A method and system for data-driven optimization of motion control of diamagnetic materials

Abstract

The application provides a kind of anti-magnetic material motion control data driven optimization method and system, and the core of the application is to define the magnetic pole direction angle of the preset magnet group in the permanent magnet array and the magnetic field distribution in multiple planes directly above the magnet configuration as optimization variables, and generate a variable combination of multiple groups of different angles corresponding to a plane;For each variable combination, calculate its magnetic field distribution in the target plane by finite element simulation, extract the index representing the performance of magnetic trap, and construct the data set corresponding to the variable combination and the performance index for machine learning modeling;Use the trained model to predict the performance of a large number of candidate variable combinations, and select the variable combination that can make the performance index optimal as the optimal magnetic pole direction.The application can simultaneously realize active constraint and collaborative control of the target anti-magnetic material in two translational degrees of freedom and one rotational degree of freedom, thereby supporting its precise positioning, stable suspension, path following, directional translation and controllable rotation in two-dimensional plane.

Description

Technical Field

[0001] This invention relates to the field of motion control technology for diamagnetic materials, specifically a data-driven optimization method and system for motion control of diamagnetic materials. Background Technology

[0002] In fields such as microelectromechanical systems (MEMS), biochip manipulation, and precision materials control, it is often necessary to achieve complex, non-contact motion control of tiny diamagnetic materials (such as graphene microsheets, polymer particles, and biological samples). This includes, but is not limited to, stable capture, precise positioning, in-plane translation, three-dimensional spatial flipping, and directional rotation. Because diamagnetic materials have negative magnetic susceptibility, they experience repulsive forces in an applied magnetic field. Utilizing this characteristic, by carefully designing the spatial distribution of a static magnetic field, a field structure with controllable magnetic field gradients and directions can be constructed in specific regions, thereby enabling effective, flexible, and stable control of various motion modes of the target diamagnetic material. This non-contact manipulation method based on static magnetic fields offers significant advantages such as no physical contact, no heat source disturbance, and no pollution, making it a highly promising technological path for achieving precise, complex, and multi-degree-of-freedom motion control.

[0003] The key to effectively controlling the movement of antimagnetic materials using magnetic fields lies in constructing a "magnetic trap" to achieve "magnetic locking" of the antimagnetic material. However, constructing an effective magnetic locking mechanism suitable for antimagnetic materials faces significant challenges. Antimagnetic materials have very low magnetic susceptibility (typically 10). -6_ 10 -4 The magnetic force exerted on a magnet is proportional to its magnetic susceptibility, volume, and the square of the magnetic field gradient, and the force is extremely weak (typically on the order of piconewtons to nanonewtons). In techniques applicable to strongly magnetic ferromagnetic materials, magnetic locking methods rely on the regular symmetrical arrangement of permanent magnets or electromagnetic coils, attempting to generate a high magnetic field gradient region in the central area by manually adjusting the magnetic pole directions or based on simple analytical models. Applying this method to diamagnetic materials has significant shortcomings: First, the total magnetic field distribution of multiple magnets has a highly nonlinear relationship with the spatial angle and position of the magnets; the trap depth (i.e., magnetic barrier strength) generated by simple symmetrical arrangements is limited, and diamagnetic materials are easily escaped by environmental disturbances; second, the system lacks a decoupling design between translational and rotational degrees of freedom, often making it difficult to avoid introducing unnecessary torque or coupled motion when achieving in-plane movement, leading to a decrease in control degrees of freedom.

[0004] Specifically, the current construction of an effective motion control and multi-degree-of-freedom magnetic locking system for antimagnetic materials mainly faces the following technical bottlenecks and inherent contradictions:

[0005] First, existing technologies largely rely on systems composed of multiple independent electromagnetic coils. While such electromagnetic schemes can dynamically adjust the magnetic field through complex real-time feedback algorithms, they inevitably result in a large system size, high energy consumption, complex control algorithms, and high costs. Furthermore, the Joule heat generated by the continuous energization of the coils introduces thermal disturbances, severely impacting long-term operational stability.

[0006] Secondly, multi-degree-of-freedom decoupled collaborative control is complex to achieve. Previous studies have often been unable to simultaneously achieve both translational and rotational magnetic control.

[0007] Furthermore, traditional design processes heavily rely on experience and iterative trial and error. Traditional design workflows are based on numerical simulations using finite element analysis software, requiring manual setting of the initial magnetic pole orientation for each magnet and searching for a better solution through extensive parameter scanning. Due to the high dimensionality of the parameter space (the three-dimensional positions and orientations of multiple magnets) and the enormous computational load, the design cycle is long, the cost is high, and it is difficult to obtain a globally optimal solution.

