kalman filter for real-time motion prediction, and an adaptive compliance estimator for safe force regulation. Compared to previous vision-only and force-only method, ex vivo experiments on porcine eyes demonstrate robust improvements: the root-mean-square tracking error reduced by 40% (to $18.5\mu m$), the maximum absolute error lowered by 2.5 times, and 96.7% of tip forces maintained within ±0.7 mN. Control delays were minimized to 0.25 s, enabling low-latency corrections beyond freehand capabilities. Our system enhances precision and safety in fragile retinal tissues, advancing the potential for reliable robot-assisted surgeries for retinal diseases.

I. Introduction

Subretinal injection is a delicate microsurgical maneuver for delivering therapeutic agents into the potential space between the retinal neuroepithelium and the retinal pigment epithelium (RPE) [1]. This approach enables targeted delivery to photoreceptors and RPE cells and has been successfully applied in gene therapy for Leber congenital amaurosis [2]. Its clinical applications continue to expand, with ongoing trials for X-linked retinitis pigmentosa [3], Bietti crystalline dystrophy [4], and dry age-related macular degeneration [5].

Because the retina and RPE are extremely fragile and possess low regenerative capacity, even minor trauma can cause permanent vision loss. Thus, safe subretinal injection requires precise, depth-controlled advancement of a microsurgical insertion through the retinal neuroepithelial layer with accurate tip placement in the potential subretinal space [6]. Freehand procedures are highly challenging due to the surgeon’s physiological hand tremor (about $182\mu \text{m}$) [7], the thinness of the retina (depending on location, about $160-290\mu \text{m})$ [8], and limited depth perception using en face viewing systems. Moreover, once the needle enters the subretinal space, the surgeon must simultaneously deliver the agent at a constant, slow rate and hold the tip perfectly still to avoid tissue damage—demands that together make sustained freehand control very difficult.

Robotic assistance offers a promising solution. Platforms developed such as [9] and [10] achieve micron-scale positioning accuracy. However, challenges remain, including retinal deformation during tool-tissue interaction and retinal motion caused by respiration and heartbeat. These uncertainties highlight the need to integrate robotic systems with advanced real-time sensing modalities for precise tool positioning and safe interaction.

Intraoperative optical coherence tomography (iOCT) combined with deep neural networks has been used to guide surgical robots by processing intraoperative B- and C-scan data. In this way, accurate tool placement despite tissue deformation is enabled [11]. Feedback-based approaches have demonstrated relatively robust subretinal injections in ex vivo porcine eyes [12]. To address retina motion, iOCT-based deep learning methods synchronize robotic tools with tissue dynamics [13], [14]. These approaches can segment surgical needles and retinal layers, especially the internal limiting membrane (ILM) and RPE, which are commonly used as markers of the retina. However, they face limitations such as latency (~ 9 Hz), insufficient training data, poor robustness to unseen conditions, and the absence of force sensing at the tool tip [12].

In terms of force-related safety measures, scleral forces are controlled in previous studies using force-sensing surgical needles equipped with fiber Bragg grating (FBG) sensors, compensating bimanual robots’ motion, minimizing scleral forces within a safe limit, both in cooperative and teleoperation modalities [15], [16].

Utilizing the needle tip’s contact force to compensate for retinal motion during subretinal injection has not yet been fully investigated. To address this gap, we propose the first adaptive tip force compensation scheme for robotic subretinal injection, dynamically estimating tissue compliance to maintain safe interaction forces amid physiological retinal motion. Our robotic system fuses iOCT-based retinal layer segmentation and short-term motion previews with FBG force sensing for post-contact regulation. A residual Kalman filter with Long Short-Term Memory (LSTM)-generated previews tracks RPE motion at 1 kHz, while a finite state machine (FSM) [17] coordinates preparation, synchronization, transition, and post-contact phases. Dual controllers blend vision- and force-based velocities through normalized, dwell-adjusted weights, with adaptive compliance tuning to prevent force excursions. The contributions of this work are as follows:

• We developed a unified control architecture—including an FSM for procedural phase management, a residual Kalman filter predictor for bridging low-rate iOCT (4 Hz) with high-rate force feedback (1 kHz), and an adaptive force compensation algorithm that online-estimates tissue compliance to generate smooth reference trajectories and correct deviations.

