Method for quickly estimating upper and lower bounds of maximum magnetic force of micro-nano robot under double synchronous rotating magnetic fields

Abstract

The invention discloses a method for quickly estimating the upper and lower bounds of the maximum magnetic force of a micro-nano robot in a double-synchronous rotating magnetic field. The method comprises the following steps: acquiring position vectors, common magnetic moment vectors, common rotating shaft unit vectors and to-be-estimated position points of two permanent magnets; calculating and superposing a total magnetic field generated by each permanent magnet at the to-be-estimated position point and a magnetic field rotating shaft; the magnetic gradient force borne by the micro-nano robot is expressed as a calculation formula related to the magnetic moment direction of the permanent magnet and the magnetic moment direction of the micro-nano robot; constructing a symmetric matrix related to a common rotating shaft of the permanent magnets and a magnetic field rotating shaft at the position point to be estimated, and taking a characteristic value of the symmetric matrix as a candidate upper bound of the normalized maximum magnetic force; constructing an auxiliary matrix based on the eigenvectors, and taking eigenvalues of the auxiliary matrix as a candidate lower bound of the normalized maximum magnetic force; and obtaining an estimation interval of the normalized magnetic gradient force maximum square according to the candidate upper and lower bounds, and outputting a modulus length estimation range. According to the method, rapid estimation of the maximum magnetic force is realized on the premise of ensuring the calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of motion control technology for micro-nano robots, and in particular to a method for rapidly estimating the upper and lower bounds of the maximum magnetic force of a micro-nano robot under a dual synchronous rotating magnetic field. Background Technology

[0002] In recent years, magnetically driven micro- and nano-robots have been extensively studied in fields such as minimally invasive medicine, targeted drug delivery, thrombus removal, and precision manipulation. Common driving methods include electromagnetic coil array driving and permanent magnet driving. Among them, permanent magnet driving systems have advantages such as simple structure, low energy consumption, and low maintenance costs, making them more suitable for deployment in small and medium-sized experimental platforms and clinical application environments.

[0003] In permanent magnet drive systems, micro- and nanorobots typically move under the influence of an external magnetic field. On one hand, the magnetic torque is used to adjust the attitude of the micro- and nanorobot, aligning its magnetic moment with the direction of the external magnetic field. On the other hand, the spatial gradient of the magnetic field generates a magnetic gradient force, which propels or pulls the micro- and nanorobot along a target direction. However, when the magnetic gradient force is too large, it may cause excessive traction on surrounding tissues or instability in the movement of the micro- and nanorobot, posing potential safety risks. Therefore, in the trajectory planning and closed-loop control design process, it is necessary to evaluate and constrain the maximum magnetic gradient force that the micro- and nanorobot may experience at a given spatial location.

[0004] Existing methods rely on numerical iteration to calculate the maximum force under different magnetic moment combinations, which involves a large amount of computation and is difficult to apply in real-time control. At the same time, it is difficult to provide safe upper and lower bounds that can be quickly evaluated, which is not conducive to the real-time verification of the controller during trajectory planning or closed-loop control.

[0005] Traditional methods often involve numerical simulation or offline search to calculate the magnetic gradient force point-by-point for the discrete permanent magnet attitude and the magnetic moment direction of the magnetic micro / nano robot, and then taking the maximum value as the estimate. This method is computationally intensive, difficult to integrate into real-time control loops, and cannot theoretically provide a clear description of the upper bound of the force, making it unsuitable for explicitly embedding magnetic gradient force constraints into the control algorithm. Summary of the Invention

[0006] The purpose of this invention is to provide a fast method for estimating the upper and lower bounds of the maximum magnetic force for micro / nano robots under dual synchronous rotating magnetic fields. This invention establishes a linear mapping relationship between the magnetic gradient force and the direction of the permanent magnet's magnetic moment, and combines this with eigenvalue analysis to obtain the upper and lower bound estimation intervals of the square of the maximum magnetic gradient force while ensuring computational efficiency. This yields the estimation range of the magnetic gradient force modulus, which can be used for real-time safety assessment in trajectory planning and closed-loop control.

