A multi-objective optimization method for robot bone resection parameters

Abstract

The present application relates to a kind of robot bone grinding parameter multi-objective optimization method, comprising: according to the real experimental measurement data of different density artificial bone block milling, via signal processing, construct robot bone grinding dataset;According to robot bone grinding dataset, via genetic algorithm optimization parameter, based on radial basis function neural network RBFNN constructs bone grinding mechanics model, obtains the mathematical representation between bone density, spindle speed and feed speed these three grinding parameters and grinding force;According to the bone grinding force model constructed, in combination with material removal rate theoretical formula, develop multi-objective exploratory differential optimization algorithm MOEDO to complete bone grinding parameter optimization;According to the technical scheme provided in the present application, can according to different optimization target weight tendency obtain the optimal grinding parameter combination corresponding to each bone layer, provide important theoretical basis and operation guidance for the grinding parameter selection of cortical bone and cancellous bone in bone grinding operation.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization method for robot bone grinding parameters, belonging to the field of robot-assisted orthopedic surgery and bone grinding processing. Background Technology

[0002] Bone grinding is a crucial step in orthopedic surgeries such as epiphyseal opening. The appropriate selection of process parameters directly affects the magnitude and fluctuation of grinding force, thus impacting surgical safety and postoperative healing quality. However, current robot-assisted bone grinding parameters still lack sufficient precision, making it difficult to achieve smooth transitions between different bone layers, easily leading to mechanical damage to bone tissue or drill breakage. Therefore, constructing a precise mapping model between grinding process parameters and grinding force, and optimizing these parameters, has significant clinical implications. Due to the anisotropy and non-homogeneity of bone tissue, and the influence of multi-physics coupling during grinding, a highly nonlinear relationship exists between process parameters and grinding force. Traditional empirical models, limited by pre-defined function forms, struggle to accurately characterize this complex mapping. Neural networks, with their powerful nonlinear fitting capabilities, offer a new technical approach for constructing high-precision grinding force models. Based on the obtained grinding force prediction model, the optimization of bone grinding process needs to consider the balance between processing efficiency and processing safety. However, existing studies mostly use single-objective optimization, which makes it difficult to reveal the true trade-off between the two. Furthermore, multi-objective genetic algorithms or particle swarm optimization algorithms still suffer from slow convergence speed and insufficient solution set distribution when dealing with continuous variable optimization, limiting their practical value in clinical decision-making. In summary, constructing a high-quality bone grinding dataset, designing a high-precision neural network model to establish the mapping relationship between process parameters and grinding force, and developing a multi-objective optimization algorithm suitable for clinical needs are of significant research value for improving the surgical quality and safety of robot-assisted bone grinding. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a multi-objective optimization method for robotic bone grinding parameters. This method can automatically optimize the combination of grinding parameters based on three grinding parameters: bone density, spindle speed, and feed rate, balancing surgical safety (minimizing grinding force) and surgical efficiency (maximizing material removal rate). This method is of great significance for determining the safety boundary of robotic bone grinding and improving surgical quality and efficiency.

[0004] This invention provides a multi-objective optimization method for robot bone grinding parameters, including:

[0005] Based on real experimental measurement data of milling artificial bone blocks of different densities, a robot bone grinding dataset was constructed through signal processing.

[0006] Based on the robot bone grinding dataset, the parameters were optimized by a genetic algorithm, and a bone grinding mechanical model was constructed based on a radial basis function neural network (RBFNN) to obtain the mathematical representation of the relationship between the three grinding parameters—bone density, spindle speed, and feed rate—and the grinding force.

[0007] Based on the constructed bone grinding force model and combined with the theoretical formula of material removal rate, a multi-objective exploratory differential optimization algorithm (MOEDO) was developed to optimize bone grinding parameters.

[0008] The aforementioned multi-objective optimization method for robot bone grinding parameters preferably involves constructing a robot bone grinding dataset based on real experimental measurement data from milling artificial bone blocks of different densities via a signal processing procedure. The specific process is as follows:

[0009] Based on the UR10 robotic arm, a six-dimensional force sensor was added, and a 5mm diameter spherical drill was selected for 800... 1640 Three densities of SAWBONES solid rigid polyurethane foam were used to simulate cancellous and cortical bone in bone grinding experiments. A design of full factors (DOE) was used to design the experimental parameters for bone grinding. All combinations of spindle speed range (12000-30000 rpm) and feed rate range (0.3-1.0 mm / s) were arranged into a test matrix, and grinding experiments were conducted accordingly. The robot moved the milling unit perpendicular to the bone surface along a straight path at a fixed linear speed, maintaining a consistent grinding depth throughout the process, and recording data from a six-dimensional force sensor as the raw signal.

