Method and system for calculating magnetic gradient force of micro-nano robot under three synchronous rotating magnetic fields

Abstract

The application discloses a kind of micro-nano robots magnetic gradient force calculation method and system under three synchronous rotating magnetic field.The method comprises the following steps: obtaining the position parameters of three synchronous rotating permanent magnets, the magnetic moment size of permanent magnet, common rotating phase, the position parameters of the space point to be calculated and the magnetic moment size of micro-nano robot;Based on magnetic dipole model, the magnetic field generated by three permanent magnets at the space point to be calculated is calculated and superimposed to obtain the total magnetic field;According to the total magnetic field, the total magnetic field direction unit vector is constructed, and the magnetic moment direction of micro-nano robot is kept consistent with the total magnetic field direction;Field matrix, magnetic gradient matrix and gradient force compact matrix are constructed, and the magnetic gradient force vector and its module length suffered by micro-nano robot at the space point to be calculated are calculated.The application can quickly complete the magnetic gradient force calculation under the action of three synchronous rotating magnetic field, and is suitable for trajectory planning, closed-loop control and safety evaluation of magnetic driving micro-nano robot.

Description

Technical Field

[0001] This invention relates to the fields of motion control and magnetic field mechanical analysis technology for magnetically driven micro / nano robots, specifically to a method and system for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field. Background Technology

[0002] In recent years, magnetically driven micro- and nano-robots have shown promising application prospects in minimally invasive medicine, targeted drug delivery, micro-assembly, thrombus removal, and precision manipulation due to their advantages such as non-contact actuation, small size, flexible movement, and adaptability to confined spaces and complex environments. Compared with electromagnetic coil actuation, permanent magnet actuation offers advantages such as relatively simple structure, lower energy consumption, convenient system maintenance, and ease of engineering implementation, thus attracting widespread attention in magnetically driven micro- and nano-robot experimental platforms and application devices.

[0003] In permanent magnet drive systems, micro- and nanorobots are typically subjected to both magnetic torque and magnetic gradient force. Magnetic torque primarily regulates the robot's attitude, aligning its magnetic moment direction with the external magnetic field. Magnetic gradient force, on the other hand, drives the robot to perform translational, traction, aggregation, or directional movements. Therefore, rapidly and accurately determining the magnetic gradient force is crucial for the structural design, workspace analysis, motion behavior prediction, trajectory planning, and control safety assessment of magnetic drive systems.

[0004] In existing technologies, the analysis of magnetic gradient forces on micro / nano robots under the action of multiple synchronously rotating permanent magnets typically relies on finite element simulation, parameter traversal search, or extensive numerical iterative calculations. While these methods can obtain relatively detailed magnetic field distributions and force results, they generally suffer from problems such as complex calculation processes, long computation times, and insufficient real-time performance. Therefore, they are difficult to meet the application requirements of online control, rapid evaluation, and real-time solutions under multi-position and multi-phase conditions.

[0005] Especially under the configuration of a three-synchronous rotating magnetic field, the increased number of permanent magnets involved in the superposition leads to a highly nonlinear and coupled relationship in the spatial distribution of the magnetic field and its gradient variation. This results in significant shortcomings in existing solution methods regarding computational efficiency, expression, and ease of engineering application. Therefore, there is an urgent need to propose a fast solution method for the magnetic gradient force of micro- and nano-robots under the condition of a three-synchronous rotating magnetic field, so as to achieve efficient estimation of the magnetic gradient force and thus provide support for trajectory planning, control analysis, and safety assessment. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for calculating the magnetic gradient force of micro / nano robots under a three-synchronous rotating magnetic field. This invention establishes a superposition model of the magnetic fields of three synchronously rotating permanent magnets at the point to be calculated, and expresses the magnetic gradient force experienced by the micro / nano robot as a compact matrix operation form. This significantly improves computational efficiency while ensuring computational accuracy, quickly obtaining the magnetic gradient force vector and its magnitude experienced by the micro / nano robot at a specified spatial point. This allows for real-time mechanical evaluation in trajectory planning, closed-loop control, and safe workspace analysis.

[0007] The technical solution of this invention: A method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field, comprising the following steps:

[0008] Step 1: Obtain the position vectors of the three synchronously rotating permanent magnets, the magnitude of the permanent magnet's magnetic moment, the common rotation phase, the position vector of the spatial point to be calculated, and the magnitude of the magnetic moment of the micro / nano robot; and define the instantaneous magnetic moment vector of the permanent magnet based on the magnitude and unit vector of the magnetic moment direction.

