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Drape-Compatible Tool-Tip Localization for Hand-Held Laparoscopic Instruments via UWB Carrier-Phase Ranging and Trocar-Constrained Geometry

Jinseok Lee, Dongho Yee, Minsung Kim, Younghoon Noh, Seonho Shim, Juahn Oh, Yechan Seo, Jiyul Lee, Seong Jeong, Hyuk Choi, Hyoun-Joong Kong

arXiv:2609.39129v1cs.RO

TL;DR

Laparoscopic video does not reliably provide tool-tip geometry when instruments or anatomy occlude the view, and drapes block optical paths on instruments. The paper estimates both tips using UWB carrier-phase distances and trocar constraints; in a metal-rich phantom, the measured distances had σ = 0.10–0.33 mm at 35–46 Hz.

  • Problem

    Endoscope video alone does not provide tool-tip geometry when tips are occluded, and drapes block optical paths on instruments.

    Source: §I · p. 2

  • Method

    The method combines pairwise UWB carrier-phase distances with IMU-measured trocar directions, reducing the two instrument antennas to two insertion-depth unknowns.

    Source: §I · p. 2, B. Single-channel carrier-phase ranging · p. 3

  • Results

    σ = 0.10–0.33 mm at 35–46 Hz for three inter-antenna distances among metal instruments in the 11-hole phantom.

    Source: §I · p. 2

  • Takeaways & Limitations

    The trocar supplies the direction missing from drape-compatible distance measurements, making tool-tip estimation possible.

    Source: §V · p. 7

    In-vivo tip localization is not yet validated; incomplete attitude from one instrument's IMU left the live-animal records as distances rather than solved tips.

    Source: §V · p. 7

Abstract

from arXiv · show

A surgical robot policy needs to know where each instrument's working end sits relative to the camera and to the other instrument, yet a laparoscopic operation leaves only the endoscope video, and a draped instrument hides every optical path on itself. We estimate the tool tips from distances and an IMU alone. The distances are measured by ultra-wideband carrier phase between antenna nodes on the handle side of the instruments: one per hand-held instrument, one on the endoscope, all outside the sterile barrier. Take the endoscope antenna as the reference. The two instrument antennas carry six coordinates while the three pairs give three distances, so the problem is short by three, and averaging cannot close that gap because what is missing is information, not precision. Carrier phase adds one more unknown per pair, an integer that leaves distance fixed only modulo lambda/2 = 23.1 mm. The trocar settles both difficulties: each shaft passes through a port whose position is known and whose direction the on-board IMU measures, so its antenna keeps a single degree of freedom, the insertion depth. Two unknowns now face three distances -- two fix the depths and the third is left over, and that spare equation exposes a wrong integer or a wrong mounting offset instead of absorbing it. The same solve returns both tool tips in the endoscope frame, without the second carrier frequency that integer resolution usually needs, so the link never leaves a single PLL lock. In an 11-hole phantom among metal instruments the three distances hold sigma = 0.10-0.33 mm at 35-46 Hz, a sterile drape pressed onto the antennas leaves the link unchanged where an optical path would be blocked, and the logger was carried into a live rabbit appendectomy.

I. INTRODUCTION

The paper estimates laparoscopic tool geometry from UWB distances and IMU-measured shaft directions, addressing optical occlusion and draping. Trocar constraints reduce the solve to two insertion depths, and carrier-phase ranging provides sub-millimeter distance measurements.

I. INTRODUCTION

  • Endoscope video alone does not provide tool-tip geometry when tips are occluded, while draping blocks optical paths on the instruments.Optical trackers require line of sight, electromagnetic trackers degrade near metal, and marker-less estimation degrades under occlusion.Source: §I · p. 2
  • Three UWB nodes range pairwise from outside the sterile barrier, where radio crosses the drape and distance requires no line of sight.The setup places one node on each hand-held instrument and one on the endoscope.Source: §I · p. 2
  • σ = 0.10–0.33 mm at 35–46 Hz for the three inter-antenna distances among metal instruments in the 11-hole phantom.The phase-based distances also outperform ToF on blind rail displacements.Source: §I · p. 2
  • Trocar constraints reduce each instrument antenna to one insertion-depth unknown, allowing three measured distances to solve for both tool tips and expose a wrong integer or mounting offset.The method uses kinematics rather than a second carrier frequency to resolve phase ambiguity while maintaining one PLL lock.Source: §I · p. 2
  • The logger recorded 11 episodes totaling 133 seconds of three-pair ranging during a live rabbit appendectomy.With the drape pressed onto both chip antennas, the round rate was unchanged and raw static σ did not move.Source: §I · p. 2

II. RELATED WORK

Prior surgical tracking approaches face line-of-sight, metal-interference, or occlusion constraints. The paper positions trocar geometry as a way to reduce unknowns and resolve carrier-phase ambiguity without adding anchors or accumulating surgeon-controlled trajectories.

