A Method for Optimizing the Magnetic Particle Concentration of a Conical Magnetic Continuum Soft Robot

Abstract

The present invention relates to a method for optimizing the magnetic particle concentration of a conical magnetic continuum soft robot, comprising: S1. Dividing the conical magnetic continuum soft robot into m voxels, randomly generating a number of conical magnetic continuum soft robot magnetic particle concentration distribution schemes as an initial population, wherein each voxel has a different magnetic particle concentration, and each individual in the initial population is a magnetic particle concentration distribution scheme of a conical magnetic continuum soft robot; S2. Optimizing the population of the current generation population to obtain a child population; S3. Determining whether the maximum terminal deflection angle in the child population and the average terminal deflection angle of all individuals in the population are less than the tolerance, if yes, obtaining the optimized magnetic particle concentration distribution scheme of the conical magnetic continuum soft robot, if not, replacing the current generation population with the child population and returning to S2. The present invention significantly improves the terminal deflection angle of the soft robot by optimizing the magnetic particle concentration distribution.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic continuous soft robots, and particularly to a method for optimizing the magnetic particle concentration of a conical magnetic continuous soft robot. Background Art

[0002] MSCR can achieve non-contact motion control under the action of an external magnetic field and is widely used in fields such as vascular navigation, targeted therapy, and precision guidance.

[0003] Currently, one method to improve the magnetic deflection performance of MSCR is to design a multi-segment magnetic structure to control the response of the robot in the magnetic field in segments. However, this structural design of multi-segment magnetic segments highly depends on the experience of researchers and the preset of specific application scenarios, and usually only suboptimal deflection effects can be obtained under specific conditions. Due to the lack of systematic optimization of the magnetic material distribution, the existing designs still have limitations in enhancing the magnetic deflection angle of the robot and are difficult to meet the requirements of large-angle deflection in complex vascular environments.

[0004] This limitation mainly stems from the deficiency of the multi-segment magnetic segment design method. The experience-based multi-segment design lacks a systematic optimization process and usually can only achieve local optimality, unable to ensure the global optimal deflection effect of MSCR in a multi-dimensional non-linear space. Therefore, there is still significant room for improvement in the existing technology in enhancing the magnetic deflection performance of MSCR.

[0005] To address the above problems, using an intelligent optimization method to optimize the magnetic particle concentration helps to overcome the deficiencies in the current design. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for optimizing the magnetic particle concentration of a conical magnetic continuous soft robot. By optimizing the magnetic particle concentration distribution, the end deflection angle of the soft robot is significantly improved, enhancing the controllability and flexibility of the robot in complex environments.

[0007] To achieve the above purpose, the present invention provides the following solution:

[0008] A method for optimizing the magnetic particle concentration of a conical magnetic continuous soft robot, comprising:

[0009] S1. Divide the conical magnetic continuous soft robot into m voxels, and randomly generate several magnetic particle concentration distribution schemes of the conical magnetic continuous soft robot as the initial population. Among them, each voxel has a different magnetic particle concentration, and each individual in the initial population is a magnetic particle concentration distribution scheme of the conical magnetic continuous soft robot;

[0010] S2. Optimize the current generation population to obtain the offspring population;

[0011] S3. Determine whether the maximum end deflection angle of the individuals in the offspring population is less than the tolerance compared with the average end deflection angle of all individuals in the population. If so, obtain the magnetic particle concentration distribution scheme of the optimized conical magnetic continuum soft robot. If not, replace the current generation population with the offspring population and return to S2.

[0012] Optionally, in S2, performing population optimization on the current generation population to obtain an offspring population includes:

[0013] Establish a finite difference model of the conical magnetic continuum soft robot;

[0014] Calculate the end deflection angle of each individual in the current generation population according to the finite difference model, and re-calibrate the end deflection angle of each individual in the current generation population using the dynamic linear calibration algorithm to obtain the probability of each individual being selected in the stochastic universal sampling algorithm;

[0015] Select several individuals according to the probability of each individual being selected, and perform genetic calculations on the selected several individuals to obtain the offspring population.

