Autonomous Steering of Concentric Tube Robots via Nonlinear Model Predictive Control

Abstract

This paper presents a Model Predictive Controller (MPC) developed for the autonomous steering of concentric tube robots (CTRs). State-of-the-art CTR control relies on differential kinematics developed by local linearization of the CTR's mechanics model and cannot explicitly handle constraints on robot's joint limits or unstable configurations commonly known as snapping points. The proposed nonlinear MPC explicitly considers constraints on the robot configuration space (i.e. joint limits) and the robot's workspace (i.e. mixed boundary conditions on robot curvature). Additionally, the MPC calculates control decisions by optimizing the model-based predictions of future robot configurations. This way, it avoids configurations it cannot recover from, joint limits, singular configurations and snapping. The proposed controller is evaluated via simulations and experimental studies with a variety of trajectories of increasing complexity. Simulation results demonstrate the capability of MPC to avoid singularities while satisfying robot mechanical constraints. Experimental results demonstrate that our solution enables following of trajectories unattainable by state-of-the-art controllers with mean error corresponding to 1% of robot arclength.

Visual servoing of continuum robots: Methods, challenges, and prospects

“…Concentric-tube robots mainly incorporate two pre-curved concentric tubes with four DOFs [30][31][32] or three pre-curved concentric tubes with six DOFs. 28,[33][34][35][36][37][38] Webster et al 39 studied the VS of a 6-DOF active cannula and then conducted experiments on a 4-DOF version of the cannula. Kesner and Howe [40][41][42][43] used a visually servoed cardiac catheter guidewire inside a flexible sheath to compensate for the beating heart motions in a mitral valve repair.…”

“…Different modelling approaches have been employed to date, but the efficiency and generalisability of the models are still debatable. Some researchers have derived the kinematic and static models using analytical/numerical modelling approaches, including constant curvature-based methods, 36,39,46,50,52,53,56,59,61,64,67,68,70,75,76,[88][89][90][94][95][96][97][98] Denavit-Hartenberg method, 54 geometric methods, 38,47,48,55,65,83,86,99,100 Cosserat rod theory, 73,85,87 Euler-Bernoulli beam theory, 81 and the principle of virtual work. 84 A set of estimation/approximation-based methods was employed to derive the Jacobian of a CR, including Fourier series, 37 local Gaussian process regression, 91 column-bycolumn independent actuation, 33 numerical approach, 35,49 datadriven method, 57 Kalman filter (KF), 45 and feed-forward neural networks.…”

“…On the other hand, non-medical imaging systems comprised of a single digital camera in different scales, 33,51,65,66,[71][72][73][74]76,83,86,90,93,97,100,104 or a stereo vision system 38,39,58,62,64,67,84,85,87,94,99 have been employed to capture the intended state of CRs. Stereo vision has been implemented either by a single stereo camera or via forming a stereo system using several digital cameras/webcams.…”

“…detection, extraction, and connection, [31][32][33]59 calculating the centre of contour, 56,66,81 and segmentation. Segmentation is the most challenging stage of preprocessing that can be performed manually 38,[40][41][42]99 or automatically utilising, for instance, shape-based 95 and threshold-based methods. 49…”

“…Camarillo et al 94 reconstructed the 3D shape of a cardiac catheter using multiple cameras and a marker-less tracking method called Shape-From-Silhouette to be used for a cardiac ablation scenario. Ott et al 46 fitting a 3D polynomial to the CR body, 85 point cloud formation from the stereo images of a catheter, 84 and the point cloud formation from the stereo images of a CTCR 38 are some of the samples reported in this regard in the surveyed papers.…”