A layout optimization method of a three-magnet rotating magnetic drive system

Abstract

This disclosure relates to a layout optimization method for a three-magnet rotary magnetic drive system, addressing the common problems of multi-degree-of-freedom magnetic drive systems that rely on multiple magnets to collaboratively generate magnetic fields for drive, including complex structures, prominent coupling between degrees of freedom, significant magnetic field crosstalk, poor output isotropy, and low space utilization. This solution systematically and multi-objectively optimizes the spatial position parameters and rotation axis pointing parameters of the three permanent magnets. Without increasing unnecessary structural complexity, it improves the minimum singular value of the control matrix, enhancing the system's effective controllability and operational stability in three-dimensional space. Simultaneously, it improves the directional uniformity of the magnetic field output and suppresses channel coupling and crosstalk, resulting in more balanced, predictable, and stable magnetic field vector control within the target area. This leads to a high-performance rotary magnetic field generator suitable for integration into the end effector of a robotic arm.

Description

Technical Field

[0001] This disclosure relates to magnetically driven continuum robots, and more particularly to a layout optimization method for a three-magnet rotary magnetic drive system. Background Technology

[0002] Magnetic field control and magnetic navigation technology has become a research hotspot in the field of microrobotics, especially in the biomedical field. Due to its unique advantages of remote, non-invasive control and good biocompatibility, the technology of using external magnetic fields to drive navigation microrobots is highly favored. Low-intensity magnetic fields can drive microrobots to perform complex diagnostic and treatment tasks such as targeted drug delivery, minimally invasive surgery, and micro-manipulation within the confined spaces of the human body. However, it is necessary to generate a spatially controllable rotating magnetic field and gradient magnetic field to meet the microrobot's posture adjustment and propulsion requirements. This places stringent demands on the performance of the magnetic field generating device and is one of the core challenges restricting the widespread adoption of this technology.

[0003] Existing multi-degree-of-freedom rotating magnetic field control devices still suffer from shortcomings in their implementation path, failing to meet engineering requirements. Schemes using only one or two rotating permanent magnets lack sufficient adjustable degrees of freedom to support continuous control of the three-dimensional rotating magnetic field vector, easily leading to control degradation in certain directions. This manifests as a low minimum singular value of the control matrix, sometimes approaching zero, resulting in insufficient magnetic field output capability and decreased control accuracy in specific directions. Even with an increase to three permanent magnets, if the spatial positions and rotation axis orientations remain empirically arranged or regularly symmetrically arranged, the system may still exhibit weak directions in certain postures or mission directions, significantly reducing the synthetic magnetic field strength and control sensitivity, making it difficult to achieve stable and reliable three-dimensional directional coverage. Furthermore, multi-magnet superposition control is generally accompanied by insufficient output isotropy and channel crosstalk issues. Adjusting a magnetic field component in one direction often triggers undesirable changes in other components, causing difficulties in channel coupling and decoupling, thus limiting the accuracy of independent multi-degree-of-freedom control and increasing the control compensation burden. Meanwhile, existing layout designs often fail to uniformly optimize the rotation axis orientation as a system variable, easily leading to insufficient axis dispersion and excessively high correlation of magnet contributions, further limiting the system's effective controllability and overall efficiency. For applications requiring spatial pose adjustment at the end effector of a robotic arm, these problems are further amplified by the limited end-effector space and installation dimensions, making it difficult for the device to achieve controllability, uniformity, and low coupling within a compact structure. Summary of the Invention

[0004] To address all or some of the aforementioned problems, this solution proposes a layout optimization method for a three-magnet rotating magnetic drive system. By optimizing the multi-magnet rotating magnetic field generation mechanism and layout parameters, the magnetic field control performance is comprehensively improved, adapting to the application requirements of advanced magnetic navigation and magnetic drive.

[0005] Firstly, this disclosure proposes a layout optimization method for a three-magnet rotation drive system, comprising: based on an initial placement layout of the three magnets, performing a global search using a differential evolution algorithm to generate candidate placement layouts, retaining candidate placement layouts that satisfy geometric hard constraints, and eliminating dynamically unexecutable placement layouts using dynamic task constraints; for each remaining candidate placement layout, calculating the three-magnet control output vector at the target point. Construct the control Jacobian matrix , Let the rotation angle of the motor with three magnets about its own rotation axis be denoted by a weighted matrix. Calculate the matrix Calculate the minimum singular value that characterizes static controllability. Set multiple static performance metrics, including static controllability. For each candidate placement layout, if any static metric exceeds a threshold, calculate the penalty value, and then obtain the total penalty value F for all metrics. The top K1 candidate placement layouts of L, from smallest to largest, are selected as candidate optimal layouts. Micro-domain robustness verification is performed to obtain the optimal layout of three magnets. The geometric hard constraints include the minimum safe distance constraint between the centers of any two magnets and the maximum span constraint of the magnet set. The micro-domain robustness verification involves applying a small perturbation to the position and axial parameters of the candidate optimal layout and re-evaluating the static index.