[0008] In summary, the contradiction between cost and accuracy in traditional simulation lies in the fact that magnetic trap optimization involves minute angular deflections. To capture this level of accuracy, the finite element mesh must be extremely fine, resulting in long simulation times per run. Traditional methods require tens of thousands of simulations to obtain a relatively good solution, which is unacceptable in practical engineering. Summary of the Invention

[0009] The technical problem to be solved by this invention is how to simultaneously achieve active constraint and coordinated control of the target antimagnetic material in two translational degrees of freedom and one rotational degree of freedom, so as to support its multi-dimensional non-contact motion such as precise positioning, stable suspension, path following, directional translation and controllable rotation in a two-dimensional plane.

[0010] The present invention solves the above-mentioned technical problems through the following technical means:

[0011] A data-driven optimization method for motion control of diamagnetic materials, applied to a motion control device for diamagnetic materials, the motion control device including an inner layer translation control array; comprising the following steps:

[0012] S1. Parametric sampling: Based on the rotationally symmetric physical structure of N permanent magnets in the inner translation control array, construct the magnetic field distribution in multiple planes with set radii within a single symmetric periodic unit, including the magnetic pole direction angle and the set height range directly above the magnet configuration. Define these as optimization variables and generate a plane corresponding to multiple sets of variable combinations with different magnetic pole direction angles.

[0013] S2. Constructing the dataset: Calculate the magnetic field distribution of each variable combination on the target plane through simulation, extract performance indicators that characterize the magnetic trap, and construct a dataset corresponding to the variable combinations and performance indicators;

[0014] S3. Machine Learning and Modeling Optimization: The dataset is used as training samples to train a machine learning model to establish a mapping relationship from variable combinations to performance indicators. The trained model is used to predict the performance of a large number of candidate variable combinations, and the variable combination that can make the performance indicators reach the optimal is selected as the optimal magnetic pole direction.

[0015] Furthermore, it also includes: S4. Verification and iterative optimization: The candidate optimal magnetic pole direction is verified by simulation technology. If the verification result does not reach the preset performance threshold, the verification data is added to the dataset, and S3 and S4 are repeated for iterative optimization. If the verification result reaches the preset performance threshold, it is determined as the final magnetic pole direction design of the permanent magnet array.

[0016] Furthermore, step S2 specifically involves: establishing a three-dimensional magnetic field model of the inner layer translation control array; calculating the magnetic field distribution at different combinations of magnetic pole orientation angles and heights of multiple permanent magnets within a single symmetrical periodic unit through parametric scanning; and extracting the corresponding maximum magnetic field value B at the edge of the magnetic trap. max Minimum magnetic field value B at the edge of the magnetic trap edge Minimum magnetic field value B at the center of the magnetic trap center Construct a dataset that includes input variables and output performance metrics.

[0017] Furthermore, during the training process in step S3, a loss function is constructed, introducing a magnetic potential well closure constraint term based on the mean square error, expressed as follows: ,in y i For the first i The actual value of each sample For the first i The predicted value of each sample; when the edge magnetic field predicted by the gradient boosting decision tree is less than the central magnetic field, a very large penalty weight is applied.

[0018] Furthermore, during the training process in step S3, a weighted coefficient scoring function is constructed to balance the difference between the maximum and minimum magnetic field values ​​within the magnetic trap range.

[0019] Furthermore, the scoring function is:

[0020]

[0021] in, The difference in magnetic field between the highest and lowest points of the magnetic trap reflects the depth of the potential trap. Represents the lowest point of the magnetic trap edge B edge With the lowest point of the entire magnetic trap magnetic field B centerThe difference in magnetic field reflects the uniformity of the magnetic trap's closure in the plane; λ 1 and λ 2 represents the weight coefficient of the corresponding term; the optimization objective is to find the factor that makes the term weighted. The optimal combination of parameters.

[0022] This invention also provides a data-driven optimization system for motion control of diamagnetic materials, applied to a motion control device for diamagnetic materials, wherein the motion control device for diamagnetic materials includes an inner layer translation control array; comprising:

[0023] Parametric sampling module: Based on the rotationally symmetric physical structure of N permanent magnets in the inner translation control array, it constructs the magnetic field distribution in multiple planes with set radii within a single symmetric periodic unit, including the magnetic pole direction angle and the set height range directly above the magnet configuration. These are defined as optimization variables, and a plane is generated corresponding to multiple sets of variable combinations with different magnetic pole direction angles.

[0024] Dataset construction module: used to calculate the magnetic field distribution of each set of variables on the target plane through simulation, extract performance indicators characterizing the magnetic trap, and construct a dataset corresponding to the variable combination and performance indicators;

[0025] Model training module: The dataset is used as training samples to train the machine learning model to establish a mapping relationship from variable combinations to performance indicators. The trained model is used to predict the performance of a large number of candidate variable combinations and select the variable combination that can make the performance indicators reach the optimal as the optimal magnetic pole direction.

