cs.ROSep 30, 2026

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

Authors: Jinseok Lee, Dongho Yee, Minsung Kim, Younghoon Noh, Seonho Shim, Juahn Oh, Yechan Seo, Jiyul Lee, +3 more

Organizations: Department of Transdisciplinary Medicine, Seoul National University Hospital. · Rosota Inc., Seoul, Republic of Korea. · Department of Mechanical Engineering, Seoul National University. · Department of Computer Science and Engineering, Seoul National University. · Department of Mechanical Engineering, Chungang University. · Eulji University College of Medicine. · Department of Medicine, Seoul National University College of Medicine. · Institute of Convergence Medicine with Innovative Technology, Seoul National University Hospital.

Abstract

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.

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