[0006] In one embodiment of the above technical solution, the static performance indicators include static uniformity, static decoupling, axial dispersion, and non-coplanar constraints, and the penalty value for each indicator is calculated as follows: when Calculate the penalty value , The minimum singularity threshold is q, which is a preset exponent. Calculate the isotropic penalty that characterizes static homogeneity : , , 'n' is the rank-related parameter corresponding to the output dimension. When the isotropic penalty exceeds a preset threshold, the penalty value is calculated. , The preset unidirectional threshold is used; Calculate the non-target channel output leakage characterizing static decoupling and normalize the sum to obtain the crosstalk value. When crosstalk exceeds the threshold, a penalty value is calculated. , The preset crosstalk threshold is used; Calculate the dispersion index of the three axes , For each rotation axis unit vector, calculate the penalty value when the axis dispersion exceeds the threshold. ; Perform non-coplanar constraint judgment when the layout envelope volume or equivalent volume ratio Below the preset threshold Calculate the penalty value ; , , , , , Preset penalty factor.

[0007] In one embodiment of the above technical solution, dynamic task constraints are used to eliminate placement layouts that are dynamically unexecutable. Specifically, for each candidate placement layout, a preset task sequence is executed to solve for its motor angle sequence. Maximum angular velocity angular acceleration and total variation of angle series ,when , If either of these conditions exceeds the motor's operating limit or the TV exceeds the threshold, the candidate placement layout will be eliminated.

[0008] In one embodiment of the above technical solution, the placement posture is: , To describe the spherical coordinate parameters of the magnet's center position, It is the polar angle between the rotation axis and the z-axis in the global coordinate system. It is the azimuth angle of the projection of the rotation axis onto the xy plane in the global coordinate system relative to the x-axis.

[0009] In one embodiment of the above technical solution, after performing a global search using the differential evolution algorithm, a local optimization algorithm with boundaries, L-BFGS-B, is used for refinement.

[0010] Secondly, this disclosure proposes a three-magnet rotary drive device, including three permanent magnets, three sets of rotary drive mechanisms, and a mounting frame. Each permanent magnet is equipped with an independent rotary drive mechanism. All magnets and drive mechanisms are integrated and assembled, and are fixedly connected to the end of a robotic arm. The robotic arm can achieve global position adjustment. The layout parameters of the three magnets are obtained by any of the above methods.

[0011] Thirdly, this disclosure proposes a computer-readable storage medium storing a computer program that can be loaded by a processor and execute any of the methods of this disclosure.

[0012] The beneficial technical effects of this invention are as follows: 1) This invention achieves high-quality rotating magnetic field control using three magnets, requiring fewer magnetic sources and resulting in a compact structure. Electromagnetic systems with more magnetic sources have a lower engineering burden in terms of size, wiring, heat dissipation, and power supply, making them easier to integrate into cavity intervention devices or confined space platforms; 2) This invention incorporates the spatial position of the magnets and the direction of the rotation axis into a unified, calculable design framework. Through index constraints and optimization solutions, reproducible layout parameters are obtained, avoiding the performance instability and difficulty in reproducibility issues caused by relying on experience-based placement or repeated debugging in existing solutions, resulting in better engineering consistency; 3) This invention is guided by controllability, explicitly suppressing weakly controllable and near-singular states during the design phase, ensuring the target point is attached to... The output capability is more balanced in all directions, reducing the situation where the field strength in certain directions is significantly weak or the attitude is sensitive, thereby improving control accuracy and stability; 4) Under the same evaluation system, the present invention simultaneously constrains uniformity and channel coupling, significantly reducing the mutual influence between shafts caused by crosstalk, making the synthesis and adjustment of the rotating magnetic field closer to independent controllability, reducing the difficulty of control compensation and increasing the available bandwidth; 5) The present invention incorporates assembly feasibility and dynamic executability into the design constraints, ensuring manufacturability and integrability through minimum spacing and size upper limit, and constraining the peak speed, acceleration and cumulative rotation angle requirements of the motor through task sequence simulation, so that the resulting layout not only has excellent static indicators, but also can achieve stable control within the actual motor capability range. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a schematic diagram of the overall framework of a three-magnet magnetic control system in one embodiment.