• We integrated iOCT vision and FBG force sensing with dynamic weight adjustment for velocity blending, enabling robust synchronization to retinal motion (reducing tracking RMSE by 40% to $18.5\mu \text{m}$) and safe tip force regulation (96.7% of samples within ±0.7 mN) in ex vivo porcine eye experiments, while minimizing control delays to 0.25 s.

II. Methods

A. iOCT Vision and FBG Force Sensing

The iOCT $B^5$-scan, which contains five evenly spaced B-scans over the 4 × 0.1 mm area, provides retinal depth images at ~ 9 Hz, segmented via a pretrained U-Net [12] to extract needle position, ILM, and RPE in image coordinates. The U-Net was trained on 1707 labeled OCT images using Dice loss and Adam optimizer under the MONAI framework; full details are reported in [12]. A lightweight LSTM model yields short-horizon RPE axial motion previews $\left({\hat{z}}_{rpe},{\hat{v}}_{rpe}\right)$ in the robot frame via calibrated 1D pixel-to-millimeter mapping as we will discuss in section II-C.1.

The FBG force-sensing needle monitors tip-tissue interaction at ~ 200 Hz. As depicted in Fig. 1, it comprises three optical fibers recessed in 120° grooves on a 0.63 mm stainless-steel shaft, each with a triplet of 3 mm gratings. The distal triplet (FBG-I) senses intraocular tip bending; proximal triplets (FBG-II/III) compensate for temperature drift and scleral loads similar to [18]. Following [18], the transverse tip force $F_t={\left[F_{tx},F_{ty}\right]}^T$ is recovered via a pseudo-inverse calibration matrix, and the controller uses $F_n={‖F_t‖}_2$ as a proxy for insertion-axis force, valid under the near-perpendicular approach geometry.

Fig. 1.

Device setup for simulating subretinal injection. A cooperative robot holds and actuates an FBG-based force-sensing needle; the eye is mounted on a motorized linear stage that imposes sinusoidal Z-motion to mimic breathing-induced retinal motion. ILM and RPE layers are indicated for context; the inset shows the schematic of the FBG force sensor.

B. Finite State Machine

The FSM (Fig. 2(a)) divides the procedure into four phases, ensuring robotic safety and precision while simulating surgical workflow.

Fig. 2.

High-level architecture of the motion compensation system for subretinal injection. (a) A finite state machine divides the procedure into preparation, pre-contact synchronization, transition, and post-contact phases, with transitions based on force thresholds, user velocity, and segmentation confidence. (b) Retina layer predictor generating short-term RPE motion previews via LSTM-based trajectory fitting and refining estimates with a residual Kalman filter updated by high-confidence iOCT frames. (c) Integrated control pipeline fusing iOCT vision (for layer segmentation and motion compensation) with FBG force sensing (for real-time tip interaction regulation), including dynamic weight adjustment for velocity blending, adaptive force control, and polynomial speed control under surgeon oversight.

Phase 1 (Preparation): iOCT segmentation identifies needle tip, ILM, and RPE positions. The robot remains stationary while collecting 15 consecutive tip positions. Noise reduction uses interquartile range (IQR) outlier removal followed by median estimation. A 1D transformation maps image pixels $p$ to robot depth $Z$ (mm) with scale $b=3.379\times {10}^{-4}\text{mm}/\text{pixel}$, enabling motion synchronization [14].

Phase 2 (Pre-Contact Synchronization): The robot maintains constant needle-to-RPE distance $\Delta d$ using vision compensation. A Kalman filter-based predictor estimates current RPE ${\hat{z}}_{RPE}$ in robot coordinates, yielding desired position: $p_{\text{des}}={\hat{z}}_{\text{RPE}}+\Delta d$.

A polynomial speed controller computes velocity toward $p_{\mathit{\text{des}}}$, clipped to maximum speed; non-zero user velocity overrides. Transition to Phase 3 occurs if FBG detects a tip force larger than a preset threshold $\left(F_{on}\right)$ for a dwell period.

Phase 3 (Transition): Relies on user input until velocity is zero. A 60-sample rolling window tracks force and $\Delta d$; upon stop, medians set target force $F_{\mathit{\text{target}}}$ and distance, advancing to Phase 4. If force drops below threshold forces $\left(F_{off}\right)$ for dwell period, revert to Phase 2.

Phase 4 (Post-Contact): Fuses force and vision with dynamic weights to track motion, prioritizing force’s 200 Hz rate over vision’s latency/noise. Surgeon input reverts to Phase 3; low force with positive user speed (retraction) reverts to Phase 2.