[0016] Optionally, constructing the finite difference model includes:

[0017] For a conical magnetic continuum soft robot with a single concentration, establish an analytical model according to the Euler-Bernoulli beam theory;

[0018] For a conical magnetic continuum soft robot with multiple concentrations, discretize the analytical model using the finite difference method to establish a finite difference model.

[0019] Optionally, selecting several individuals according to the probability of each individual being selected includes:

[0020] Generate a roulette wheel according to the probability of each individual being selected, randomly generate the position of the initial pointer according to the roulette wheel and calculate the spacing between the pointers;

[0021] Obtain the position of each pointer according to the position of the initial pointer and the spacing between the pointers;

[0022] Select several individuals according to the position of each pointer.

[0023] Optionally, performing genetic calculations on the selected several individuals to obtain the offspring population includes:

[0024] Perform elitism, crossover, and mutation operations on the selected several individuals to obtain the offspring population, where the elitism operation is to obtain the magnetic particle concentration distribution scheme with the maximum end deflection angle, the crossover operation is to exchange the voxels of different individuals, and the mutation operation is to change the voxels of individuals.

[0025] Optionally, the objective function of the genetic calculation is to maximize the end deflection angle of the conical magnetic continuous soft robot.

[0026] Optionally, obtaining the magnetic particle concentration distribution scheme of the optimized conical magnetic continuous soft robot further includes: S4. Fitting the magnetic particle concentration distribution scheme of the optimized conical magnetic continuous soft robot by using a piecewise linear fitting method.

[0027] Optionally, fitting the magnetic particle concentration distribution scheme of the optimized conical magnetic continuous soft robot by using a piecewise linear fitting method includes:

[0028] S41. Obtain a sliding window with a preset length, and align the starting position of the sliding window with the starting position of the optimized magnetic particle concentration distribution scheme;

[0029] S42. Obtain the magnetic particle concentration that appears the most times within the sliding window, and set all the magnetic particle concentrations within the sliding window to the magnetic particle concentration that appears the most times;

[0030] S43. Move the sliding window backward along the optimized magnetic particle concentration distribution scheme by the preset length, and repeat steps S42 - S43 until the sliding window reaches the end voxel of the optimized conical magnetic continuous soft robot.

[0031] The beneficial effects of the present invention are as follows:

[0032] 1. Improve deflection performance: By optimizing the magnetic particle concentration distribution, the end deflection angle of the soft robot is significantly improved, enhancing the maneuverability and flexibility of the robot in complex environments.

[0033] 2. Precise control and optimization: Using a genetic algorithm combined with a finite difference model, the distribution of magnetic particles is gradually optimized to maximize the end deflection angle of the soft robot, achieving precise control of the behavior of the soft robot.

[0034] 3. Improve optimization efficiency and effect: Through genetic operations such as dynamic linear calibration, elitism, crossover, and mutation, the diversity of the population and the genetic process are optimized, making the optimization process more efficient, and the finally generated soft robot has better performance.

[0035] 4. Piecewise fitting: Using a piecewise linear fitting algorithm to fit the optimized magnetic particle concentration distribution, making the optimization result more valuable for practical applications and improving the operability of the soft robot in specific application scenarios. Description of the Drawings

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0037] Figure 1 Flowchart of the method for optimizing the magnetic particle concentration of a conical magnetic continuous soft robot according to an embodiment of the present invention;

[0038] Figure 2 Schematic diagram of the curve coordinates of the conical magnetic soft robot according to an embodiment of the present invention;

[0039] Figure 3 Flowchart of the genetic algorithm for the method of optimizing the magnetic particle concentration of a conical magnetic continuous soft robot according to an embodiment of the present invention;

[0040] Figure 4 Schematic diagram of the piecewise linear fitting result according to an embodiment of the present invention;

[0041] Figure 5 Optimization result diagram of the conical magnetic continuous soft robot according to an embodiment of the present invention. Detailed implementation manners

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0043] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the drawings and specific implementation manners.

[0044] The genetic algorithm is an optimization method that simulates natural selection and genetic mechanisms. It avoids local optimal solutions by global search and maintaining population diversity, and is applicable to various complex and large-scale problems. It does not require the gradient information of the objective function, so it is particularly useful for problems that are difficult to differentiate. In addition, the genetic algorithm is easy to parallel process and combine with other algorithms, improving the search efficiency and the quality of the solution.

