A motion simulation method of a micro-nano robot

Abstract

The application discloses a motion simulation method of a micro-nano robot, comprising the following steps: S1, converting the micro-nano robot into a robot particle and setting robot parameters, and discretizing a complex environment into a plurality of environment particles and setting environment parameters; S2, collecting a first distance between the robot particle and the environment particles, and retaining the first distance not exceeding a preset cut-off radius; S3, calculating a local softening condition of the environment particles according to the robot parameters, the environment parameters and the distance; S4, obtaining a compensation force according to the local softening condition, and calculating an environmental force applied to the robot particle according to an external magnetic field and the environment particles; S5, superimposing and processing the compensation force and the environmental force to obtain simulation parameters of the robot particle; and ending the simulation and outputting a simulation result after a preset termination condition is reached. The application can obtain reliable simulation results and intuitively obtain the motion condition of the micro-nano robot in a complex elastic environment.

Description

Technical Field

[0001] This invention relates to the field of robot simulation, and more particularly to a motion simulation method for micro-nano robots. Background Technology

[0002] Microrobots are miniature robots commonly used in complex elastic environments with a certain degree of stiffness, such as biological tissues, gel networks, and porous media. When moving in these complex elastic environments, microrobots come into contact with the environment, causing localized softening at the contact points. This localized softening leads to deformation of the contact areas within the complex elastic environment.

[0003] Traditional methods for simulating micro- and nano-robots employ meshing of complex elastic environments or constructing constitutive matrices for these environments to characterize the mechanical changes caused by the micro- and nano-robots. While this approach can capture the local softening characteristics of complex elastic environments, it requires reconstructing the mesh and constitutive matrix for each calculation, resulting in significant computational costs. Furthermore, the forces exerted by multiple micro- and nano-robots on the complex elastic environment can easily accumulate unbounded, distorting the simulation results. Setting the elastic parameters of the complex elastic environment to fixed parameters reduces computational costs, but it remains difficult to characterize the local softening characteristics of different parts of the complex elastic environment caused by the micro- and nano-robots.

[0004] Therefore, there is an urgent need for a method to achieve efficient simulation of micro- and nano-robots in complex elastic environments without changing the elastic parameters of the environment. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a motion simulation method for micro-nano robots, simulating the motion of multiple micro-nano robots in a complex elastic environment; the sampling time is determined based on a preset sampling interval and a preset total number of time steps; the motion simulation method includes: Step S1, converting the micro-nano robots into robot particles, setting robot parameters for the robot particles, and discretizing the complex elastic environment into a set of environmental particles, setting environmental parameters for the environmental particles; Step S2, continuously collecting a first distance between the robot particles and the environmental particles according to a preset sampling frequency, and constructing a first nearest neighbor list containing multiple first particle pairs based on the first distance; each first particle pair consists of one robot particle and one environmental particle, and the first distance corresponding to each first particle pair is not greater than a preset cutoff radius; Step S3, based on the robot parameters, the environmental parameters, and the first distance corresponding to each first particle pair collected at the current sampling time... Step S4: Processing to obtain the local softening state of the environmental particles after the interaction between the robot particle and the environmental particles in each first particle pair; Step S5: Processing to obtain the compensation force applied to each robot particle based on the local softening state and the environmental parameters, and processing to obtain the multiple environmental forces acting on each robot particle based on the force applied to each robot particle by the external magnetic field and the environmental particles respectively; Step S6: Processing to obtain the motion simulation parameters of each robot particle based on the superposition of the compensation force and the environmental forces; Repeating Step S3 at each sampling time to update the local softening state; Repeating Step S4 and Step S5 at each time step; Continuously executing the motion simulation method until the preset termination condition is reached, the simulation ends, and the motion simulation parameters of all robot particles and the contact situation between the robot particles and the environmental particles recorded during the simulation are integrated into the motion simulation result of the micro-nano robot and output.

[0006] Preferably, the contact situation is obtained by processing in the following manner: During the simulation, it is determined whether the center distance between the robot particle and the environment particle is not greater than the sum of the radius of the robot particle and the radius of the environment particle; if yes, the first counter records once and the second counter records once; if no, the second counter records once; after the simulation ends, the ratio between the number of records by the first counter and the number of records by the second counter is calculated, and the contact rate of the robot particle during the simulation is output according to the ratio as the contact situation.

[0007] Preferably, the environmental parameters include a softening radius parameter, a half-effect saturation parameter, a saturation index, and a minimum stiffness ratio parameter. Step S3 processes the local softening situation according to the following steps: Step S31, processing the softening radius parameter and the first distance in the first particle pair to obtain the total local softening dose experienced by the environmental particles; Step S32, processing the total local softening dose, the half-effect saturation parameter, and the saturation index to obtain the corresponding softening effect of the environmental particles; Step S33, processing the softening effect and the minimum stiffness ratio parameter to obtain the effective stiffness ratio of the environmental particles, as the local softening situation.