The FSM integrates with the robot’s velocity-control mode (1 kHz servo loop), allowing seamless surgeon override for shared control.

C. Retinal Position Predictor

The predictor uses a residual Kalman filter (KF) to estimate RPE position/velocity in real-time, bridging iOCT’s 4 Hz rate with force’s 200 Hz via LSTM previews (Fig. 2(b)).

1). Preview Generation:

A pretrained lightweight LSTM network [14] with two stacked layers, 64 hidden units each, with dropout, forecasts the next two ILM $z$-positions from the last five historical positions (in pixels); we use this model without retraining. Current $z_0$, first prediction $z_1$ (horizon $\Delta t_h$), and second $z_2\left(2\Delta t_h\right)$ fit quadratic trajectory: $z(t)=a{t}^2+bt+z_0$ where

$$a=\frac{z_2-2z_1+z_0}{2\Delta t_h^2},b=\frac{z_1-z_0}{\Delta t_h}-a\Delta t_h.$$ (1)

If implied acceleration $\left|2a\right|$ exceeds threshold, fallback to linear $(a=0)$. Discretize into sequences $z_{\mathit{\text{seq}}},v_{\mathit{\text{seq}}}(v(t)=2at+b)$; linear interpolation evaluates nominal $z_n(t),v_n(t)$ at time $t$, with constant-velocity extrapolation beyond horizon.

2). Residual Kalman Filter:

The KF tracks residuals $x=[\delta z,\delta v{]}^T$ relative to preview, where $\delta z,\delta v$ is the position and velocity difference between LSTM prediction and current KF estimation, propagating at control rate and correcting on iOCT arrivals. The measurement model is:

$${\mathbf{x}}_k=\left[\begin{array}{cc}1& \Delta t\\ 0& 1\end{array}\right]{\mathbf{x}}_{k-1}+{\mathbf{w}}_{k-1},{\mathbf{w}}_{k-1}~𝒩(\mathbf{0},\mathbf{Q}).$$ (2)

where $\Delta t$ is the time step. The process noise covariance $\mathbf{Q}$ is scaled with $\Delta t$ and tuned to accommodate variability in breath-like retinal motion. The initial state is set to zero, with a diagonal covariance matrix reflecting uncertainties in position and velocity. The final estimates are computed as ${\hat{z}}_{\mathit{\text{rpe}}}=z_n(t)+\delta z$ for position and ${\hat{v}}_{\mathit{\text{rpe}}}=v_n(t)+\delta v$ for velocity.

3). OCT Update:

Upon arrival of an OCT frame, providing the segmented RPE position $z_{\text{img}}$ (in mm), segmentation confidence ${\text{conf}}_{\text{seg}}\in [\mathrm{0,1}]$, and timestamp $t_{\text{img}}$, the residual measurement is computed as $y_{\text{res}}=z_{\text{img}}-z_n\left(t_{\text{img}}\right)$. The observation model is

$$y=[\mathrm{1,0}]\mathbf{x}+v,v~𝒩\left(0,R_{\text{img}}\right)$$ (3)

The measurement noise variance $R_{\text{img}}$ scales exponentially with staleness and $\left(1-{\text{conf}}_{\mathit{\text{seg}}}\right)$ to penalize low-confidence segmentations. The KF performs the correction step using the innovation covariance $S=\mathbf{H}{\mathbf{P}\mathbf{H}}^{\top }+R_{\text{img}}$ and Kalman gain $\mathbf{K}=\mathbf{P}{\mathbf{H}}^{\top }/S$. The state and covariance are then updated as

$$\mathbf{x}\leftarrow \mathbf{x}+\mathbf{K}\left(y_{\text{res}}-\mathbf{H}\mathbf{x}\right),\mathbf{P}\leftarrow (\mathbf{I}-\mathbf{K}\mathbf{H})\mathbf{P}.$$ (11)

This predictor feeds the robot’s high-rate loop, enabling low-latency motion compensation.

D. Adaptive Force Compensation Algorithm

We adopt an adaptive force control scheme based on the estimation of tissue compliance, ensuring that the needle maintains safe interaction forces.

