Adorno, Bruno Vilhena

Mcgrath, Brendan

Tang, Yuan

Weightman, Andrew

English

The University of Manchester - Institutional Repository

The University of Manchester ResearchAutomated Robotic Needle Puncture for PercutaneousDilatational TracheostomyLink to publication record in Manchester Research ExplorerCitation for published version (APA):Tang, Y., Mcgrath, B., Weightman, A., & Adorno, B. V. (in press). Automated Robotic Needle Puncture forPercutaneous Dilatational Tracheostomy. In 5TH UK ROBOT MANIPULATION WORKSHOPPublished in:5TH UK ROBOT MANIPULATION WORKSHOPCiting this paperPlease note that where the full-text provided on Manchester Research Explorer is the Author Accepted Manuscriptor Proof version this may differ from the final Published version. If citing, it is advised that you check and use thepublisher's definitive version.General rightsCopyright and moral rights for the publications made accessible in the Research Explorer are retained by theauthors and/or other copyright owners and it is a condition of accessing publications that users recognise andabide by the legal requirements associated with these rights.Takedown policyIf you believe that this document breaches copyright please refer to the University of Manchester’s TakedownProcedures [http://man.ac.uk/04Y6Bo] or contact uml.scholarlycommunications@manchester.ac.uk providingrelevant details, so we can investigate your claim.Download date:24. May. 20245TH UK ROBOT MANIPULATION WORKSHOP 1Automated Robotic Needle Puncture forPercutaneous Dilatational TracheostomyYuan Tang, Brendan McGrath, Andrew Weightman and Bruno V. AdornoI. INTRODUCTIONPercutaneous Dilatational Tracheostomy (PDT) is routinelyperformed on patients who require prolonged mechanicalventilation [1]. Without the direct visualization of the trachea,the position of the PDT needle puncture is determined bypalpating the patient’s neck and operators’ skills, resultingin large position and angular errors and associated damagecaused by the needle tip [2]. The allowable puncture precisionin current clinical practice is ±30◦ of midline deviation aslong as the puncture position is close to the midline plane [3],which requires a long learning process for operators to achievesuch precision every time.Robotic technologies have been widely adopted in variousminimally-invasive surgeries (MISs), demonstrating the poten-tial to replace some manual procedures. A few prototypeswere developed to perform PDT but none of them provideguidance for PDT puncture or automate the insertion process[4], [5]. Robotic systems that provide guidance using sensorsand automate the needle puncture will not only achieve highprecision but also release the operator’s action from thisstep, decreasing the procedure complexity and easing clinicaltraining. To achieve precise incision and prevent any damagecaused by the robots, we use constrained controllers based onVector-Field Inequalities (VFIs) [6]. In this framework, thedynamics between obstacles in the workspace and the robot isgiven by differential inequalities in a constrained optimizationproblem, being suitable to generate safe motions during theinsertion procedure.This research aims to adopt a robotic system that replacesthe manual needle puncture and automates the process to im-prove puncture precision and ease the PDT training. Measuringthe direction of the midline and the destination position be-tween tracheal rings manually using electromagnetic sensors,the robot manipulator is guided using the pose information andVFI-based constrained control laws to automatically completethe puncture without colliding with the patient’s body oraccidentally hitting nearby tissues.II. SYSTEM OVERVIEW AND PROBLEM FORMULATIONPuncture procedure is divided into two steps. During thefirst step, the end-effector moves to the start position to alignwith the midline without colliding with the patient’s body.Y. Tang, A. Weightman