[0015] Figure 2 This is a schematic diagram illustrating the parametric modeling and magnetic field mapping relationship of a magnet system in one embodiment.

[0016] Figure 3 This is a flowchart of a multi-magnet system layout optimization algorithm in one implementation.

[0017] Figure 4 This is a simulation diagram of the spatial layout and magnetic dipole parameterization of a multi-magnet system in one implementation method. Detailed Implementation

[0018] According to the background technology, existing multi-degree-of-freedom magnetic drive systems mostly rely on multiple magnets to generate magnetic fields in concert to achieve drive. They generally suffer from problems such as complex structure, prominent coupling between degrees of freedom, obvious magnetic field crosstalk, poor output isotropy, and low space utilization. These defects make it difficult for the system to achieve independent and precise control of each degree of freedom, and hinder the compact design of the device, thus limiting the promotion and application of this technology in fields such as precision control.

[0019] Based on this, the core technical problem that this invention aims to solve is to provide a three-magnet multi-degree-of-freedom magnetic drive system with optimized magnet layout. By introducing a multi-objective optimization design method based on ε-constraint strategy, the invention coordinates core indicators such as magnetic field isotropy, decoupling performance, magnetic field crosstalk, and layout compactness. By improving the minimum singular value of the system and optimizing the magnet layout, the invention significantly improves the isotropy and decoupling performance of magnetic field control, reduces magnetic field crosstalk, simplifies the system structure, and improves compactness, thereby achieving precise and stable control of multi-degree-of-freedom magnetic fields.

[0020] The following description, in conjunction with the accompanying drawings, clearly and completely describes how the technical solution of this case is implemented. Obviously, the described embodiments are only a part of the embodiments of this case, and not all of them. Based on the embodiments in this case, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this application.

[0021] The three permanent magnet rotating magnetic field control device in this solution uses three permanent magnets as the core unit for generating the magnetic field. Its overall structure is adapted to the installation requirements of the robotic arm's end effector, allowing it to adjust its spatial posture along with the robotic arm and achieve magnetic field control over the target working area. The three permanent magnets are arranged around the target working area, each driven by an independent motor mechanism, enabling single-degree-of-freedom rotation around its preset axis. By adjusting the direction of the magnetic dipoles, the synergistic superposition and precise control of multiple magnetic sources within the target area are achieved. The three permanent magnets are mounted on a support frame or modular base, which is rigidly connected to the robotic arm's end effector. Their spatial layout is uniformly described by a set of structural parameters, specifically including the distance between the center of the permanent magnet and the target working point, the spatial azimuth and polar angle positions, and the installation orientation of each permanent magnet's rotation axis in the global coordinate system.

[0022] This invention designs and optimizes the structural parameters of the spatial layout of a three-magnet rotating magnetic field device, which can improve the uniformity of magnetic field direction coverage within a limited installation space, while effectively reducing coupling and crosstalk problems generated during multi-magnet collaborative control.

[0023] In the design and optimization of the structural parameters of a three-magnet rotating magnetic field device, a multi-objective optimization framework based on an ε-constraint strategy was constructed for the three permanent magnet system to jointly determine the spatial layout parameters and rotation axis orientation of the permanent magnets. The optimization process focuses on minimizing the singularity of the magnetic field control matrix, while performance indicators such as magnetic field isotropy, channel crosstalk level, and rotation axis dispersion are uniformly incorporated as constraints or auxiliary optimization objectives into the solution process. By setting clear threshold requirements for each indicator and simultaneously evaluating the feasibility and performance of the parameters during the global search, this invention obtains a combination of three-magnet layout parameters that satisfies the constraints and has balanced performance. This ensures that the system maintains stable controllability, good directional uniformity, and low control coupling within the target area, while adapting to the limited load and installation dimensions of the robotic arm end effector. This design and optimization achieves a reasonable balance between performance, structural compactness, and engineering feasibility of the three-permanent magnet rotating magnetic field control device, while also considering the integration requirements of the robotic arm.

[0024] In another embodiment, the focus is on the optimized design and controllable implementation of a three-magnet rotating magnetic field system. The core is to transform the empirical selection of the magnet's spatial layout and rotation axis orientation into a calculable, constrained, and reproducible engineering design process. This transformation enables the resulting structure to possess stable controllability, good directional uniformity, and low channel coupling near the target point, while simultaneously meeting the motor's dynamic capability requirements for covering the task sequence. For ease of implementation, the device structure and method flow are also provided, along with a complete explanation of key parameters, modeling relationships, index definitions, optimization solutions, and verification processes, in conjunction with the accompanying drawings.

