A. Bicchi

E. De Momi

E. Votta

F. Fati

M. Quacquarelli

English

Archivio istituzionale della ricerca - Politecnico di Milano

Optimizing Heart Valve Surgery with Model-Free Catheter ControlA. Bicchi1, F. Fati1, M. Quacquarelli1, E. Votta1, and E. De Momi11Politecnico di Milano, Department of Electronics Information and BioengineeringINTRODUCTIONMinimally Invasive Surgery (MIS) is nowadays the mostwidely adopted approach for treating structural heart dis-ease. Despite the superior safety achieved, and efficacy,MIS procedures are technically demanding, requiring ahigh level of dexterity to precisely maneuver the catheterand thus showing a notoriously steep learning curve. Toaddress these issues, we aim at introducing a variableshared autonomy robotic platform for intra-proceduralsupport, by robotizing the commercial MitraClip𝑇𝑀System (MCS). The MCS allows the treatment of mitralregurgitation by percutaneously implanting a clip thatgrasps the valve leaflets with a tendon-driven catheter.In this paper we propose a position control strategy thatguarantees good trajectory tracking in the intracardiacphase of the procedure, i.e. from the transseptal punctureto the positioning of the clip in the valve, see Fig. 2. Inthe field of control of catheter robots, a good model ofthe system is key to obtaining reliable control. Severalmodel-based control approaches have been proposed inthe literature [1]. The constant curvature model is the best-known one but implies significant and oversimplifyingassumptions about the catheter. The Cosserat Rod model,on the other hand, aims at providing a higher-fidelitydescription of the robot’s behavior, but it is too com-putationally expensive to be usable online [2], [3]. Data-driven model-free controllers represent a valid alternativeto analytical models, considering their potential in modeluncertainties that strongly influence soft robot control[3]. In [4], authors proposed a formulation for learn-ing the inverse kinematics of a continuum manipulatorwhile integrating the end-effector position feedback. Inthis paper, we present a Neural Network based InverseKinematic Controller (IKC), shown in the scheme in Fig.1, to control the tip position of the catheter. The inputs ofthe net are the target tip pose at the next time instant ?̄?𝑘+1,the current state of the 3 motors, 𝒒𝑘 , and the current tippose 𝒑𝑘 , while the output is the state of the 3 motors atthe next time instant 𝒒𝑘+1. Our goal is to build a robustcontrol starting from the state-of-the-art one applied tothe MCS presented in [5] by X. Zhang et all. Moreover,we characterize the control model proposed, by testing itsperformance robustness at different motors’ velocities.Fig. 1 Scheme of the Inverse Kinematic Controller. Theinputs are the desired pose at time 𝑘 + 1, ?̄?𝑘+1, thecurrent servomotors position, 𝒒𝑘 , and the current tip pose?̂?𝑘 , measured by the Electromagnetic (EM) sensor. Thetip pose is expressed as a vector with the position andorientation expressed as a quaternion. The output is theposition of the servomotor at the next time instant, 𝒒𝑘+1.MATERIALS AND METHODSThe proposed control exploits the Multi-Layer Perceptron(MLP) neural network to learn the non-linear map:( ?̄?𝑘+1, 𝒒𝑘 , ?̂?𝑘) → (𝒒𝑘+1). (1)In order to identify the aforementioned map, we exploredthe whole catheter’s workspace ”,i.e. the intracardiac-simulated environment within the robot can move fromthe transseptal puncture site to the Mitral Valve (see Fig.2),” and we built a representative data set where knownconfigurations of the motors’ state were mapped to thecorresponding tip poses, which were measured by usingthe Electromagnetic (EM) Sensor Aurora® NDI. In orderto make the measurement of the tip pose independentfrom the magnetic field generator position, we referredthe tip pose with respect to a fixed sensor at the base (Fig.2). The data acquired were then sampled and processed,obtaining a final training data set of 3500 points. Thearchitecture of the implemented MLP features an inputlayer of 17 neurons ( ?̄?𝒌+1, 𝒒𝑘 , ?̂?𝑘), two hidden layers ofrespectively 56 and 60 neurons with hyperbolic tangentactivation functions, and an output layer of 3 neurons(𝒒𝑘+1) with linear activation functions. The system iscomposed of a set of two Nema 23 Stepper motors(JoyNano), and one linear actuator Nema 17 BipolarStepper Motor (Sainsmart) that are used respectively topull tendons, for bending the catheter in mediolateral(ML) and anteroposterior (AP) planes, and to move the tipin the forward direction (LIN). Each motor is controlled bya DM556 driver (Jadeshay) and connected to an ArduinoUno microcontroller. To study the performances of theFig. 