Electromagnetic Actuation System

Abstract

An electromagnetic actuation system comprising: a) one or more magnetic robots within a workspace; b) three independent robotic arms, each comprising a movable electromagnetic coil; and c) a positioning system for tracking the one or more magnetic robots, wherein the three independent robotic arms are controlled using multi-objective optimization to capture a coil configuration space for providing a magnetic field for manipulating the one or more magnetic robots within the workspace. Methods for using the electromagnetic actuation system are also provided.

Description

[Technical Field]

[0001] The present invention relates generally to electromagnetic actuation systems, and more particularly to a robotic-assisted reconfigurable electromagnetic actuation system with a human-scale workspace. [Background technology]

[0002] In recent years, the development of small-scale magnetic robots has attracted attention due to their ability to navigate within confined spaces for a wide range of applications, including targeted drug delivery, in vivo cell transport, and minimally invasive therapy, and has the potential to revolutionize biomedical research [1]–

[10] . These magnetic robots derive power from an external magnetic field generated by a magnetic actuation system. Therefore, magnetic robots can be considered end-effectors of larger robotic systems that involve external magnetic field sources.

[0003] Much of the progress has been made in the development of magnetic actuation systems, which can be divided into two broad categories based on their different magnetic field sources: electromagnetic actuation (EMA) systems and permanent magnet actuation (PMA) systems [5],

[11] ,

[12] . Here, we focus on EMA systems with cylindrical electromagnetic coils (hereafter referred to as coils). The advantages and limitations of these two types of systems have been investigated and demonstrated according to their characterization

[13] –

[18] . It has been concluded that each magnetic field source has its merits, and its selection should be made according to the actual scenario. For example, when considering systems where the magnetic field strength changes rapidly and can even be turned on or off at will, or where high-frequency magnetic field modulation is present (e.g., torque-based control of helical swimming robots), EMA systems are the preferred choice due to their comparatively superior characteristics. In addition, PMA systems are more suitable for thermally sensitive or wide-area applications than EMA systems, but their control frequencies are relatively low.

[0004] Considering the advantages and disadvantages of the two different types of magnetic field sources, magnetic actuation systems have been designed extensively over the past two decades and are primarily classified as fixed and moving systems

[19] . Generally, conventional fixed EMA systems with coils are typically utilized to manipulate microscale devices under a microscope, such as OctoMag

[20] and system expansions

[13] ,

[21] ,

[22] . Their advantages lie in their high magnetic field precision and various modalities. Unfortunately, these systems suffer from limitations such as a relatively limited workspace, poor accessibility, and rapid decay of magnetic field strength with increasing distance. Furthermore, some potential issues that hinder the expansion of coils include increased inductance and resistive heating of the coil, which requires a cooling system to mitigate

[23] . Therefore, building a fixed EMA system with a human-scale workspace remains a major challenge.

[0005] Recent research efforts have been directed toward developing mobile magnetic actuation systems with relatively large workspaces by combining the advantages of fixed magnetic actuation systems with the avoidance of their drawbacks. In particular, many studies have explored the idea of ​​using robotically operated mobile systems, due to the benefit of robotic arms providing a much larger workspace. Mahoney and Abbott proposed a robotically operated single-permanent magnet system using a six-degree-of-freedom robotic arm to control a five-degree-of-freedom mockup capsule, demonstrating a higher level of magnetic control.

[24] Pittiglio et al.

[25] presented a PMA system with dual permanent magnets actuated by two robotic arms to control gradient magnetic fields in 3D space and five independent gradients. However, this can generate undesirable transient behavior in Cartesian space and does not consider the singularity of the robotic arm. However, these mobile PMA systems may address tasks requiring high-frequency or uniform magnetic fields, as well as situations in which the magnetic field must be turned off throughout the workspace. Another approach is to design a mobile EMA system with a moving coil to achieve faster response and on / off capabilities, thereby expanding the workspace without increasing the coil size. In previous studies, moving EMA systems such as BigMag

[26] and DeltaMag

[27] were designed with moving coils that are coupled but provide a relatively large workspace. To independently control the coils' orientation and avoid potential barriers within the workspace, an EMA system named RoboMag was developed. This system utilizes three moving coils that are independently operated by a desktop robot platform

[28] . This system has an adjustable, hemispherical workspace with a diameter of 203 mm and primarily focuses on magnetic torque control.

[0006] The above analysis of existing magnetic actuation systems reveals that there is a trade-off between torque generation, force generation, and workspace accessibility when designing a magnetic actuation system. The objective of this study is to design a magnetic actuation system that not only generates a rotating magnetic field but also handles the combination of magnetic field and force with five degrees of freedom control in a human-scale workspace. Furthermore, the safety of the entire magnetic operation must be ensured. Due to the objectives and needs derived from the intended application, the following design requirements must be considered during the development process: 1) It is important to ensure that the designed system provides sufficient clearance around the human patient to meet the spatial requirements of possible integration with medical devices in the operating room. 2) The generated magnetic field is expected to be shut off in a timely manner to ensure safety when necessary. Furthermore, it is essential to provide a wider range of controllable magnetic fields. 3) The feasibility of magnetic field and gradient generation must be considered to operate different types of magnetic robots, such as helical robots operated by high-frequency rotating magnetic fields and capsule robots under force control.

[0007] In light of the above analysis, a mobile EMA system is a good option to meet these requirements. As described in

[29] , the minimum number of coils for five degrees of freedom of heading and position control is five, as long as non-magnetic restoring forces exist. In fact, designing a five-coil mobile system while providing a workspace large enough to meet clinical requirements is a major challenge. Therefore, for a mobile EMA system with a human-scale workspace, it is crucial that the coil configuration is flexible and the number of coils is as small as possible. Specifically, three linearly independent coils can be simultaneously actuated, which only requires modulating the current in each coil to generate the required 3D magnetic field and ensuring good magnetic field isotropy within a small target area [9]. Furthermore, this three-coil configuration has substantially more open access to the workspace to meet the design requirements. However, two critical issues must be further discussed and addressed. At a higher level, how do we establish a less actuated scheme to ensure an ideal magnetic field and corresponding precise force control? At a lower level, how do we design a new mobile platform capable of imparting sophisticated magnetic manipulation to a human-scale workspace?

[0008] To address these issues, which have largely been unresolved by previously reported work and ideas on the RoboMag concept, a newly designed system has been developed that enables both magnetic field and force control in a human-scale workspace. This significant improvement is primarily due to the decoupled 3D spatial motion of three coils mounted on three independent 6-DOF robotic arms, as well as the proposed control method for magnetic manipulation. The major contributions of this work can be summarized as follows: 1) The design, modeling, and control of a new robot-assisted electromagnetic actuation system capable of reconfigurable coil configurations under a novel control strategy for a human-scale workspace are reported. Furthermore, a ROS-based software framework and simulation environment are presented, which can significantly improve the efficiency of algorithm development and provide better visualization for surgeons. Furthermore, automatic magnetic field calibration software for a single coil has been developed to improve the accuracy of magnetic field calibration. This software is open source and available online at http: / / github.com / caimingxue / TRORALE. 2) A performance-guided optimization method for generating a rotating magnetic field with high isotropy is presented. Unlike previously reported control strategies, the proposed method can provide an isotropic magnetic field by ensuring an optimized coil configuration based on specific application scenarios. 3) Unlike existing mobile EMA systems that primarily focus on rotating magnetic field control, the field-priority force control method is developed, which manipulates a combination of magnetic field and force for five-degree-of-freedom control. 4) By demonstrating the successful maneuvering of a helical robot and a mock-up capsule in different scenarios, this study demonstrates a feasible and sophisticated EMA platform whose performance is comparable to or even superior to previously reported mobile EMA systems.

[0009] The approach presented here could provide a basis for developing flexible, high-performance mobile EMA systems that require a human-scale workspace for clinical applications in the operating room. Summary of the Invention

[0010] The present invention provides an electromagnetic actuation system, in one embodiment, comprising: a) one or more magnetic robots within a workspace; b) three independent robotic arms, each arm comprising a movable electromagnetic coil; and c) a positioning system for tracking the one or more magnetic robots, wherein the three independent robotic arms are controlled using multi-objective optimization to secure a coil configuration space for providing a magnetic field for manipulating the one or more magnetic robots within the workspace.