[0025] (I) Overall Framework of Magnetic Control System like Figure 1As shown, the device uses three permanent magnets as the core unit for generating the magnetic field. Its overall structure is adapted to the installation requirements of the robotic arm's end effector, allowing for spatial posture adjustment along with the robotic arm to control the magnetic field of the target working area. Specifically, it consists of three permanent magnet assemblies M1 / M2 / M3; three sets of rotary drive mechanisms; a mounting frame; and a control and computing unit. Each permanent magnet is equipped with an independent rotary drive mechanism. All magnets and drive mechanisms are integrated and fixedly connected to the end effector of the robotic arm, enabling global position adjustment by the robotic arm. The three magnets are arranged around the target point in the working space. Each magnet is rigidly connected to its corresponding drive mechanism and rotates around a preset rotation axis. The drive mechanism is preferably a servo motor or stepper motor with an encoder to achieve angle closed-loop and repeatable positioning. By adjusting the direction of the magnetic dipoles, the synergistic superposition and precise control of the magnetic fields from multiple sources within the target area are achieved. The mounting frame for the three permanent magnets is used to fix the magnet positions and ensure assembly accuracy. The control and computing unit is used to solve for layout parameters, simulate and evaluate task sequences, and issue angle commands during runtime. The mounting frame is rigidly connected to the end effector of the robotic arm, or the mounting frame is rigidly connected to the end effector of the robotic arm via a base. The target point is preferably the center of the workspace or a reference point for treatment and operation. This invention uses the magnetic field and magnetic field gradient at the target point as the control output, which can be used to control only the magnetic field vector or to simultaneously constrain the gradient components to meet more complex manipulation requirements.

[0026] (II) Parametric Modeling and Magnetic Field Mapping Relationship like Figure 2 As shown, to make the three-magnet layout computable, a unified parametric description is used for each magnet, specifically including the distance between the permanent magnet center and the target working point, the spatial azimuth and polar angle positions, and the installation orientation of each permanent magnet's rotation axis in the global coordinate system. Static indices and static geometric constraints are then defined based on this. For the three-magnet system, the runtime control input is the motor rotation angle of each magnet around its own rotation axis, denoted as: , For three-dimensional real space, .

[0027] To uniformly describe the spatial arrangement and magnetic field output relationship of the three permanent magnets, this invention first establishes a global Cartesian coordinate system. This coordinate system is denoted as... The origin of the global coordinate system is set at a reference point in the target working area, preferably the center point of the workspace surrounded by three magnets or the target point to be controlled by the expected magnetic field. The x, y, and z axes of the global coordinate system are determined according to the system installation reference. When the system is loaded onto the end effector of the robotic arm, the global coordinate system is preferably aligned with the end effector flange coordinate system, or a fixed relationship is established with the robotic arm tool coordinate system through a known rigidity transformation. The end effector flange coordinate system is used as the local coordinate system. The local coordinate system can be mapped to the global coordinate system through fixed extrinsic parameters.

[0028] The magnetic field at the target point is calculated using the magnetic dipole model. The magnetic field gradient G allows for quantifiable evaluation of the system's output capability, enables optimization solutions, and allows for comparisons of the same aperture across two-magnet, three-magnet, and four-magnet systems. The control output vector is defined as ( (in 8-dimensional real space)

[0029] in, This represents the magnetic field vector at the target point. For the independent components of the magnetic field gradient tensor at the target point, defined as

[0030] in The coordinates of the target point The j-th component, Since there is no current in the workspace and the static magnetic condition is satisfied, the magnetic field satisfies... and Therefore, the trace of the gradient tensor is zero and satisfies symmetry. To avoid redundancy, this scheme uses five independent gradient components commonly used in magnetic control. The remaining components are determined by the constraint relationships.

[0031]

[0032]

[0033]

[0034] therefore, It also covers the magnetic field control capability related to magnetic torque and the gradient control capability related to magnetic traction force, providing a unified interface for the subsequent construction of controllability indices based on the Jacobian matrix.

[0035] At the structural design level, each magnet is described using a five-parameter standardized approach. The position is mapped from spherical coordinates to Cartesian coordinates, and the rotation axis orientation is defined by Euler angles to define the rotation matrix. This ensures that the layout and axial description are consistent, reproducible, and can be directly used as optimization variables.

[0036] Specifically, the magnet placement pose is used as an optimization variable. The i-th magnet is described using five geometric variables and defined as follows: , where N is the number of magnets, and we choose N=3.