[0008] Preferably, the environmental parameters further include the basic stiffness of the environmental particle and the equilibrium position of the environmental particle; step S4 obtains the compensation force by: obtaining the first displacement of the environmental particle relative to the equilibrium position at the current time step, and combining the first displacement, the effective stiffness ratio, and the basic stiffness to obtain the compensation force to be applied to the robot particle in the corresponding first particle pair.

[0009] Preferably, the environmental forces include the magnetic driving force exerted by the external magnetic field on the robot particle, and the contact force, friction force, and viscous damping force exerted by the environmental particles on the robot particle in the corresponding first particle pair.

[0010] Preferably, the robot parameters include the magnetic moment vector of the micro / nano robot; step S4 obtains the magnetic driving force by processing the magnetic field vector of the external magnetic field and the magnetic moment vector of the micro / nano robot to obtain the magnetic driving force applied to the corresponding robot particle.

[0011] Preferably, step S4 is performed to obtain the contact force and the friction force in the following manner: the contact force between the robot particle and the environmental particle is obtained by using a spring-damped model, and the friction force between the robot particle and the environmental particle is obtained by using a Coulomb friction model.

[0012] Preferably, step S4 is performed to obtain the viscous damping force by calculating the viscous damping force exerted by the environmental particles on the robot particles based on the relative velocity between the robot particles and the environmental particles.

[0013] Preferably, step S5 includes: step S51, based on a preset integration time step, integrating the force superimposed by the compensation force and the environmental force using a time integrator, and outputting the half-step velocity information of the robot particle in the current time step by combining the velocity information of the robot particle in the previous time step; in the first time step, the velocity information of the robot particle in the previous time step is 0; step S52, updating the position information of the robot particle in the current time step according to the half-step velocity information of the current time step; step S53, updating the first distance according to the updated position information, and recalculating the compensation force and the environmental force applied to the robot particle in the first particle pair; step S54, processing the recalculated compensation force and the recalculated environmental force to obtain the velocity information of the robot particle in the current time step; the velocity information of the current time step is used to update the half-step velocity information of the next time step.

[0014] Preferably, after the simulation is completed, the following steps are performed: Step B1, calculate the average velocity of the micro-nano robot based on the position information within all the time steps; Step B2, calculate the normalized velocity of the micro-nano robot by combining the average velocity and a preset reference velocity; Step B3, determine the motion partition of the micro-nano robot by combining the contact situation and the normalized velocity; The motion simulation result includes the average velocity, the normalized velocity, and the motion partition of the robot particle.

[0015] The following beneficial effects can be obtained by using the present invention: 1. By defining the distance between robot particles and environment particles used for subsequent calculations through a preset cutoff radius, and constructing a particle pair with one robot particle corresponding to one environment particle, the unbounded superposition of the forces of robot particles corresponding to multiple micro-nano robots on the same environment particle is prevented, thus ensuring the reliability of the simulation.

[0016] 2. By calculating the local softening caused by robot particles and environmental particles, the compensation force that needs to be applied to the robot particles is calculated, as well as the environmental forces exerted on the robot particles by the external magnetic field and environmental particles. The compensation force and environmental forces are superimposed and combined with the contact between robot particles and environmental particles to integrate the motion simulation results of the micro-nano robot, which intuitively shows the motion of the micro-nano robot in a complex elastic environment. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the simulation method of the present invention; Figure 2This is a schematic diagram of the process for processing environmental particles to achieve local softening in this invention. Figure 3 This is a schematic diagram of the process for simulating superimposed forces and outputting simulation parameters in this invention; Figure 4 This is a schematic diagram of the process for obtaining motion simulation results in this invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0020] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0021] This invention provides a motion simulation method for micro / nano robots, simulating the motion of multiple micro / nano robots in a complex elastic environment; the sampling time is determined based on a preset sampling interval and a preset total number of time steps; such as Figure 1As shown, the motion simulation method includes: Step S1, converting the micro / nano robot into robot particles, setting robot parameters for the robot particles, and discretizing the complex elastic environment into a set of environmental particles, setting environmental parameters for the environmental particles; Step S2, continuously collecting the first distance between the robot particles and environmental particles according to a preset sampling frequency, and constructing a first nearest neighbor list containing multiple first particle pairs based on the first distance; each first particle pair consists of one robot particle and one environmental particle, and the first distance corresponding to each first particle pair is not greater than a preset cutoff radius; Step S3, processing the robot parameters, environmental parameters, and the first distance corresponding to each first particle pair collected at the current sampling time to obtain the environmental particle generation after the interaction between the robot particle and the environmental particle in each first particle pair. The local softening condition is determined; step S4, the compensation force applied to each robot particle is obtained based on the local softening condition and environmental parameters, and the multiple environmental forces acting on each robot particle are obtained based on the forces exerted on each robot particle by the external magnetic field and environmental particles respectively; step S5, the motion simulation parameters of each robot particle are obtained based on the superposition of the compensation force and environmental forces; step S3 is repeated at each sampling time to update the local softening condition; steps S4 and S5 are repeated at each time step; the motion simulation method is continuously executed until the preset termination condition is reached and the simulation ends, and the motion simulation parameters of all robot particles and the contact between robot particles and environmental particles recorded during the simulation are integrated into the motion simulation results of the micro-nano robot and output.