[0045] In summary, in order to improve the deflection performance of the magnetic particle type magnetic continuous soft robot, this embodiment provides a feasible solution for optimizing the design of the magnetic particle type magnetic continuous soft robot based on the genetic algorithm.

[0046] As Figure 3, this embodiment provides a method for optimizing the magnetic particle concentration of a conical magnetic continuum soft robot, including:

[0047] S1. Divide the conical magnetic continuum soft robot into m voxels, and randomly generate several magnetic particle concentration distribution schemes of the conical magnetic continuum soft robot as the initial population. Among them, each voxel has a different magnetic particle concentration, and each individual in the initial population is a magnetic particle concentration distribution scheme of a conical magnetic continuum soft robot;

[0048] S2. Optimize the current generation population to obtain the offspring population;

[0049] S3. Determine whether the maximum end deflection angle of the individuals in the offspring population is less than the tolerance compared with the average end deflection angle of all individuals in the population. If so, obtain the optimized magnetic particle concentration distribution scheme of the conical magnetic continuum soft robot. If not, replace the current generation population with the offspring population and return to S2.

[0050] Further, the optimization of the current generation population in S2 to obtain the offspring population includes:

[0051] Establish a finite difference model of the conical magnetic continuum soft robot;

[0052] Calculate the end deflection angle of each individual in the current generation population according to the finite difference model, and recalibrate the end deflection angle of each individual in the current generation population using the dynamic linear calibration algorithm to obtain the probability of each individual being selected in the stochastic universal sampling algorithm;

[0053] Select several individuals according to the probability of each individual being selected, and perform genetic calculations on the selected several individuals to obtain the offspring population.

[0054] Furthermore, constructing the finite difference model includes:

[0055] For a conical magnetic continuum soft robot with a single concentration, establish an analytical model according to the Euler-Bernoulli beam theory;

[0056] For a conical magnetic continuum soft robot with multiple concentrations, discretize the analytical model using the finite difference method to establish a finite difference model.

[0057] Specifically, the analytical model of the conical soft robot is:

[0058]

[0059] Among them, EI represents the flexural rigidity of the soft robot, dθ / ds is the curvature at any position of the soft robot, s represents the arc length from the origin to any point P on the neutral axis of the soft robot, as Figure 2 shown, d AThe distal diameter of the soft robot is \(D\), and the length of the soft robot is \(L\). The angle between the external magnetic field direction and the initial direction of the soft robot is \(\varphi\), the external magnetic field strength is \(B\), the magnetization intensity of the soft robot is \(M\), the angle between any position on the soft robot and the reference direction is \(\theta(s)\), and \(Q(s)=[(1 - \alpha)x+\alpha L]\). 2 is the volume correction term, \(d\) B is the proximal diameter of the soft robot, and \(\alpha = d\) B / \(d\) A (\(\alpha>1\)).

[0060] The soft robot is discretized into \(K\) equal - length units. Then the curvature can be approximately expressed as \(\kappa(s)=\frac{d\theta}{ds}\approx\frac{\theta i -\theta i-1}{{\Delta s}}\), where \(\Delta s=\frac{L}{K}\), and \(\theta i represents the angle between the \(i\) - th element and the reference direction. \(E i is the Young's modulus of the \(i\) - th element, and \(I i is the moment of inertia of the \(i\) - th element. Therefore, the analytical model of the soft robot can be discretized into a finite - difference model by using the finite - difference method:

[0061]

[0062] where \(M q is the magnetization intensity of the \(q\) - th unit, \(\theta q is the angle between the \(q\) - th unit and the reference direction, \(Q q is the volume correction term of the \(q\) - th unit, and \(\Delta s\) is the length of the divided unit.

[0063] Furthermore, according to the probability of each individual being selected, several individuals are selected, including:

[0064] Generate a roulette wheel according to the probability of each individual being selected, randomly generate the position of the initial pointer on the roulette wheel and calculate the spacing between the pointers;

[0065] According to the position of the initial pointer and the spacing between the pointers, obtain the position of each pointer;

[0066] According to the position of each pointer, select several individuals.