[0037] Position parameters The spherical coordinate parameters used to describe the center position of each magnet are converted to global Cartesian coordinates:

[0038] Axial parameters Used to describe the orientation of the magnet's local coordinate system relative to the global coordinate system. It is the polar angle between the rotation axis and the z-axis in the global coordinate system. This is the azimuth angle of the projection of the rotation axis onto the xy-plane in the global coordinate system relative to the x-axis. This scheme uses Euler ZY rotation, rotating around the z-axis and then around the y-axis to construct a rotation matrix from local to global: , and This is the standard rotation matrix around the global y-axis and z-axis.

[0039] At the dynamic parameter level, the controllable degrees of freedom of the system are the motor rotation angles of each magnet. The unit direction of the magnetic dipole moment. Written as:

[0040] And to provide its pair for subsequent construction of the Jacobian matrix. The derivative form:

[0041] Therefore, the structural design parameters of each magnet are composed of five elements. It is confirmed that a total of 15 structural variables need to be designed for the three magnets, while only adjustments are needed during runtime. This can generate different magnetic fields and gradient outputs.

[0042] (III) Constructing a core evaluation and constraint system Based on the aforementioned device and parameterization, a core evaluation and constraint system is constructed. By introducing a weight matrix, key indicators such as minimum singularity, isotropy, crosstalk, and axial dispersion are simultaneously constrained. This structurally suppresses weakly controllable directions and near-singular states, avoids directional capability imbalance, reduces channel coupling, and improves control precision.

[0043] First, this solution sets up geometric hard constraints to ensure manufacturability and assemblability, avoiding assembly interference and magnet collisions; and maintains a safe distance from the human body, with the center-to-center distance between any two magnets satisfying the minimum safe distance constraint.

[0044] At the same time, an upper limit is set on the overall layout scale, for example, constrained by the maximum span (workspace) of the magnet assembly:

[0045] in, To maximize workspace, ensuring a compact structure that can be integrated into the designated equipment space.

[0046] Secondly, to ensure the inherent controllability of the layout at the structural level, this invention defines and constrains static performance indicators. These static performance indicators include static uniformity, static decoupling, axial dispersion, and non-coplanar constraints.

[0047] Before quantifying static performance metrics, we first establish a linearized mapping from input to output near the target point and characterize the layout quality by manipulating the Jacobian matrix.

[0048] Specifically, the Jacobian of the magnetic field with respect to the magnetic moment is obtained directly:

[0049] This matrix depends only on the geometric relative position vector. , and control angle Irrelevant.

[0050] Gradient components are defined as , regarding the formula Taking the derivative, we can obtain the first... The explicit form of the gradient components contributed by each magnet:

[0051] in The symbol for Kronecker. express The One portion, express The Each component.

[0052] Further Taking the derivative, we can obtain the sensitivity in the form of a third-order tensor.

[0053] in These are the standard basis vectors of the global coordinate system. To maintain consistency with the five independent gradient components mentioned earlier, definition Then the first A pair of magnets The derivative can be written as Explicit matrix:

[0054] Each row takes the corresponding get; For any target point The task output vector can be written as

[0055] because and For control angle The dependence is solely through the magnetic moment reflect, The Jacobian matrix can be obtained using the chain rule. List

[0056] Finally, the control Jacobian matrix is ​​obtained by concatenating the columns to obtain the Jacobian matrix. : When N=3, we have

[0057] Next, considering that the output components include magnetic field and gradient with different dimensions, this scheme introduces a weighting matrix. and based on the matrix Define static performance metrics.

[0058] Specifically, static controllability is achieved by minimizing singular values. Representation, defined as: It reflects the system's weakest control capability. The larger the value, the less likely it is to exhibit weakly controllable or near-singular states; therefore, this scheme will improve... This serves as the core design guiding principle. With controllability as the core guiding principle, weakly controllable and near-singular states are explicitly suppressed during the design phase, making the output capabilities in all directions near the target point more balanced. This can reduce situations where the field strength in certain directions is significantly weak or attitude sensitivity is high, thereby improving control accuracy and stability.

[0059] when Calculate the penalty value if the value is less than the minimum singular value lower bound threshold. , It is the lower limit threshold for the minimum singular value.

[0060] Static homogeneity is characterized by an isotropic penalty, let: , Where n is the rank-related parameter corresponding to the output dimension, and the isotropic penalty is defined as... .when When the value approaches 0, it indicates that the control matrix is ​​closer to the ideal equilibrium in terms of energy distribution and correlation, and the correlation is lower.

[0061] When the isotropic penalty exceeds a preset threshold, the penalty value is calculated. , This is a preset threshold for the same direction.