[0022] The complex elastic environment involved in this application refers to a non-uniform elastic medium with a certain stiffness, such as biological tissue, gel networks, and porous media. For example, when it is necessary to obtain information about tumor sites in a patient's human tissue or to inject drugs, macroscopic methods can easily damage the human tissue. Therefore, micro- and nano-robots are needed to enter the human tissue for operations.

[0023] Micro- and nano-robots are miniature devices measuring in the micrometer or nanometer scale (depending on the application) that can perform tasks such as motion, targeting, manipulation, and sensing under external control. Micro- and nano-robots are typically composed of functional materials (such as polymers, metals, and biodegradable materials), and do not have their own batteries or drive circuits; they rely on external fields for propulsion.

[0024] The micro-nano robot used in this application is a magnetically controlled robot, which drives the movement of discrete robot particles through an externally applied magnetic field.

[0025] Before the simulation begins, the total time step and sampling interval of the simulation process are set based on external factors such as the simulation environment and the selection of the micro / nano robot, ensuring that the sampling time is the ratio of the total time step to the sampling interval. For example, the total time step is set... Sampling interval Therefore, there are 1000 sampling moments in the total time step.

[0026] Specifically, based on the spatial resolution of the complex elastic environment, it is discretized into a large number of environmental particles. Each environmental particle carries parameters such as initial position coordinates, initial velocity, mass, and boundary markers. A regular mesh or equivalent discrete network is used to discretize the complex elastic environment. After discretization, elastic connections are established between adjacent environmental particles, and parameters such as the basic stiffness and damping parameters of the environmental particles are defined. An elastic network discrete model of the target complex elastic environment is constructed through these elastic connections to calculate the elastic restoring force between environmental particles, which is then converted into a force acting on the robot particles. Furthermore, during the construction of the elastic network discrete model, the environmental particles at the model boundaries are fixed to prevent displacement and thus avoid changes to the overall model. Simultaneously, the free movement capability of the environmental particles within the model is preserved, allowing them to interact with the robot particles and produce a softening effect.

[0027] Because robotic particles cluster on a large scale in complex elastic environments, the dynamics of a single micro / nano robot can be simplified to that of a single robotic particle. Under the influence of environmental particles and external fields (such as an external magnetic field), the robotic particles spontaneously form different topological shapes, collectively constituting a chain-like model of the robot. The chain-like topological shape reflects the actual geometry of the micro / nano robot (such as a flagellated chain, a multi-segmented helix, etc.). Based on the geometry of the micro / nano robot, its inherent property parameters, such as the equivalent magnetic moment and the coefficient of friction, are obtained for subsequent calculations of the environmental forces acting on the corresponding robotic particles.

[0028] The simulation method disclosed in this application is implemented based on simulation software. After discretizing robot particles and environment particles, robot parameters are preset for the robot particles and environmental parameters are preset for the environment particles. The robot parameters and environmental parameters are input into the simulation software to provide data support for subsequent simulation steps.

[0029] During the simulation, the first distance between robot particles and environmental particles is collected according to the preset sampling frequency.

[0030] Specifically, the computational domain used for simulation calculations in a complex elastic environment (i.e., simulating robot particles and environment particles within the computational domain) is divided into multiple regular spatial bins, each with a side length not less than a preset cutoff radius. For each robot particle and environment particle in a spatial bin, corresponding particles are searched for in their respective bins and adjacent bins and paired to form particle pairs, avoiding global traversal. For example, to construct a particle pair between a robot particle and an environment particle, a robot particle in a certain bin is selected, and a particle pair is constructed between it and every environment particle in its respective bin and adjacent bins, and saved to the first nearest neighbor list. The actual Euclidean distance between the two particles in the constructed particle pair is calculated as the first distance. Particle pairs with an actual Euclidean distance not greater than the cutoff radius are retained in the first nearest neighbor list for subsequent calculations, while other particle pairs exceeding the cutoff radius are discarded.

[0031] The above pairing process reduces the overall search complexity of the computational domain from... Reduce to (N is the total number of particles in the computational domain).

[0032] Furthermore, a cutoff radius is set to reasonably define the range of softening effects between robot particles and environmental particles, without calculating softening effects between particles exceeding the cutoff radius.

[0033] The cutoff radius is defined by the following formula: (1) in, The cutoff radius; This is the preset cutoff ratio coefficient; This is the softening radius parameter.

[0034] The cutoff ratio is a dimensionless parameter used to represent the ratio between the cutoff radius and the softening radius. A larger cutoff ratio results in a larger cutoff radius, which includes more particles and requires the simultaneous calculation of more particle pairs, leading to higher computational accuracy, but also a higher computational cost.

[0035] The softening radius parameter is a preset property parameter of the environmental particles, which will also be used in the following text to calculate the local softening of the environmental particles.

