Enhanced Accuracy in Magnetic Actuation: Closed-loop Control of a Magnetic Agent with Low-Error Numerical Magnetic Model Estimation

Abstract

Magnetic actuation holds promise for wirelessly controlling small, magnetic surgical tools and may enable the next generation of ultra minimally invasive surgical robotic systems. Precise torque and force exertion are required for safe surgical operations and accurate state control. Dipole field estimation models perform well far from electromagnets but yield large errors near coils. Thus, manipulations near coils suffer from severe (10×) field modeling errors. We experimentally quantify closed-loop magnetic agent control performance by using both a highly erroneous dipole model and a more accurate numerical magnetic model to estimate magnetic forces and torques for any given robot pose in 2D. We compare experimental measurements with estimation errors for the dipole model and our finite element analysis (FEA) based model of fields near coils. With five different paths designed for this study, we demonstrate that FEA-based magnetic field modeling reduces positioning root-mean-square (RMS) errors by 48% to 79% as compared with dipole models. Models demonstrate close agreement for magnetic field direction estimation, showing similar accuracy for orientation control. Such improved magnetic modelling is crucial for systems requiring robust estimates of magnetic forces for positioning agents, particularly in force-sensitive environments like surgical manipulation.

Keywords: Closed-loop Control; Magnetic Modeling; Magnetic Robots; Medical Robotics.

Fig. 1:

The MagnetoSuture™ system, consisting of an array of 4 coils surrounding a central Petri dish. a) High-level depiction of the mechatronic components and PID control block diagram. b) A side view of the system. The camera at the top allows for real-time magnetic agent localization and recording of experiments. c) Top view from camera. d) The four coils surround the dish in the cardinal directions, enabling actuation of a magnetic field by powering the coils. e) The magnetic agent has a cylindrical needle-like shape and is magnetized axially. The green marker facilitates detection of the south pole of the magnet.

Fig. 2:

All the plots in this figure are for a unit current activation of the represented coil. The circle represents the Petri dish (region of interest). a-b) Magnetic field intensity using the dipole model and FEA results, respectively. c-d) Magnetic field gradient generated using the dipole model and FEA results, respectively.

Fig. 3:

Experimental characterization of (a) the magnetic field and (b) the magnetic gradient along the coil axis for a 1 A input current.

Fig. 4:

Representation of singular locations in the Petri dish (region of interest), vary with the change in magnetic agent’s orientation. Petri dish diameter is 85 mm. Electromagnetic coils on each sides are representative.

Fig. 5:

Among 5 trials for each path, the experiment with median position RMS error is presented. a) Representative sample of the experiments conducted (snapshots of the tracking of (P4) with an FEA-based magnetic model). b) Five different paths are implemented to compare the effect of modeling on the PID controller. The XY trajectory, time vs. position error, orientation (modulated in 0° - 360° range), and coil currents are provided in each column, from left to right, respectively.

Fig. 6:

a) Comparative box-and-whisker plots for average position RMS errors for both magnetic models. b) Corresponding orientation RMS errors for the same experiments.

Fig. 7:

All the plots in this figure are for a unit current activation of the represented coil. a-b) Normalized percentage error in the magnetic field strength between the dipole model and the FEA-based model. c-d) Normalized percentage error in the magnetic gradient along the axis of the coil between the dipole model and the FEA-based model. e-f) Absolute orientation error in the magnetic direction between the dipole model and the FEA-based model.

Fig. 8:

The computational cost of the individual processes that are taking place sequentially in a typical system loop. The subroutines can be classified as localization, controller, magnetic model-related computations, and other processes such as visuals, data savings, inter-process communications. Adding the FEA-based model slightly increases the overall loop time. The resultant loop rate reduces from 19.88 Hz to 19.49 Hz.