[0009] Step 2: Based on the magnetic dipole model, calculate the magnetic field generated by the three permanent magnets at the point to be calculated, and then vector-superimpose the corresponding magnetic fields of each permanent magnet to obtain the total magnetic field at the point to be calculated.

[0010] Step 3: Construct a unit vector for the direction of the total magnetic field based on the total magnetic field, and make the unit vector for the magnetic moment direction of the micro-nano robot consistent with the unit vector for the direction of the total magnetic field;

[0011] Step 4: Based on the relative positional relationship between the three permanent magnets and the spatial point to be calculated, construct the field matrix and magnetic gradient matrix, and further construct the gradient force compact matrix;

[0012] Step 5: Based on the gradient force compact matrix, the magnitude of the permanent magnet magnetic moment, the magnitude of the micro / nano robot magnetic moment, and the unit vector of the total magnetic field direction, calculate the magnetic gradient force vector acting on the micro / nano robot at the spatial point to be calculated.

[0013] Step 6: Output the magnetic gradient force vector and its magnitude.

[0014] In the above-mentioned method for calculating the magnetic gradient force of micro / nano robots under a three-synchronous rotating magnetic field, in step 2, for the i-th permanent magnet, the position vector between the spatial point p to be calculated and the i-th permanent magnet is first calculated. The relative position vectors between them:

[0015] ;

[0016] And the relative position unit vector:

[0017] ;

[0018] Where i = 1, 2, 3;

[0019] Then, based on the magnetic dipole model, calculate the magnetic field generated by the i-th permanent magnet at the point in space to be calculated:

[0020] ;

[0021] In the formula, The permeability of free space, It is a third-order identity matrix. This refers to the instantaneous magnetic moment vector of a synchronously rotating permanent magnet;

[0022] The total magnetic field is obtained by vector superposition of the magnetic fields of the three permanent magnets:

[0023] .

[0024] In the aforementioned method for calculating the magnetic gradient force of micro / nano robots under a three-synchronous rotating magnetic field, step 3, the instantaneous magnetic moment vector of the permanent magnet is expressed as:

[0025] ;

[0026] in, The magnitude of the magnetic moment of the permanent magnet. The unit vector of the magnetic moment direction of the permanent magnet;

[0027] Normalizing the total magnetic field yields the unit vector of the total magnetic field direction:

[0028] ;

[0029] If the direction of the magnetic moment of the micro / nano robot is aligned with the direction of the total magnetic field, then the magnetic moment vector of the micro / nano robot can be expressed as:

[0030] ;

[0031] in, The magnetic moment of the micro / nano robot is denoted by .

[0032] In the aforementioned method for calculating the magnetic gradient force of micro / nano robots under a three-synchronous rotating magnetic field, step 4 involves constructing the field matrix corresponding to the i-th permanent magnet:

[0033] ;

[0034] And construct the magnetic gradient matrix , and ,in:

[0035] ;

[0036] ;

[0037] ;

[0038] Then, the gradient force compact matrix is ​​constructed as follows:

[0039] ;

[0040] The gradient force compact matrix is ​​used to characterize the mapping relationship of magnetic gradient forces under the combined action of three synchronously rotating permanent magnets.

[0041] In the aforementioned method for calculating the magnetic gradient force of micro / nano robots under a three-synchronous rotating magnetic field, step 5, the magnetic gradient force vector at the spatial point to be calculated is expressed as:

[0042] ;

[0043] In the formula, The magnitude of the magnetic moment of the micro / nano robot; This represents the magnitude of the magnetic moment of the permanent magnet.

[0044] In the aforementioned method for calculating the magnetic gradient force of micro / nano robots under a three-synchronous rotating magnetic field, step 6 involves repeatedly executing steps 1 to 5 for multiple discrete rotating phases within one rotation cycle to obtain the periodic response results of the magnetic gradient force as a function of the rotating phase.

[0045] The aforementioned method for calculating the magnetic gradient force of micro-nano robots under a three-synchronous rotating magnetic field involves repeatedly executing steps 1 to 6 at multiple spatial points to construct a magnetic gradient force distribution map, a safe workspace distribution map, or a centerline path force characteristic distribution map within the workspace.