[0036] Furthermore, the nearest neighbor list is continuously updated at a preset sampling frequency, and the pairing process described above is executed with each update. Within the interval between two samplings of the first distance, the real-time coordinates of each particle can be updated, but the original connection relationships are preserved. Even if the first distance between the robot particle and the environment particle in the particle pair stored in the first nearest neighbor list exceeds the cutoff radius, it is still retained in the first nearest neighbor list. Only the first distance is updated according to the updated real-time coordinates, and the particle pair is updated again when the first nearest neighbor list is updated next time. Particle pairs with a first distance exceeding the cutoff radius are no longer retained, thus balancing computational accuracy and efficiency.

[0037] In subsequent simulations, particle pairs from the updated nearest neighbor list were used for calculations to avoid the unbounded superposition of a large number of robot particles in the same region, which could lead to unstable simulation results. By defining the computational domain with spatial binaries, the stability and reproducibility of the simulation results were ensured.

[0038] When implementing the simulation method in this application, all robot particles in the computational domain are simulated simultaneously according to the particle pairs in the first nearest neighbor list, and the corresponding simulation results are output.

[0039] Furthermore, the local softening situation includes the total local softening dose, softening effect, and effective stiffness ratio of the environmental particles at the current sampling time. The total local softening dose represents the cumulative intensity of the softening effect caused by all robotic particles within a pre-set cutoff radius. The softening effect represents the degree and effect of stiffness reduction in the environmental particles due to the action of robotic particles. The effective stiffness ratio represents the remaining stiffness of the environmental particles relative to the basic stiffness after softening.

[0040] At each sampling time, the local softening of environmental particles and the contact between robot particles and environmental particles are calculated. The calculation of the local softening at each sampling time is updated for subsequent calculation of compensation forces.

[0041] The local softening pattern reflects the reduction in the support provided to the robot particle by the softening of environmental particles. Based on this, the required compensating force is calculated and applied to the robot particle's center of mass. The compensating force is then superimposed with the environmental forces acting on the robot particle to form the resultant force on the robot particle at the current time step. This resultant force is then input into a time integrator for integration.

[0042] Furthermore, by integrating the net force acting on the robot particle, the velocity information of the robot particle at the corresponding time step is calculated. After the simulation, the motion of the robot particle in the corresponding complex elastic environment is determined based on the global velocity information and contact conditions of the robot particle.

[0043] The local softening of environmental particles is calculated at each sampling time, while the resultant force on the robot particles and the integral of that force need to be calculated at each time step. Therefore, the local softening condition used at each time step within each sampling interval is the same.

[0044] The preset termination condition can be that all the total number of steps in all time steps has been completed, or that the motion simulation result meets expectations, such as the motion of the robot particles becoming smoother. The termination condition is set by the user by inputting it into the simulation software before the simulation begins.

[0045] In a preferred embodiment of the present invention, the contact status is obtained by the following steps: determining whether the center distance between the robot particle and the environment particle is not greater than the sum of the radii between the robot particle and the environment particle; if yes, the first counter records once and the second counter records once; if no, the second counter records once; after the simulation ends, the ratio between the number of records by the first counter and the number of records by the second counter is calculated, and the contact rate of the robot particle during the simulation time is output according to the ratio as the contact status.

[0046] Specifically, robot particles and environment particles have a center of mass. Based on the distance from the center of mass to the edge of the particle, the first radius of each robot particle and the second radius of each environment particle are obtained in advance.

[0047] At each sampling time, based on the particle pairs in the first nearest neighbor list, the distance from the centroid of the corresponding robot particle to the centroid of the environment particle, i.e., the center distance, is calculated. Furthermore, the sum of the first radius and the second radius, i.e., the radius sum, is calculated. It is determined whether the center distance is not greater than the radius sum; if so, the robot particle and the environment particle are considered to be in contact; otherwise, they are considered not to be in contact. Based on the determination result, the corresponding counter is started counting.

[0048] Furthermore, after the simulation terminates, the ratio of the count of the first counter to the count of the second counter is calculated to obtain the corresponding contact rate between the robot particle and the environmental particles, which is used to characterize the contact frequency between the robot particle and the environmental particles.

[0049] In a preferred embodiment of the present invention, the environmental parameters include the softening radius parameter, the half-effect saturation parameter, the saturation index, and the minimum stiffness ratio parameter; such as Figure 2 As shown, step S3 calculates the local softening situation according to the following steps: Step S31, calculate the total local softening dose of the environmental particles based on the softening radius parameter and the first distance in the first particle pair; Step S32, calculate the softening effect of the corresponding environmental particles based on the total local softening dose, the half-effect saturation parameter and the saturation index; Step S33, calculate the effective stiffness ratio of the environmental particles based on the softening effect and the minimum stiffness ratio parameter, as the local softening situation.

[0050] Specifically, the softening radius parameter, half-effect saturation parameter, saturation index, and minimum stiffness ratio parameter are preset by the user according to different environments. The softening radius parameter represents the effective range of the robot particles' softening effect on environmental particles, determining the maximum range of the robot particles' softening contribution. The half-effect saturation parameter is the total local softening dose required for the softening effect to reach half of its maximum value, representing the dose threshold at which softening begins to take effect significantly. The saturation index represents the rate and steepness of the increase in softening effect with the local softening dose, determining how quickly the softening changes from weak to strong. The minimum stiffness ratio parameter limits the lower limit of the effective stiffness of environmental particles after softening, preventing the effective stiffness from approaching zero or becoming negative, and ensuring the mechanical stability of the system.