[0011] The present invention also provides a method for using the electromagnetic actuation system of the present invention, in one embodiment, the method comprising: a) inserting the one or more magnetic robots into a cavity, the cavity being within the workspace, and b) providing parameters to the system to achieve a coil configuration space for manipulating the one or more magnetic robots to achieve a desired motion.

[0012] The invention and its features can be best understood from the following detailed description and illustrative drawings. [Brief explanation of the drawings]

[0013] [Figure 1]This figure shows an overview of the RARE framework. RARE is a magnetic actuation system designed to perform autonomous magnetic manipulation in a human-scale workspace. (a) is the simulation environment developed based on the ROS architecture. (b) is the real-world RARE system developed. The system consists of three moving coils actuated by three independent six-degree-of-freedom robotic arms, enabling precise magnetic manipulation in a human-scale workspace. In addition, a low-level controller STM32 and three coil drivers are deployed to manipulate the current flowing through the coils. (c) is a schematic diagram of the hardware flow. (d) is the software flow architecture. (e) is the GUI for the magnetic field / force control unit. (f) is the image processing result for the perception unit. (g) is the GUI for the robot arm motion and planning unit. [Figure 2] Figure 1 shows the visualization window, which contains all information about the magnetic robot's movements, the robot arm's posture, and the phantom used in the experiment, while the magnetic field can also be displayed to the researcher in a clear overview. [Figure 3] This figure shows the automated collection of magnetic field data readings from a magnetic sensor via a robotic arm (Video S2). (a) is the GUI developed for magnetic field data collection. (b) is the filtering of magnetic field data readings from the magnetic sensor. (c) is the verification of the linear relationship between the magnetic field and the current. [Figure 4] 1 shows the definition of the world frame and coil frame for describing the coil configuration. The orientation of the coil frame is described using five elements (L, θ, φ, α, β) expressed in the world frame. [Figure 5] FIG. 1 illustrates a concise procedure for performance-guided optimization method for coil configuration design. [Figure 6] FIG. 1 illustrates an analysis of the convergence of the optimization process by computing hypervolumes. [Figure 7]This figure shows the comparison results of the performance metrics between two randomly sampled coil configurations and the optimized coil configuration. Coil configuration #1 and coil configuration #2 are sampled from the coil configuration space. Then, the performance metrics for the three coil configurations are calculated. Meanwhile, the current consumption is calculated by summing the currents collected under five rotation angles for a given rotating magnetic field. Without loss of generality, four cases under different rotating magnetic field directions n are implemented and evaluated. [Figure 8] FIG. 1 illustrates the NSGA-II algorithm for solving the MOO problem. [Figure 9] Figure 1 shows the performance of the magnetic field-dominated force control method in the case where the magnetic field and force have the same directional vector. (a-1)-(c-1) characterize the desired and actual force results along x, y, and z when the force amplitude is 12 mN. (a-2)-(c-2) illustrate the percentage error of the force under four different desired force amplitudes: 6 mN, 12 mN, 18 mN, and 24 mN. [Figure 10] Figures 10A-10C show the performance of the magnetic field-dominated force control method in cases where the magnetic field and force have different direction vectors. Figures 10A-10C show the desired and actual force results along x, y, and z when the force amplitude is 12 mN ... [Figure 11] Figure 1 shows the experimental setup. (a) Magnetic helical swimmer. (b) Mock-up capsule. (c) Human body model phantom. (d) PVC tube. (e) Cubic container. [Figure 12]Figure 1 shows the results of magnetically actuating a helical swimmer under the guidance of the proposed rotating magnetic field control method. Case I (a)–(c) shows the actuation of the helical swimmer in a curved tube under different combinations of magnetic field amplitude and frequency (Video S3). (a-1)–(c-1) demonstrate the movement of the helical swimmer in a simulated tubular environment and display the isotropic unit rotating magnetic field within a cubic domain under the optimized coil configuration. (a-2)–(c-2) illustrate the real-world diagram. (a-3)–(c-3) show the real-time position of the helical swimmer in the top-view image frame. Case II (d)–(f) shows the actuation of the helical swimmer in a straight tube at a distance of 80 mm to the top surface of the phantom (Video S4). (d-1)–(f-1) provide a newly optimized coil configuration that differs from the coil configuration in Case I. (d-2)~(f-2) illustrate the real-time position of the helical swimmer in the top camera frame. (d-3)~(f-3) display the isotropy of the unit rotation field under the newly optimized coil configuration. (d-4)~(f-4) show the real-time position of the helical swimmer in the side camera frame. [Figure 13] A capsule is magnetically propelled through a C-tube under the guidance of a magnetic field-dominated force control method (Video S5). Six different combinations of magnetic fields and forces are applied to propel the capsule through the C-tube. The simulated and real-world diagrams show the real-time capsule pose and corresponding coil configurations. The red arrow in the top view indicates the capsule's direction of travel. [Figure 14]This figure shows the results of magnetic propulsion of a mockup capsule under the guidance of the magnetic field-dominated force control method to track an N-shaped path in 3D space (Video S6). The overall process can be divided into three operational stages. (a)-(b) show operational stage 1, where the capsule's direction of travel remains horizontal (along the y-axis) and the force is along the yz plane. (b)-(c) show operational stage 2, where the angle between the capsule's direction of travel and the applied force direction is 180 degrees. (c)-(d) show operational stage 3, where the capsule's direction of travel remains vertical (along the z-axis) and the force is along the y-axis. [Figure 15] FIG. 1 illustrates the overall concept of the proposed system integrated with a C-arm fluoroscopy device. DETAILED DESCRIPTION OF THE INVENTION

[0014] The present invention provides an electromagnetic actuation system, in one embodiment, comprising: a) one or more magnetic robots within a workspace; b) three independent robotic arms, each arm comprising a movable electromagnetic coil; and c) a positioning system for tracking the one or more magnetic robots, wherein the three independent robotic arms are controlled using multi-objective optimization to secure a coil configuration space for providing a magnetic field for manipulating the one or more magnetic robots within the workspace.

[0015] In one embodiment, one or more of the three independent robotic arms comprises a moving stage.

[0016] In one embodiment, the workspace is adjusted by the reach and position of any of the three independent robotic arms.

[0017] In one embodiment, the workspace is a human-scale workspace.

[0018] In one embodiment, the positioning system includes one or more selected from a video camera and a C-arm fluoroscope.

[0019] In one embodiment, the one or more magnetic robots include a helical robot or a capsule robot.

[0020] In one embodiment, the magnetic field is controlled using a performance-guided optimization method or a field priority force control method.

[0021] In one embodiment, the magnetic field is a rotating magnetic field having high isotropy or a magnetic field that provides five degrees of freedom control to the one or more magnetic robots.

[0022] In one embodiment, the performance-guided optimization method comprises:

[0023]

number

[0024]

number

[0025] In one embodiment, the magnetic field dominated force control method comprises:

[0026]

number

[0027]

number

[0028]

number

[0029] In one embodiment, the multi-objective optimization is performed using the formula:

[0030]

number

[0031] In one embodiment, the three independent robotic arms are controlled using software comprising: a) a magnetic field control unit for receiving parameters for achieving desired motion for the one or more magnetic robots; b) a perception unit for collecting and processing data from the positioning system; c) a robot arm motion and planning unit for implementing coordinated motion control of the three independent robotic arms; and d) an algorithm unit for generating control commands based on feedback of position and environmental information for the three independent robotic arms.

[0032] The present invention also provides a method for using the electromagnetic actuation system of the present invention, in one embodiment, the method comprising: a) inserting the one or more magnetic robots into a cavity, the cavity being within the workspace, and b) providing parameters to the system to achieve a coil configuration space for manipulating the one or more magnetic robots to achieve a desired motion.

[0033] In one embodiment, the cavity is in a human subject.

[0034] In one embodiment, the one or more magnetic robots include a helical robot or a capsule robot.