II. RELATED WORK

  • Optical tracking held 1.6–2.0 mm registration error across six NDI trackers, while EM held 2.8–3.3 mm and metal interference caused most EM failures.Marker-less endoscopic estimation degrades under occlusion, with the best SurgRIPE entry rising from 3.0 to 12.4 mm.Source: §II · p. 2
  • Hand-held laparoscopy obeys the trocar's remote centre of motion, but less rigidly than robotic RCM mechanisms because the abdominal wall enforces the fulcrum,,, [11],.Earlier uses narrowed continuous searches through pivot calibration or image lines through the insertion point; this work estimates half-wavelength integers jointly with insertion depths.Source: §II · p. 2
  • Three distances cannot place two free antennas in space, and averaging cannot repair the underdetermination,.Fixed anchors and accumulated measurements are usual remedies,, but anchors are impractical in the field and surgeons determine trajectories.Source: §II · pp. 2–3
  • UWB carrier-phase distance requires resolving an integer ambiguity, and the trocar supplies a geometric constraint for that search.Dual-frequency switching achieved sub-millimeter median error but had 10.2 cm error with a metal reflector 20 cm off line of sight.Source: §II · p. 3

A. Platform: three UWB nodes on hand-held instruments

The platform uses three external UWB nodes on a standard laparoscopic setup. Its single-channel ranging protocol is designed to preserve phase continuity and provide pairwise measurements for the trocar-constrained solve.

A. Platform: three UWB nodes on hand-held instruments

  • Three identical nodes mount on the two hand-held instruments and the endoscope, with every node outside the sterile barrier and nothing added to the part entering the patient.Each node combines a UWB board, IMU, battery, and printed mount.Source: A. Platform: three UWB nodes on… · p. 3

B. Single-channel carrier-phase ranging

  • The three nodes range pairwise on channel 5, with the radio layer organized around keeping the phase chain unbroken.All three distances are collected at 35–46 rounds/s per pair, with no failed exchange in 125,176 rounds.Source: B. Single-channel carrier-phase ranging · p. 3
  • One channel avoids PLL re-locks that re-randomize phase and caused the two-channel version to slip a cell every 30–60 seconds.The two-channel synthetic wavelength also admitted near-coincident false fixes at ±21 and ±72 mm.Source: B. Single-channel carrier-phase ranging · p. 3
  • A post-final packet measures residual carrier-frequency error, keeping block-mean phase coherence at 0.964 under forced PLL re-lock every two seconds, versus 0.885 uncorrected.Carrier phase fixes distance modulo 23.1 mm.Source: B. Single-channel carrier-phase ranging · p. 3
  • A per-round SNR and circular-consistency gate rejects measurements at multipath amplitude nulls, while ToF only seeds an episode's absolute offset.ToF is not fused into the phase distance because antenna-delay bias re-randomizes by ±70–100 mm per boot.Source: B. Single-channel carrier-phase ranging · p. 3

C. Ambiguity-grid Kalman filter

The ambiguity-grid filter tracks phase-derived distance and uses accelerometer readings to gate integer-slip corrections. The trocar-constrained solve reduces each instrument to one insertion-depth unknown, using three pairwise distances to test integer hypotheses and recover both tool tips.