[0051] The first distance between environmental particles and robot particles is obtained through the first nearest neighbor list.

[0052] Furthermore, the total local softening dose is calculated using the following formula: (2) in, The softening contribution of robot particle i to environmental particle j; r ij For robot particles i With environmental particles j The distance; σ s This is the softening radius parameter; The total local softening dose of environmental particle i; r cut The cutoff radius is [value].

[0053] The softening effect of environmental particles is calculated using the following formula: (3) in, The softening effect of environmental particle i; The total local softening dose of environmental particle i; The preset saturation index; This is the preset half-effect saturation parameter.

[0054] In one embodiment, the saturation index ranges from [1, 6].

[0055] The effective stiffness ratio of environmental particles is calculated using the following formula: (4) in, The effective stiffness ratio of environmental particle i; This is the preset minimum stiffness ratio parameter; This refers to the softening effect of environmental particle i.

[0056] In one embodiment, the minimum stiffness scaling parameter ranges from (0, 1).

[0057] In a preferred embodiment of the present invention, the environmental parameters further include the basic stiffness of the environmental particle and the equilibrium position of the environmental particle; step S4 calculates the compensation force in the following manner: obtain the first displacement of the environmental particle relative to the equilibrium position at the current time step, and calculate the compensation force to be applied to the robot particle by combining the first displacement, the effective stiffness ratio and the basic stiffness.

[0058] Specifically, the basic stiffness and the equilibrium position of the robot particle are fixed parameters in each complex elastic environment, obtained directly from the complex elastic environment being simulated before the motion simulation method begins. The basic stiffness represents the initial stiffness of the environment particle. The equilibrium position represents the position of the environment particle when it is not acted upon by the robot particle.

[0059] Furthermore, the compensating force applied to the robot particle is calculated using the following formula: (5) in, The force generated by the softening effect of the environmental particle i will be applied to the center of mass of the robot particle.

[0060] The effective stiffness ratio of environmental particle i; Let i be the first displacement of the environmental particle i relative to its equilibrium position.

[0061] Specifically, this is achieved by calculating the difference between the basic stiffness and the effective stiffness (i.e., As a compensation term, the compensation force acting on the robot particle is then obtained.

[0062] For each particle pair in the first nearest neighbor list, the total local softening dose, softening effect, effective stiffness ratio, and compensation force are calculated sequentially. The compensation forces acting on the robot particles are superimposed into a resultant force and written into the time integrator.

[0063] In a preferred embodiment of the present invention, the environmental forces include the magnetic driving force exerted on the robot particle by the external magnetic field, as well as the contact force, friction force and viscous damping force exerted on the robot particle by the environmental particles.

[0064] In a preferred embodiment of the present invention, the robot parameters include the magnetic moment vector of the micro-nano robot; step S4 is processed in the following manner to obtain the magnetic driving force: the magnetic driving force is calculated based on the magnetic field vector of the external magnetic field and the magnetic moment vector of the micro-nano robot.

[0065] Specifically, the magnetic drive force includes magnetic drive torque and magnetic drive force.

[0066] The magnetic driving force of the robot particles corresponding to the external magnetic field acting on the micro / nano robot is calculated using the following formula: (6) in, It is a magnetic driving force; The preset magnetic moment vector of the micro / nano robot; Let be the external magnetic field vector at time step t; It is the magnetic driving torque; The amplitude of the planar rotating magnetic field; It is the rotational angular frequency; This represents the amplitude of the axial bias magnetic field; e x , e y , e z All of these are coordinate basis vectors of the world coordinate system preset in this simulation.

[0067] Furthermore, magnetic driving force is used to control the translational motion of the robot particles. Magnetic driving torque is used to control the rotational motion of the robot particles.

[0068] Specifically, the translational and rotational motions of robot particles include motion frequency, contact posture, and propulsion efficiency.

[0069] The motion frequency of the robot particles is controlled by their rotational angular frequency. The rotational angular frequency directly controls the rotation period of the external magnetic field, thus determining the rotational frequency of the robot chain. The higher the rotational frequency, the faster the robot's contact rhythm with the environment. The rotational period satisfies the formula: (7) in, T is the rotation period; ω is the rotational angular frequency.

[0070] The contact attitude is jointly determined by the ratio of the axial bias magnetic field to the planar rotating magnetic field. When the amplitude of the axial bias magnetic field is 0, the magnetic field is in... In-plane rotation, the robot chain in the robot chain model tends to move in the plane; when the amplitude of the axial bias magnetic field is not zero, the magnetic field rotation surface tilts, causing the rotation posture of the robot chain in the robot chain model to deviate from pure planar motion, thereby changing the contact geometry and contact angle between the robot and the environment.