This controller receives raw force data $F_{\text{mea}}(t)=F_n(t)$ from the FBG sensor, filtering it through an exponential moving average (EMA) filter to yield a smoothed signal $F_{\text{fil}}(t)$:

$$F_{\text{fil}}(t)=\alpha F_{\text{mea}}(t)+(1-\alpha )F_{\text{fil}}(t-\Delta t),$$ (4)

where $\alpha$ and $\Delta t$ are the smoothing coefficient and sampling interval, respectively. The controller then generates a smooth reference trajectory $F_d(t)$ to prevent abrupt loading during injections:

$$F_d(t)=F_{\text{target}}+\Delta F{e}^{-\lambda \left(t-t_0\right)},{\dot{F}}_d(t)=-\lambda \Delta F{e}^{-\lambda \left(t-t_0\right)},$$ (5)

where $F_{\text{target}}$ is the desired steady-state force learned from phase 3, $\Delta F$ defines the initial force offset, $\lambda$ controls the convergence speed, and $t_0$ is the time when compensation begins.

The force error is defined as $e_{\mathit{\text{force}}}(t)=F_{\text{fil}}(t)-F_d(t)$. If the error exceeds a predefined threshold $T$, an adaptive control law is triggered. The desired velocity command, generated by the adaptive controller, is defined by:

$$v_{\mathit{\text{force}}}(t)=\hat{\gamma }(t){\dot{F}}_d(t)-K_f{e}_{\mathit{\text{force}}}(t),$$ (6)

where $\hat{\gamma }(t)$ is the adaptive estimation of tissue compliance, and $K_f$ is a proportional gain empirically tuned for stability and responsiveness. The tissue compliance parameter $\hat{\gamma }(t)$ is updated adaptively via:

$$\dot{\hat{\gamma }}(t)=-\Gamma {\dot{F}}_d(t)e(t),$$ (7)

where $\Gamma$ is the adaptation gain, controlling how rapidly the controller adapts to variations in the tissue’s mechanical properties. The adaptive force compensation ensures rapid yet stable correction of force deviations, maintaining safe interaction levels during dynamic retinal motion.

E. iOCT Vision Based Control Algorithm

The iOCT-based control computes the desired needle position $p_{\text{des}}$. Velocity toward $p_{\text{des}}$ uses proportional control with saturation:

$$v_{\text{vis}}=\text{min}\left(k_v\left|p_{\text{des}}-p_{\text{rob}}\right|,v_{\text{max}}\right)\cdot \text{sgn}\left(p_{\text{des}}-p_{\text{rob}}\right)+{\hat{v}}_{\text{rpe}}$$ (8)

where $k_v$ is the gain, $v_{\text{max}}$ the maximum velocity, $p_{\text{rob}}$ the current robot position, and ${\hat{v}}_{\text{rpe}}$ the predicted RPE velocity for feedforward compensation.

F. Dynamic Weight Adjustment

In Phase 4, the fused velocity is computed as a weighted combination of the vision-based velocity and the force-based velocity, as shown in Fig. 2(c):

$$v_{\text{fused}}=w_{\text{vis}}{v}_{\text{vis}}+w_{\text{force}}{v}_{\text{force}},$$ (9)

where $v_{\text{vis}}$ is the vision-based velocity, $v_{\text{force}}$ is the force-based velocity. Initial weights are $w_{\text{vis}}=0.3$ and $w_{\text{force}}=0.7$, since we trust force data more during contact. These weights are dynamically adjusted if certain error conditions persist for longer than the dwell threshold ${\tau }_d$. Specifically:

- Force error condition: If the absolute difference between the measured force $F_{\text{fil}}$ and the target force $F_{\text{target}}$ exceeds the force margin, i.e.,

$$e_F=\left|F_{\text{fil}}-F_{\text{target}}\right|>F_{\text{margin}}$$ (10)

then increment $w_{\text{force}}$ by the step size $\Delta w$. This adjustment prioritizes the force-based estimate to better align the system with the desired target force.

- RPE stability condition: Experimental observations revealed segmentation errors from the neural network, leading to unstable RPE position. To address this, if the variance of the recent RPE estimates exceeds the threshold, i.e.,

$$\text{Var}\left({\hat{z}}_{\text{RPE}}\right)>{\sigma }_{\text{thresh}}^2,$$ (11)

then increment $w_{\text{force}}$ by $\Delta w$. This shifts more trust toward the force-based estimate during periods of noisy or unreliable segmentation.