[0062] Static decoupling is characterized by crosstalk. This scheme calculates the output leakage of non-target channels by exciting them one by one with a single-channel unit command, and then normalizes and accumulates the results to obtain the crosstalk value ct. The smaller the crosstalk, the weaker the channel coupling and the easier it is to control independently. Under the same evaluation system, the uniformity of synchronous constraints and channel coupling are significantly reduced, which reduces the inter-axis mutual influence caused by crosstalk. This makes the synthesis and adjustment of the rotating magnetic field closer to independent controllability, reduces the difficulty of control compensation, and increases the available bandwidth.

[0063] When crosstalk exceeds the threshold, a penalty value is calculated. , This is the preset crosstalk threshold.

[0064] To avoid a decrease in effective degrees of freedom due to the three rotation axes being too close together, this scheme further introduces an axis dispersion index, assuming that the unit vector of each rotation axis is... ,definition: , A smaller value indicates that the axial direction is closer to orthogonal dispersion, which is more conducive to improving isotropy and reducing crosstalk.

[0065] When the axis dispersion exceeds the threshold, a penalty value is calculated. .

[0066] To prevent structural degradation caused by the near-coplanar positioning of the three magnets, this scheme also introduces non-coplanar constraints, employing layout envelope volume or equivalent volume ratio. As a soft constraint indicator, it is required to be no lower than a preset threshold. To ensure three-dimensional spatial distribution. When Higher than the preset threshold Calculate the penalty value at that time. .

[0067] In the above penalty calculation, q is a preset exponent, q=1,2,3 or4, with 2 being the preferred value.

[0068] For optimization problems involving multiple coexisting indices, this solution employs an ε-constraint strategy to achieve controllable trade-offs. Upper threshold values ​​for indices such as isotropy, crosstalk, axis dispersion, and non-coplanarity are determined through machine sampling. And set a minimum singularity lower limit threshold. In the optimization evaluation, when If any static index exceeds the threshold, it is directly determined as infeasible and a penalty is applied; for layouts that are close to the threshold boundary but still feasible, a soft penalty is introduced to give the final solution a margin, thereby improving the ability to adapt to assembly errors and calibration errors.

[0069] The optimization problem can be represented as: min , , , , , , This is a preset penalty factor. The smaller L is, the better the placement parameters of the three magnets, specifically referring to the position and axial parameters of the three magnets.

[0070] (iv) Layout optimization algorithm for multi-magnet system To ensure efficient solution and stable convergence, this scheme adopts a two-stage solution path. First, based on the initial placement layout of the three magnets, a differential evolution algorithm is used for global search to obtain candidate placement layouts. Then, the L-BFGS-B local optimization algorithm with boundaries is used for refinement to obtain the candidate placement layout parameters that satisfy the constraints and have the best performance. A soft penalty is introduced for layouts close to the threshold to improve the adaptability to assembly and calibration errors.

[0071] To ensure that the optimization results meet the requirements of real tasks, this solution introduces dynamic task constraints. It evaluates the peak speed, peak acceleration and cumulative angle requirements of the motor using representative task sequences, eliminates dynamically unexecutable placement layouts, and ensures that the system does not experience actuator saturation or insufficient response in actual control.

[0072] Specifically, a representative task sequence is constructed as a preset task sequence, and the required angle sequence of the corresponding motor is solved for each candidate placement layout. Maximum angular velocity angular acceleration and total variation of the angle sequence:

[0073] when or When the motor's operating limit is exceeded or the TV exceeds the threshold, the corresponding candidate placement layouts are determined to be dynamically unexecutable placement layouts and are removed to avoid motor saturation and response lag.

[0074] The above solution steps include: defining discrete angular velocity and angular acceleration based on the angle increment.

[0075] Based on this, peak angular velocity and peak angular acceleration are defined as dynamic intensity indicators:

[0076] in Corresponding magnet number. The above indicators are used to characterize the maximum demand level of motor rotation and acceleration / deceleration. The sampling period is... Discrete time is defined as , , This represents the total number of discrete moments contained in the sequence.

[0077] In practical control processes, in addition to being constrained by continuous angular velocity, discrete control updates are also limited by the amplitude of single-step angle changes. This paper defines the maximum single-step angle change as:

[0078] To measure the cumulative change of the angle sequence and the smoothness of control throughout the task, the total variation (TV) of a single magnet is introduced, with the maximum total variation among all magnets used as the evaluation metric for system-level smoothness and executability. A larger value indicates that at least one motor needs to complete a large cumulative rotation during the task, which usually leads to higher energy consumption, mechanical wear and control complexity.