[0010] Based on each sampling time, obtain Fx, Fy, and Fz from the original signal, and obtain the resultant force F as:

[0011]

[0012] Based on the resultant force signal of the sampling points, a Butterworth low-pass filter is first used to remove high-frequency noise, and then the signal is smoothed by a moving average algorithm to extract the average resultant force F in the stable grinding region. Finally, the average value is correlated with the corresponding bone density and grinding parameters to construct a complete robot bone grinding dataset.

[0013] The aforementioned multi-objective optimization method for robot bone grinding parameters preferably involves optimizing parameters using a genetic algorithm based on a robot bone grinding dataset, constructing a bone grinding mechanical model based on a radial basis function neural network (RBFNN), and obtaining mathematical representations of the relationship between three grinding parameters—bone density, spindle speed, and feed rate—and grinding force. The specific process is as follows:

[0014] Based on the constructed robotic bone grinding dataset, a bone grinding mechanical model is built using a radial basis function neural network (RBFNN), which can be represented as follows:

[0015]

[0016] Where m is the number of radial basis function units in the hidden layer, and each unit maps the input to a high-dimensional space using a Gaussian function. For the input vector, For the first The output value of each output neuron For the hidden layer The nth neuron to the output layer The weights of each neuron, For radial basis functions RBF, For the output layer Bias of each neuron;

[0017] To obtain the best data fitting effect of the bone grinding mechanical model, this invention uses a genetic algorithm to optimize two key parameters in RBFNN: the expansion parameter of the radial basis function and the number of hidden layers. With the goal of minimizing the root mean square error (RMSE), the global optimal search is achieved through iterative calculation, thereby determining the optimal parameter configuration.

[0018] Based on the optimal grinding parameter configuration obtained through training, an RBFNN grinding force model is constructed. The input bone grinding data is mapped to a high-dimensional space, and the average grinding force is fitted by nonlinear transformation regression. This achieves a mathematical representation of the relationship between the three grinding parameters—bone density, spindle speed, and feed rate—and the grinding force.

[0019] The aforementioned multi-objective optimization method for robot bone grinding parameters preferably involves developing a multi-objective exploratory differential optimization algorithm (MOEDO) based on a constructed bone grinding force model and the theoretical formula for material removal rate to optimize the bone grinding parameters. The specific process is as follows:

[0020] Material removal rate refers to the amount of bone material removed by grinding per unit time, which can be expressed as:

[0021]

[0022] in, For grinding depth, The radius of the drill bit. For feed rate, Material removal rate;

[0023] To address the complex nonlinear coupling and objective conflict between grinding force and material removal rate in bone grinding process parameter optimization, this invention introduces a multi-objective exploratory differential optimization (MOEDO) algorithm. Based on the classic multi-objective differential evolution framework MODE, this algorithm designs a two-stage perturbation strategy and a dynamic Pareto solution set maintenance mechanism, aiming to ensure solution set quality while taking into account convergence speed and global search capability.

[0024] In MOEDO, each individual is represented by a position vector. Let represent a candidate solution, where To determine the dimension of the decision variables, and to maintain search continuity, each individual maintains a memory vector. It records the position information of its previous generation. In each iteration, the algorithm first selects the mean of the top three individuals as the guiding solution based on the non-dominated ranking results of the current population. It is used to guide individuals to high-quality areas and define local reference points to characterize the individual's local environment. To guide the solution and the midpoint of the memory vector, it can be represented as:

[0025]

[0026] A dynamic perturbation vector is constructed based on this reference point. ,in This indicates element-wise multiplication, which increases the disturbance amplitude as the reference point coordinates increase, thus achieving adaptive step size adjustment;

[0027] The core of MOEDO lies in its two-stage perturbation mutation mechanism, which uses probability... Execution development phase (local fine-grained search), with probability The exploration phase is executed (global diversity enhancement), in which probability... Adaptive adjustment based on the number of iterations;