- Positional gap condition: Provided that the segmentation results are stable (i.e., low variance in RPE estimates), if the gap between the robot’s position $p_{\text{rob}}$ and the RPE estimate falls below the maintained distance $\Delta d$ minus a safety margin, i.e.,

$$g=p_{\text{rob}}-{\hat{z}}_{\text{RPE}}<\Delta d-g_{\text{margin}}$$ (12)

then increment $w_{\text{vis}}$ by $\Delta w$. This emphasizes the vision-based estimate to avoid over-penetration and maintain the desired separation.

After adjustment, renormalize weights as

$$w_{\text{vis}}\leftarrow \frac{w_{\text{vis}}}{w_{\text{vis}}+w_{\text{force}}},w_{\text{force}}\leftarrow 1-w_{\text{vis}}.$$ (13)

III. Experiments

A. Experiment Setup

The experimental setup, depicted in Fig. 3, comprises a robot developed before [19] configured in velocity-control mode, integrated with a Galil 4088 servo drive, which maintains a joint-velocity control loop operating at 1 kHz. Simultaneously, sensor data acquisition occurs at 200 Hz. The robotic instrument features a custom-designed 33-gauge injection needle embedded with three circumferentially arranged FBG strain sensors of $80\mu \text{m}$ diameter each. The sensors interface with an optical interrogator (SM130-700, Micron Optics, USA), enabling precise, real-time measurement of the needle-tip force. Surgical visualization is facilitated by a Leica Proveo 8 microscope, augmented by integrated intra-operative optical coherence tomography (iOCT), with the live B-scan image displayed on an auxiliary monitor (see Fig. 3, left panel).

Fig. 3.

Experimental setup. A Leica Proveo 8 ophthalmic microscope provided scanning OCT (optical coherence tomography) imaging. A Galil motion controller, interfaced via ROS, commanded the Robot SHER 2.0. Tip forces were measured with a fiber-optic force-sensing needle connected to an optical interrogator. The eye was secured in a 3D-printed holder mounted on a motorized linear stage to impose programmable motion.

Experiments are conducted using freshly enucleated ex vivo porcine eyes, which are securely mounted on a piezo-actuated linear stage (P-611, Physik Instrumente), capable of replicating physiological retinal motion through precise displacement along the needle-insertion axis. High-level system control, data logging, and visualization tasks are executed using open-source middleware running on a workstation equipped with Ubuntu 20.04.

B. Experimental Procedure

Each experimental trial commences with meticulous mounting and registration of the ex vivo porcine eye onto the linear stage, secured within a 3D-printed orbital socket. The linear stage immediately initiates sinusoidal movements with amplitudes of $100\mu \text{m}$ at 8 breaths per minute (bpm) to simulate physiological retinal pulsations from the trial outset. The amplitude (0.2 mm peak-to-peak) lies at the center of the 0.1–0.3 mm physiological range reported via iOCT [20], and the frequency of 8 bpm falls within the 6.4–19.5 bpm range observed under patient sedation [21]. Under real-time microscopic and iOCT guidance, the surgeon positions the FBG-instrumented needle tip above the subretinal space via a pre-established sclerotomy. With data recording (robot joint kinematics, linear stage displacement, iOCT frames, and filtered tip-force measurements) initiated immediately after calibration, the system then progresses through the FSM phases detailed in Section II-B:

Phase 1 (Preparation/Calibration): Stationary hold for enabling iOCT segmentation, noise reduction, and LSTM-based motion learning from 15 consecutive frames, with 1D pixel-to-millimeter calibration. Phase 2 (Pre-Contact Synchronization): Maintain constant needle-to-RPE distance $(\Delta d\approx 1\text{mm})$ via vision compensation for 5 s. Phase 3 (Transition): Surgeon manually inserts needle into subretinal space until it reaches RPE layers and stops, setting $F_{\text{target}}$ and distance medians. Phase 4 (Post-Contact): Activate vision–force fusion for motion compensation, maintaining $F_n$ within ±0.7 mN. Retraction and Re-Synchronization: The surgeon manually retracts the needle, reverting to Phase 2 for 5 seconds to assess re-calibration. Throughout the procedure, the operator always holds a physical emergency-stop button, allowing for immediate termination of robot motion in the event of unsafe behavior.