[0007] The technical solution of this invention: a fast estimation method for the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous swirl magnetic fields, comprising the following steps:

[0008] Step 1: Obtain the position vector, common magnetic moment vector, unit vector of rotation axis, and position point to be estimated for two identical permanent magnets;

[0009] Step 2: Calculate the magnetic field generated by each permanent magnet at the position to be estimated based on the magnetic dipole model, and superimpose them to obtain the total magnetic field;

[0010] Step 3: Express the magnetic gradient force on the micro-nano robot as a symmetric matrix form related to the magnetic moment direction of the permanent magnet and the magnetic moment direction of the micro-nano robot;

[0011] Step 4: Construct a symmetric matrix related to the rotation axis through linear mapping and calculate its eigenvalues ​​as candidate upper bounds for the square of the maximum value of the normalized magnetic gradient force.

[0012] Step 5: Construct an auxiliary matrix based on the eigenvectors and calculate its eigenvalues ​​as candidate lower bounds for the square of the normalized magnetic gradient force.

[0013] Step 6: Obtain the estimated range of the square of the normalized magnetic gradient force based on the candidate upper and lower bounds, and output the estimated range of the magnitude of the magnetic gradient force.

[0014] In the above-mentioned method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous swirl magnetic fields, step 2 first calculates the relative position vector and unit vector between each permanent magnet and the position to be estimated:

[0015] ;

[0016] ;

[0017] In the formula: It is a relative position vector. Let be the position vector of the point to be estimated. It is a unit vector of relative position. The position vector of a permanent magnet in a fixed coordinate system; Number the permanent magnets;

[0018] Then, based on the magnetic dipole model, the magnetic field vector generated by each permanent magnet at the position to be estimated is solved separately:

[0019]

[0020] In the formula: The magnetic field vector generated at the location point to be estimated of the permanent magnet; It is a physical quantity representing the strength and direction of the magnetism of a permanent magnet; Permeability of free space; It is the identity matrix;

[0021] Finally, the magnetic field vectors corresponding to the two permanent magnets are superimposed to obtain the total magnetic field at the location to be estimated.

[0022] In the aforementioned method for rapid estimation of the upper and lower bounds of the maximum magnetic force on micro / nano robots under dual synchronous swirl magnetic fields, step 3, the magnetic gradient force experienced by the micro / nano robot is expressed as:

[0023] ;

[0024] In the formula: The permeability of free space, The magnitude of the magnetic moment of the micro / nano robot; The magnitude of the magnetic moment of a single permanent magnet, It is a unit vector of relative position. The magnetic moment unit vector of the permanent magnet. It is the transpose symbol. , , They are the first The magnetic gradient matrix corresponding to each permanent magnet , and A 3×3 matrix with orientation; Let be the unit vector of the magnetic moment of the micro / nano robot. It is a constant related to the magnitude of the magnetic moment and the free permeability. For the reason and The constructed gradient force matrix.

[0025] In the aforementioned method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous swirl magnetic fields, step 4 is based on linear mapping. The unit vector of the magnetic moment of any permanent magnet Mapped to gradient force matrix Construct a symmetric matrix:

[0026] ;

[0027] In the formula: The constructed constrained symmetric matrix, Let the unit vector be the common axis of rotation of the permanent magnets. It is the transpose symbol. is the component of the magnetic gradient force in the direction vector of the magnetic moment;

[0028] ;

[0029] In the formula, It is the identity matrix. It is a relative position vector. It is the outer product of the relative position vectors of the two permanent magnets. It is a unit vector of relative position. Number the permanent magnets;

[0030] Calculate the largest eigenvalue of a symmetric matrix and corresponding feature vectors and the largest eigenvalue This serves as one of the upper bounds of the square of the normalized magnetic gradient force.