[0079] By ensuring manufacturability and integrability through minimum spacing and upper size limits, and by constraining the peak speed, acceleration and cumulative angle requirements of the motor through task sequence simulation, the resulting layout not only has excellent static performance, but also achieves stable control within the actual motor capability range.

[0080] In terms of robustness, this scheme employs micro-neighborhood robustness verification, applying small perturbations to the position and axial parameters of the candidate optimal layout and recalculating. Along with isotropy and other indicators, worst-case scenarios are incorporated into the scoring or penalty to prevent layouts that perform well only at ideal parameter points and are sensitive to errors from being selected. The number of candidate optimal layouts can be the top 10% in ascending order of L value; the specific percentage can be changed.

[0081] Based on simulation comparison results, such as Figure 4 As shown, in the unoptimized three-magnet layout, the magnets are often approximately coplanar or the rotation axes are highly correlated, resulting in a weakening of the magnetic field output capability in some directions and a decrease in the minimum singular value. The initial values ​​were too low, resulting in increased isotropic penalties and significant channel crosstalk. After optimization, the magnets exhibit a more dispersed three-dimensional distribution in space, with each rotation axis tending to separate from the others, reducing axial correlation. This allows the minimum singular value to remain stably above the set threshold within the target region, while simultaneously decreasing crosstalk and improving isotropic performance. Under the same dynamic task sequence, this layout further demonstrates reduced required peak angular velocity and total variation, thereby reducing the dynamic load on the actuator and improving the stability of the control process.

[0082] Simulation results show that the three-magnet layout obtained through ε-constrained multi-objective optimization achieves more stable controllability and directional uniformity near the target point, significantly improves the control capability in the weakest direction, and markedly reduces channel crosstalk. Furthermore, even with geometric constraints, it can still output a feasible solution that is assemblable and structurally compact. Simultaneously, this scheme was validated under representative task sequences to meet the dynamic requirements of the motor. The optimized layout is within acceptable ranges for peak speed, peak acceleration, and cumulative rotation angle, satisfying the actuator's controllability requirements.

[0083] Furthermore, this scheme compared two-magnet, three-magnet, and four-magnet systems under the same simulation caliber. The results showed that the three-magnet scheme achieved a more reasonable trade-off between structural complexity and control performance, verifying the feasibility and effectiveness of this scheme.

[0084] In summary, this solution provides a layout optimization method for a three-magnet rotary drive system, enabling the magnets to be integrated into the end effector of a robotic arm in a compact structure, while still achieving stable multi-degree-of-freedom magnetic field control capabilities within a limited installation space. This solution systematically and multi-objectively optimizes the spatial position parameters and rotation axis pointing parameters of the three permanent magnets, improving the minimum singular value of the control matrix without increasing unnecessary structural complexity. This enhances the system's effective controllability and operational stability in three-dimensional space, while simultaneously improving the directional uniformity of the magnetic field output and suppressing channel coupling and crosstalk. This results in more balanced, predictable, and stable magnetic field vector control within the target area, thus forming a high-performance rotary magnetic field generator and design method suitable for integration into the end effector of a robotic arm. The three-magnet rotary magnetic field control system obtained by this solution can achieve high-quality rotary magnetic field control, requires fewer magnetic sources, has a compact structure, and reduces the engineering burden of electromagnetic systems with more magnetic sources in terms of size, wiring, heat dissipation, and power supply, making it easier to integrate into related intracavity intervention equipment or confined space platforms.

[0085] This invention can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of the invention.

[0086] For example, a layout optimization method for a three-magnet rotary drive system is as follows: Figure 3 As shown, the process includes: an initial placement layout based on three magnets; a global search using a differential evolution algorithm to generate candidate placement layouts; retention of candidate placement layouts that satisfy geometric hard constraints; and elimination of dynamically unexecutable placement layouts using dynamic task constraints; for each remaining candidate placement layout, calculation of the three-magnet control output vector at the target point. Construct the control Jacobian matrix , Let the rotation angle of the motor with three magnets about its own rotation axis be denoted by a weighted matrix. Calculate the matrix Calculate the minimum singular value that characterizes static controllability. Set multiple static performance metrics, including static controllability. For each candidate placement layout, if any static metric exceeds a threshold, calculate the penalty value, and then obtain the total penalty value F for all metrics. The top K1 candidate placement layouts of L, from smallest to largest, are selected as candidate optimal layouts. Micro-domain robustness verification is performed to obtain the optimal layout of three magnets. The geometric hard constraints include the minimum safe distance constraint between the centers of any two magnets and the maximum span constraint of the magnet set. The micro-domain robustness verification involves applying a small perturbation to the position and axial parameters of the candidate optimal layout and re-evaluating the static index.