To evaluate controller robustness and adaptability, experiment with 10 different ex vivo porcine eyes, resulting in a comprehensive dataset of 12 trials. For a subset of porcine eyes, multiple trials are performed at the same retinal site to enable direct, within-site comparisons among the compensation methods. All data are synchronously logged via open-source middleware for subsequent analysis

IV. RESULTS AND DISCUSSION

A. Motion Compensation Performance

Fig. 4 illustrates the trajectories of the needle tip, ILM, and RPE across a representative trial, converted from iOCT pixel coordinates (px) to the robot’s local frame (mm) using the calibration factor. The observed trajectories confirm seamless FSM progression: the needle remains stationary during initial registration (Phase 1), achieving stable pre-contact offsets amid simulated motion (Phase 2). Post-insertion (Phase 3), the fused controller tracks RPE fluctuations with minimal deviation (Phase 4), and retraction enables prompt resynchronization (back to Phase 2) without loss of registration accuracy.

Fig. 4.

Trajectories of the needle tip (blue), ILM (orange), and RPE (green) during a representative trial, transformed from iOCT pixel coordinates to the robot’s local frame. Shaded regions mark experimental phases: Phase 1 (registration, purple), Phase 2 (pre-contact with motion compensation, green), Phase 3 (insertion, yellow), and Phase 4 (tracking, red).

Table I reports tracking performance across 12 experimental trials using ex vivo porcine eyes. In Phase 2 (pre-contact synchronization, relying solely on iOCT vision-based control), we evaluated errors using a known fixed offset (350 px ≈ 1.183 mm). In Phase 4 (post-contact regulation, integrating FBG force sensing with vision via dynamic weight adjustment), the offset was estimated robustly as the median of the observed separations, then subtracted so that metrics summarize the residual tracking error $e_t=z_{\text{pred}}-z_{\text{true}}$, in which $z_{\text{pred}}$ is the position of the needle with offset, and $z_{\text{true}}$ is the position of the RPE layer in OCT coordinate.

TABLE I.

Tracking Error Statistics Across 12 Trials. Columns report mean, median, sample std, min/max, quartiles, robust spread (Robust $\sigma =\text{IQR}/1.349)$, and CV. Conversion: $1\text{PX}=3.379\mu \text{M}$.

Phase	Metric ($\mathit{\mu }\mathbf{m}$)	Mean	Median	Std	Min	Max	IQR	Q1	Q3	Robust $\mathit{\sigma }$	CV (%)
Phase 2	Offset	1182.650	1182.650	0.000	1182.650	1182.650	0.000	1182.650	1182.650	0.000	0.000
	RMSE	31.009	31.127	1.537	28.725	33.290	1.260	30.323	31.584	0.934	4.958
	MAE	26.738	26.501	1.477	24.842	29.249	1.020	26.120	27.140	0.756	5.523
	MaxAE	60.744	60.417	3.670	56.243	66.016	4.798	58.224	63.018	3.557	6.041
	P95AE	53.104	53.729	3.795	47.637	57.686	4.916	50.665	55.581	3.645	7.146
Phase 4	Offset	273.236	266.255	34.652	230.887	320.184	48.158	250.921	299.079	35.699	12.682
	RMSE	18.517	18.993	1.466	16.422	20.240	1.828	17.503	19.331	1.355	7.920
	MAE	15.050	15.300	1.588	12.891	17.152	2.021	13.935	15.956	1.498	10.552
	MaxAE	44.184	43.184	4.568	40.349	53.044	2.352	41.626	43.978	1.743	10.340
	P95AE	35.233	35.175	2.318	31.888	38.838	1.801	34.266	36.067	1.335	6.579

We report: Root Mean Square Error (RMSE) as the overall performance across different cases; Mean absolute error (MAE) as the typical absolute deviation; Maximum Absolute Error (MaxAE) as the worst case; 95th Percentile Absolute Error (P95AE) as the tail behavior at the 95th percentile; Robust $\sigma =\text{IQR}/1.349$ as the outlier-resistant spread; and Coefficient of Variation (CV %) as the unitless relative variability.

In Phase 2, the vision-only controller achieves a mean RMSE of $31.01\mu \text{m}$ and MAE of $26.74\mu \text{m}$, with a MaxAE of $60.74\mu \text{m}$. The P95AE stands at $53.10\mu \text{m}$, indicating reliable but limited precision at larger initial offsets (mean: $1182.65\mu \text{m}$ from the RPE). These errors arise from iOCT’s 4 Hz update rate, segmentation noise, and uncompensated retinal motion, which can lead to over- or under-estimation of the needle-RPE distance $\Delta d$. While sufficient for initial alignment, this phase risks ILM perforation if motion previews deviate significantly.