[0026] Furthermore, the feature is that it also includes: a verification and iterative optimization module: used to verify the candidate optimal magnetic pole direction through simulation technology; if the verification result does not reach the preset performance threshold, the verification data is added to the dataset, and S3 and S4 are repeated for iterative optimization; if the verification result reaches the preset performance threshold, it is determined as the final magnetic pole direction design of the permanent magnet array.

[0027] Furthermore, the specific execution process of the dataset construction module is as follows: A three-dimensional magnetic field model of the inner layer translation control array is established; through parametric scanning, the magnetic field distribution at different combinations of magnetic pole orientation angles and heights of multiple permanent magnets within a single symmetrical periodic unit is calculated; and the corresponding maximum magnetic field value B at the edge of the magnetic trap is extracted. max Minimum magnetic field value B at the edge of the magnetic trap edge Minimum magnetic field value B at the center of the magnetic trap center Construct a dataset that includes input variables and output performance metrics.

[0028] Furthermore, during training, a loss function is constructed, introducing a magnetic potential well closure constraint term based on the mean squared error, expressed as follows: ,iny i For the first i The actual value of each sample For the first i The predicted value of each sample; when the edge magnetic field predicted by the gradient boosting decision tree is less than the central magnetic field, a very large penalty weight is applied; during training, a weight coefficient scoring function is constructed to balance the difference between the maximum and minimum magnetic field values ​​within the magnetic trap range; the scoring function is:

[0029]

[0030]

[0031] in, The difference in magnetic field between the highest and lowest points of the magnetic trap reflects the depth of the potential trap. Represents the lowest point of the magnetic trap edge B edge With the lowest point of the entire magnetic trap magnetic field B center The difference in magnetic field reflects the uniformity of the magnetic trap's closure in the plane; λ 1 and λ 2 represents the weight coefficient of the corresponding term; the optimization objective is to find the factor that makes the term weighted. The optimal combination of parameters.

[0032] The advantages of this invention are:

[0033] This invention collapses a magnet array into a symmetrical periodic cell and extracts magnetic field data from multiple planes within the three-dimensional model of this symmetrical periodic cell. This extraction method transforms the three-dimensional magnetic field problem into a two-dimensional feature extraction problem, preserving key physical information while significantly reducing the complexity of data processing and model training. The innovative introduction of rotational symmetry dimensionality reduction and machine learning models significantly improves the efficiency and global optimality of magnetic trap performance design. The entire control process does not rely on electromagnetic coils or external power supplies, achieving truly passive, heatless, multi-degree-of-freedom motion control. It enables stable magnetic trap capture with translational degrees of freedom, thus achieving independent and precise control of translational and rotational motions without the need for power supply or heat sources. Methodologically, the innovative introduction of rotational symmetry dimensionality reduction and machine learning models significantly improves the efficiency and global optimality of magnetic trap performance design.

[0034] The innovation of this application lies in the complexity of multi-degree-of-freedom magnetic control physical coupling, the high cost of traditional trial-and-error design, and the difficulty in ensuring trap stability due to the weak magnetic force of diamagnetic materials. Through an optimization strategy that integrates data-driven approaches and physical constraints, a non-intuitive but physically optimal magnetic pole configuration design was successfully achieved. Its advantages include a fully permanent magnet device, passive and heat-free operation, compact structure, and stable control. The optimization method is both efficient and universal, scalable to different scales, materials, and target scenarios, providing reliable technical support for fields such as precision micromanipulation and space experiments. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the magnet array structure in Embodiment 2 of the present invention;

[0036] Figure 2 for Figure 1 Schematic diagram of the magnet angles of the inner and outer rings;

[0037] Figure 3 for Figure 1 Magnet array structure and magnetic field distribution diagram, in which Figure 3 (b) in the middle is Figure 3 The one-dimensional distribution of the magnetic field in (a) is shown in the figure. Figure 3 (c) shows the horizontal direction (0°) Figure 3 The magnetic field distribution of the magnet shown by the red line in (a) is shown in the image. Figure 3 (d) in the middle shows the direction along 45° ( Figure 3 The magnetic field distribution of the magnet shown by the blue line in (a) in the image;

[0038] Figure 4 For Figure 3 For example, this paper shows the relationship between the three selected sampling points and the corresponding two weighting systems and the magnetic pole direction angle. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] Example 1

[0041] This invention provides a data-driven optimization method for motion control of diamagnetic materials, which is applied to a motion control device for diamagnetic materials, the motion control device for diamagnetic materials including an inner layer translation control array.