[0035] Rapid technological advances in remote-controlled magnetic robots for biomedical applications have strongly promoted the successful development of electromagnetic actuation systems due to their ability to meet demanding magnetic requirements. However, the actuation of magnetic robots in human-scale scenarios via reported electromagnetic actuation systems still suffers from many challenges, such as the sophistication of the magnetic field and the lack of sufficient workspace for clinical use in humans. To address these critical issues, a robot-assisted reconfigurable electromagnetic actuation system, called RARE, for controlling magnetic fields (up to 17 mT) and gradients (up to 120 mT / m) in a human-scale workspace is reported. Reconfigurable coil configuration is achieved by using three movable electromagnetic coils attached to three independent robot arms. Furthermore, to improve development efficiency, a robot operating system (ROS)-based simulation environment with clear visualization is detailed. To leverage the sophisticated magnetic field generation, a performance-guided optimization method is first introduced to generate a rotating magnetic field with high isotropy in the target region by optimizing the designed evaluation metrics. A field-dominant force control method is then formulated to manage the magnetic field and force for five-degree-of-freedom (5DOF) control. The average force percentage error across all sampled direction vectors is 3.87% when the magnetic field and force are in the same direction and 9.8% when the magnetic field and force are in different directions. Finally, extensive experiments were performed to demonstrate the sophisticated performance of the system's platform in a human-scale workspace, demonstrating its potential for clinical application.

[0036] This section describes the design workflow and key components of RARE, which are key design aspects that enable the setup to perform sophisticated magnetic manipulation in a human-scale workspace. Sophistication refers to a scalable workspace, flexible magnetic field manipulability, and the ability to manipulate a wide variety of magnetic robots.

[0037] A. Overview of RARE

[0038] Guided by the objectives and needs, a robot-assisted reconfigurable electromagnetic actuation system (RARE) was developed, as shown in Figure 1 (Video S1). Table I summarizes the RARE's technical specifications. The developed RARE consists of three moving coils attached to three independent six-degree-of-freedom robot arms to generate magnetic fields and gradients in a scalable workspace. The size of the coils varies primarily depending on the reach of the robot arms used and the relative installation positions of the three robot arms. Three reconfigurable coil poses, i.e., coil configurations, can be achieved by managing the three robot arms for different application scenarios. The robot arm (SJ-603-A, Anno Robot, Shenzhen, China) has a spherical workspace with a radius of 540 mm and can carry a maximum load of 3 kg with a repeatability of 0.1 mm. A positioning system enables the RARE to autonomously track the magnetic robot and reconstruct the phantom for path planning. Each robotic arm is mounted on a movable platform (Fig. 1(a)), allowing it to be moved to the operating room and integrated with medical devices such as X-ray fluoroscopes.

[0039] [Table 1]

[0040] B. Hardware Design

[0041] The following describes the general hardware design workflow of RARE used in this study.

[0042] 1) Coil Design: In contrast to other systems that use coils as large as possible to generate higher magnetic fields, the robotic arm used in RARE can only carry a maximum payload of 3 kg, which limits the maximum weight of the coil. Furthermore, for larger coils, which pose a challenge for mobile EMA systems, the heat dissipation of the coil must be considered. Therefore, the main considerations during the coil design process are weight, diameter, and magnetic field generation capability, which are guided by simulation results using finite element (FE) analysis software (COMSOL Multiphysics, COMSOL Inc., Stockholm, Sweden). Finally, a coil with a ferromagnetic core to increase the magnetic field strength is fabricated, weighing 1.2 kg. The detailed specifications of the designed coil are shown in Table I.

[0043] 2) Positioning System: RARE currently uses two orthogonal digital cameras (MER2-160-227U3C, DaHeng) to capture the top and side views of the workspace, respectively. The frame rate of the two cameras is 50 Hz with a downsampled image resolution of 1280 × 1024 pixels. Image processing methods are used to reconstruct the environmental information and spatial position of the magnetic robot for experimental measurement and closed-loop feedback control. While not a clinically relevant imaging device like ultrasound-guided navigation

[30] ,

[31] , visual tracking of the magnetic robot is sufficient for proof-of-concept experiments.

[0044] 3) Low-Level Embedded Controller: To realize real-time control of the current flowing through the coil, the control board STM32 functions as a low-level embedded controller and receives the commanded current value from the high-level master computer. The received digital current is then coded into PWM and then sent to a servo driver (ESCON 70 / 10, Maxon Inc.) with a maximum output current of 10 A, as illustrated in Figure 1(b). A 1000 W power supply is provided as the energy source. All control commands are sent from the high-level master computer to the STM32 or the robot arm control box via socket communication (TCP / IP). The entire hardware flow is illustrated in Figure 1(c).

[0045] C. Software architecture and simulation environment design

[0046] With the advancement of robotics technology, several user-friendly interactive software frameworks and robotics simulation platforms, such as Pybullet

[32] , have emerged. However, the small magnetic robots involved in this study remain few in number. Therefore, a good software architecture and simulation environment are essential and important. On the one hand, it can provide better visualization of medical tasks and intuitive interaction for surgeons. On the other hand, the simulation environment serves as a testbed for researchers to conveniently debug and tune algorithms. Furthermore, it has the added advantage of allowing researchers to verify their ideas in a simulation environment with parameters set closest to realistic conditions before the actual application of the algorithm.

[0047] 1) Software Architecture: The overall software architecture is detailed in Figure 1(d), highlighting the interaction between different functional units and the low-level controller's communication with the high-level master computer. All software is deployed within the ROS architecture and runs on a Linux OS installed on a desktop with Ubuntu 18.04, using the Python language. This desktop is equipped with 32 GB RAM and an Nvidia RTX-3080 GPU. RARE's software is primarily developed based on five control units, which interact with each other via ROS communication. Specifically, the magnetic field / force control unit receives commanded magnetic field / force parameters to drive the desired motion of the magnetic robot (see Figure 1(e)). Real-time video frames from two cameras are collected and processed via the perception unit to track the magnetic robot's motion (see Figure 1(f)). The robot arm motion and planning unit is primarily responsible for executing coordinated motion control of the three robot arms, which differ according to the ROS-Moveit interface (see Figure 1(g)). The algorithm unit creates control commands based on feedback of the robot's state and environmental information. The designed software can integrate a user-friendly control and optimization library for algorithm development, as well as other real-time physics engines, thereby supporting more realistic physical interactions.

[0048] 2) Visualization: As illustrated in Figure 2, a customized visualization interface (RViz) in ROS was built to help surgeons clearly overview the execution of medical tasks. This GUI includes the coils, the phantom used in these scenarios, a magnetic field display window, and the magnetic robot, as well as three robotic arms, each equipped with their motion information. For visualization, a model of the magnetic robot was built in Solidworks and then imported into RViz. In addition, a visualization toolkit (VTK)-based visualization window was developed in Python, in which arrows represent the composite 3D magnetic field generated by the three coils. The visualization was synchronized with the real-world platform, providing a solution for remote control of the inventive system.

[0049] 3) Simulation Environment: To demonstrate the magnetic manipulation and evaluate the proposed controller, a simulation environment was designed based on the characteristics of a real environment, as illustrated in Figure 1(a). The simulation environment consists of three main parts: robot arm kinematics, magnetic field modeling, and magnetic robot dynamics. Specifically, the robot arm kinematics is developed for real-time path planning and collision detection. To account for realistic scenarios, the simulated magnetic field is generated by a model of a real coil. To evaluate the behavior of the magnetic robot and accurately mimic real-world scenarios, the magnetic robot dynamic model is implemented in Python and interacts with modules via the ROS API. The simulator currently supports the control of helical and capsule robots. In the future, more effort will be spent on addressing more realistic physical interactions.

[0050] D. Calibration

[0051] Developing an accurate calibration for RARE is essential for the accurate operation of the magnetic robot. In this study, an eye-based calibration should be performed to determine the relative pose between the robot arm and the camera. The easy handeye package

[33] provides easy-to-understand software for performing eye-based calibration. Here, particular emphasis is placed on the magnetic field calibration for the coils.