C. Ambiguity-grid Kalman filter

  • The filter treats near-grid innovations as measurement artifacts unless accelerometer speed exceeds the absorption gate, with a 231 mm/s binding limit and a fivefold margin over freehand phantom speeds.The accelerometer only gates and scales the filter; if it drops out, tracking falls back to phase alone.Source: C. Ambiguity-grid Kalman filter · p. 3

D. Trocar-constrained solve: from three distances to two tool tips

  • Each trocar confines an instrument antenna to an IMU-measured shaft line, leaving insertion coordinate s_i as its only unknown.The tip is computed from the port, shaft direction, IMU attitude, mount offset, and shaft length; the endoscope antenna is treated as fixed.Source: D. Trocar-constrained solve: from… · pp. 3–4
  • Three pairwise carrier-phase measurements provide three equations for two insertion depths and three integer-slip variables.For a fixed integer hypothesis, the continuous problem is solved by nonlinear least squares; hypotheses include the null and single-pair corrections through ±5 cells.Source: D. Trocar-constrained solve: from… · pp. 4–5
  • A wrong single-pair integer cannot be absorbed by the two depths, so it appears in the residual; once depths are fixed, the same solve returns both tips in the endoscope frame.A correction is committed only when the residual margin exceeds 3 mm for five consecutive solves; correct offsets close at 0.4 mm, versus 36 mm for a wrong offset sign.Source: D. Trocar-constrained solve: from… · p. 5

E. Detachable module and mounting calibration

The logger is a detachable clip-on module that leaves laparoscopic instruments unmodified. The same module and mount were used across phantom and in-vivo instruments, with only shaft length and antenna offset changed in the model.

E. Detachable module and mounting calibration

IV. EXPERIMENTS AND RESULTS

The experiments used a calibrated two-node rail setup, a trocar-based phantom setup, and a live rabbit appendectomy. Phantom sessions included static and freehand manipulation, while rail protocols assessed drape conditions and blind displacements.

A. Experimental setup

  • The rail setup tested two mounted nodes at 150–400 mm separation against a 0.01 mm-resolution caliper, with five blind displacements spanning 25–53 mm.The rail tests preceded the three-node build and used a two-channel link.Source: A. Experimental setup · p. 5
  • Drape tests recorded 120 seconds at 250.00 mm bare, loosely draped, and with drape pressed onto both antennas; pressed-drape displacement trials had four runs, with one excluded.Source: A. Experimental setup · p. 5
  • The 11-hole phantom held the endoscope node centrally and instrument nodes on a gripper and cutter through two other ports; 39 usable episodes covered freehand and stationary manipulation.A separate freehand ablation used 16 episodes at v_max = 25 mm/s; tool-tip tests scored closure and parked-tip repeatability.Source: A. Experimental setup · p. 5
  • The logger was carried into a live rabbit appendectomy using the phantom settings, and every precision measurement followed a 15-minute warm-up.Baselines were same-radio, same-round ToF, raw phase, and a supervisory stack without the Kalman filter.Source: A. Experimental setup · p. 5

B. Radio layer: keeping the phase chain continuous

Packet-path and phase-chain changes improved ranging cadence and phase stability. The three-node single-channel schedule sustained pair-specific rates without failed exchanges, while correction and quality gating addressed drift and low-SNR rounds.

B. Radio layer: keeping the phase chain continuous

C. Rail: continuity and the sterile drape

Rail tests show continuous phase tracking through freehand motion and drape contact, while phantom tests quantify static precision and examine ToF initialization and integer-slip detection.

C. Rail: continuity and the sterile drape

  • A 75 s freehand sequence followed every transition and held four dwells at 21, 155, 151 and 132 mm with σ = 0.72–1.00 mm.On the bare rail, five blind displacements had 2.8 mm mean absolute error and zero grid slips.Source: C. Rail: continuity and the sterile… · p. 5
  • With the drape pressed onto both antennas, the three blind displacements were tracked at 0.81 mm mean absolute error.The drape left round rate, first-path SNR and raw static σ unchanged; ToF errors were 6.7–149 mm.Source: C. Rail: continuity and the sterile… · p. 6

D. Phantom: static precision, ToF and grid integrity

  • 0.22, 0.33 and 0.10 mm median σ on AB, CB and AC, respectively, across stationary phantom episodes.The measurements cover 15, 14 and 16 episodes, respectively.Source: D. Phantom: static precision, ToF and… · p. 6, Figure 6 · p. 7
  • Across two power cycles, ToF median shifted +35.2 mm and single-shot σ grew from 31 to 105 mm, so ToF seeds only an episode’s absolute offset.The second boot turned bimodal; a bias that redraws at each boot cannot be averaged away.Source: D. Phantom: static precision, ToF and… · p. 6
  • At vmax = 25 mm/s, the ablation confirmed six slips over 31.4 pair-minutes, compared with none confirmed over 30.7 pair-minutes of motion.The main detector raised 31 candidates across 22 freehand episodes; none of the witnessed candidates fell in the defined slip band.Source: D. Phantom: static precision, ToF and… · pp. 6–7

E. Trocar-constrained solve

The trocar-constrained solve uses the three pairwise ranges to estimate two insertion depths, with the remaining equation exposing inconsistent assumptions. Phantom results show that integer corrections are often withheld when evidence is insufficient, while tip accuracy is sensitive to IMU attitude.