[0042] The specific steps are as follows:

[0043] Step 1: This step completes the spatial dimension collapse and symmetry group mapping, as well as parameterized sampling: Utilizing the rotationally symmetric physical structure of N permanent magnets in the inner layer translation control array, the N permanent magnets can be arranged in a ring with the same diameter, or arranged in multiple layers of inner and outer rings. Regardless of the arrangement, a rotation group C can be established. N The equivalence class mapping operator; transforms the original N-dimensional angle search space Φ = [θ1, θ2, ..., θ N Through linear transformation Mapping to a single symmetric periodic unit [0, π / N] achieves dimensional collapse and parameter reduction of the design space, reducing the search space from 180... N The exponential scale of the problem is directly reduced to a 2D continuous optimization problem within a single sector. The magnetic pole orientation angle within a single symmetric periodic unit and the magnetic field distribution of multiple (usually 11) target planes (circular cross-sections) with a set radius (usually 0.6 cm) within a set height h (usually within 1 cm) directly above the magnet configuration are defined as optimization variables, and a plane is generated corresponding to multiple sets of variable combinations with different angles.

[0044] Step 2: Dataset Construction Based on Finite Element Simulation: A three-dimensional magnetic field model of the permanent magnet array is established using finite element analysis tools. Through parametric scanning, the magnetic field distribution under different combinations of magnetic pole orientation angles and different permanent magnet heights h within a single symmetrical periodic unit is calculated. The magnetic field characteristic value B of the corresponding target plane (the cross-section of the designed magnetic field distribution) is extracted. max (Maximum magnetic field value at the edge of the magnetic trap), B edge (Minimum magnetic field at the edge of the magnetic trap), B center (The magnetic trap center is the minimum magnetic field value within the data extraction range), constructing an original physical dataset (θ1, θ2, ... θ) containing input variables and output performance indicators. n h, B max B edge B center ); where n is the number of permanent magnets in a single symmetric periodic unit, θ n Let be the magnetic pole direction angle of the nth permanent magnet, and h be the height of the center point of the permanent magnet from the target plane.

[0045] It should be noted that, since this embodiment focuses on the magnetic field distribution on the target plane, the 3D model is a complete simulation based on the actual size and parameters. Therefore, the magnetic field data of the cross section on the target plane is extracted from the 3D model. The most realistic method would be to use the data of the entire cross section as training data, but this would drastically increase the amount of data. To improve the efficiency of subsequent model calculations, three key points are selected on a target plane. The specific process is as follows:

[0046] 1) Set the target plane: In the finite element software, set a horizontal section 0.8 mm above the upper surface of the outer ring magnet;

[0047] 2) Define key sampling points: Set a point at the center of the cross-section (corresponding to the trap center);

[0048] 3) Select several points evenly at the edge of the cross section (such as on a circle with a radius of 0.6 cm) to capture the extreme values ​​of the edge magnetic field;

[0049] 4) Data Extraction: For each combination of angle and height, run a magnetic field simulation to read the magnetic field values ​​at three key points (B). max B center B edge );

[0050] 5) Construct a two-dimensional table: For each input group (θ1, θ2, ... θ... n Each group of outputs (B, h) max B center B edge ).

[0051] This extraction method transforms the three-dimensional magnetic field problem into a feature extraction problem on a two-dimensional plane, which not only preserves key physical information but also significantly reduces the complexity of data processing and model training.

[0052] Step 3: Machine Learning Model Training: Using the dataset, train the model using the Gradient Boosting Decision Tree (GBDT) algorithm, establishing design variables θ1, θ2, ... θ n h, and the magnetic field characteristic value B max B edge B center The high-dimensional nonlinear mapping relationship between them forms a numerical prediction surrogate model with low computational cost; at the same time, the loss function is reconstructed: a magnetic potential well closure constraint term is introduced on the basis of mean squared error (MSE), and the loss function is expressed as: For indicator functions, where y i For the first i The actual value of each sample For the first i The predicted values ​​of each sample; when the predicted edge magnetic field is less than the central magnetic field (i.e. no effective magnetic trap is formed), a very large penalty weight is applied; based on the attenuation characteristics of the permanent magnet magnetic field and the characteristics of the required magnetic trap, the predictive agent model is subject to monotonicity constraints. During the splitting process of the decision tree node, a physical monotonicity judgment operator that the magnetic field attenuates with increasing distance is embedded to eliminate prediction branches that do not conform to the common sense of electromagnetic physics.

[0053] Step 4: Multi-objective weight optimization strategy: Based on the locking stiffness requirements of the diamagnetic material, and to more comprehensively measure the magnetic locking effect of the magnetic trap, this embodiment constructs a weight coefficient scoring function for the magnetic trap. Through this function, the goal is to obtain the weight parameter combination that maximizes the score. The function expression is as follows:

[0054]

[0055]