[0031] In the aforementioned method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous swirl magnetic fields, step 5 involves constructing the auxiliary matrix as follows:

[0032] ;

[0033] In the formula, is the unit vector of the rotation axis of the magnetic field at the location to be estimated;

[0034] Calculate the largest eigenvalue of the auxiliary matrix and their corresponding eigenvectors This serves as a candidate lower bound for the square of the normalized magnetic gradient force.

[0035] In the aforementioned method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous swirl magnetic fields, step 6 is based on the feature vector. as well as Construct matrices respectively:

[0036] ;

[0037] ;

[0038] calculate and The largest eigenvalues ​​are denoted as follows: and ;

[0039] Define normalized magnetic gradient force ,therefore ;

[0040] According to the inequality:

[0041] ;

[0042] The estimated interval for the square of the normalized magnetic gradient force acting on the micro / nano robot at the location to be estimated is obtained. ,in, , ;

[0043] Estimation range of the maximum magnitude of the output magnetic gradient force .

[0044] The aforementioned method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous swirl magnetic fields, wherein the symmetric matrix Auxiliary matrix ,matrix sum matrix The largest eigenvalue is obtained by numerical eigenvalue decomposition.

[0045] A magnetic gradient force estimation system, comprising:

[0046] The calculation module is used to execute the methods described above;

[0047] The storage module is used to store the permanent magnet position parameters, magnetic moment parameters, rotation axis parameters, and parameters of the position point to be estimated;

[0048] The output module is used to output the estimated range of the maximum value of the magnetic gradient force.

[0049] The aforementioned system is coupled to a magnetically driven microrobot control system to evaluate the magnetic gradient force in real time during trajectory planning or closed-loop control, and to issue an alarm or adjust parameters when the force exceeds a safety threshold.

[0050] In the aforementioned system, the storage module is also used to store the magnetic gradient force estimation results at different spatial points in order to construct a safe workspace distribution map.

[0051] The aforementioned system is characterized in that the calculation module automatically recalculates and updates the magnetic gradient force estimation interval when the position of the permanent magnet or the position to be estimated is updated.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. This invention establishes a linear mapping relationship between the magnetic gradient force and the magnetic moment direction of the permanent magnet, transforming the solution of the maximum magnetic gradient force into the eigenvalue decomposition of a finite-dimensional symmetric matrix. This avoids the high-dimensional nonlinear search and numerical iteration of traditional methods, significantly reducing the computational load. It can be directly embedded into the real-time control loop to meet the real-time requirements of trajectory planning and closed-loop control.

[0054] 2. This invention clearly provides the upper and lower bound estimation intervals of the square of the maximum magnetic gradient force. The conservative upper bound can effectively avoid the risk of tissue damage or robot motion instability caused by excessive magnetic gradient force, while the lower bound estimation can provide a quantitative evaluation basis for the effectiveness of the control strategy, achieving a balance between safety and control efficiency.

[0055] 3. This invention does not require additional sensors. It can complete the calculation by relying only on existing available parameters such as the position of the permanent magnet, the magnetic moment, the rotation axis parameters, and the position point to be estimated. It is easy to integrate into the magnetic drive platform of the robotic arm and the permanent magnet, and is compatible with the drive system of various devices such as magnetic micro-nano robots, magnetically controlled capsules, and magnetic conduits.

[0056] 4. The method of the present invention is not limited to a specific permanent magnet arrangement or robot type, and can be extended to various magnetically driven micro-nano robot application scenarios such as minimally invasive medicine, targeted drug delivery, thrombus removal, and precision operation, providing a unified theoretical tool and engineering implementation scheme for safety control in different scenarios.