E. Trocar-constrained solve

  • 0.4 mm three-pair residual RMS with correct mounting offsets contrasts with 36 mm for the wrong offset sign; a stationary tip held within a median 1.8 mm during manipulation.The spare equation makes wrong assumptions visible in the residual rather than absorbing them into the two depths.Source: E. Trocar-constrained solve · p. 7
  • Figure 8 depicts the three-node logger during live rabbit appendectomy, with an endoscope-view inset from the same episode.The supplied passage describes deployment, not a solved-tip accuracy result.Source: Figure 8 · p. 7
  • Wrong offset signs raised residual RMS to 26.9 mm, while one-cell slips produced 1.5, 2.4, and 4.3 mm residuals on AB, AC, and CB, reaching about 13 mm in the worst poses.One-cell slips can remain below the 3 mm commit margin, so the arbiter often stays silent.Source: E. Trocar-constrained solve · p. 7
  • 63% of 200 injected slips received the correct integer correction, while 61 remained uncorrected and 13 received a wrong cell; no false fixes occurred in 200 slip-free poses.The ±5-cell hypothesis set committed no false fix in the slip-free trials.Source: E. Trocar-constrained solve · p. 7
  • 0.92 mm median tip error with exact attitude and 0.5 mm range noise rises to 3.6 and 7.4 mm with 1° and 2° attitude errors, respectively.The passage attributes the larger errors to attitude entering through both the lever arm and solved depth.Source: E. Trocar-constrained solve · p. 7

F. In-vivo deployment

The logger was deployed during a live rabbit appendectomy using the phantom setup's mounts and logging chain, with no hardware added inside the animal.

F. In-vivo deployment

  • 11 episodes totaling 133 s of three-pair ranging and 6.0 pair-minutes of motion exposure were logged during live rabbit appendectomy.The working ends were inside the animal.Source: F. In-vivo deployment · p. 7
  • The logger used the same mounts and logging chain as in the phantom while operating through the trocars.The passage reports deployment, not validated in-vivo tip localization.Source: F. In-vivo deployment · p. 7
  • Nothing was added to the part of either instrument entering the animal during the deployment.The logger was mounted on the surgeon’s hand-held instruments.Source: F. In-vivo deployment · p. 7

V. DISCUSSION AND LIMITATIONS

The logger combines carrier-phase distances with trocar geometry to estimate tool tips, but the evidence supports sub-millimeter ranging more strongly than validated in-vivo tip localization. Its practical scope is also bounded by attitude quality, relative ranging, and assumptions about ports, packaging, and the endoscope.

V. DISCUSSION AND LIMITATIONS

  • In-vivo tip localization remains unvalidated: incomplete attitude from one instrument’s IMU left the in-vivo records as distances rather than solved tips.The authors state that more in-vivo episodes are needed.Source: §V · p. 7
  • With fused IMU, median tip error is 3.6–7.4 mm; the system delivers sub-millimeter distances and millimeter-level tips, and better attitude buys more than better ranging.Source: §V · p. 8
  • Ranging is relative and integer resolution is bounded rather than proven; ToF bias changes at each power cycle, so absolute tip accuracy against surveyed fiducials was not measured.When ToF wandered during manipulation, some candidates could not be decided.Source: §V · p. 8
  • A shifting abdominal-wall pivot can bias solved depth, and the development-board nodes need sterilizable packaging before clinical use.The endoscope is treated as fixed; movement would add a third insertion depth.Source: §V · p. 8

VI. CONCLUSION

  • Carrier phase held inter-antenna distances to σ = 0.10–0.33 mm among metal instruments, and the logger recorded a live rabbit appendectomy without adding hardware inside the animal.The trocar reduces the geometry to two insertion depths with one equation to spare, and the solve returns both tips in the endoscope frame.Source: §VI · p. 8
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