[0046] A rapid calculation system for magnetic gradient force of magnetically driven micro / nano robots is provided to realize the aforementioned method for calculating the magnetic gradient force of micro / nano robots under a three-synchronous rotating magnetic field, comprising:

[0047] The input module is used to obtain the position parameters, magnetic moment parameters, common rotation phase, position parameters of the spatial point to be calculated, and magnetic moment parameters of the micro-nano robot of the three synchronously rotating permanent magnets.

[0048] The calculation module, connected to the input module, is used to calculate the magnetic gradient force vector and its magnitude at the spatial point to be calculated for the micro-nano robot based on the parameters obtained by the input module.

[0049] An output module, connected to the calculation module, is used to output the calculation results of the magnetic gradient force.

[0050] The aforementioned magnetically driven micro / nano robot magnetic gradient force rapid calculation system, the output module is specifically used to output the magnetic gradient force calculation results, the magnetic gradient force distribution results in the workspace, or the over-threshold alarm information.

[0051] The aforementioned magnetic gradient force rapid calculation system for magnetically driven micro / nano robots is communicatively connected to the control system of the magnetically driven micro / nano robots.

[0052] During the trajectory planning phase, the system is used to perform rapid calculation of the magnetic gradient force on discrete points on the candidate path;

[0053] During the closed-loop control phase, the system updates the magnetic gradient force calculation results based on the real-time position of the micro-nano robot, so that the control system can perform parameter correction, path adjustment, or safety verification.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] 1. This invention establishes a magnetic field superposition model of three synchronously rotating permanent magnets and transforms the solution of magnetic gradient force into a concise matrix operation, avoiding the high computational burden caused by traditional finite element simulation, discrete search and a large number of numerical iterations, and can significantly improve the computational efficiency of magnetic gradient force.

[0056] 2. This invention can directly calculate the magnetic gradient force vector and its magnitude at a specified spatial point on a micro-nano robot, which facilitates the rapid acquisition of mechanical information during trajectory planning, workspace analysis and control parameter tuning.

[0057] 3. This invention can complete the calculation by relying only on parameters such as the position of the permanent magnet, the magnitude of the magnetic moment, the common rotation phase, the magnitude of the magnetic moment of the micro-nano robot, and the position of the spatial point to be calculated. The model is clear, easy to implement in a program, and easy to integrate with robotic arm platforms, vision measurement systems, and magnetic drive controllers.

[0058] 4. This invention can be used for rapid calculation of magnetic gradient force at a single spatial point, as well as for batch calculation at multiple spatial points and multiple rotation phases, thereby facilitating the construction of magnetic gradient force distribution maps in the workspace, safe workspace distribution maps, and path direction force characteristic distribution maps.

[0059] 5. This invention is applicable to the mechanical analysis and safety assessment of various magnetically driven devices such as magnetically driven micro-nano robots, magnetically controlled capsules, and magnetic conduits, and has good versatility and engineering application value. Attached Figure Description

[0060] Figure 1 This is a schematic diagram showing the geometric arrangement of the three synchronously rotating permanent magnets of the present invention and the relative positional relationship of the spatial points to be calculated.

[0061] Figure 2 The geometric arrangement of the three permanent magnets and the relative positions of the spatial points to be calculated are given.

[0062] Figure 3In this embodiment of the invention, the magnetic gradient force modulus of the three magnetic dipole system at eight representative spatial locations varies with the synchronous rotation angle. A schematic diagram of the change curve. Detailed Implementation

[0063] The present invention will be further described below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0064] Example 1: A method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field, wherein the geometric arrangement of the three permanent magnets and the relative positional relationship of the spatial points to be calculated are as follows. Figure 1 As shown. The method includes the following steps:

[0065] Step 1: Parameter Acquisition and Magnetic Moment Definition

[0066] In a fixed coordinate system, obtain the spatial positions of the three synchronously rotating permanent magnets, denoted as follows: Three permanent magnets have the same magnetic moment magnitude and rotate synchronously with a common rotational phase under the same drive. Based on the unit vector of the magnetic moment magnitude and direction of the permanent magnets, the instantaneous magnetic moment vector of the permanent magnets is defined. Specifically, the instantaneous magnetic moment vector of the permanent magnets is expressed as:

[0067] ;

[0068] in, The magnitude of the magnetic moment of the permanent magnet. is the unit vector of the magnetic moment direction of the permanent magnet.