[0057] 5. When the position of the permanent magnet or the position to be estimated by the robot is updated, the magnetic gradient force estimation interval can be automatically and quickly recalculated. In conjunction with the construction of the safe workspace distribution map, the control system can dynamically adjust the drive parameters and avoid dangerous paths, thus achieving dynamic safety assurance throughout the entire process. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the structure of the dual synchronous rotating permanent magnets superimposed with a rotating magnetic field according to the present invention. Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0060] Example: A fast method for estimating the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous swirl magnetic fields, including the following steps:

[0061] Step 1: Obtain the position vector, common magnetic moment vector, unit vector of rotation axis, and position point to be estimated for two identical permanent magnets;

[0062] In this step, the geometric center positions of two identical permanent magnets are obtained in a fixed coordinate system. Two permanent magnets have the same magnetic moment magnitude, and their magnetic moment directions always remain parallel. They can be represented by a common magnetic moment vector. This indicates that the unit vector of the rotation axis of the two permanent magnets rotating synchronously is obtained. Select the location point to be estimated. This point can be located anywhere within the target workspace, near the midpoint of the line connecting the two permanent magnets; the magnetic moment of the micro / nano robot can be obtained. And denote its magnetic moment unit vector as .

[0063] Step 2: Calculate the magnetic field generated by each permanent magnet at the position to be estimated based on the magnetic dipole model, and superimpose them to obtain the total magnetic field;

[0064] In this step, for the first One permanent magnet ( =1,2), define its position relative to the point to be estimated. The relative position vectors and unit vectors between them are as follows:

[0065] ;

[0066] The magnetic dipole model is used to describe the state of a single permanent magnet at a point. The generated magnetic field vector, the first The magnetic field generated by a permanent magnet can be written as:

[0067]

[0068] In the formula: The magnetic field vector generated at the location point to be estimated of the permanent magnet; It is a physical quantity representing the strength and direction of the magnetism of a permanent magnet; Permeability of free space; It is an identity matrix with a size of 3×3;

[0069] Two permanent magnets at point The total magnetic field is the sum of the individual magnetic fields:

[0070] .

[0071] Step 3: Express the magnetic gradient force on the micro-nano robot as a symmetric matrix form related to the magnetic moment direction of the permanent magnet and the magnetic moment direction of the micro-nano robot;

[0072] In this step, let the unit vector of the permanent magnet's magnetic moment be... The unit vector of the magnetic moment of the micro / nano robot is Under the action of two synchronously rotating permanent magnets, the derived expression for the magnetic gradient force can be written as follows: The quadratic form:

[0073]

[0074] In the formula: The permeability of free space, The magnitude of the magnetic moment of the micro / nano robot; The magnitude of the magnetic moment of a single permanent magnet, It is a unit vector of relative position. The magnetic moment unit vector of the permanent magnet. It is the transpose symbol. Let be the unit vector of the magnetic moment of the micro / nano robot. It is a constant related to the magnitude of the magnetic moment and the free permeability. , For the reason and The constructed gradient force matrix has a size of 3×3; , , They are the first The magnetic gradient matrix corresponding to each permanent magnet , and A 3x3 matrix with orientation:

[0075] ;

[0076] ;

[0077] ;

[0078] in, , , .

[0079] Step 4: Construct a symmetric matrix related to the rotation axis through linear mapping and calculate its eigenvalues ​​as candidate upper bounds for the square of the maximum value of the normalized magnetic gradient force.

[0080] In this step, a 3×3 matrix is ​​further introduced to construct the symmetric matrix related to the rotation axis. So that it satisfies relation (6):

[0081] ;

[0082] From this we can obtain Explicit form:

[0083] ;

[0084] In the formula, It is the outer product of the relative position vectors of the two permanent magnets; ;

[0085] This formula allows direct calculation of geometric quantities. , With matrix Calculate ;

[0086] Then based on linear mapping The unit vector of the magnetic moment of any permanent magnet Mapped to gradient force matrix Construct a symmetric matrix:

[0087] ;

[0088] In the formula: The constructed constrained symmetric matrix, Let the unit vector be the common axis of rotation of the permanent magnets. , ; It is the transpose symbol. is the component of the magnetic gradient force in the direction vector of the magnetic moment;

[0089] Calculate the largest eigenvalue of a symmetric matrix and corresponding feature vectors and the largest eigenvalue As a candidate upper bound for the square of the normalized magnetic gradient force maximum value.