[0052] Investigations into single-coil magnetic field calibration have been presented in

[30] ,

[34] . These rely on magnetic field data from magnetic sensors and finite element method (FEM) simulations performed with COMSOL, typically relying heavily on data from FEA. However, FEM modeling typically does not take into account manufacturing imperfections, inhomogeneous materials, or the presence of unmodeled disturbances. In addition, the measured magnetic field data is obtained by manually moving a commercially available magnetic sensor through a workspace marked with numerous grids, requiring significant engineering effort. The calibrated magnetic field is then calculated using the calibration formula in

[34] and stored as a lookup table. Apart from single-coil magnetic field calibration, a system-wide calibration method has been introduced for fixed EMA systems consisting of multiple coils, using a static 3D magnetic sensor array placed in the center of the workspace

[35] ,

[36] . This study focuses primarily on single coils. To address the above challenges, automated magnetic field data collection software is first developed to record pairs of coil position and magnetic field data, taking advantage of the high positioning accuracy of the robot arm in this study. The recorded discrete magnetic field data are then used to obtain a continuous representation of the magnetic field using linear interpolation, instead of a lookup table. Details of the proposed automated magnetic field calibration routine are shown in Figure 3 (Video S2). To the inventors' knowledge, this is the first study aimed at open-source software for automated coil magnetic field calibration.

[0053] As shown in Figure 3(a), the software designed 33 × 50 grid cells on the YZ plane with 3 mm spacing in each direction. The coil should traverse all grid cells via the robot arm for magnetic field sampling. The grid cell size can be arbitrarily changed based on the actual situation. In Figure 3(b), a commercially available 3D magnetic field sensor (TLE493D W2B6, Infineon Inc.) is placed at a fixed position for magnetic field data sampling. Note that the raw measurements from the magnetic sensor contain some noise. Therefore, to reduce the influence of such measurement noise, an extended Kalman filter (EKF) method is applied. Figure 3(b) reports the comparison results before and after filtering. Furthermore, to avoid the nonlinear effects of ferromagnetic material saturation, the linear relationship between the commanded current applied to the coil and the generated magnetic field must be characterized. From the results in Figure 3(c), a roughly linear magnetic field-current relationship can be observed. Finally, together with the sampled magnetic field data, a 3D vector magnetic field interpolation function based on a regular grid interpolator is established to calculate magnetic field values ​​across 3D space.

[0054] To verify the performance of the proposed magnetic field calibration routine, four points in the workspace are selected to measure the actual magnetic field. Meanwhile, the calibrated magnetic field is also calculated according to the interpolation function. Furthermore, the calibration method in

[34] , which uses FEM and measurement data to generate a look-up table, was used for comparison. Table II shows the measured magnetic field B meas , the calibrated magnetic field B in

[34] F EM , and the calibrated magnetic field Bours derived by this method are summarized, respectively. Note that the frame of sampled points is represented by the tip center of the coil, and the commanded current is set to 1 A. Then, to further analyze the difference in calibration performance between this method and the method in

[34] , B FEM and B meas The ratio of the size of B ours and B meas The ratio of the size of FEM and Bmeas The angle between and B ours and B meas The angle between was calculated. The results show that the magnetic field amplitude ratio in this method is very close to 1, which means that the calibrated results agree well with the measured values. Furthermore, the angle error in this method is relatively smaller than that in

[34] . In general, the manufacturing tolerance of the coil and misalignment during system assembly are likely to be the main error sources.

[0055] [Table 2]

[0056] III. Magnetic Actuation Background

[0057] A. Notation

[0058] In this document, scalars are represented by standard lowercase symbols (e.g., v), and column vectors are represented by bold lowercase letters (e.g., v=[v x v y v y ]t) Uppercase blackboard bold symbol

[0059]

number

[0060]

number

[0061]

number

[0062] The left superscript indicates the quantity represented with respect to a particular frame (e.g., i v denotes the vector v expressed in frame i).

[0063]

number

[0064]

number

[0065] Magnetic Actuation Modeling

[0066] In this part, the position under the world frame w w p r Dipole moment m at {m} r {A·m 2}, a magnetic robot made of a magnetic material having a position w p c Dipole moment m at {m} c {A·m 2 It is shown how a magnetic robot experiences a force F{N} and a torque T{Nm} when subjected to an applied magnetic field b(p){T} generated by a coil with a}. Two assumptions must be made: 1) The resultant magnetic field is assumed to be the sum of the individual coil contributions. Since saturation of the core material is never achieved in this study, the superposition assumption is shown to be valid. 2) In many instances, it can be assumed that the magnetic robot will always attempt to align with the applied field.

[0067] In RARE, all generated fields and forces are calculated with respect to the world frame. Therefore, it is necessary for each coil to transform its field into the world frame. Since the calibrated field is expressed in coil frame c, we use the following equation to obtain the field for the kth coil (k=1,2,3) in the world frame:

[0068]

number

[0069]

number

[0070]

number

[0071] Subsequently, the magnetic field generated by the three coils is

[0072]

number

[0073]

number

[0074]

number

[0075] Applied magnetic field b( w p r The equation for the magnetic torque T acting on the magnetic robot when subjected to a force is expressed as

[37] ,

[38] .

[0076]

number

[0077]

number

[0078] The torque is the result of the tendency of the magnetic robot's dipole moment to align with the direction of the applied magnetic field. For low Reynolds number magnetic robots, this torque acts by adjusting the direction of the applied magnetic field to control the robot's direction, as long as the magnetic field strength is high enough to reject external disturbances. Therefore, it is more convenient to linearize the system by directly specifying the desired magnetic field instead of the magnetic torque. In the following part, torque control will be exemplified using magnetic field control.

[0079] Similarly, the magnetic force can be expressed as follows, emphasizing the magnetic gradient as a controllable parameter

[39] :

[0080]

number

[0081] From (3) and (4), it may be observed that to fully independently control torque and force in an isotropic magnetic manipulation workspace, by changing only the current, it is necessary to have at least eight fixed coils. It is easy for RARE to implement magnetic field control by following the inverse mapping of (2). The desired solution i d teeth,

[0082]

number

[0083] IV. Performance-guided rotating magnetic field control method

[0084] The most common application of rotating magnetic fields is to induce corkscrew motion in magnetic robots. The magnetic field generates a torque, which acts as a force, aligning the robot's dipole moment with the field. For example, a helical swimmer can move at extremely low Reynolds numbers under a rotating magnetic field

[40] . In the case of RARE, different coil configurations can achieve various local magnetic field distributions. However, determining the appropriate configuration for a specific task is essential but intractable. In this section, we rigorously analyze the key points for generating a rotating magnetic field with high isotropy to ensure control agility.

[0085] A.Problem

[0086] One of the goals of RARE is to provide a desired and controllable rotating magnetic field for magnetic manipulation. Clearly, systems like OctoMag can ensure that a small central region with an isotropic magnetic field distribution exists at the center of the workspace. Additionally, several performance metrics, including manipulability and minimum singular value, have been defined to characterize the effectiveness of different fixed systems

[36] ,

[41] . There has been no published research analyzing the magnetic field distribution according to these metrics for mobile EMA systems. How to produce a highly isotropic rotating magnetic field by managing the coil configuration using the desired performance metrics is a more challenging issue. The basic idea is to set a score for each performance metric, which serves as a performance goal for evaluating a given coil configuration. Therefore, performance-guided optimization techniques can guide users to efficiently explore this design domain while optimizing for a given performance goal.

[0087] Nevertheless, due to the nonlinear relationship between the objectives and the degrees of freedom for the three coils (each coil has five degrees of freedom, ignoring rotation along its main axis), finding the ideal three-coil configuration for a rotating magnetic field in the target region is not easily achievable. Multi-objective optimization (MOO)

[42] techniques can provide a solution for managing the multi-objective functions. Below, an investigation is conducted on how to apply this method to solve the problem.

[0088] B. Definition of evaluation metrics

[0089] To evaluate the rotating field control capability of any coil configuration, different evaluation indices can be defined. Here, we consider the characteristics of an ideal rotating field across a target region from two aspects: magnetic field isotropy and magnetic field actuation matrix isotropy.

[0090] Magnetic field isotropy: For applications requiring a rotating magnetic field, a magnetic field with isotropic properties can provide reliable operation and avoid unexpected magnetic forces on gradient-sensitive magnetic robots. With a preferred coil configuration, it is expected that the sampled magnetic field will match the desired magnetic field distribution. To this end, a measurement of isotropy can be calculated by sampling the magnetic field in multiple directions across the target area. To simplify the calculations without loss of generality, the desired magnetic field is expressed as a unit magnetic field.