[0069] In this embodiment, the vacuum permeability is taken as:

[0070] ;

[0071] The characteristic spacing between adjacent permanent magnets is taken as:

[0072] ;

[0073] The magnetic moment parameter of the permanent magnet is taken as follows:

[0074] ;

[0075] The magnetic moment parameters of the micro / nano robot are taken as follows:

[0076] ;

[0077] The unit vector of the common rotation axis of the driving magnets is taken as:

[0078] ;

[0079] The positions of the three permanent magnets are set as follows:

[0080] ;

[0081] ;

[0082] ;

[0083] That is, the three permanent magnets are arranged in an equilateral triangle with a side length of 350 mm in the xy plane.

[0084] Under synchronous rotation conditions, the instantaneous magnetic moment direction unit vector of a permanent magnet can be expressed as:

[0085] ;

[0086] In the formula, They are in common rotation phase.

[0087] Therefore, the instantaneous magnetic moment vector of the permanent magnet is:

[0088] ;

[0089] Simultaneously, the magnitude of the magnetic moment of the spatial point p to be calculated and the micro / nano robot are obtained. The magnetic moment of the micro-nano robot can be pre-measured using a vibrating sample magnetometer (VSM) or a calibration system based on Helmholtz coils.

[0090] Figure 2 This is a schematic diagram illustrating the coordinate system definition of three synchronously rotating permanent magnets in an embodiment of the present invention; wherein x, y, and z form a global rectangular coordinate system, the three permanent magnets are arranged in an equilateral triangle in the xy plane, and each permanent magnet rotates synchronously around its own axis with the same angular velocity Ω. This indicates the initial orientation direction of the magnetic moment of the permanent magnet.

[0091] Step 2: Calculate the total magnetic field;

[0092] For the i-th permanent magnet, calculate its relative position vector with the spatial point to be calculated:

[0093] ;

[0094] And the corresponding unit vector:

[0095] ;

[0096] According to the magnetic dipole model, the magnetic field generated by the i-th permanent magnet at the point in space to be calculated is:

[0097] ;

[0098] The total magnetic field generated by the three permanent magnets is:

[0099] .

[0100] Step 3: Determine the direction of the magnetic moment of the micro / nano robot;

[0101] Normalizing the total magnetic field yields the unit vector of the total magnetic field direction:

[0102] ;

[0103] In this embodiment, it is assumed that the magnetic moment direction of the micro / nano robot is consistent with the direction of the total magnetic field. Therefore, the magnetic moment vector of the micro / nano robot is represented as:

[0104] .

[0105] Step 4: Construct the field matrix and magnetic gradient matrix;

[0106] Define the field matrix corresponding to the i-th permanent magnet as:

[0107] ;

[0108] Further define the gradient matrix

[0109] ;

[0110] ;

[0111] ;

[0112] Based on this, construct the gradient force compact matrix:

[0113] ;

[0114] Step 5: Construct the gradient force compact matrix and calculate the magnetic gradient force;

[0115] The magnetic gradient force experienced by the micro / nano robot at the spatial point to be calculated is:

[0116] ;

[0117] The magnitude of the magnetic gradient force is:

[0118] ;

[0119] The total magnetic field modulus is:

[0120] ;

[0121] Step 6: Output the results;

[0122] Output the current spatial point to be calculated and the current synchronous rotation angle. Total magnetic field modulus under the condition and magnetic gradient force mode .

[0123] By repeating the above steps for multiple discrete synchronous rotation angles within one rotation cycle, the periodic response results of the total magnetic field modulus and the magnetic gradient force modulus as a function of the synchronous rotation angle can be obtained.

[0124] By repeating the above steps at multiple spatial points, the total magnetic field and magnetic gradient force distribution at different locations within the workspace can be obtained; by repeating the above steps along a given path, the magnetic field and force characteristics distribution along the path can be obtained, which can be used to analyze the magnetic field variation and force variation at different locations.

[0125] The following explanation of this embodiment is based on the calculation results of representative spatial points.