[0028] During the development phase, two sub-modes are used to generate test vectors based on whether the memory vector equals the current position. If the memory equals the current position (the individual has not moved effectively), then the synergistic effect of memory and guided solution is emphasized, which can be expressed as:

[0029]

[0030] If the memory vector is not equal to the current position (the individual has moved), a nonlinear random perturbation is introduced to enhance the local exploration capability, which can be expressed as:

[0031]

[0032] in As a random perturbation factor, the logarithmic transformation produces a negative value with variable amplitude, enhancing local exploration capabilities;

[0033] In the exploration phase, the classic differential mutation approach is adopted: two distinct individuals are randomly selected. Construct difference vectors Then the test vector is:

[0034]

[0035] scaling factor , by adaptive parameters The decision made To balance population diversity and convergence, the adaptive parameters in the above formula... The current iteration progress changes dynamically with each iteration. And introduce random factors (obey (uniform distribution)

[0036] The generated new solution After boundary constraint processing to ensure that each component lies within the feasible region, it can be represented as:

[0037]

[0038] in, The solution vector is the first The components of the dimension, and These are the upper and lower bounds of the dimension, respectively. This is the number of variable dimensions in the optimization problem. This step ensures that all candidate solutions are within the feasible search space.

[0039] MOEDO employs a dynamic Pareto solution set maintenance mechanism, effectively reducing computational overhead while ensuring solution set quality through non-dominated solution selection and elite retention strategies. New individuals are merged with their parent population after generation. Let the... The Pareto solution set is The offspring population is Mixed population construction The new generation of Pareto solutions, selected through non-dominated sorting, can be represented as:

[0040]

[0041] in, yes The set of all non-dominated solutions, the dominance relation can be defined as:

[0042]

[0043] in, and To find the point in the search space, It is the first With the above update mechanism, MOEDO can achieve multi-objective optimization of bone grinding process parameters while maintaining high-quality non-dominated solutions and taking into account the diversity of solution sets.

[0044] Based on the grinding force model and material removal rate theoretical formula constructed above, and with the objectives of minimizing grinding force and maximizing material removal rate, a MOEDO optimization algorithm is constructed for bone mineral density of 800. 1640 The feed rate and spindle speed under two working conditions are iteratively optimized to obtain the optimal front edge under the corresponding bone density. This Pareto front edge can provide the selection basis for the optimal parameter combination for different grinding scenarios and provide key reference parameters for subsequent controller design.

[0045] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0046] Based on real experimental measurement data of milling artificial bone blocks of different densities, a robotic bone grinding dataset is constructed through signal processing. Using this dataset, parameters are optimized via a genetic algorithm, and a bone grinding mechanics model is constructed based on a radial basis function neural network (RBFNN) to obtain mathematical representations of the relationship between three grinding parameters—bone density, spindle speed, and feed rate—and grinding force. Based on the constructed bone grinding force model and combined with the theoretical formula for material removal rate, a multi-objective exploratory differential optimization algorithm (MOEDO) is developed to optimize the bone grinding parameters. According to the technical solution provided by this invention, the optimal combination of grinding parameters for each bone layer can be obtained based on different optimization objective weight tendencies, providing important theoretical basis and operational guidance for the selection of grinding parameters for cortical and cancellous bone in actual epiphyseal plate bone bridge grinding surgery. Attached Figure Description

[0047] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort or labor.

[0048] Figure 1 This is a schematic diagram of the multi-objective parameter optimization method for bone grinding provided in this invention example;

[0049] Figure 2This is an example of an orthopedic robot experimental platform provided by the present invention, (a) robot system, (b) end effector, (c) bone grinding material, and (d) schematic diagram of bone grinding.

[0050] Figure 3 This is a schematic diagram of the dataset signal preprocessing provided in the example of the present invention;

[0051] Figure 4 This is a schematic diagram of the RBFNN network structure provided in the example of this invention;

[0052] Figure 5 This is a schematic diagram of the RBFNN parameter optimization process based on genetic algorithm provided in the example of the present invention;

[0053] Figure 6 This is a schematic diagram of the training set prediction fitting results provided in the example of the present invention;

[0054] Figure 7 This is a schematic diagram of the test set prediction fitting results provided in the example of the present invention;

[0055] Figure 8 This is a schematic diagram of the bone grinding material removal process provided in the example of the present invention;

[0056] Figure 9 This is a schematic diagram of the RBFNN-MOEDO hybrid optimization process provided in the example of this invention;