[0087] For example, a three-magnet rotary drive device or system includes three permanent magnets, three sets of rotary drive mechanisms, and a mounting frame. Each permanent magnet is configured with an independent rotary drive mechanism. All magnets and drive mechanisms are integrated and assembled, and are fixedly connected to the end of a robotic arm, which performs global position adjustment. The layout parameters of the three magnets are obtained using the method described above.

[0088] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0089] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0090] The computer program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, Python, etc., and conventional procedural programming languages ​​such as "C" or similar languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing state information from the computer-readable program instructions. This electronic circuitry can execute the computer-readable program instructions to implement various aspects of the invention.

[0091] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein. The scope of the invention is defined by the appended claims.

Claims

1. A layout optimization method for a three-magnet rotary drive system, characterized in that, include: Based on the initial placement layout of three magnets, a differential evolution algorithm is used for global search to generate candidate placement layouts. Candidate placement layouts that satisfy the geometric hard constraints are retained, and dynamic task constraints are used to eliminate dynamic non-executable placement layouts. For each remaining candidate placement layout, calculate the three-magnet control output vector at the target point. Construct the control Jacobian matrix , The rotation angle of a motor with three magnets rotating around its own axis; Introducing a weighted matrix Calculate the matrix Calculate the minimum singular value that characterizes static controllability. ; Multiple static performance metrics, including static controllability, are set. For each candidate placement layout, if any static metric exceeds a threshold, a penalty value is calculated, thereby obtaining the total penalty value F for all metrics. ; Several candidate placement layouts are selected from L in ascending order as candidate optimal layouts, and micro-domain robustness verification is performed to obtain the optimal layout of the three magnets. The geometric hard constraints include the minimum safe distance constraint between the centers of any two magnets and the maximum span constraint of the magnet set. The micro-domain robustness verification is to apply a small perturbation to the position and axial parameters of the candidate optimal layout and then re-evaluate the static index.

2. The method according to claim 1, characterized in that, Static performance indicators also include static uniformity, static decoupling, axial dispersion, and non-coplanar constraints. The penalty values ​​for each indicator are calculated as follows: when Calculate the penalty value , The minimum singularity threshold is q, which is a preset exponent. Calculate the isotropic penalty that characterizes static homogeneity : , , 'n' is the rank-related parameter corresponding to the output dimension. When the isotropic penalty exceeds a preset threshold, the penalty value is calculated. , The preset unidirectional threshold is used; Calculate the non-target channel output leakage characterizing static decoupling and normalize the sum to obtain the crosstalk value. When crosstalk exceeds the threshold, a penalty value is calculated. , The preset crosstalk threshold is used; Calculate the dispersion index of the three axes , For each rotation axis unit vector, calculate the penalty value when the axis dispersion exceeds the threshold. ; Perform non-coplanar constraint judgment when the layout envelope volume or equivalent volume ratio Below the preset threshold Calculate the penalty value ; , , , , , Preset penalty factor.

3. The method according to claim 1, characterized in that, Dynamic task constraints are used to eliminate placement layouts that are dynamically unexecutable. Specifically, for each candidate placement layout, a preset task sequence is executed to solve for its motor angle sequence. Maximum angular velocity angular acceleration and total variation of angle series ,when , If either of these conditions exceeds the motor's operating limit or the TV exceeds the threshold, the candidate placement layout will be eliminated.

4. The method according to claim 1, characterized in that, The placement posture is as follows: , To describe the spherical coordinate parameters of the magnet's center position, It is the polar angle between the rotation axis and the z-axis in the global coordinate system. It is the azimuth angle of the projection of the rotation axis onto the xy plane in the global coordinate system relative to the x-axis.

5. The method according to claim 1, characterized in that, After performing a global search using the differential evolution algorithm, the algorithm is then refined using the local optimization algorithm with boundaries, L-BFGS-B.

6. A three-magnet rotary drive device, comprising three permanent magnets, three sets of rotary drive mechanisms, and a mounting frame, wherein each permanent magnet is configured with an independent rotary drive mechanism, all magnets and drive mechanisms are integrated and assembled, and are integrally fixed to the end of a robotic arm, and the robotic arm achieves global position adjustment, characterized in that: The layout parameters of the three magnets are obtained by any one of the methods in claims 1-5.

7. A computer-readable storage medium, characterized in that: The computer program is stored that can be loaded by a processor and executed according to any one of claims 1 to 5.

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