[0126] To characterize the magnetic field distribution characteristics within the workspace under the action of three synchronous rotating magnetic fields, this embodiment selects eight representative spatial points for total magnetic field calculation. The selected spatial points are (0,0,0), (20,0,0), (0,20,0), (0,0,20), (20,20,0), (20,0,20), (0,20,20), (20,20,20) mm. For each representative spatial point, at a given synchronous rotation angle... The total magnetic field modulus was calculated under different conditions. Table 1 shows the calculated total magnetic field results at eight representative spatial points under different synchronous rotation angles. Table 1: Calculated Total Magnetic Field Results (mT) at Eight Representative Spatial Points:

[0127]

[0128] As shown in Table 1, at the same spatial point, the total magnetic field modulus will change with synchronous rotation. The variation in magnitude indicates a significant angular correlation between the combined magnetic field formed by the three synchronously rotating permanent magnets and the changes in the total magnetic field modulus at different spatial points, suggesting that the spatial superposition of the three magnets creates a non-uniform magnetic field distribution within the workspace. The differences between single-axis, dual-axis, and multi-axis offset points reflect the influence of spatial position variations on the local magnetic field strength. These results can be used to assist in determining the distribution of magnetic field strength within the workspace and provide a foundation for subsequent magnetic gradient force analysis.

[0129] Furthermore, to characterize the distribution of magnetic gradient force within the workspace under the action of three synchronous rotating magnetic fields, this embodiment also selects the aforementioned eight representative spatial points for magnetic gradient force calculation. For each representative spatial point, the synchronous rotation angle is calculated separately. The magnetic gradient force modulus at different synchronous rotation angles is shown in Table 2.

[0130] Table 2 Calculation results of magnetic gradient force at eight representative spatial points :

[0131]

[0132] As shown in Table 2, the magnitude of the magnetic gradient force depends not only on the spatial position but also on the synchronous rotation angle. The magnetic gradient force is relatively small near the origin, indicating a weaker magnetic gradient effect in the central region. The magnitudes of the magnetic gradient force at single-axis, dual-axis, and multi-axis offset points significantly increase, indicating that the magnetic gradient force on the micro / nano robot becomes more pronounced as its spatial position deviates from the center and is amplified by the superposition of multiple permanent magnets. Furthermore, the magnetic gradient force values ​​at the same point differ under different synchronous rotation angles, demonstrating a significant angle-dependent force characteristic of the three synchronous rotating magnetic fields.

[0133] Figure 3 The magnetic gradient force modulus of the three magnetic dipole system at eight representative spatial locations in this embodiment of the invention varies with the synchronous rotation angle. The curve showing the change of the horizontal axis; where the horizontal axis is... The vertical axis represents the synchronous rotation angle of the permanent magnet, and the vertical axis represents the magnitude of the magnetic gradient force. The curves of different colors correspond to the magnetic gradient force variation characteristics at eight spatial locations.

[0134] from Figure 3 As can also be seen from Table 2, under the parameter conditions selected in this embodiment, some spatial points are... and The magnetic gradient force modulus at that time was significantly higher than and The corresponding value at that time indicates that the synchronous rotation angle of the driving magnet has a direct impact on the local magnetic field gradient distribution. Therefore, when performing trajectory planning, workspace safety assessment, or control parameter tuning, it is necessary to consider not only the spatial location itself, but also the influence of the synchronous rotation angle on the instantaneous force state.

[0135] In practical applications, the real-time positions of the three permanent magnets can be obtained through encoders, robotic arm kinematic models, or position sensors. Simultaneously, the spatial position of the micro / nano robot to be evaluated can be obtained based on trajectory planning or visual measurement. The control software first calculates the relative positional relationship and unit vector between each permanent magnet and the point to be calculated in space, then calculates the magnetic field generated by each permanent magnet, and obtains the total magnetic field result.

[0136] After obtaining the position correlation matrix, the field matrices, magnetic gradient matrix, and gradient force compact matrix are constructed according to steps 4 and 5, thus expressing the total magnetic field and magnetic gradient force in a compact form. At this point, for any given spatial point to be calculated and synchronous rotation angle, the magnitudes of the total magnetic field and magnetic gradient force experienced by the micro / nano robot can be quickly obtained.

[0137] In a magnetic drive control system, the above calculations can be performed one by one on discrete points on several candidate paths during the trajectory planning stage to obtain the total magnetic field and magnetic gradient force at the corresponding points. If the magnetic gradient force modulus at certain path points exceeds a preset safety threshold at a specific synchronous rotation angle, the path is considered to have potential risks, which can be avoided by adjusting the relative positions of the three permanent magnets, limiting the movement range of the micro-nano robot, replanning the path, or correcting the drive parameters.