[0071] The propulsion efficiency is determined by both the amplitude of the planar rotating magnetic field and the environmental factors. Within a certain range, the larger the amplitude of the planar rotating magnetic field, the greater the magnetic driving torque, and the stronger the rotational drive obtained by the robot chain in the robot chain model.

[0072] In a preferred embodiment of the present invention, step S4 is performed to obtain the contact force and friction force by: calculating the contact force between the robot particle and the environmental particle using a spring damping model, and calculating the friction force between the robot particle and the environmental particle using a Coulomb friction model.

[0073] Specifically, the magnitude of the contact force is equivalent to the restoring force generated when an environmental particle, after being softened by a robotic particle, tends to return to its equilibrium position. This restoring force also acts on the robotic particle in the calculated particle pair.

[0074] When the spring-damped model uses a linear model, the restoring force is calculated using Hooke's Law: (8) in, The restoring force of environmental particle i; Let i be the equivalent stiffness of the environmental particle i. Let i be the first displacement of the environmental particle i relative to its equilibrium position; The effective stiffness ratio of environmental particle i; Let i be the basic stiffness of the environmental particle.

[0075] This formula corresponds to the calculation of the compensation force mentioned above, where the restoring force is precisely the restoring force of the effective stiffness.

[0076] When the spring damping model adopts a nonlinear model, the nonlinear restoring force can be expressed in either a power-law form or a piecewise linear form. When the power-law form is adopted, the restoring force changes nonlinearly with the displacement amplitude. When the piecewise linear form is adopted, different equivalent stiffnesses are used to calculate the restoring force before and after a preset displacement threshold.

[0077] Specifically, the nonlinear restoring force is calculated using the following formula in the power-law form: (9) in, The restoring force of environmental particle i; Let i be the equivalent stiffness of the environmental particle i. Let i be the first displacement of the environmental particle i relative to its equilibrium position; The nonlinear stiffness index is preset and remains unchanged during the simulation.

[0078] Furthermore, the frictional force between the robot particle and the environment particles is calculated using the Coulomb model or the regularized Coulomb model. This frictional force is limited by the normal contact force. (10) in The frictional force is tangential; The friction coefficient between environmental particles is recorded in the discrete model of the elastic network. The contact force is in the normal direction.

[0079] If the contact situation at the current sampling moment is such that the robot particle and the environmental particle are not in contact, the friction force is 0.

[0080] In a preferred embodiment of the present invention, step S4 is performed to obtain the viscous damping force by calculating the viscous damping force exerted by the environmental particle on the robot particle based on the relative velocity between the robot particle and the environmental particle.

[0081] Specifically, a second distance between two environmental particles is acquired according to a preset sampling frequency, and a second nearest neighbor list is constructed based on this distance. The viscous internal resistance between environmental particles is obtained from the environmental particle pairs in the second nearest neighbor list. Then, combining the viscous internal resistance with the relative velocity between the robot particle and the environmental particles, the viscous damping force exerted by the environmental particles on the robot particles is calculated. The viscous damping force is proportional to the relative velocity and in the opposite direction, serving to dissipate kinetic energy and suppress numerical oscillations.

[0082] Furthermore, the velocity information of the robot particles is calculated in subsequent time integrators, and the velocity of the robot particles calculated in the previous time step is used for each calculation of the viscous damping force. The first calculation of the resultant force is considered as if no viscous damping force has been generated. The velocities of environmental particles are recorded in the discrete model of the elastic network and are also considered as parameters that do not change.

[0083] In a preferred embodiment of the present invention, such as Figure 3 As shown, step S5 includes: Step S51, based on a preset integration time step, using a time integrator to integrate the force superimposed by the compensation force and the environmental force, and combining the velocity information of the robot particle in the previous time step to output the half-step velocity information of the robot particle in the current time step; in the first time step, the velocity information of the robot particle in the previous time step is 0; Step S52, updating the position information of the robot particle in the current time step according to the half-step velocity information of the current time step; Step S53, updating the first distance according to the updated position information, and recalculating the compensation force and the environmental force applied to the robot particle in the first particle pair; Step S54, processing the recalculated compensation force and the recalculated environmental force to obtain the velocity information of the robot particle in the current time step; the velocity information of the current time step is used to update the half-step velocity information of the next time step.

[0084] Specifically, within each time step, the information of the current time step is read, and the resultant force after the superposition of the compensating force and the environmental force is integrated using the velocity Verlet method or the equivalent explicit symplectic integral method: (11) in, The half-step velocity of the robot particle is calculated by the first integration within the current time step; The velocity information of the robot particles calculated in the previous time step; The preset time step; The resultant force input to the time integrator at the current time step; The equivalent mass of the robot particle.

[0085] Subsequently, the position of the robot particles is updated based on the half-step velocity: (12) in, This represents the updated position of the robot particle at the current time step. This represents the position of the robot particle before the update at the current time step.

[0086] As the robot particle's position is updated, the Euclidean distance between the robot particle and the environment particle in the first nearest neighbor list is also updated. This changes the compensating force and the environmental force. The resultant force of the compensating force and the environmental force is then calculated again following the steps described above, and subsequently input into the time integrator to obtain the robot particle's velocity information. (13) in, The velocity information of the robot particles at the current time step is obtained after a second update based on the half-step velocity, and is used as the basis for calculating the half-step velocity information in the next time step; This is the resultant force obtained after the update and recalculation.