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[0094] Operating matrix A b Isotropy of the magnetic field: the ability to perform a specific action at any position and orientation without singularities is of paramount importance. In the case of RARE, this analysis is based on the magnetic field actuation matrix A, as described in Section III. b It provides information similar to the classical Jacobian matrix in robotics, which can be used to characterize control isotropy.

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[0098] According to the above analysis, the magnetic field isotropy index

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[0101] C. Defining the Coil Configuration Space

[0102] To perform MOO to generate an optimized coil configuration, we must first construct a search space that includes some design constraints on the coil orientation. To this end, we create a world frame O to describe the coil configuration, as shown in Figure 4. w-xyz and coil frame O c-xyz is defined. First, each coil needs to be kept at a proper distance from the human patient to avoid obstacles. In addition, the entire configuration of the three robotic arms needs to have enough clearance for the operating table and the imaging system. As a result, the configuration adopted is one in which two robotic arms are installed on one side of the operating table and the third robotic arm is located on the other side of the table. The three coils are always above the human patient, which is reasonable for practical applications. As described in Figure 4, the generalized coordinates of each coil frame are defined by five elements with respect to the world frame:

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[0105] The set of orientation parameters of the three coils was considered as the coil configuration space (CCS). The CCS for the optimization problem was

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[0107] Constraints on each element in X should be carefully considered because they can reduce the feasible region in the objective space, resulting in obtaining a suboptimal solution.

[0108] Performance-guided optimization methods

[0109] During coil configuration optimization, locating all coils as close as possible to the target region can improve the magnetic field strength-to-current ratio, i.e., torque generation. Nevertheless, magnetic field isotropy performance may be compromised or conflicts may occur. This indicates that improving one performance metric can compromise another. Therefore, compromises should be made regarding application specifications.

[0110] The weighted sum method is widely used due to its convenience; however, weight values ​​should be assigned carefully because they are not necessarily linearly proportional to the objective function values, and different weights may result in the same optimal solution on the Pareto front. Multi-objective optimization (MOO) methods are used to find optimal solutions to optimization problems with multiple objectives, often in conflict with each other. Given a designed coil configuration space and a set of performance evaluation functions, MOO can extract the Pareto set, i.e., the coil configuration with the optimal tradeoff. As an authoritative algorithm in MOO, the nondominated sorting genetic algorithm (NSGA)-II is popular due to its simple structure and powerful global search ability

[43] , which can provide an effective method for accelerating and solving MOO problems.

[0111] Based on the above analysis, by combining the four evaluation indices and the defined CCS, the process of finding the optimal coil configuration for magnetic field control is formulated as a multi-objective optimization problem to maximize the performance criteria.

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[0114] Below we will introduce how to implement this MOO problem.

[0115] The brief procedure of the performance-guided optimization method for coil configuration design is listed in Figure 5. During optimization, first, for a sampled coil configuration x in CCS X, 27 unit magnetic fields with different directions from the 3D space are calculated.

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[0121] Once the values ​​of the four objective functions are obtained, the NSGA-II algorithm is deployed in a multithreaded manner to calculate a set of non-dominated solutions, i.e., a Pareto front. Compared to single-threaded programming, the execution efficiency of multithreaded programming is improved by approximately 50%. However, a significant difficulty lies in how to narrow down the Pareto set for practical applications to only a single suitable solution, i.e., how to select an appropriate coil configuration for further control from the obtained set. The weighted sum method is widely used due to its convenience, but the weight values ​​should be assigned carefully because they are not necessarily linearly proportional to the values ​​of the objective functions and it is not easy to ensure these weights. In this study, a solution was selected from the optimized set using the pseudo-weight vector method. The pseudo-weight w for the i-th objective function is i teeth,

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[0123] This formula is for each objective function

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[0125] It should be noted that it is impossible to know whether the algorithm has converged to the true optimal solution due to the unknown actual Pareto front. Hypervolume is a very well-known performance metric for multi-objective problems. This hypervolume exemplifies the volume between a given reference point and the provided solution. At this time, the performance metric is maximized. Figure 6 reports that the algorithm converged most of its progress during the optimization, indicating that the optimization process has converged.

[0126] E. Analysis of the optimized coil configuration

[0127] To investigate the magnetic field isotropy and magnetic field generation capability of the optimized coil configuration compared with other coil configurations, the four proposed evaluation metrics and the current consumption for a given rotating magnetic field were quantified. Figure 7 reports the detailed results. In addition to the optimized coil configuration, two other coil configurations from CCS X were sampled for comparison. Without loss of generality, the parameter L was kept constant in all three cases. As expected, the evaluation metrics show that the optimized coil configuration outperforms the other two cases. Meanwhile, the current consumption was evaluated by generating a unit rotating magnetic field for four different rotating magnetic field directions n. For each direction, current values ​​were collected at a 60° offset angle per loop, and the cumulative current of each coil was calculated. It was observed that the current consumption of the optimized coil configuration was, in most cases, smaller than the other two coil configurations. The current consumption of the optimized coil configuration was 13% lower than that of coil configuration #1 and 29.6% lower than that of coil configuration #2. Additionally, for these three configurations, the maximum difference in current consumption between any two coils is 6.6 A (coil configuration #1), 6.1 A (coil configuration #2), and 2.6 A (optimized coil configuration), respectively. Indeed, the smallest singular values ​​and inverse condition numbers also reveal the system's ability to amplify current for all directions of the magnetic field. In terms of current consumption, the worst coil configuration is unsurprisingly coil configuration #2, since it has the smallest σ3 and 1 / κ.

[0128] V. Magnetic Field Priority Force Control Method

[0129] As explained in Section III, for RARE, magnetic field control can be effectively realized by (2) and (3). In contrast, force control is more complex to analyze than magnetic field control because it requires a five-element gradient vector to determine the resultant three-element force vector, as exemplified in (4). For fixed EMA systems such as OctoMag, magnetic force can only be controlled by modulating the current. However, leveraging coil configurations and currents to manage the combination of magnetic field and force control is important for RARE.

[0130] A.Problem

[0131] For an unconstrained capsule robot, it is reasonable to assume that the capsule's dipole moment always attempts to align with the applied magnetic field (capsule trajectory control), allowing the generated force to control the capsule's movement. Because no force is applied to the robot in the absence of a magnetic field, magnetic field control should be considered if a magnetic gradient is expected to be applied to the robot. As described in

[29] , a static system requires eight independent magnetic field sources to control the magnetic field and force. The difficulty lies in how to achieve magnetic field and force control using the three moving coils of the RARE. From the perspective of magnetic task space control, it is not easy to present an explicit expression to describe the relationship between a given magnetic field, force, and the orientation and current of these three coils. Note that each coil has a total of six degrees of freedom for control: five degrees of orientation (ignoring rotation along the coil axis) and one degree of current. Below, a detailed solution to this problem is reported based on a field-dominated force control method.

[0132] B. Method

[0133] To achieve the control of the magnetic field and force by the three moving coils, the dipole moment m of the magnetic robot is rA field-first force control method is proposed under the assumption that m is always aligned with the applied magnetic field. Note that the force control varies depending on the applied magnetic field, and at least three coils are required to implement 3D magnetic field control. Therefore, for a given magnetic field and force, the proposed field-first force control method guarantees magnetic field control and optimizes the actual force to the given force with an acceptable error. m r It is clear that the value of m only affects the amplitude of the force generated. Therefore, in this further study, we will use the unit dipole moment m r In addition to controlling the magnetic field and forces during the operation of a magnetic robot, it is important to ensure that each robot arm has robust manipulability to avoid singularities for specific joint configurations. Therefore, the manipulability of the three robot arms is also emphasized in this study.