[0090] Step 5: Construct an auxiliary matrix based on the eigenvectors and calculate its eigenvalues ​​as candidate lower bounds for the square of the normalized magnetic gradient force.

[0091] In this step, the auxiliary matrix is ​​constructed as follows:

[0092] ;

[0093] In the formula, Let be the unit vector of the rotation axis of the magnetic field at the location to be estimated. , ;

[0094] Calculate the largest eigenvalue of the auxiliary matrix and their corresponding eigenvectors This serves as a candidate lower bound for the square of the normalized magnetic gradient force.

[0095] Step 6: Obtain the estimated range of the square of the normalized magnetic gradient force based on the candidate upper and lower bounds, and output the estimated range of the magnitude of the magnetic gradient force.

[0096] In this step, based on feature vectors Construct the following two matrices:

[0097] ;

[0098] ;

[0099] The matrices were obtained respectively. and The largest eigenvalue is denoted as and These two can be considered as two candidate lower bounds for the square of the maximum magnetic gradient force.

[0100] For ease of calculation, a normalized magnetic gradient force is defined. ,therefore ;

[0101] Based on the above matrix and eigenvalue relationships, the normalized magnetic gradient force satisfies the following inequality:

[0102] ;

[0103] in, , ;

[0104] Based on this Then at the specified location point The range of the magnitude estimation for the maximum normalized magnetic gradient force experienced by the micro / nano robot is as follows: This can be used for real-time safety assessment of magnetic gradient force during trajectory planning and closed-loop control. The above interval gives the value at a specified point. Given the positions of the two permanent magnets and the direction of the rotation axis, what is the estimated range of the maximum magnitude of the magnetic gradient force experienced by the micro / nano robot? It can be used directly to determine whether the current driving scheme meets the preset safety threshold.

[0105] The present invention will be further described below with reference to specific application examples.

[0106] like Figure 1 As shown, in a fixed coordinate system In this configuration, two identical permanent magnets are mounted on the end effector of the robotic arm or on an independent support, with their geometric centers positioned at the following locations: The two permanent magnets have the same magnetic moment magnitude, their magnetic moment directions remain parallel, and they rotate around a common axis of rotation as a unit vector. Synchronous rotation. Micro- and nano-robots (such as helical magnetic microrobots) are positioned at a certain location within a fluid or gel-filled workspace between two permanent magnets. .

[0107] In practical applications, the real-time position of the two permanent magnets can be obtained through an encoder or robotic arm model. and the direction of rotation axis Simultaneously, the spatial location to be evaluated can be obtained based on trajectory planning or visual measurement. The control software first calculates... and Then calculate the magnetic field generated by each permanent magnet. And obtain the total magnetic field.

[0108] In obtaining the location-related matrix Then, a linear mapping is constructed based on steps 3 and 4. and symmetric matrices Thus, the magnetic gradient force can be written as In this case, for any condition satisfying the constraints... The magnetic gradient force modulus can be obtained through get.

[0109] To estimate in all allowed The maximum magnetic gradient force under the combination is constructed in this embodiment according to the steps in the invention description, by forming a matrix. Obtained through numerical eigenvalue decomposition Then calculate as well as The estimated interval.

[0110] In a magnetic drive control system, discrete points on several candidate paths can be selected during the trajectory planning stage. Perform the above calculations one by one to obtain the corresponding upper bound of the maximum magnetic gradient force. If certain points on certain paths If the path exceeds a pre-set safety threshold, it is considered to be potentially dangerous and can be avoided by adjusting the relative position of the permanent magnet, limiting the range of motion of the micro-nano robot, or replanning the path.