and B. V. Adorno are with the ManchesterCentre for Robotics and AI, University of Manchester, Manchester,UK (yuan.tang@manchester.ac.uk, andrew.weightman@manchester.ac.uk,bruno.adorno@manchester.ac.uk)B. McGrath is with Manchester University NHS Foundation Trust, Manch-ester, UK (brendan.mcgrath@manchester.ac.uk)During the second step, the robot advances the needle alongthe midline until its tip reaches the puncture destination point.We use a constrained control law to generate the velocitycontrol inputs u ≜ q̇. The desired task vector for the PDTpuncture is given by xd ∈ Rm and ẋd is a feedforward term.The task error is given by x̃ ≜ x − xd, where x is the taskvector, usually measured externally or estimated using forwardkinematics. The control input u is given byu ∈ argmin ∥Jq̇ + ηx̃− ẋd∥22 + λ2 ∥q̇∥22subject to W (q)q̇ ⪯ w(q),(1)where J ∈ Rm×n is the task Jacobian for an n-DOF robotand an m-DOF task, and η ∈ (0,∞) is a proportional gaindetermining the convergence rate and λ ∈ R is the dampingfactor. The ℓ (scalar) linear constraints in the control inputsare represented by W ∈ Rℓ×nand w ∈ Rℓ.The VFIs consist of differential inequalities used to preventcollisions between the robot and geometrical primitives. Adifferentiable signed distance d (q (t)) ∈ R between twocollidable entities is defined, such that ḋ (q (t)) = Jd (q) q̇,with Jd ≜ ∂d(q)/∂q being the distance Jacobian. Then, givena constant safe distance ds ∈ [0,∞) anda signed error distanced̃(t) ≜ d(t)− ds, enforcing the inequality˙̃d(t) ⩾ −ηdd̃(t) ⇐⇒ −Jdq̇ ⩽ ηdd̃(t) (2)ensures that d̃(t) ≥ d̃(0)e−ηdt [6]. Therefore, if d(0) ≥ ds,then d(t) ≥ ds for all t > 0. An analogous reasoning applieswhen the inequality is reversed. If the goal is ensure d(t) ≤ ds,it suffices to enforce˙̃d(t) ≤ −ηdd̃(t) ⇐⇒ Jdq̇ ⩽ −ηdd̃(t). (3)a) First step: In the first step, the robot moves the needletip to the puncture start location with the z-axis aligned withthe puncture direction (midline) and positioned above thetarget puncture position with distance df along the midline(see Fig. 1). To avoid any part of the robot arm hitting thepatient’s body, we define a cylinder with a radius dc to coverthe patient’s body. While moving the robot end-effector to thepuncture start position, any point on robot links should notenter the restricted cylinder.The desired task vector in (1) is given by xd ≜vec8(xpx1), with xp being the unit dual quaternion represent-ing the rigid motion from the global frame to a frame locatedat the insertion point, with the z-axis pointing outward, andx1 = (r1 +12εp1r1), with p1 = df k̂ and r1 = ı̂ (i.e., r1is a rotation of π rad around the x-axis). The vec8 operator5TH UK ROBOT MANIPULATION WORKSHOP 2Fig. 1. (A) Simulation setup. Midline vectors were randomly selected from four octants to simulate different patient anatomy. (B) Time response of thedistance between the needle tip to the puncture destination in Step 2. (C) Time response of the needle-to-midline (line-to-line) angle in Step 2. (D) Timeresponse of the needle tip-to-midline (point-to-line) distance in Step 2. (E) Time response of the needle-to-midline (line-to-line) distance in Step 2.maps the eight dual quaternion coefficients to a vector. Thetask vector is given by x = vec8 x, with x being the dualquaternion representing the end-effector pose [7]. Because thedesired set-point is constant, ẋd = 0.b) Second step: During the second step, two new prim-itives are defined to restrict the needle tip motion to insidea cylinder with small radius dr around the puncture midlineinsertion, and to avoid rotating it outside a maximum allowableangle θp.In this step, the needle tip position is controlled instead ofits pose to release DOFs. Therefore, the task vector in (1)becomes x ≜ vec3 p, where p ∈ Hp is the pure quaterniondescribing the needle position. The desired time-varying taskvector is given by xd(t) = vec3 pd(t), where pd(t) ∈ Hp isgenerated