2 MitraClip𝑇𝑀 System. The image shows theentire catheter workspace after the transseptal punctureapproaching the mitral valve, in the intracardiac phase.The reference systems of the base (fixed point) and tip arealso shown.Fig. 3 Box plots show the distribution of the ED, (2),using the IK controller at two motors’ velocities. The redline represents the mean ED obtained by [5], with the PIDcontroller.proposed IK controller, the system was tested in trackingfive desired trajectories. The trajectories were recordedindependently from the data-set acquisition. For all ofthem, the catheter moved from the transseptal puncturesite to the final target on the mitral valve, see Fig. 2,following different paths. Moreover, two different motors’velocities (60 rpm for AP and ML motors, 120 rpm for LINone, 90 rpm for AP and ML, then 270 rpm for LIN) wereset to simulate slow and fast actuation and characterize thecontroller behavior. Each trajectory was repeated 3 timesat each speed, and the results were averaged. To evaluatethe performance of the control for the path following theEuclidean Distance (ED) was used:𝐸𝐷 =√︃(?̂?𝑘 − ?̄?𝑘)2 + ( ?̂?𝑘 − ?̄?𝑘)2 + ( ?̂?𝑘 − 𝒛𝑘)2 (2)between the desired position of the tip [?̄?𝑘 , ?̄?𝑘 , 𝒛𝑘] andthe measured one [?̂?𝑘 , ?̂?𝑘 , ?̂?𝑘].RESULTSOur study compared the performances of data-drivenmodel-free control with the PID model-based control pro-posed by [5]. The box plots in Fig. 3 show the distributionof the estimated position error ED with the proposed IKCapplied for the two motors’ velocities tested. The medianof the error with slower motors’ velocities is 1.98 mm,with respect to the 5.5 mm obtained at higher velocity.Moreover in Fig. 3 is reported with a red line the meanvalue of the error obtained with the PID controller in [5],which is 5 mm. The data-driven controller outperformedthe PID when the motors velocities are set to small values,with an average improvement in tracking error of 3.02mm. Overall, the results suggest that data-driven model-free control can be a promising alternative to model-basedcontrol in challenging scenarios.DISCUSSIONIn conclusion, this paper introduces a machine learningmodel-free kinematic controller for continuum tendon-driven robots and the preliminary validation results of arobotic-assisted system in comparison with a PID state-of-the-art control. Experimental results demonstrated theeffectiveness of the proposed method in path tracking ifwe stay under a curtain motor’s velocity. Future worksmay compare the proposed method with other controllersbased on a data-driven model. Additionally, anotherpromising alternative could be the implementation of adata-driven controller which exploits a different architec-ture, such as the Radial Basis Function Neural Network[6], which could be useful to compensate for modelinguncertainties and unknown external disturbances, thusachieving better tracking performance. Recurrent NeuralNetworks [7] could be also a suitable solution for con-trolling our system, since their ability to capture temporalcharacteristics.In conclusion, we would like to acknowledge the EuropeanUnion’s EU Research and Innovation program Horizon2020 under the project ARTERY, grant agreement No.101017140.REFERENCES[1] C. Della Santina, C. Duriez, and D. Rus, “Model based control ofsoft robots: A survey of the state of the art and open challenges,”arXiv preprint arXiv:2110.01358, 2021.[2] T. da Veiga, J. H. Chandler, P. Lloyd, G. Pittiglio, N. J. Wilkinson,A. K. Hoshiar, R. A. Harris, and P. Valdastri, “Challenges ofcontinuum robots in clinical context: a review,” Progress inBiomedical Engineering, vol. 2, no. 3, p. 032003, 2020.[3] D. Wu, X. T. Ha, Y. Zhang, M. Ourak, G. Borghesan,K. Niu, F. Trauzettel, J. Dankelman, A. Menciassi, and E. Van-der Poorten, “Deep-learning-based compliant motion control ofa pneumatically-driven robotic catheter,” IEEE Robotics and Au-tomation Letters, vol. 7, no. 4, pp. 8853–8860, 2022.[4] A. Centurelli, L. Arleo, A. Rizzo, S. Tolu, C. Laschi, andE. Falotico, “Closed-loop dynamic control of a soft manipulatorusing deep reinforcement learning,” IEEE Robotics and Automa-tion Letters, vol. 7, no. 2, pp. 4741–4748, 2022.[5] X. Zhang, M. C. Palumbo, F. Perico, M. Magro, A. Fortuna,T. Magni, E. Votta, A. Segato, and E. De Momi, “Roboticactuation and control of a catheter for structural intervention cardi-ology,” in 2022 IEEE/RSJ International Conference on IntelligentRobots and Systems (IROS). IEEE, 2022, pp. 5907–5913.[6] J. Xie, Y. Qian, D. Hu, and W. Liu, “Neural network adaptivetracking control for continuum robots considering modeling un-certainties,” in 2022 China Automation Congress (CAC). IEEE,2022, pp. 2176–2181.[7] A. Hashemi, G. Orzechowski, A. Mikkola, and J. McPhee, “Multi-body dynamics and control using machine learning,” MultibodySystem Dynamics, pp. 1–35, 2023.

Optimizing Heart Valve Surgery with Model-Free Catheter Control

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Optimizing Heart Valve Surgery with Model-Free Catheter Control

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