Multi-Point Orientation Control of Discretely-Magnetized Continuum Manipulators

Abstract

In the past decade, remote actuation through magnetic fields has been used for position and orientation control of continuum manipulators (CMs) with a single magnet at the distal tip. By leveraging multiple points of actuation along the length of the CM it is possible to achieve increasingly complex shapes, which could be of interest in complex navigation tasks, for example, in minimally invasive surgery. In this study we present an approach for multi-point orientation control of discretely magnetized CMs. The approach is demonstrated with a manipulator that contains two permanent magnets, which are each actuated inside a non-homogeneous magnetic field. We formulate an accurate field model that conforms to Maxwell's equations and apply this to the available actuation system. Furthermore, Cosserat rod theory is used to model the manipulator deformation under external wrenches, and is utilized to numerically compute a Jacobian necessary to calculate the actuation inputs. During experiments, a stereo vision setup is used for manipulator shape feedback. Target orientations are manually provided as input to show independent orientation control of the two permanent magnets. Additionally, simulations with an extended virtual clone of the electromagnetic system are performed to show the capability of achieving more complex manipulator shapes. In both scenarios, it is observed that the algorithm is able to independently control the orientation of two interconnected magnets in a non-uniform magnetic field.

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

“…The CR can also be made of ferromagnetic materials in submillimeter scale. 80 In this regard, the literature includes two pairs of Helmholtz coils, [81][82][83] BigMag, 84,85 OctoMag, 86,87 and Delta-Mag 88 actuation systems. Ullrich et al 86 steered a catheter with a curved needle attached at the CR tip using OctoMag for eye surgery.…”

“…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.…”

“…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.…”

“…Since the controller was based on the static model, the interaction control with the environment did not guarantee an oscillation-free behaviour. Richter et al 85 reported the shape control of a CR by the multi-point PI orientation control of two permanent magnets discretely located along the body of a CR. The controller, established based on a static Cosserat rod model of the CR, showed an accurate and independent 2D control of the magnets.…”