Phase 4 demonstrates substantial improvements through vision-force fusion, reducing the mean RMSE to $18.52\mu \text{m}$ (40% lower than Phase 2) and MAE to $15.05\mu \text{m}$ (44% reduction). The MaxAE drops to $44.18\mu \text{m}$ (27% improvement), and P95AE to $35.23\mu \text{m}$ (34% better), at a closer mean offset of $273.24\mu \text{m}$. The CV for RMSE decreases from 4.96% to 7.92% (noting the smaller offset scale), reflecting enhanced stability. Dynamic weights prioritize the high-rate (200 Hz) FBG feedback during contact, mitigating vision latency and ensuring sub-millisecond corrections.

These reductions underscore the superiority of the combined approach: vision provides layer previews and depth estimation, while force ensures safe tip-tissue interaction. The 40% RMSE improvement enhances precision, minimizing RPE trauma risks in the fragile subretinal space ($160-290\mu \text{m}$ thick [8]). Safety is bolstered by adaptive compliance estimation $(\hat{\gamma }(t))$ and dwell-adjusted blending, preventing force spikes during motion. Compared to ex vivo benchmarks in the previous work [14], where inside-retina RMSE reached $36.25\mu \text{m}$ (MaxAE: $200\mu \text{m}$) without force integration, our fused method halves errors ($18.52\mu \text{m}$ RMSE), achieving 2.5× better MaxAE control. Robust spread (IQR/1.349) remains low (Phase 4: $1.36\mu \text{m})$, indicating outlier resistance even under segmentation variance $(>{\sigma }_{\text{thresh}}^2\text{triggers}{w}_{\text{force}}\text{increase})$. Overall, the algorithm yields micron-scale precision $(<20\mu \text{m}\text{RMSE})$, surpassing freehand tremor ($182\mu \text{m}$ [7]) and prior vision-only systems ($31\mu \text{m}$ RMSE [14]), while force limits ensure safety thresholds.

B. Comparison in Control Delay

Fig. 5 illustrates the control delay observed under three different control modalities: vision-only, force-only, and combined vision–force. The plots compare the $z$-position of the linear stage, which represents retinal motion, and the needle tip position controlled by the robotic end-effector. The temporal offset $\Delta$ between the two signals is reported as the difference in sample index, with a sampling rate of approximately $4Hz$ (i.e., one sample index corresponds to 0.25 $s$).

Fig. 5.

Example of control delay under three modalities: vision-only (top), force-only (middle), and combined vision–force (bottom). The plots compare retinal motion represented by the linear stage (orange) with the corresponding needle tip position (blue). The shaded red region highlights the temporal offset $(\Delta )$ between the two signals, where one sample index corresponds to 0.25 s at a 4 Hz acquisition rate.

The results show that the vision-only controller exhibits the largest delay, with $\Delta =3$ (~ 0.75 s). This outcome is expected, as the vision-based control relies solely on OCT images, which are limited by their acquisition rate of 4 Hz. By contrast, both the force-only and combined vision–force controllers demonstrate substantially reduced delays, with $\Delta =1$ (~ 0.25 s). This improvement is attributed to the high sampling rate (1 kHz) of the force sensor, enabling faster response to retinal motion.

All data are collected in ex vivo porcine eye experiments. The offset measurements are in the robot’s local frame for both the linear stage motion and the needle tip position. These results confirm that force sensing substantially reduces control delay. Integrating vision and force yields latency comparable to force-only control while preserving spatial awareness. The force-only modality is spatially blind: the FBG sensor measures relative force changes but cannot determine the needle’s position relative to ILM or RPE. Consequently, it may maintain nominally correct force while the tip has breached the target layer, or fail to re-establish standoff after retraction. Vision feedback resolves this by continuously providing layer distances, enabling the fused controller to enforce both force and positional safety.

C. Comparison in Force Threshold Control

Fig. 6 presents representative compensation performance assessed via tip-force measurements. Experiments were conducted on ex vivo porcine eyes using a consistent setup, with sinusoidal retinal motion imposed by a linear translation stage (amplitude $100\mu \text{m}$; frequency 8 bpm) and forces recorded at the needle tip by a force-sensing needle. Under force-only compensation, despite a target constraint of ±0.7 mN, the tip contact force frequently exceeded this bound. In contrast, the combined force+vision strategy achieved markedly better regulation, with tip forces rarely breaching the threshold. A more detailed numeric performance comparison is shown in Table II.