using a quintic polynomial to ensure we can defineboth start and end velocities and accelerations for the needletip [8]. The vec3 operator maps the three coefficients of a purequaternion to a vector in R3. The feedforward term is givenby ẋd(t) = vec3 ṗd(t).c) Constraints: The definition of constraints is done byusing elements of the dual quaternion algebra [6]. For instance,to ensure that a given point pr ∈ Hp in the robot is outsidethe cylinder enclosing the patient, we consider the patient’scylinder’s midline given by a Plücker line, lp = lp+εpp× lp,with lp ∈ Hp being the line direction and pp ∈ Hp beingan arbitrary point in the midline. Then, it suffices to find the(squared) distance between pr and lp and its correspondingJacobian, to define an inequality such as (2). An analogousreasoning is done to maintain any desired point inside theguiding cylinder described in Section II-0b, but an inequalitysuch as (3) is used instead [6].Finally, to constrain the needle tip orientation in the secondstep, we constrain the angle between the needle tip and thepuncture guideline by using a conic constraint that is alsotransformed into an inequality such as (3) [9].d) Simulation: Simulations were conducted using Cop-peliaSim (Coppelia Robotics, Ltd., Switzerland) to evaluatethe precision of the robotic puncture. The puncture start pointis defined along the midline with a 30 cm distance from thedestination. Midline vectors were randomly generated from thefour octants in the global frame. The trajectory was generatedusing designated puncture duration T = 10 s with initial andfinal velocities and accelerations equal to zero. Fig. II(b-e)show the time response for different aspects of the punctureprocedure. We define the maximum allowed tip angle asθp = 0.5◦ and the radius of the cylinder around the guidingmidline as dr = 0.2mm.III. CONCLUSION AND FUTURE WORKThe constrained control using VFIs to ensure safe robotictracheostomy has been verified in simulation. Future work willfocus on replicating the results obtained in simulation on a realrobot operating on a mannequin.REFERENCES[1] C. G. Durbin, “Tracheostomy: why, when, and how?” Respiratory care,vol. 55, no. 8, pp. 1056–1068, 2010.[2] G. Servillo and P. Pelosi, Percutaneous tracheostomy in critically illpatients. Springer, 2015.[3] M. Rudas, “The role of ultrasound in percutaneous dilatational tra-cheostomy,” Australasian Journal of Ultrasound in Medicine, vol. 15,no. 4, pp. 143–148, 2012.[4] M. Botyrius, Q. Liu, C. M. Lim, and H. Ren, “Design conceptualizationof a flexible robotic drill system for minimally invasive tracheostomy,”in 2018 IEEE International Conference on Real-time Computing andRobotics (RCAR). IEEE, 2018, pp. 584–588.[5] X. Xiao, H. Poon, C. M. Lim, M. Q.-H. Meng, and H. Ren, “Pilot study oftrans-oral robotic-assisted needle direct tracheostomy puncture in patientsrequiring prolonged mechanical ventilation,” Frontiers in Robotics and AI,vol. 7, p. 575445, 2020.[6] M. M. Marinho, B. V. Adorno, K. Harada, and M. Mitsuishi, “Dynamicactive constraints for surgical robots using vector-field inequalities,” IEEETransactions on Robotics, vol. 35, no. 5, pp. 1166–1185, 2019.[7] B. V. Adorno, “Robot kinematic modeling and control based on dualquaternion algebra—part i: Fundamentals.” 2017.[8] M. W. Spong, S. Hutchinson, and M. Vidyasagar, Robot modeling andcontrol. John Wiley & Sons, 2020.[9] J. J. Quiroz-Omaña and B. V. Adorno, “Whole-body control with (self)collision avoidance using vector field inequalities,” IEEE Robotics andAutomation Letters, vol. 4, no. 4, pp. 4048–4053, 2019.

Automated Robotic Needle Puncture for Percutaneous Dilatational Tracheostomy

https://pure.manchester.ac.uk/ws/files/297777666/Abstract.pdf

Automated Robotic Needle Puncture for Percutaneous Dilatational Tracheostomy

Abstract

Similar works

Full text

Available Versions

The University of Manchester - Institutional Repository