[0087] Furthermore, the time step is preset in the time integrator to satisfy: (14) in, The preset safety factor; The minimum equivalent mass pre-set in the robot chain model; The maximum equivalent stiffness is preset in the discrete model of the elastic network.

[0088] Setting an upper limit for the integration step size by defining the time step size is a sufficient condition for the stability of explicit time integration. As long as the time step size satisfies this constraint, the explicit velocity Verlet integral or the equivalent symplectic integral can maintain long-term stability.

[0089] If the time step set by the user does not meet the constraints, the system executing the simulation will issue a warning or terminate the calculation before the simulation starts, prompting the user to reduce the time step.

[0090] In a preferred embodiment of the present invention, such as Figure 4 As shown, the following steps are performed after the simulation: Step B1, calculate the average velocity of the micro-nano robot based on the position information within all time steps; Step B2, calculate the normalized velocity of the micro-nano robot by combining the average velocity and the preset reference velocity; Step B3, determine the motion partition of the micro-nano robot by combining the contact situation and the normalized velocity; The motion simulation results include the average velocity, normalized velocity and motion partition of the robot particles.

[0091] Specifically, based on the motion trajectory formed by the position information of the robot particle within the simulation time, and combined with a preset time window width, a sliding time averaging is performed on the micro-nano robot corresponding to the robot particle to calculate the average velocity of the micro-nano robot within the simulation time: (15) Average speed; For the trajectory of motion; This represents the width of the time window.

[0092] Furthermore, the normalized velocity of the micro / nano robot is calculated using the following formula: (16) in, Normalized speed; This is the preset reference speed.

[0093] The reference speed is a dimensionless index, which can be taken as the speed of a micro-nano robot moving in a free environment (with minimal or zero basic stiffness).

[0094] For each micro-nano robot, the motion zone of the micro-nano robot is determined by combining the normalized velocity (or average velocity) and contact rate calculated after the simulation.

[0095] Specifically, the motion zones include the free-penetration zone, the transition zone, and the obstructed zone.

[0096] When the normalization velocity is not less than 0.8 and not greater than 0.55, the micro-nano robot is in the free penetration zone.

[0097] The micro-nano robot is in the transition zone when either the normalized velocity or the contact rate satisfies the following conditions: the normalized velocity is greater than 0.55 and less than 0.8, and the contact rate is greater than 0.1 and less than 0.2.

[0098] When the normalized velocity is no greater than 0.55 and the contact is no less than 0.2, the micro-nano robot is in the obstructed zone.

[0099] When the normalized velocity is not less than 0.8 and the contact is not less than 0.2, or when the normalized velocity is not greater than 0.55, the micro-nano robot is in the transition zone.

[0100] In one embodiment, simulations were performed on the same group of micro-nano robots using soft gel, neutral gel, and hard gel, respectively. The average velocity of the soft gel was used as the reference velocity. In two simulations, the rotational angular frequencies of the external magnetic field were set to 1 Hz and 5 Hz, respectively. In the soft gel, the normalized velocities of the micro-nano robots at 1 Hz and 5 Hz were both 1; in the neutral gel, the normalized velocities of the micro-nano robots at 1 Hz and 5 Hz were 0.702 and 0.721, respectively; and in the hard gel, the normalized velocities of the micro-nano robots at 1 Hz and 5 Hz were 0.408 and 0.386, respectively.

[0101] In one embodiment, simulations were performed on the same group of micro / nano robots using soft gel, neutral gel, and hard gel, respectively, resulting in 48 sets of data. 37 sets of data represent the micro / nano robots in the free-penetration region, 7 sets represent the micro / nano robots in the transition region, and 4 sets represent the micro / nano robots in the obstructed region. For the micro / nano robots in the free-penetration region, the median normalized velocity was 0.944, and the median contact rate was 0.037; for the micro / nano robots in the transition region, the median normalized velocity was 0.669, and the median contact rate was 0.148; for the micro / nano robots in the obstructed region, the median normalized velocity was 0.469, and the median contact rate was 0.22. Therefore, the calculated high velocity boundary of the micro / nano robots is: The low speed boundary is: The low contact rate boundary is: The high contact rate boundary is: .

[0102] The above description is merely a preferred embodiment of the present invention and does not limit the implementation and protection scope of the present invention. Those skilled in the art should realize that any equivalent substitutions and obvious changes made based on the description and illustrations of the present invention should be included within the protection scope of the present invention.