[0134] A coil configuration space CCS, which is identical to the CCS described in Section IV, was first designed. The field-dominant force control method not only optimizes the error between the desired force and the actual force, but also considers the manipulability of the robot arm. The manipulability of the robot arm is important for operation in a large workspace. The manipulability of the robot arm is a preferred performance index for the optimization function. Therefore, the MOO problem is formulated as follows:

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[0138] C. Feasibility Assessment

[0139] As a difficult high-dimensional problem to solve, verifying the feasibility of the proposed method—that is, assessing whether the magnetic robot can be operated with a desired set of magnetic fields and forces while remaining in any pose during operation—is rather challenging. Without loss of generality, to simplify the quantitative analysis of the proposed method, a direction vector space for a desired set of magnetic fields and forces is defined, and then two cases are analyzed in detail as follows. 1) Definition of the Direction Vector Space: With the definition of the magnetic field direction vector space b, it is easy for RARE to achieve any desired magnetic field control throughout the entire workspace, as shown in Section III. Specifically, b is composed of 50 direction vectors sampled from 3D space. Regarding the force direction vector space f, since three coils must be placed on a human patient under practical scenarios, a coil configuration under this constraint would undoubtedly induce a magnetic attractive force between the magnetic robot and the three-coil system. Therefore, it is impractical for RARE to generate a magnetic force with a component along the negative z direction. From the above analysis, S b and S f is intuitively defined as follows:

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[0141] Based on the designed magnetic field and force direction vector space, two different cases are identified to exploit and demonstrate the feasibility and effectiveness of this method.

[0142] 2) Case I: Magnetic Field and Force Have the Same Direction Vector: The first case, where the magnetic field and force have the same direction vector, was implemented to characterize the performance of the method. This case is suitable for many real-world scenarios, such as maneuvering a capsule robot through a tubular environment, where the magnetic force direction and the capsule's direction of travel (magnetic field direction) must be aligned with the centerline of the tube. To facilitate understanding of the evaluation process, the dipole moment m r is the unit moment

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[0145] During this evaluation, to ensure that the applied magnetic field and force have the same directional vector, the inventors remapped all directional vectors to a common directional vector.

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[0148] During optimization, the magnetic field control was assigned a higher priority and guaranteed, so more attention was paid to the feasibility of force generation. An evaluation metric, force percentage error ε, was defined to describe the difference between the desired and actual force values, which is as follows:

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[0150] The overall results are detailed in Figure 9. Based on the applied unit dipole moment and unit magnetic field, the desired force F with four different amplitudes is d The actual force obtained under 50 sampled direction vectors was observed using the desired force amplitude F d From (a-1) to (c-1) in Figure 9, the result is that the actual force F a It was observed that there was a good correspondence between the components of F and the desired value. The average force percentage error ε across all 50 directional vectors was 3.87%. In addition, the feasibility of three other cases was investigated, as illustrated in Figure 9 (a-2) to (c-2), and the force percentage error was used to determine the results. When the desired force value F d It can be seen that the force percentage error ε becomes large when ε is far from ε = 12 mN. This can be explained by the fact that once the magnetic field amplitude and dipole moment are determined, the actual force is limited to a reasonable range. This range can be roughly approximated in advance under a specific coil configuration. Another possible reason is that the manipulability index of the robot arm is taken into account during optimization, and some poor configurations for the robot arm are not allowed, which may adversely affect the force percentage error. This suggests that the manipulability index is explored and improved at the expense of the force control error.

[0151] Case II: When the magnetic field and force have different direction vectors: To further verify the feasibility of the proposed method, the case where the magnetic field direction and the force direction do not coincide with each other was considered.

[0152] First, S bfrom the magnetic field direction vector, and S f The force direction vector was randomly sampled from the . The same procedure illustrated in Case I was used to obtain the actual force generated. The results are reported in Figure 10. Notably, as shown in Figure 10 (a-1) to (c-1), the desired force F d When F is 12 mN, the generated force still corresponds well with the desired value for most directional vectors. The average force percentage error across all 50 directional vectors is 9.8%. Similarly, the actual force under the other three desired forces is observed, and the distribution of the force percentage error is shown in Figure 10 (a-2) to (c-2). This result shows that F d This reflects the deviation of the actual force from the desired value when the force amplitude is decreased or increased around = 12 mN. Furthermore, it was observed that the overall performance of this case was worse than that of Case I. This suggests that the space of achievable forces for our system is compromised when the magnetic field direction vector does not coincide with the force direction vector.

[0153] D.Analysis

[0154] The analysis of field-dominated force control provides insight into how to control the magnetic field and force for RARE-mediated magnetic manipulation in the workspace. The main limiting factors preventing the reduction of the magnetic field percentage error can be summarized in two aspects. One is the constraint on the coil configuration space, which ensures collision-free manipulation among the three robot arms. The other is related to the manipulability index of the robot arms. As one of the objective functions of optimization, this may reduce the accuracy of force control. Therefore, some solutions to the negative effects of these two limiting factors during force generation are suboptimal but within an acceptable range.

[0155] VI. Experiments and Results

[0156] To verify the performance of the presented RARE platform for magnetic manipulation and the proposed method, several sets of experiments were conducted under different scenarios. These included steering a helical swimmer swimming within a human body model phantom and propelling a mockup capsule within the same phantom and a cubic container, respectively. Thanks to the simulator environment, the control method and related parameters could be debugged and tuned by conducting these experiments in advance in a simulated environment. Real-world experiments based on the proposed control method with pre-tuned parameters could then be conducted. This means that fine-tuning is required here, rather than endless tuning from scratch to find the optimized parameters. Please see the attached video for a visualization of a typical example of the following experiments.

[0157] A. Experimental Setup

[0158] A typical use case of RARE is to operate a helical robot under the guidance of a rotating magnetic field. First, a magnetic helical swimmer capable of meeting the objectives and requirements for further demonstration was designed and fabricated using standard manufacturing processes. As illustrated in Figure 11(a), the helical swimmer contains a grade N52 NdFeB permanent magnet (2 mm diameter, 2.5 mm height) at its head position, with its dipole moment oriented perpendicular to the swimmer's main axis. In addition, to demonstrate the field-driven force control method, a mockup capsule was selected and designed, as illustrated in Figure 11(b). The capsule requires magnetic torque to adjust its direction and force to move. The capsule contains a magnet (4 mm diameter, 6 mm height) with its dipole moment oriented parallel to its main axis. Note that magnetic robots in many medical applications need to navigate through tubular tissues or the human GI system. The experimental phantom in this study is intended to emulate a real-world scenario. Therefore, a full-scale human body model phantom was utilized to mimic a human-scale scenario, the key dimensions of which are shown in Figure 11(c). To better mimic tubular tissue in the human body environment, a PVC tube with an inner diameter of 10 mm (see Figure 11(d)) was attached to a hard-to-reach location on the human body phantom model. The tube was filled with 80% glycerol to mimic a low-Reynolds-number environment. Furthermore, in Figure 11(e), an additional cubic container, also filled with 80% glycerol, was utilized to maneuver the capsule in 3D space. While these phantoms are not representative of real-world medical scenarios, they are sufficient for proof-of-concept experiments.

[0159] B. Evaluation of rotating magnetic field control

[0160] Rotating a helical swimmer under an applied rotating magnetic field is easy to visualize and therefore helps understand the coupling effect between the magnetic field source and the helical swimmer. The performance of the rotating magnetic field is evaluated under two different cases. In the first case, the helical swimmer is immersed in viscous oil in a curved tube attached to the inner wall of a human body model phantom, as shown in Figure 12(a-3), for ease of fixation and imaging. For the second case, to verify whether the helical swimmer has good swimming performance under the new coil configuration, a straight tube (see Figure 12(d-4)) within the phantom was designed, with a distance of 80 mm from the top surface of the phantom. Prior to this demonstration, the centerline of the tube was reconstructed as the desired path of the helical swimmer. Then, the position of the helical swimmer, p r can be calculated based on the image provided by the top-view camera. For two different cases, the corresponding coil configurations are controlled according to Algorithm 1. Based on the generated coil configurations, a rotating magnetic field with zero magnetic force amplitude is applied in a plane perpendicular to the centerline of the tube. This causes the helical swimmer to rotate and spiral through the silicone oil. At every instant, the positions of the three coils and the corresponding currents are calculated to ensure that the direction of the rotating magnetic field is always aligned with the centerline of the tube.