[0111] During the closed-loop control process, the control system updates the estimated position of the micro-nano robot in real time. At the same time, the calculation method of this invention can also be used to quickly estimate the maximum magnetic gradient force at the current point. If the estimation result shows... When the target magnetic moment approaches or exceeds the safety threshold, the system can dynamically reduce the driving magnetic moment, decrease the rotation frequency, or adjust the target position to achieve online safety protection.

[0112] Table 1 shows the results of using the method of the present invention in several typical spatial locations. The upper bound of the square of the maximum value of the magnetic gradient force obtained by the lower estimation and the lower world The results comparison table demonstrates the effectiveness of the fast estimation method of the present invention.

[0113] Table 1. Comparison of Magnetic Gradient Force Estimation Results at Typical Locations:

[0114]

[0115] In Table 1, the location of the origin ( =[0 0 0]ᵀ): and All values ​​are 0, indicating that when the location to be estimated coincides with the geometric center of the permanent magnet, the gradient of the magnetic fields generated by the two permanent magnets after superposition is 0, and the maximum value of the magnetic gradient force is 0, which is consistent with the physical characteristics of the magnetic dipole model.

[0116] Single-axis offset position (e.g.) =[20 0 0]ᵀ、[0 20 0]ᵀetc).

[0117] Slightly larger (e.g., [20 0 0]ᵀ line:) =23.64, (= 21.14), indicating that the estimated interval is compact, without obvious redundancy, reflecting the advantages of "fast estimation" and "high precision" of the present invention;

[0118] The numerical differences at different coaxial offset positions (such as at 20 mm on the x-axis = 23.64, at 20 mm on the z-axis = 13.34), reflecting the spatial differences in the magnetic field distribution of the permanent magnet, verifying that the method can adapt to the force estimation requirements at different positions.

[0119] Multi-axis offset positions (such as = [20 20 0]ᵀ, [20 20 20]ᵀ, etc.):

[0120] The difference from is still small (such as for the row [20 20 20]ᵀ: = 37.33, = 32.99), indicating that even at complex spatial positions, the method can still stably output accurate upper and lower bounds;

[0121] The overall value is higher than that of the single-axis offset position, conforming to the physical law that "the magnetic gradient force increases as the distance from the permanent magnet decreases".

[0122] The data in Table 1 verifies the core advantages of the present invention: without numerical iteration, a compact estimated interval can be quickly obtained only through matrix eigenvalue decomposition, and the results are stable under different spatial positions and can be directly used for trajectory planning (to avoid paths exceeding the safety threshold) and closed-loop control (updating the position in real time and adjusting parameters).

[0123] Embodiment 2: This embodiment provides a system for implementing the method described in Embodiment 1, including:

[0124] Calculation module: Using a general microcontroller or industrial computer, with the ability of matrix operation and numerical eigenvalue decomposition, pre-storing the algorithm logic of the fast estimation method described in the claims, and capable of receiving external parameter inputs and performing the calculation of the upper and lower bounds of the magnetic gradient force.

[0125] Storage module: Selecting a general storage medium, used to solidify basic parameters such as the position vector of the permanent magnet, the common magnetic moment vector, and the unit vector of the rotation axis, and at the same time caching the data of the position points to be estimated, the real-time calculation results, and the historical estimation records, supporting data reading, writing, and updating.

[0126] Input module: Through an encoder, a positioning sensor, or a communication interface, obtaining the real-time position parameters of two identical permanent magnets, the information of the rotation axis direction, and the coordinate data of the position points to be estimated (the position where the micro-nanorobot is located), ensuring the real-time and accurate transmission of parameters.

[0127] Output module: Includes communication interface and alarm unit, which can output the estimated range of the maximum magnitude of magnetic gradient force to the magnetic drive micro robot control system. When the estimated value exceeds the preset safety threshold, it triggers an alarm signal or sends parameter adjustment command to the control system.