[0056] in, The difference in magnetic field between the highest and lowest points of the magnetic trap reflects the depth of the potential trap. Represents the lowest point of the magnetic trap edge B edge With the lowest point of the entire magnetic trap magnetic field B center The difference in magnetic field reflects the uniformity of the magnetic trap's closure in the plane; λ 1 and λ 2 represents the weight coefficient of the corresponding term; the optimization objective is to find the factor that makes the term weighted. Maximize the combination of parameters. For example... Figure 4 The diagram illustrates the optimized key parameters and their corresponding physical target response trends when the weighting coefficient λ1 varies within the range of 0 to 1. Taking the inner-layer translation control array consisting of eight permanent magnets in the inner and outer rings, as shown in Example 2, as an example... Figure 4 (a) and Figure 4 Figure (b) shows the changes in the inner ring magnet angle θ1 and the outer ring magnet angle θ2, respectively. Through five iterations (Top-1 to Top-5), when λ1=1 and λ2=0, the system tends towards a parameter combination (3°, 180°, 0.8 mm) that significantly enhances the potential well depth; however, when the weights are biased towards edge uniformity (λ1=0, λ2=1), the optimal parameters shift to (85°, 116°, 0.8 mm). While this configuration is beneficial for edge closure, it comes at the cost of sacrificing potential well depth. Analysis shows that, due to... As λ1 changes very drastically The change in λ1 is very slow, therefore the influence of λ1 is dominant in the magnetic trap optimization process. Therefore, this embodiment ultimately selects a weight configuration of λ1=1 and λ2=0, focusing the optimization entirely on maximizing the magnetic potential well depth. This decision stems not only from the support of data trends—the potential well depth term is dominant—but also from physical logic: in antimagnetic locking, a sufficiently deep potential well is a fundamental prerequisite for resisting external disturbances and achieving stable magnetic control. Experimental results show that the array optimized with this single objective, while achieving a deep potential well, still possesses good edge closure characteristics, verifying the effectiveness and rationality of this weighting strategy.

[0057] Step 5: Configuration verification and device implementation: The optimal parameter combination obtained by optimization is fed back to the finite element model for high-precision verification, and the azimuth angle of each mounting slot on the permanent magnet fixing plate is determined according to the verified angle parameters.

[0058] Step 6: Return the results of the model prediction screening and verify them using the finite element method.

[0059] The core of this invention lies in providing a data-driven optimization method and a hydromagnetic array device based on this method, for achieving multi-degree-of-freedom decoupled control of diamagnetic materials. Various modifications and extensions can be made without departing from the principles of this invention.

[0060] (1) Scalability of system scale: All geometric dimensions of the permanent magnet array (including magnet unit size and array radius) can be scaled up or down proportionally to meet the manipulation requirements of diamagnetic objects of different scales from micrometers to centimeters. The optimization method described above can redetermine the optimal parameters for any target scale.

[0061] (2) Replaceability of components and configurations: The shape, material and quantity of permanent magnet units can be adjusted according to actual applications. The arrangement of the inner array can be varied while satisfying the principle of functional decoupling, and the Hellback ring that provides a uniform magnetic field in the outer layer can also adopt other multi-pole permanent magnet structures that can generate magnetic fields with the same direction.

[0062] (3) Extensibility of design objectives and methods: The objective function of the optimization method can be flexibly defined as a trade-off between indicators such as trap depth and field uniformity. The machine learning model used can be replaced with other applicable regression or surrogate models.

[0063] (4) Universality of application objects: The manipulated objects are not limited to specific antimagnetic materials, but can be applied to various antimagnetic materials, such as biological cells, polymer microspheres, silicon-based devices, etc.

[0064] (5) Wide range of applications: The technical solution of the present invention can be widely applied to multiple technical fields such as micro-nano assembly, biological operation, precision sensing, teaching demonstration and space experiment.

[0065] (6) The data-driven magnetic field configuration optimization method described in this invention has universality. By defining the optimization objective function as generating a maximum magnetic field strength at the target point, this method can also be used to design permanent magnet arrays that attract and lock ferromagnetic materials (i.e., construct "magnetic peaks"). Therefore, the core method of this invention can be widely applied to occasions requiring non-contact stable positioning and manipulation of antimagnetic or ferromagnetic materials.

[0066] Example 2

[0067] Based on the method described in Example 1, this embodiment constructs a permanent magnet array capable of capturing diamagnetic materials and optimizes the data using the method of Example 1. In this embodiment, eight permanent magnets form an inner and outer ring layer to create a translation control array, as shown below. Figure 1 , Figure 2 As shown, the structure consists of an inner ring of 4 permanent magnets, an outer ring of 4 permanent magnets, and an outer layer of 12 permanent magnets forming a Hellback ring. The inner and outer rings, a total of 8 magnets, provide magnetic traps for translational freedom capture. The 12 permanent magnets in the Hellback ring form a magnetic field with consistent direction and uniform amplitude, providing rotational freedom capture. Each permanent magnet is cubic (1cm side length, 1.4T remanence), with its center located on the same plane and distributed at equal angles on three concentric circles centered at the device's center O. The azimuth angles of the inner ring permanent magnets are 0°, 90°, 180°, and 270°, with a radius of 1.3cm; the azimuth angles of the outer ring permanent magnets are 45°, 135°, 225°, and 315°, with a radius of 1.7cm; similarly, the Hellback ring has a radius of 3cm. The magnetic poles point with the Z-axis at 0 degrees. The optimization process using the method described in Example 1 is as follows:

[0068] like Figure 3 As shown in (a), due to the C4 symmetry (star-shaped rotational symmetry) distribution of the eight permanent magnet units in the inner translation control array, the magnetic field distribution of the entire system exhibits periodic rotational symmetry. Therefore, when designing space exploration, it is not necessary to independently search for the angles of all eight magnets; instead, calculations can be performed within a basic sector (e.g., 0°~45°), and the magnetic field distribution of the remaining sectors can be obtained through rotational symmetry mapping. This means that in the specific finite element calculation, only one sector needs to be calculated, which is only 1 / 4 of the total calculation, greatly reducing the computational load.

[0069] Within the aforementioned basic sector, design variables θ1 and θ2 are established and combined with h to form input data. This data is then input into the target model obtained in Example 1, thereby optimizing the inner ring magnetic pole direction angle to 3° and the outer ring magnetic pole direction angle to 180° (clockwise rotation of the Z-axis is positive). The magnetic trap is a circle with a diameter of 12 mm, located at a cross-section 0.8 mm above the upper surface of the outer ring magnet, with a magnetic trap depth difference of 0.095 T.

[0070] To further quantify the locking capability of this magnetic trap, such as Figure 3 As shown, the curves of magnetic field variation with position were extracted along two typical directions. Figure 3 (a) shows the magnetic trap magnet layout for magnetic locking of XY degrees of freedom, with red indicating magnets in the 3° magnetic pole direction and blue markings indicating magnets in the 180° direction. Figure 3The two-dimensional magnetic field distribution in (b) provides a key perspective for understanding the constraint performance of the system: the optimized potential well presents as a completely closed trapping region in the plane, with a smooth and continuous central trough region. Although the potential well depth exhibits anisotropy, the magnetic field strength shows a monotonically increasing trend when moving outward from the center in any direction. This means that when the levitated body deviates in any direction, it will be subjected to a restoring force pointing towards the center. The experimentally observed stable locking phenomenon confirms that under this closed and continuous potential well topology, even if there are differences in the absolute depth in different directions, the resulting restoring force gradient is sufficient to macroscopically resist environmental disturbances (such as weak airflow and vibration), thereby achieving effective three-degree-of-freedom passive magnetic control. This result also shows that in the design of antimagnetic locking systems, the global closure and gradient continuity of the potential well are as important as the absolute depth, and both together determine the actual robustness of the system. Figure 3 (c) shows the magnetic field distribution along the horizontal direction (0°), with the difference between the maximum and minimum magnetic fields being approximately 0.095 T, forming a potential well with significant depth and a steep gradient. Figure 3 (d) in the figure shows the magnetic field distribution along the 45° direction (i.e., the case where the magnetic field difference is the smallest), with a difference of about 0.03 T. Although it is lower than the horizontal direction, it still presents a continuous potential well structure with a clear gradient.

[0071] The magnetic array provided in this embodiment offers high-performance magnetic locking, high reliability, and zero energy consumption, thus solving the problems of bulky size, heat generation, and complex control associated with electromagnetic solutions. The device is entirely composed of permanent magnets, requiring no power supply and generating no heat. Its robust structure makes it suitable for long-term, stable, and precision control environments. Through data-driven optimization, a non-intuitive but physically optimal magnetic pole orientation was obtained, significantly improving the trapping force and stability against magnetic materials.

[0072] It should be noted that the specific embodiments described above are merely preferred methods for achieving the purpose of this invention and are not intended to limit the invention.

[0073] Example 3

[0074] Based on the optimized permanent magnet array capable of capturing diamagnetic materials obtained in Example 2, a motion control device for diamagnetic materials was fabricated and verified.

[0075] like Figure 1 As shown, this embodiment constructs a permanent magnet magnetic trap array according to the optimal magnetic pole direction combination (3° for the inner ring and 180° for the outer ring) obtained from the invention. The array consists of 4 permanent magnets in the inner ring, 4 permanent magnets in the outer ring, and 12 permanent magnets in the outer Hellback ring, with the centers of all permanent magnets located in the same plane.

[0076] (1) Fabrication of magnet fixing structure

[0077] First, design the permanent magnet mounting disk using 3D modeling software. This disk can then be manufactured using 3D printing or CNC machining, including:

[0078] 1) Mounting slots for four permanent magnets in the inner ring;

[0079] 2) Mounting slots for the four permanent magnets on the outer ring;

[0080] 3) Mounting slots for 12 permanent magnets of the circumferentially distributed Herbak ring.

[0081] Each slot is arranged strictly according to the aforementioned structural radius and azimuth angle, and the slots are manufactured using 3D printing. The depth of each slot is designed to be 10mm, consistent with the thickness of the permanent magnet used, so that the permanent magnet is completely embedded in the slot.