[0161] Figures 12(a)-(c) report the experimental results of the first case, including the simulated environment, real-world scenario, and image sequences for magnetic field visualization (Video S3). As shown in Figure 12(a), at the beginning of this experiment, the magnetic field amplitude and frequency are set to 4 mT and 2.5 Hz, respectively. Similarly, in Figure 12(b), 3 mT and 2 Hz are set as the amplitude and frequency for the rotating magnetic field to drive the helical swimmer through the curved section of the tube. Finally, as shown in Figure 12(c), larger magnetic field parameters are applied to operate the helical robot and reach the target position. On the other hand, to illustrate the rotating magnetic field isotropy under the optimized coil configuration, a cubic space (10 × 10 × 10 mm) centered on the helical swimmer is used. 3 ) is established to show the real-time magnetic field. Note that the actual magnetic field was scaled to unit field and three different rotation angles were sampled, as shown in Figure 12 (a-1) to (c-1). The results show that rotating magnetic fields with high isotropy can be generated over a range of amplitudes and frequencies to actuate the motion of a helical swimmer within a curved tube.

[0162] To further demonstrate the adaptability of this method to different scenarios, a new coil configuration for the second case is obtained through optimization, as shown in Figure 12(d-1). The experimental results are illustrated in Figure 12(d)–(f) (Video S4). It can be observed that the new coil configuration differs from the first case because there is a significant distance deviation between the coil and the helical swimmer. This is because potential collisions between the coil and the human body model phantom are considered during optimization. Nevertheless, the experimental results reflect that the helical swimmer still has good swimming performance. In addition, as shown in Figure 12(d-3)–(f-3), the new coil configuration also exhibits good magnetic field isotropy under the three sampled rotation angles.

[0163] In summary, the experimental results for two different cases fully demonstrate the effectiveness of the proposed method in controlling a rotating magnetic field with high isotropy.

[0164] C. Evaluation of magnetic field-driven force control in a 2D tubular environment

[0165] To evaluate the performance of the field-driven force control method, a demonstration is conducted in which a mockup capsule is propelled through a C-shaped PVC tube. More specifically, the tube is fixed to the inner wall of an anthropomorphic phantom, and the relative position between the tube and the phantom is manually determined. The field-driven force control method must ensure that the direction of travel of the mockup capsule is along the centerline of the tube and generate a propulsive force to move the capsule through the tube. Indeed, as illustrated in Case I of Section VC, the desired field and force have the same direction vector aligned with the centerline of the tube.

[0166] The experimental results are shown in Figure 13(a)-(f) (Video S5). During operation, the desired direction of the capsule is determined by the current position p rOtherwise, the capsule would be unable to move due to the constraints of the tube's inner wall. In addition, a constant perpendicular magnetic force is continuously applied to counteract the capsule's gravity. One fact that needs to be clarified is that transitioning from one coil configuration to another takes time (sometimes more than 2 seconds). This time varies depending on the trajectory execution time of the robot arm. For example, transitioning from Figure 13(a) to Figure 13(b) (real world) requires a certain amount of time for the robot arm to adjust its posture. The robot arm's movement speed can be adjusted to a higher value, but this may cause chattering and security risks. If real-time adjustment of the coil configuration based on the capsule's real-time position is adopted, this will affect the smoothness of the control procedure. Therefore, a trade-off method is to divide the movement path into different regions according to the curvature. In each region, a corresponding coil configuration is generated based on Algorithm 2 to generate the desired magnetic field and force. Note that the magnetic field is turned off during the transition to avoid unexpected capsule behavior.

[0167] D. Evaluation of magnetic field-driven force control in a 3D workspace

[0168] To further demonstrate the effectiveness of the proposed magnetic-field-driven force control method, an experiment was performed to enable the capsule to track a planned path in a 3D workspace with different moving directions, i.e., to achieve five-degree-of-freedom attitude control. The capsule was assumed to be immersed and floating in silicone oil so that its moving direction was aligned with the applied magnetic field. Both top and side cameras were employed to track the capsule's 3D position. It should be noted that the side cameras' capture of high-quality images was somewhat difficult due to the low transparency of the anthropomorphic phantom's side walls. Therefore, to avoid image blurring, a cubic container was selected to replace the anthropomorphic phantom as the experimental phantom.

[0169] Figure 14 reports the experimental results of capsule navigation under 5-DOF attitude control. The capsule follows an N-shaped path in 3D space with its travel direction pointing in a given direction (Video S6). The entire experimental process is divided into three motion stages. Specifically, for each motion stage, the desired force direction vector is not aligned with the magnetic field direction vector. That is, the travel direction does not match the motion direction, similar to Case II in Section VC. Due to the limited bandwidth of the robot arm, it is not practical to generate new coil configurations at a sufficiently fast manipulation speed to respond in time to rapid changes in the magnetic field and force direction. In addition, if real-time control of the coil configuration is required, vibrations may exist in the capsule's motion. These factors suggest that it is better to reduce unnecessary coil configuration transitions as much as possible during operation.

[0170] Based on the above analysis, a control strategy for propelling the capsule in 3D space is formulated. During each operational phase, the corresponding coil configuration is optimized according to Algorithm 2 to generate the desired magnetic field and force. The capsule's movement speed mainly depends on the magnitude of the applied force and must be reduced before approaching the next operational phase. In particular, if the magnetic field and force direction vectors remain unchanged, changes in the magnetic field and force magnitude with the same scaling factor only affect the current, not the coil configuration. Naturally, a proportional-integral-derivative (PID) method is used to calculate the scaling factor, thereby further modulating the magnetic field and force amplitude simultaneously. Note that the magnetic field magnitude should maintain sufficient strength to successfully align the capsule's direction of travel to a given direction. Furthermore, the current change is sufficiently fast, reaching 20 Hz. The results reflect that, under the guidance of the control strategy of the present invention, the capsule can follow the planned path in three operational phases. By relying on the RARE system and the corresponding control strategy, the experiments presented herein demonstrated the effectiveness of controlling the capsule for visual inspection.

[0171] VII. Discussion

[0172] Most current designs of EMA systems are limited primarily by limited workspace, oversized or complex designs, and low sophistication in magnetic field generation

[44] . These limitations limit the performance of EMA systems reported in operating rooms. Therefore, a novel EMA system was established to be suitable for human-scale workspace applications, which allows for improved sophistication in magnetic manipulation and patient access. Through multiple simulations and experiments, the feasibility of this system was demonstrated for autonomous magnetic manipulation, including actuating a helical swimmer via a rotating magnetic field in a human body model phantom, and similarly successfully propelling a mockup capsule using a field-driven force control method. The experimental results demonstrated that the system developed in this invention exhibited high sophistication in magnetic manipulation and flexible workspace, thereby enabling it to adapt to variable environments with limited access and visibility. It is worth mentioning that the developed simulation environment plays an essential role in algorithm development and evaluating the robustness of the algorithm, thereby easily avoiding unexpected movements. This provides a good validation platform with an emphasis on the safety of the surgical staff, the human patient, and the robotic system. Although this study demonstrates substantial results, several limitations exist in the current methods and results that still need to be addressed.

[0173] Currently, the magnetic manipulation paradigm in this study relies primarily on visual feedback, which is not suitable for in vivo procedures. To successfully transition to in vivo work, medical imaging devices must be fully considered to improve clinically relevant applications. In these situations where information about the magnetic robot's position is required, the use of an X-ray fluoroscopy scanner for real-time tracking can be considered a feasible alternative. As a result, the coil configuration and layout of the three robotic arms should provide an open space that allows the fluoroscopy scanner to actively monitor the status of the magnetic robot during operation. One of the exquisite performance features of this system is reflected in the feasible workspace and the mobile wheeled robotic arms. This is achieved by the reconfigurable coil configuration achieved by the three robotic arms and the mobile wheeled platform, as shown in Figure 15. Thanks to the mobile platform, the developed system can be wheeled into the operating room without changing the room layout and can be easily integrated with a C-arm and fluoroscopy scanner. This can be considered an important advantage of using this robotic system for clinical applications guided by fluoroscopy in the operating room. However, assuming that the system of the present invention can be wheeled in and out as needed, a major challenge is the accuracy of the calibration of the three robotic arms with the fluoroscopy scanner. A possible solution is to design a mechanical positioning mechanism to ensure that the three robotic arms can be fixed in the desired position before each task. In addition, this study recognized that the automated calibration process for the three robotic arms in the presence of fluoroscopy equipment requires further research.