[0128] In system deployment, two identical permanent magnets are mounted on the drive mechanism (such as the end effector of a robotic arm or a fixed bracket), ensuring that their magnetic moments are always parallel and that they can rotate synchronously around a common axis of rotation. The input module establishes a communication connection with the position detection device of the permanent magnets and the rotation axis control unit. The calculation module, storage module, and input / output module are integrated through a standard communication bus or interface to complete the algorithm program burning and basic parameter initialization storage, and preset the magnetic gradient force safety threshold (set according to the application scenario requirements). The detection device for the position point to be estimated (such as a visual positioning system or position sensor) is connected to the input module to collect the position coordinates of the micro-nano robot in the workspace in real time and transmit them to the system.

[0129] The system's workflow is as follows: After the system starts, the storage module loads the preset permanent magnet magnetic moment parameters, initial position vector, and rotation axis unit vector, and the calculation module completes the initialization preparation.

[0130] The input module receives the position update data of the permanent magnet, the rotation axis direction information, and the coordinate data of the position point to be estimated in real time, and transmits them synchronously to the calculation module and the storage module for caching.

[0131] The calculation module calls the method described in the claims and performs the following operations in sequence: calculates the total magnetic field of the two permanent magnets at the position to be estimated based on the magnetic dipole model; expresses the magnetic gradient force in a symmetric matrix form; constructs a symmetric matrix and an auxiliary matrix related to the rotation axis, and obtains candidate upper and lower bounds through numerical eigenvalue decomposition; and finally determines the estimation interval of the square of the maximum value of the magnetic gradient force and the estimation range of the modulus.

[0132] The output module feeds back the calculated estimated interval to the magnetically driven microrobot control system in real time for safety verification of trajectory planning or closed-loop control.

[0133] When the position of the permanent magnet or the position to be estimated cached in the storage module is updated, the calculation module automatically triggers the recalculation process to update the magnetic gradient force estimation range; if the estimated value exceeds the safety threshold, the output module immediately issues an alarm and links the control system to adjust the drive parameters or motion trajectory.

[0134] The storage module continuously records the magnetic gradient force estimation results at different spatial locations, gradually building safe distribution data of the workspace to provide a basis for subsequent control strategy optimization.

[0135] 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, rapid estimation and safe control of magnetic gradient force can be achieved.

[0136] 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 principle 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 fast method for estimating the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous swirl magnetic fields, characterized by: Includes the following steps: Step 1: Obtain the position vector, common magnetic moment vector, unit vector of rotation axis, and position point to be estimated for two identical permanent magnets; Step 2: Calculate the magnetic field generated by each permanent magnet at the position to be estimated based on the magnetic dipole model, and superimpose them to obtain the total magnetic field; Step 3: Express the magnetic gradient force on the micro-nano robot as a symmetric matrix form related to the magnetic moment direction of the permanent magnet and the magnetic moment direction of the micro-nano robot; Step 4: Construct a symmetric matrix related to the rotation axis through linear mapping and calculate its eigenvalues ​​as candidate upper bounds for the square of the maximum value of the normalized magnetic gradient force. Step 5: Construct an auxiliary matrix based on the eigenvectors and calculate its eigenvalues ​​as candidate lower bounds for the square of the normalized magnetic gradient force. Step 6: Obtain the estimated range of the square of the normalized magnetic gradient force based on the candidate upper and lower bounds, and output the estimated range of the magnitude of the magnetic gradient force.

2. The method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous rotating magnetic fields according to claim 1, characterized in that: In step 2, the relative position vector and unit vector between each permanent magnet and the point to be estimated are first calculated: ； ； In the formula: It is a relative position vector. Let be the position vector of the point to be estimated. It is a unit vector of relative position. The position vector of a permanent magnet in a fixed coordinate system; Number the permanent magnets; Then, based on the magnetic dipole model, the magnetic field vector generated by each permanent magnet at the position to be estimated is solved separately: In the formula: The magnetic field vector generated at the location point to be estimated of the permanent magnet; It is a physical quantity representing the strength and direction of the magnetism of a permanent magnet; Permeability of free space; It is the identity matrix; Finally, the magnetic field vectors corresponding to the two permanent magnets are superimposed to obtain the total magnetic field at the location to be estimated.