[0138] During closed-loop control, when the control system updates the estimated position of the micro-nano robot in real time, it can also call the calculation method of this embodiment to quickly estimate the total magnetic field and magnetic gradient force at the current point. If the estimation result shows that the magnetic gradient force corresponding to a certain synchronous rotation angle is close to or exceeds the safety threshold, the system can dynamically reduce the driving magnetic moment, adjust the motion path, or correct the target position, thereby achieving online safety protection.

[0139] This embodiment demonstrates that the method of the present invention can not only quickly complete the total magnetic field calculation of multiple representative spatial points under the action of three synchronous rotating magnetic fields, but also simultaneously obtain the magnetic gradient force results under the corresponding synchronous rotation angle conditions, and provide quantitative basis for trajectory planning, workspace evaluation and closed-loop control.

[0140] Example 2: This example provides a magnetic gradient force calculation system for a magnetically driven micro / nano robot to implement the method described in Example 1, comprising:

[0141] Calculation module: Employs an industrial computer, embedded controller, or host computer program, and has matrix operation capabilities to perform rapid calculations of magnetic field and magnetic gradient force based on input parameters;

[0142] Storage module: Used to store the position parameters, magnetic moment parameters, spatial point parameters to be calculated, historical calculation results, and safety threshold parameters of the three permanent magnets;

[0143] Input module: used to receive position update data of three synchronously rotating permanent magnets, rotation phase information, and spatial position data of the micro-nano robot;

[0144] Output module: Used to output total magnetic field results, magnetic gradient force results, distribution map results or alarm signals, and communicate with the magnetically driven micro-nano robot control system.

[0145] During system deployment, three synchronously rotating permanent magnets are mounted on the drive mechanism to ensure that they rotate synchronously under the control system. The input module establishes a communication connection with the permanent magnet position detection device, visual positioning system, or other position sensors to collect the spatial position data of the three permanent magnets and the micro-nano robot in real time.

[0146] After the system starts, the storage module loads the preset permanent magnet magnetic moment parameters, initial position parameters, and safety thresholds, and the calculation module enters standby mode. After the input module receives the position and phase data in real time, the calculation module calls the method of Example 1 to calculate the relative position vector, total magnetic field, total magnetic field direction, field matrix, magnetic gradient matrix, gradient force compaction matrix, and magnetic gradient force vector in sequence, and sends the results to the output module.

[0147] The output module feeds back the calculated total magnetic field and magnetic gradient force results to the magnetic drive control system in real time for trajectory planning, closed-loop control, and safety verification. When the magnetic gradient force at a certain path point or the current real-time position exceeds a preset threshold, the output module immediately triggers an alarm and coordinates with the control system to adjust the drive parameters or motion trajectory.

[0148] The storage module can also continuously record the total magnetic field results and magnetic gradient force results at different spatial points, gradually building magnetic field distribution data and safety distribution data within the workspace, providing a basis for subsequent control strategy optimization.

[0149] This embodiment, through its universal design, is compatible with permanent magnets, micro-nano robots, and detection equipment of different specifications. By simply adjusting the parameter configuration and safety threshold according to the actual application scenario, it can achieve rapid calculation and safe control of the total magnetic field and magnetic gradient force under the action of three synchronous rotating magnetic fields.

[0150] The above embodiments are merely preferred embodiments of the present invention. Those skilled in the art can make several improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field, characterized in that: Includes the following steps: Step 1: Obtain the position vectors of the three synchronously rotating permanent magnets, the magnitude of the permanent magnet's magnetic moment, the common rotation phase, the position vector of the spatial point to be calculated, and the magnitude of the magnetic moment of the micro / nano robot; and define the instantaneous magnetic moment vector of the permanent magnet based on the magnitude and unit vector of the magnetic moment direction. Step 2: Based on the magnetic dipole model, calculate the magnetic field generated by the three permanent magnets at the point to be calculated, and then vector-superimpose the corresponding magnetic fields of each permanent magnet to obtain the total magnetic field at the point to be calculated. Step 3: Construct a unit vector for the direction of the total magnetic field based on the total magnetic field, and make the unit vector for the magnetic moment direction of the micro-nano robot consistent with the unit vector for the direction of the total magnetic field; Step 4: Based on the relative positional relationship between the three permanent magnets and the spatial point to be calculated, construct the field matrix and magnetic gradient matrix, and further construct the gradient force compact matrix; Step 5: Based on the gradient force compact matrix, the magnitude of the permanent magnet magnetic moment, the magnitude of the micro / nano robot magnetic moment, and the unit vector of the total magnetic field direction, calculate the magnetic gradient force vector acting on the micro / nano robot at the spatial point to be calculated. Step 6: Output the magnetic gradient force vector and its magnitude.