[0174] Experimental results on the operation of a helical swimmer demonstrate that the proposed performance-guided optimization framework successfully generates coil configurations with favorable performance metrics while performing various tasks. An important aspect of the inventive concept that has not been fully addressed in this study is the kinematic singularity of the robot arm. It should be noted that rotating magnetic field control only requires current changes. This is because the robot arm can move close to the helical swimmer and move along the helical swimmer by maintaining the coil configuration within the workspace. Specifically, singularities at specific workspace points can be avoided by considering the manipulability of each robot arm as an objective function during optimization. However, this can result in a decrease in the isotropy of the magnetic field generation. In fact, multiple validations in a simulation environment have shown that the optimized results are met even without considering manipulability. This is because the simulation environment can always cover the specific workspace. To reduce current consumption, the optimized results tend to maintain the coils at a close distance from the magnetic robot. As a result, if a task requires a large distance to avoid obstacles in the workspace, a new coil configuration will be optimized by varying the parameter L in the coil configuration space. The advantage of using a simulation environment is that new coil configurations can be run in the simulation environment to evaluate whether the current configuration is near a kinematic singularity. Note that the value of the parameter L depends primarily on the obstacles between the coil and the magnetic robot, which allows a conservative value to be given for complex environments at the expense of slightly higher currents.

[0175] Regarding kinematic singularities during field-dominated force control, the manipulability of each robot arm is considered as an objective function during optimization to maintain the largest possible manipulability ellipsoid volume. Unlike rotational field control, field-dominated force control requires transitioning between different coil configurations to generate the desired magnetic field and force. Therefore, to ensure that the robot arm is as far away from the singularity as possible, the manipulability of the robot arm must be considered by slightly sacrificing force control performance. The most likely limiting factor for this method is the transition phase between the two different coil configurations. For example, during capsule actuation, the magnetic field is turned off during the transition phase to avoid unexpected capsule movement. This is because it is not easy to control the movement and magnetic field generation of three robot arms to maintain the expected capsule position and heading. Meanwhile, a low-bandwidth robot arm takes time to complete the transition phase, and the capsule is subject to the effects of gravity during this phase. In experiments, a silicone oil environment provided damping that could ensure the capsule's positional stability in a short period of time. However, this phenomenon would fail in the case of high flow velocities, such as pulsatile blood flow, which may require a high-bandwidth robotic arm to improve response time. Another issue worth considering is the N-shaped path created by closed-loop tracking in 3D space. Note that scaling the field and force amplitudes with a common scaling factor calculated by the PID method can only be achieved by varying the current. This strategy is intended to control the capsule's velocity while reducing unwanted coil configuration transitions. However, as the desired force magnitude approaches zero, the applied magnetic field also approaches zero. In the presence of large disturbances, this could cause the capsule's dipole moment to become misaligned with the applied magnetic field. As a result, the assumption that the magnetic robot's dipole moment is aligned with the applied magnetic field becomes invalid. In conclusion, to improve stability during magnetic manipulation, robust control algorithms and advanced strategies for coil configuration transitions should be further investigated.

[0176] On the other hand, improvements can be made with respect to the static glycerol environment. For real-world scenarios, a dynamic environment is essential and requires further research

[45] ,

[46] . On the other hand, environmental disturbances still pose considerable challenges to current control methods. To overcome this limitation, a possible solution is to use learning-based techniques in this system to obtain automated and precise motion control

[47] ,

[48] . Previously reported work

[39] detailed a reinforcement learning method for a magnetic robot to reject unknown flow velocities. The designed simulation environment can also provide a training environment for reinforcement learning to create robust policies.

[0177] From the above analysis, it is clear that the current version of the system still has some limitations, and it remains unclear whether such a system enables safe magnetic manipulation in clinically relevant scenarios. The system designed and presented in this study provide a novel solution for implementing magnetic manipulation with compelling performance. Improvements in the sophistication of the system could potentially benefit other medical applications, such as drug delivery. Apart from untethered magnetic robots, magnetic catheters could also be steered under the guidance of the system developed in this invention. In the next generation of systems, some improvements could be adjusted accordingly. The research presented here is expected to provide readers with a rule-of-thumb guideline in terms of combining magnetic actuation robotics with robotic platforms, as well as benefit future healthcare.

[0178] VIII. Conclusion

[0179] In summary, a mobile EMA system that relies on three robotic arms for autonomous magnetic manipulation in a human-scale workspace has been developed. Specifically, with three moving coils attached to three independent robotic arms, the developed system can provide sufficient air space for sophisticated magnetic field generation and integration with medical imaging systems. Meanwhile, the development of a simulation environment is beneficial for algorithm development. To improve the accuracy of magnetic field modeling, an automatic magnetic field configuration and interpolation scheme is detailed. To ensure the precision of magnetic field generation, a performance-guided optimization procedure is first implemented to control the coil configuration and generate a rotating magnetic field with high isotropy. A comparative study is also conducted to verify the optimized results. A field-dominated force control method is then proposed and analyzed, which can achieve the operation of a capsule robot with five degrees of freedom in 3D space. Validation experiments highlight the sophistication and effectiveness of the designed system in magnetic manipulation. Overall, the results reported in this study reveal the potential capabilities of our system in clinically relevant scenarios.

[0180] Future research will focus on improving the system design and demonstrating the clinical feasibility of the present system, while advanced control strategies will be developed to improve the efficiency and safety of autonomous robot navigation under the present system in dynamic environments.

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Claims

1. a. one or more magnetic robots within a workspace; b. three independent robotic arms, each equipped with a movable electromagnetic coil; c. a positioning system for tracking the one or more magnetic robots; wherein the three independent robotic arms are controlled using multi-objective optimization to reserve coil configuration space for providing magnetic fields for manipulating the one or more magnetic robots within the workspace.

2. The electromagnetic actuation system of claim 1 , wherein one or more of the three independent robotic arms comprises a moving stage.

3. The electromagnetic actuation system of claim 1 , wherein the workspace is adjusted by the reach and position of any of the three independent robotic arms.

4. The electromagnetic actuation system of claim 1 , wherein the workspace is a human-scale workspace.

5. The electromagnetic actuation system of claim 1 , wherein the positioning system includes one or more selected from a video camera and a C-arm fluoroscope.

6. The electromagnetic actuation system of claim 1 , wherein the one or more magnetic robots include a helical robot or a capsule robot.

7. The electromagnetic actuation system of claim 1 , wherein the magnetic field is controlled using a performance-guided optimization method or a field-driven force control method.

8. The electromagnetic actuation system of claim 7 , wherein the magnetic field is a rotating magnetic field having high isotropy or a magnetic field that provides five degrees of freedom control for the one or more magnetic robots.

9. The performance-guided optimization method comprises: [Equation 1] providing the coil configuration space based on During the ceremony, [Equation 2] 8. The electromagnetic actuation system of claim 7.

10. The magnetic field dominant force control method comprises: [Equation 3] providing the coil configuration space based on During the ceremony, [Equation 4] and F ｄ denotes the desired force value, F(x) denotes the actual force value under a specific coil configuration x, and the manipulability [Equation 5] 8. The electromagnetic actuation system of claim 7, wherein:

11. The multi-objective optimization is performed using the formula: [Equation 6] The electromagnetic actuation system of claim 1 , further comprising determining a single solution using a pseudo weight vector approach using:

12. the three independent robotic arms: a. a magnetic field control unit for receiving parameters to achieve a desired motion for the one or more magnetic robots; b. a perception unit for collecting and processing data from said positioning system; c) a robot arm motion and planning unit for performing coordinated motion control of the three independent robot arms; d. an algorithm unit for generating control commands based on feedback of position and environmental information of the three independent robotic arms; 10. The electromagnetic actuation system of claim 1, controlled using software comprising:

13. a. inserting the one or more magnetic robots into a cavity, the cavity being within the workspace; b. providing parameters to the system to achieve a coil configuration space for manipulating the one or more magnetic robots to achieve a desired motion; 10. A method for using the electromagnetic actuation system of claim 1, comprising:

14. The method of claim 13 , wherein the cavity is in a human subject.

15. The method of claim 13 , wherein the one or more magnetic robots include a helical robot or a capsule robot.

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