Claims

1. A motion simulation method for micro / nano robots, characterized in that, Simulations were performed to demonstrate the movement of multiple micro-nano robots in a complex elastic environment. The sampling time is determined based on the preset sampling interval and the preset total number of time steps; The motion simulation method includes: Step S1: Convert the micro-nano robot into robot particles, set robot parameters for the robot particles, and discretize the complex elastic environment into a set of environmental particles, set environmental parameters for the environmental particles. Step S2: According to a preset sampling frequency, continuously collect the first distance between the robot particle and the environmental particle, and construct a first nearest neighbor list containing multiple first particle pairs based on the first distance; Each first particle pair consists of one robot particle and one environment particle, and the first distance corresponding to each first particle pair is not greater than a preset cutoff radius. Step S3: Based on the robot parameters, the environmental parameters, and the first distance corresponding to each first particle pair collected at the current sampling time, process to obtain the local softening situation of the environmental particles after the robot particle in each first particle pair interacts with the environmental particles; Step S4: Based on the local softening condition and the environmental parameters, the compensation force applied to each robot particle is obtained, and based on the force exerted on each robot particle by the external magnetic field and the environmental particles, the multiple environmental forces acting on each robot particle are obtained. Step S5: Obtain the motion simulation parameters of each robot particle based on the superposition of the compensation force and the environmental force; Step S3 is repeated at each sampling time to update the local softening status; Steps S4 and S5 are repeated at each time step. The motion simulation method is continuously executed until the preset termination condition is reached, at which point the simulation ends. The motion simulation parameters of all the robot particles and the contact between the robot particles and the environmental particles recorded during the simulation process are integrated into the motion simulation results of the micro-nano robot and output. The environmental parameters include softening radius parameter, half-effect saturation parameter, saturation index, minimum stiffness ratio parameter, basic stiffness of the environmental particles, and equilibrium position of the environmental particles. Step S3 obtains the localized softening condition by processing according to the following steps: Step S31: The total local softening dose of the environmental particles is obtained by processing the softening radius parameter and the first distance in the first particle pair. Step S32: Based on the total local softening dose, the half-effect saturation parameter, and the saturation index, the corresponding softening effect of the environmental particles is obtained; Step S33: The effective stiffness ratio of the environmental particles is obtained by processing the softening effect and the minimum stiffness ratio parameter, which is used as the local softening condition. The compensation force is obtained in step S4 using the following method: The first displacement of the environmental particle relative to the equilibrium position at the current time step is obtained. The first displacement, the effective stiffness ratio, and the basic stiffness are combined to obtain the compensation force to be applied to the robot particle in the corresponding first particle pair.

2. The motion simulation method according to claim 1, characterized in that, The contact condition was obtained by processing it in the following way: During the simulation, it is determined whether the center distance between the robot particle and the environment particle is not greater than the sum of the radii of the robot particle and the environment particle. If so, the first counter records once, and the second counter records once; If not, the second counter records once; After the simulation ends, the ratio between the number of records of the first counter and the number of records of the second counter is calculated, and the contact rate of the robot particle in the simulation process is output according to the ratio as the contact situation.

3. The motion simulation method according to claim 1, characterized in that, The environmental forces include the magnetic driving force exerted by the external magnetic field on the robot particle, and the contact force, friction force, and viscous damping force exerted by the environmental particles on the robot particle in the corresponding first particle pair.

4. The motion simulation method according to claim 3, characterized in that, The robot parameters include the magnetic moment vector of the micro / nano robot; The magnetic drive force is obtained in step S4 using the following method: The magnetic driving force applied to the corresponding robot particle is obtained by processing the magnetic field vector of the external magnetic field and the magnetic moment vector of the micro / nano robot.

5. The motion simulation method according to claim 3, characterized in that, The contact force and the frictional force are obtained in step S4 using the following method: The contact force between the robot particle and the environmental particle is obtained by using a spring-damping model, and the frictional force between the robot particle and the environmental particle is obtained by using a Coulomb friction model.

6. The motion simulation method according to claim 3, characterized in that, The viscous damping force is obtained in step S4 using the following method: The viscous damping force exerted by the environmental particles on the robot particles is calculated based on the relative velocity between the robot particles and the environmental particles.

7. The motion simulation method according to claim 1, characterized in that, Step S5 includes: Step S51: Based on the preset integration time step, a time integrator is used to integrate the force superimposed by the compensation force and the environmental force, and the half-step velocity information of the robot particle in the current time step is output by combining the velocity information of the robot particle in the previous time step. In the first said time step, the velocity information of the robot particle in the previous said time step is 0; Step S52: Update the position information of the robot particle in the current time step according to the half-step velocity information of the current time step; Step S53: Update the first distance according to the updated position information, and recalculate the compensation force and the environmental force applied to the robot particle in the first particle pair; Step S54: The velocity information of the robot particle in the current time step is obtained by processing the recalculated compensation force and the recalculated environmental force. The velocity information of the current time step is used to update the half-step velocity information of the next time step.

8. The motion simulation method according to claim 7, characterized in that, Perform the following steps after the simulation is complete: Step B1: Calculate the average velocity of the micro-nano robot based on the position information within all the time steps; Step B2: Calculate the normalized speed of the micro-nano robot by combining the average speed and the preset reference speed. Step B3: Based on the contact situation and the normalized velocity, determine the motion zones of the micro-nano robot; The motion simulation results include the average velocity, the normalized velocity, and the motion partition of the robot particles.

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