[0082] (2) Embedding and fixing of permanent magnets

[0083] The permanent magnets are embedded in the slots according to the marked orientation. To ensure structural stability, white glue is used to bond and fix the permanent magnets together. All permanent magnets are embedded in a tight fit, leaving no obvious gaps, thereby ensuring that the direction of the magnetic dipole is consistent with the direction of the slot.

[0084] During 3D modeling, the aforementioned angles were directly applied to the orientation of the slots. Therefore, once the magnets are inserted into the slots, they automatically acquire the preset magnetic pole orientation. Since the dipole orientation is the internal magnetization direction, the magnet's orientation is determined solely by its external shape. Thus, the structured slot design can accurately achieve the target angle. Similarly, the magnetization orientation of the Hellbach rings is arranged according to the Hellbach array principle, resulting in a directional magnetic field with consistent direction in the central region of the array. They are also fixed with white glue, and their position and orientation are guaranteed by the slot structure, requiring no additional adjustment.

[0085] Functional verification of multi-degree-of-freedom magnetic manipulation

[0086] This embodiment demonstrates the actual control effect of the device on antimagnetic materials through a physical experiment.

[0087] A graphite sheet with a side length of 10 mm and a thickness of approximately 0.5 mm was used as a typical antimagnetic material sample. Water was poured into a shallow dish until the liquid level was 0.8 mm above the upper surface of the outer ring magnet. This liquid level was used as the target plane for the magnetic trap. The antimagnetic sheet was gently placed 0.8 mm directly above the central area of ​​the device described in Example 1, at the target plane magnetic trap location.

[0088] Verification of translational freedom control: It can be observed that the graphite sheet is automatically captured and stably locked at a certain equilibrium position above the magnet surface. At this time, the robotic arm slowly and smoothly moves the entire magnetic locking head device horizontally. The suspended graphite sheet can accurately follow the movement trajectory of the magnetic trap center, achieving synchronous two-dimensional translational motion in the plane. This proves that the device has achieved effective locking and driving of the X-axis and Y-axis translational degrees of freedom.

[0089] Rotational Degree of Freedom Manipulation Verification: While maintaining stable suspension of the graphite sheet, the end effector of the robotic arm slowly rotates the entire device around its vertical central axis (Z-axis). It can be observed that the suspended graphite sheet also rotates synchronously around the Z-axis. This phenomenon originates from the uniform magnetic field with consistent direction provided by the outer Hellbach ring in the central region, achieving directional constraint and drive of the rotational degree of freedom.

[0090] The above experimental results show that the pure permanent magnet array device provided by the present invention can successfully achieve stable suspension, translational locking and rotational guidance of antimagnetic materials in a two-dimensional plane without any energized components or active control, verifying the effectiveness and practicality of its multi-degree-of-freedom integrated control.

[0091] Example 4

[0092] In this embodiment, the eight permanent magnets from Embodiment 2 are placed on the same circular ring, and the magnetic pole orientation angle and height of the permanent magnets are obtained through optimization. Additionally, nine permanent magnets are placed on three circular rings of different diameters, and the magnetic pole orientation angle and height of the permanent magnets are obtained through optimization. Verification results from Embodiment 3 show that neither of these configurations can achieve the effect of the structure shown in Embodiment 2.

[0093] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A data-driven optimization method for motion control of diamagnetic materials, applied to a motion control device for diamagnetic materials, wherein the motion control device for diamagnetic materials includes an inner layer translation control array; characterized in that, Includes the following steps: S1. Parametric sampling: Based on the rotationally symmetric physical structure of N permanent magnets in the inner translation control array, construct the magnetic field distribution in multiple planes with set radii within a single symmetric periodic unit, including the magnetic pole direction angle and the set height range directly above the magnet configuration. Define these as optimization variables and generate a plane corresponding to multiple sets of variable combinations with different magnetic pole direction angles. S2. Constructing the dataset: Calculate the magnetic field distribution of each variable combination on the target plane through simulation, extract performance indicators that characterize the magnetic trap, and construct a dataset corresponding to the variable combinations and performance indicators; S3. Machine Learning and Modeling Optimization: The dataset is used as training samples to train a machine learning model to establish a mapping relationship from variable combinations to performance indicators. The trained model is used to predict the performance of a large number of candidate variable combinations and select the variable combination that can make the performance indicators reach the optimal as the optimal magnetic pole direction. During the training process in step S3, a weighted coefficient scoring function is constructed to balance the difference between the maximum and minimum values ​​of the magnetic field within the magnetic trap range. The scoring function is: in, The difference in magnetic field between the highest and lowest points of the magnetic trap reflects the depth of the potential trap. Represents the lowest point of the magnetic trap edge B edge With the lowest point of the entire magnetic trap magnetic field B center The difference in magnetic field reflects the uniformity of the magnetic trap's closure in the plane; λ 1 and λ 2 represents the weight coefficient of the corresponding term; the optimization objective is to find the factor that makes the term weighted. The optimal combination of parameters.