Fig. 6.

Comparison of raw tip force data across 140 sample points for three compensation methods: no compensation (blue), force-only (orange), and force + vision (green). The light yellow band indicates the mean force ±0.7 mN, demonstrating reduced variability with advanced compensation.

TABLE II.

Comparison of force-only vs. force+vision methods on force variation during compensation. Retina movement is around $100\mu m$ amplitude, 8 bpm. Threshold $\tau =0.7mN$.

Metric	Force	Force+Vision
Mean (mN)	1.055	1.142
Median (mN)	0.974	1.106
Std (mN)	0.548	0.296
MaxAE (mN)	1.017	0.929
Proportion within $\pm \tau$ (%)	77.5	96.7
Significance tests ($p$-values)
Mann–Whitney U (raw values)	0.103
Chi-square (within $\pm \tau$)	0.00002**

^**p < 0.001 (statistically significant).

The combined force–vision method demonstrated improved stability, as reflected in a lower standard deviation (0.296 mN vs. 0.548 mN) and reduced maximum absolute error (0.929 mN vs. 1.017 mN). In addition, the proportion of forces within the safety threshold $\pm \tau =0.7\text{mN}$ increased markedly from 77.5% to 96.7%. Statistical analysis confirmed that while the Mann–Whitney U test did not indicate a significant difference in the overall distribution of force values $(p=0.103)$, the chi-square test showed a highly significant improvement in the proportion of forces within the safe range $(p=0.00002)$. These results indicate that integrating vision feedback with force control enhances both stability and safety by reducing force excursions beyond the clinical threshold.

The vision-only strategy revealed persistent, periodic force spikes at the needle tip. Due to latency in the vision pipeline (Fig. 5), the controller exhibits a ~ 0.75 s lag relative to retinal motion. As the retina reverses direction from its inferior extreme (near the negative displacement peak) and moves upward, the robot continues to advance, driving the needle deeper into the RPE. This over-penetration produces transient force excursions and a quasi-sinusoidal force trace with pronounced peaks near the motion extrema (Fig. 7). Although no consensus “safe” tip-force threshold for subretinal injection has been established, we observed several failed insertions associated with excessive forces and damaged RPE layer in Fig. 8.

Fig. 7.

Contact force at the needle tip under vision-only control. The measured tip force (blue) shows periodic spikes corresponding to retinal motion extrema. The red dashed line indicates the baseline force, representing the minimal contact level when the retina is stationary.

Fig. 8.

Example of failed insertion under vision-only control, showing RPE damage due to excessive force. The needle shaft (red line) and tip (pink dot) penetrate the retinal layers.

In our study, force-sensing micro-needles could allow surgeons to detect abnormal resistance in real time and halt penetration before tissue damage occurs. We attempted to predict the regularity of retinal movement during surgery. However, ocular motion may vary due to physiological factors such as patient anxiety or deep breathing. Because current imaging systems do not provide true real-time feed-back, small delays may introduce bias. Future improvements in image processing speed could enable real-time monitoring and more accurate motion compensation.

All experiments used open-sky ex vivo porcine eyes lacking physiological intraocular pressure (IOP), and the singleaxis sinusoidal motion omits heartbeat perturbations and irregular breathing [20], [21]; the reported metrics therefore represent a controlled baseline. Future work will extend to closed-globe eyes with physiological IOP, multi-axis motion profiles, and ultimately in vivo validation.

V. Conclusion

This work presented an adaptive tip-force compensation framework for robotic subretinal injection, integrating iOCT vision and FBG force sensing through a unified architecture comprising an FSM for procedural coordination, an LSTM-enhanced residual Kalman filter for motion prediction, and an adaptive compliance estimator for force regulation. Ex vivo experiments on porcine eyes under simulated respiratory motion yielded a 40% reduction in tracking RMSE relative to vision-only control (to $18.5\mu \text{m}$), 2.5 × improvement in maximum error over prior benchmarks [14], 96.7% of tip forces within ±0.7 mN, and control delays of only 0.25 s. These results demonstrate that fusing anatomical context with high-rate real time force feedback enables micron-scale precision and safe tool–tissue interaction, advancing the potential for reliable robot-assisted subretinal therapeutics.