[0067] Specifically, the probability \(p\) of each individual being selected n is:

[0068]

[0069] where \(\beta\) is a scaling factor, and its value range is \(\beta\in(0,1)\), is the end - deflection angle of the \(n\) - th individual in the population, is the end deflection angle of the j-th individual in the population, is the minimum value of the end deflection angles of all individuals in the population, ξ is a constant, and its value range is ξ ∈ [0.9, 0.999], and l is the current iteration number.

[0070] In this embodiment, the specific implementation process of selecting several individuals is as follows: First, according to the probability p of each individual being selected n generate a roulette wheel, then randomly generate the position of the initial pointer and calculate the distance between the pointers, and finally determine the position of each pointer according to the position of the initial pointer and the pointer distance, and select 100 individuals to participate in the subsequent genetic calculation.

[0071] Furthermore, performing genetic calculation on the selected several individuals to obtain the offspring population includes:

[0072] Performing elitism, crossover, and mutation operations on the selected several individuals to obtain the offspring population. Among them, the elitism operation is to obtain the magnetic particle concentration distribution scheme with the largest end deflection angle, the crossover operation is to exchange the voxels of different individuals, and the mutation operation is to change the voxels of the individuals.

[0073] Specifically, the specific implementation process of the genetic calculation is: optimizing the population through elitism, crossover, and mutation operations. Among them, the proportion of individuals participating in elitism is 10%, which means that the individual with the largest end deflection angle will directly enter the offspring population. The proportion of individuals participating in the crossover operation is 80%, which means that offspring are generated from two magnetic particle concentration distribution schemes. The proportion of individuals participating in the mutation operation is 10%, which means that the magnetic particle concentration distribution scheme is randomly modified with a certain probability, thereby increasing the population diversity.

[0074] Furthermore, the objective function of the genetic calculation is to maximize the end deflection angle of the conical magnetic continuous soft robot.

[0075] Specifically, the objective function for optimizing the magnetic particle concentration distribution of the soft robot is:

[0076] θ max = max(θ K )

[0077] where θ K is the end deflection angle of the conical magnetic continuous soft robot. Under the given boundary condition θ0 = 0, it can be solved according to the finite difference model.

[0078] Further, obtaining the magnetic particle concentration distribution scheme of the optimized conical magnetic continuous soft robot further includes: S4. Using the piecewise linear fitting method to fit the magnetic particle concentration distribution scheme of the optimized conical magnetic continuous soft robot.

[0079] Further, using the piecewise linear fitting method to fit the magnetic particle concentration distribution scheme of the optimized conical magnetic continuous soft robot includes:

[0080] S41. Obtain a sliding window of a preset length, and align the starting position of the sliding window with the starting position of the optimized magnetic particle concentration distribution scheme;

[0081] S42. Obtain the magnetic particle concentration that appears most frequently within the sliding window, and set all the magnetic particle concentrations within the sliding window to the magnetic particle concentration that appears most frequently;

[0082] S43. Move the sliding window backward along the optimized magnetic particle concentration distribution scheme by a preset length, and repeat steps S42 - S43 until the sliding window reaches the end voxel of the optimized conical magnetic continuous soft robot.

[0083] The following further elaborates on the present invention:

[0084] As Figure 1 shown, a method for optimizing the magnetic particle concentration of a conical magnetic continuous soft robot includes the following steps:

[0085] The first step: For a conical magnetic continuous soft robot with a single concentration, establish an analytical model based on the Euler - Bernoulli beam theory:

[0086]

[0087] Among them, EI represents the flexural rigidity of the soft robot, dθ / ds is the curvature at any position of the soft robot, s represents the arc length from the origin to any point P on the neutral axis of the soft robot. As Figure 2 shown, d A is the distal diameter of the soft robot, d B is the proximal diameter of the soft robot, α = d B / d A (α > 1), L is the length of the soft robot, is the angle between the external magnetic field direction and the initial direction of the soft robot, B is the external magnetic field strength, M is the magnetization intensity of the soft robot, θ(s) is the angle between any position on the soft robot and the reference direction, Q(s) = [(1 - α)x + αL] 2 is the volume correction term.