2. The data-driven optimization method for motion control of diamagnetic materials according to claim 1, characterized in that, Also includes: S4. Verification and Iterative Optimization: The candidate optimal magnetic pole direction is verified by simulation technology. If the verification result does not reach the preset performance threshold, the verification data is added to the dataset, and S3 and S4 are repeated for iterative optimization. If the verification result reaches the preset performance threshold, it is determined as the final magnetic pole direction design of the permanent magnet.

3. The data-driven optimization method for motion control of diamagnetic materials according to claim 1 or 2, characterized in that, Step S2 specifically involves: establishing a three-dimensional magnetic field model of the inner layer translation control array; calculating the magnetic field distribution at different magnetic pole orientation angles and heights of multiple permanent magnets within a single symmetrical periodic unit through parametric scanning; and extracting the corresponding maximum magnetic field value B at the edge of the magnetic trap. max Minimum magnetic field value B at the edge of the magnetic trap edge Minimum magnetic field value B at the center of the magnetic trap center Construct a dataset that includes input variables and output performance metrics.

4. The data-driven optimization method for motion control of diamagnetic materials according to claim 3, characterized in that, The single symmetric periodic unit includes two permanent magnets.

5. A data-driven optimization method for motion control of diamagnetic materials according to claim 1 or 2, characterized in that, In step S3 of the training process, a loss function is constructed, and a magnetic potential well closure constraint term is introduced based on the mean square error. The expression is as follows: ,in y i For the first i The actual value of each sample For the first i The predicted value of each sample; when the edge magnetic field predicted by the gradient boosting decision tree is less than the central magnetic field, a very large penalty weight is applied.

6. A data-driven optimization system for motion control of diamagnetic materials, applied to a motion control device for diamagnetic materials, wherein the motion control device for diamagnetic materials includes an inner layer translation control array; characterized in that, include: Parametric sampling module: Based on the rotationally symmetric physical structure of N permanent magnets in the inner translation control array, it constructs the magnetic field distribution in multiple planes with set radii within a single symmetric periodic unit, including the magnetic pole direction angle and the set height range directly above the magnet configuration. These are defined as optimization variables, and a plane is generated corresponding to multiple sets of variable combinations with different magnetic pole direction angles. Dataset construction module: used to calculate the magnetic field distribution of each set of variables on the target plane through simulation, extract performance indicators characterizing the magnetic trap, and construct a dataset corresponding to the variable combination and performance indicators; Model training module: The dataset is used as training samples to train the machine learning model to establish a mapping relationship from variable combination to performance index. The trained model is used to predict the performance of a large number of candidate variable combinations and select the variable combination that can make the performance index reach the optimal as the optimal magnetic pole direction. During training, a weighted scoring function is constructed to balance the difference between the maximum and minimum magnetic field values ​​within the magnetic trap range; The scoring function is: in, The difference in magnetic field between the highest and lowest points of the magnetic trap reflects the depth of the potential trap. Represents the lowest point of the magnetic trap edge B edge With the lowest point of the entire magnetic trap magnetic field B center The difference in magnetic field reflects the uniformity of the magnetic trap's closure in the plane; λ 1 and λ 2 represents the weight coefficient of the corresponding term; the optimization objective is to find the factor that makes the term weighted. The optimal combination of parameters.

7. The data-driven optimization system for motion control of diamagnetic materials according to claim 6, characterized in that, Also includes: Verification and Iterative Optimization Module: This module is used to verify the candidate optimal magnetic pole direction through simulation technology. If the verification result does not reach the preset performance threshold, the verification data is added to the dataset, and S3 and S4 are repeated for iterative optimization. If the verification result reaches the preset performance threshold, it is determined as the final magnetic pole direction design of the permanent magnet.

8. A data-driven optimization system for motion control of diamagnetic materials according to claim 6 or 7, characterized in that, The specific execution process of the dataset construction module is as follows: A three-dimensional magnetic field model of the inner layer translation control array is established; through parametric scanning, the magnetic field distribution of multiple permanent magnets within a single symmetrical periodic unit at different combinations of magnetic pole orientation angles and heights is calculated; and the corresponding maximum magnetic field value B at the edge of the magnetic trap is extracted. max Minimum magnetic field value B at the edge of the magnetic trap edge Minimum magnetic field value B at the center of the magnetic trap center Construct a dataset that includes input variables and output performance metrics.

9. A data-driven optimization system for motion control of diamagnetic materials according to claim 6 or 7, characterized in that, During training, a loss function is constructed, introducing a magnetic potential well closure constraint term based on the mean squared error, expressed as follows: ,in y i For the first i The actual value of each sample For the first i The predicted value of each sample; when the edge magnetic field predicted by the gradient boosting decision tree is less than the central magnetic field, a very large penalty weight is applied.

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