3. The method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous rotating magnetic fields according to claim 1, characterized in that: In step 3, the magnetic gradient force experienced by the micro / nano robot is expressed as: ； In the formula: The permeability of free space, The magnitude of the magnetic moment of the micro / nano robot; The magnitude of the magnetic moment of a single permanent magnet, It is a unit vector of relative position. The magnetic moment unit vector of the permanent magnet. It is the transpose symbol. , , They are the first The magnetic gradient matrix corresponding to each permanent magnet , and A 3×3 matrix with orientation; Let be the unit vector of the magnetic moment of the micro / nano robot. It is a constant related to the magnitude of the magnetic moment and the free permeability. For the reason and The constructed gradient force matrix.

4. The method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous rotating magnetic fields according to claim 3, characterized in that: In step 4, based on linear mapping The unit vector of the magnetic moment of any permanent magnet Mapped to gradient force matrix Construct a symmetric matrix: ; In the formula: The constructed constrained symmetric matrix, Let the unit vector be the common axis of rotation of the permanent magnets. It is the transpose symbol. is the component of the magnetic gradient force in the direction vector of the magnetic moment; ； In the formula, It is the identity matrix. It is a relative position vector. It is the outer product of the relative position vectors of the two permanent magnets. It is a unit vector of relative position. Number the permanent magnets; Calculate the largest eigenvalue of a symmetric matrix and corresponding feature vectors and the largest eigenvalue This serves as one of the upper bounds of the square of the normalized magnetic gradient force.

5. The method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous rotating magnetic fields according to claim 4, characterized in that: In step 5, the auxiliary matrix is ​​constructed as follows: ； In the formula, is the unit vector of the rotation axis of the magnetic field at the location to be estimated; Calculate the largest eigenvalue of the auxiliary matrix and their corresponding eigenvectors This serves as a candidate lower bound for the square of the normalized magnetic gradient force.

6. The method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous rotating magnetic fields according to claim 5, characterized in that: In step 6, based on the feature vector as well as Construct matrices respectively: ； ； calculate and The largest eigenvalues ​​are denoted as follows: and ; Define normalized magnetic gradient force ,therefore ; According to the inequality: ； The estimated interval for the square of the normalized magnetic gradient force acting on the micro / nano robot at the location to be estimated is obtained. ,in, , ; Estimation range of the maximum magnitude of the output magnetic gradient force .

7. The method for fast estimation of the upper and lower bounds of the maximum magnetic force of micro / nano robots under dual synchronous rotating magnetic fields according to claim 6, characterized in that: The symmetric matrix Auxiliary matrix ,matrix sum matrix The largest eigenvalue is obtained by numerical eigenvalue decomposition.

8. A magnetic gradient force estimation system, characterized in that, include: A calculation module is configured to perform the method as described in any one of claims 1 to 7; The storage module is used to store the permanent magnet position parameters, magnetic moment parameters, rotation axis parameters, and parameters of the position point to be estimated; The output module is used to output the estimated range of the maximum value of the magnetic gradient force.

9. The system according to claim 8, characterized in that, The system is coupled to the magnetically driven microrobot control system and is used to evaluate the magnetic gradient force in real time during trajectory planning or closed-loop control, and to issue an alarm or adjust parameters when the force exceeds a safety threshold.

10. The system according to claim 8, characterized in that, The storage module is also used to store the magnetic gradient force estimation results at different spatial points in order to construct a safe workspace distribution map; When the position of the permanent magnet or the position to be estimated is updated, the calculation module automatically recalculates and updates the magnetic gradient force estimation interval.

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