[0088] Discretize the soft robot into K equal - length units, then the curvature can be approximately expressed as κ(s) = dθ / ds ≈ (θ i - θ i-1 ) / Δs, where Δs = L / K, θ i represents the angle between the i - th equation and the reference direction, E iis the Young's modulus of the i-th equation, I i is the moment of inertia of the i-th equation. Therefore, the analytical model of the soft robot can be discretized into a finite difference model by using the finite difference method:

[0089]

[0090] where, M q is the magnetization of the q-th unit, θ q is the angle between the q-th unit and the reference direction, Q q is the volume correction term of the q-th unit, and Δs is the length of the divided unit.

[0091] Step 2: Define the objective function for optimizing the magnetic particle concentration distribution of the soft robot as:

[0092] θ max = max(θ K )

[0093] where, θ K is the end deflection angle of the conical magnetic continuous soft robot. Under the given boundary condition θ0 = 0, it can be solved according to the finite difference model.

[0094] And set the range constraint of the magnetic particle concentration δ ∈ {0%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%}.

[0095] Step 3: In the initialization stage of the genetic algorithm, first, the soft robot is divided into 100 voxels with equal length, and each voxel represents a different magnetic particle concentration δ ∈ {0%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%}. Then, 100 magnetic particle concentration distribution schemes of the soft robot are randomly generated as the initial population, where each individual represents a single magnetic particle concentration distribution scheme.

[0096] Step 4: First, calculate the end deflection angle of each individual in the current population according to the finite difference model To increase the relative difference between different individuals in the population and thus enhance the optimization ability of the algorithm, the dynamic linear calibration algorithm is used to recalibrate the end deflection angle of each individual in the population, and obtain the probability p of each individual being selected in the stochastic universal sampling algorithm n :

[0097]

[0098] where, β is the scaling factor, and its value range is β ∈ (0, 1), is the end deflection angle of the n-th individual in the population, is the minimum value of the end deflection angles of all individuals in the population, c is a constant, and its value range is ξ ∈ [0.9, 0.999], and l is the current iteration number.

[0099] Step 5: First, according to the selection probability p of each individual n Generate a roulette wheel, then randomly generate the position of the initial pointer and calculate the spacing between the pointers. Finally, determine the position of each pointer based on the position of the initial pointer and the pointer spacing, and select 100 individuals to participate in the subsequent genetic calculation.

[0100] The specific implementation process of the genetic calculation is as follows: Optimize the population through elitism, crossover, and mutation operations. Among them, the proportion of individuals participating in elitism is 10%, which means that the individuals with the largest end deflection angle will directly enter the offspring population. The proportion of individuals participating in the crossover operation is 80%, which means that offspring are generated from two magnetic particle concentration distribution schemes. The proportion of individuals participating in the mutation operation is 10%, which means that the magnetic particle concentration distribution scheme is randomly modified with a certain probability, thereby increasing the population diversity;

[0101] The 100 selected soft robots generate 100 second-generation soft robots through 10% elitism, 80% crossover, and 10% mutation. Among them, 10% elitism means that 10 soft robots with the largest end deflection angle do not change their magnetic particle concentration distribution scheme and directly enter the next-generation population; 80% crossover means that among the remaining 90 soft robots, we randomly select 80 soft robots and pair them up to exchange some of their voxels; 10% mutation means that among the remaining 10 first-generation soft robots, each soft robot will change some of its voxels with a certain probability to generate new soft robots.

[0102] Step 6: Iteratively execute the genetic operations in Step 4 and Step 5, that is, replace the offspring population obtained after the genetic calculation with the previous-generation population for population optimization until the maximum end deflection angle in a certain generation of soft robots is less than the tolerance compared with the average end deflection angle of all individuals in the population.