2. The method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field as described in claim 1, characterized in that: In step 2, for the i-th permanent magnet, first calculate the position vector between the spatial point p to be calculated and the i-th permanent magnet. The relative position vectors between them: ； And the relative position unit vector: ； Where i = 1, 2, 3; Then, based on the magnetic dipole model, calculate the magnetic field generated by the i-th permanent magnet at the point in space to be calculated: ； In the formula, The permeability of free space, It is a third-order identity matrix. This refers to the instantaneous magnetic moment vector of a synchronously rotating permanent magnet; The total magnetic field is obtained by vector superposition of the magnetic fields of the three permanent magnets: 。 3. The method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field as described in claim 1, characterized in that: In step 3, the instantaneous magnetic moment vector of the permanent magnet is expressed as: ； in, The magnitude of the magnetic moment of the permanent magnet. The unit vector of the magnetic moment direction of the permanent magnet; Normalizing the total magnetic field yields the unit vector of the total magnetic field direction: ； If the direction of the magnetic moment of the micro / nano robot is aligned with the direction of the total magnetic field, then the magnetic moment vector of the micro / nano robot can be expressed as: ； in, The magnetic moment of the micro / nano robot is denoted by .

4. The method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field as described in claim 1, characterized in that: In step 4, the field matrix corresponding to the i-th permanent magnet is constructed: ； And construct the magnetic gradient matrix , and ,in: ； ； ； Then, the gradient force compact matrix is ​​constructed as follows: ； The gradient force compact matrix is ​​used to characterize the mapping relationship of magnetic gradient forces under the combined action of three synchronously rotating permanent magnets.

5. The method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field according to claim 4, characterized in that: In step 5, the magnetic gradient force vector at the spatial point to be calculated is expressed as: ； In the formula, The magnitude of the magnetic moment of the micro / nano robot; This represents the magnitude of the magnetic moment of the permanent magnet.

6. The method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field according to claim 5, characterized in that: In step 6, steps 1 to 5 are repeated for multiple discrete rotation phases within one rotation cycle to obtain the periodic response results of the magnetic gradient force as a function of the rotation phase.

7. The method for calculating the magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field according to claim 1 or 6, characterized in that: Repeat steps 1 to 6 at multiple spatial points to construct a magnetic gradient force distribution map, a safe workspace distribution map, or a centerline path force characteristic distribution map within the workspace.

8. A rapid calculation system for magnetic gradient force of a magnetically driven micro / nano robot, used to implement the method for calculating magnetic gradient force of a micro / nano robot under a three-synchronous rotating magnetic field as described in any one of claims 1 to 7, characterized in that, include: The input module is used to obtain the position parameters, magnetic moment parameters, common rotation phase, position parameters of the spatial point to be calculated, and magnetic moment parameters of the micro-nano robot of the three synchronously rotating permanent magnets. The calculation module, connected to the input module, is used to calculate the magnetic gradient force vector and its magnitude at the spatial point to be calculated for the micro-nano robot based on the parameters obtained by the input module. An output module, connected to the calculation module, is used to output the calculation results of the magnetic gradient force.

9. The magnetic gradient force calculation system for magnetically driven micro / nano robots according to claim 8, characterized in that, The output module is specifically used to output the magnetic gradient force calculation results, the magnetic gradient force distribution results in the workspace, or the over-threshold alarm information.

10. The magnetic gradient force calculation system for magnetically driven micro / nano robots according to claim 8, characterized in that, The system is communicatively connected to the magnetically driven micro / nano robot control system. During the trajectory planning phase, the system is used to perform rapid calculation of the magnetic gradient force on discrete points on the candidate path; During the closed-loop control phase, the system updates the magnetic gradient force calculation results based on the real-time position of the micro-nano robot, so that the control system can perform parameter correction, path adjustment, or safety verification.

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