[0103] Step 7: First, set a sliding window with N voxels in length and align the starting position of the window with the starting position of the optimized magnetic particle concentration distribution of the soft robot. Then find the magnetic particle concentration δ that appears the most times within this window m , and then set the magnetic particle concentration at all positions within this window to δ m , and then move this window backward along the magnetic particle concentration distribution of the optimized soft robot by N voxels. Finally, repeat the above process until the window reaches the end voxel of the optimized soft robot. Figure 4 Schematic diagram of the piecewise linear fitting result. Figure 5Shows the final result of the optimization of the conical MSCR magnetic powder concentration.

[0104] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for optimizing the magnetic particle concentration of a conical magnetic continuous soft robot, characterized in that Including: S1. Divide the conical magnetic continuous soft robot into m voxels, and randomly generate several magnetic particle concentration distribution schemes of the conical magnetic continuous soft robot as the initial population. Among them, each voxel has a different magnetic particle concentration, and each individual in the initial population is a magnetic particle concentration distribution scheme of a conical magnetic continuous soft robot; S2. Optimize the current generation population to obtain the offspring population; The population optimization of the current generation population in S2 to obtain the offspring population includes: Establish a finite difference model of the conical magnetic continuous soft robot; Calculate the end deflection angle of each individual in the current generation population according to the finite difference model, and recalibrate the end deflection angle of each individual in the current generation population using the dynamic linear calibration algorithm to obtain the probability of each individual being selected in the stochastic universal sampling algorithm; According to the probability of each individual being selected, select several individuals, and perform genetic calculations on the selected several individuals to obtain the offspring population; Constructing the finite difference model includes: For a conical magnetic continuous soft robot with a single concentration, establish an analytical model according to the Euler-Bernoulli beam theory; For a conical magnetic continuous soft robot with multiple concentrations, discretize the analytical model using the finite difference method to establish a finite difference model; S3. Judge whether the maximum end deflection angle of the individuals in the offspring population is less than the tolerance compared with the average end deflection angle of all individuals in the population. If so, obtain the optimized magnetic particle concentration distribution scheme of the conical magnetic continuous soft robot. If not, replace the current generation population with the offspring population and return to S2; Obtaining the optimized magnetic particle concentration distribution scheme of the conical magnetic continuous soft robot further includes: S4. Fit the optimized magnetic particle concentration distribution scheme of the conical magnetic continuous soft robot using the piecewise linear fitting method.

2. The method for optimizing the magnetic particle concentration of the conical magnetic continuous soft robot according to claim 1, characterized in that Selecting several individuals according to the probability of each individual being selected includes: Generate a roulette wheel according to the probability of each individual being selected, randomly generate the position of the initial pointer according to the roulette wheel and calculate the distance between the pointers; According to the position of the initial pointer and the distance between the pointers, obtain the position of each pointer; Select several individuals according to the position of each pointer.

3. The method for optimizing the magnetic particle concentration of the conical magnetic continuous soft robot according to claim 1, wherein Performing genetic calculations on the selected several individuals to obtain the offspring population includes: Perform elitism, crossover, and mutation operations on the selected several individuals to obtain the offspring population. Among them, the elitism operation is to obtain the magnetic particle concentration distribution scheme with the maximum end deflection angle, the crossover operation is to exchange the voxels of different individuals, and the mutation operation is to change the voxels of individuals.

4. The method for optimizing the magnetic particle concentration of the conical magnetic continuous soft robot according to claim 1, wherein The objective function of the genetic calculation is to maximize the end deflection angle of the conical magnetic continuous soft robot.

5. The method for optimizing the magnetic particle concentration of the conical magnetic continuous soft robot according to claim 1, wherein Fitting the optimized magnetic particle concentration distribution scheme of the conical magnetic continuous soft robot using the piecewise linear fitting method includes: S41. Obtain a sliding window with a preset length, and align the starting position of the sliding window with the starting position of the optimized magnetic particle concentration distribution scheme; S42. Obtain the magnetic particle concentration with the highest occurrence frequency within the sliding window, and set all the magnetic particle concentrations within the sliding window to the magnetic particle concentration with the highest occurrence frequency; S43. Move the sliding window backward by the preset length along the optimized magnetic particle concentration distribution scheme, and repeat steps S42 - S43 until the sliding window reaches the end voxel of the optimized conical magnetic continuous soft robot.

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