[0057] Figure 10 This is a schematic diagram of possible solutions for MRR and grinding force target space provided by the embodiments of the present invention;

[0058] Figure 11 This is a schematic diagram of the Pareto front under different optimizers provided in the examples of this invention; Specific Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0060] This invention provides a multi-objective parameter optimization method for robotic bone grinding. Please refer to [link / reference]. Figure 1 This is a schematic diagram of the multi-objective parameter optimization method for robotic bone grinding provided by the present invention. Without being limited to the above, the multi-objective parameter optimization method for bone grinding is applicable to the field of orthopedic surgery, providing important theoretical basis and operational guidance for the selection of grinding parameters for cortical and cancellous bone in bone grinding surgery. The method includes the following steps:

[0061] Step 101: Based on real experimental measurement data of milling artificial bone blocks of different densities, a robot bone grinding dataset is constructed through signal processing. The specific process is as follows:

[0062] Data collection for bone grinding experiments was conducted based on the constructed orthopedic robot experimental platform, such as... Figure 2 As shown, the bone grinding experiment used a UR10 robotic arm with a repeatability of 0.1 mm, with a high-speed drill attached to its end effector. To measure the grinding force, a Robotqi six-dimensional force sensor was installed between the robotic arm end effector and the drill, and the grinding force was measured in the time domain at a sampling frequency of 100 Hz. A 5 mm diameter spherical drill with 14 cutting edges and a helix angle of 35 degrees was selected as the grinding drill bit. Because the mechanical and thermal properties of bone tissue are influenced by many factors such as age, sex, and race, researchers recommended using standard artificial bone blocks for the bone processing experiment. Therefore, an 800... 1640 These two densities of SAWBONES solid rigid polyurethane foam simulate cancellous bone, dense cancellous bone, and cortical bone. Furthermore, because pediatric epiphyseal plate bone bridge lesions are small and extremely prone to damage, the safety requirements for operation are extremely high. Therefore, a spindle speed range of 12,000-30,000 rpm and a feed rate range of 0.3-1 mm / s were selected for grinding experiments.

[0063] The bone grinding experiment process is as follows Figure 2 As shown in (d), the X-axis, Y-axis, and Z-axis of the spherical drill at the end of the robot are calibrated. The X-axis is perpendicular to the bone surface being ground, the Y-axis is the feed direction, and the Z-axis is perpendicular to both the X-axis and Y-axis. The feed speed f of the spherical drill along the Y-axis and the spindle speed n of the spherical drill are measured. In each experimental run, the robot moves the milling unit along a straight path at a fixed linear speed perpendicular to the bone surface, maintaining a grinding depth of 0.5 mm. The data from the six-dimensional force sensor is recorded as the raw signal.

[0064] Based on the designed grinding parameter constraints, a design of factors (DOE) was completed to simulate clinical parameters, serving as the training dataset for constructing the neural network force model. All possible combinations of grinding parameters were arranged into a test matrix, as shown in Table 1. The spindle speed for bone grinding ranged from 12000 to 3000 rpm, and the feed rate ranged from 0.3 to 1 mm / s. The bone grinding experiments were conducted in a randomized order, with each experiment in the matrix repeated twice to ensure measurement repeatability. Furthermore, additional test experiments were performed beyond the designed test matrix parameters, as shown in Table 2, serving as the test dataset to verify the effectiveness of the constructed grinding force model.

[0065] Table 1. Full Factorial Experiment Design Matrix (Training Set)

[0066]

[0067] Table 2 Test Set Experimental Parameter Design

[0068] Bone mineral density 800 / 1640 kg / m³ Spindle speed (rpm) Feed rate (mm / s) Experiment 1 20000 0.3 Experiment 2 24000 0.4 Experiment 3 18000 0.6 Experiment 4 28000 0.7 Experiment 5 25000 0.9

[0069] Based on each sampling time, Fx, Fy, and Fz are obtained from the original signal. The resultant force F is obtained by summing the force components in the three dimensions, which can be expressed as:

[0070]

[0071] Based on the resultant force signal from the sampling points, a Butterworth low-pass filter is used to remove high-frequency noise. The cutoff frequency is set to 1Hz, and the sampling frequency is 100Hz. The filtered signal is as follows: Figure 3 As shown. Moving averages are used to smooth the signal, as shown in the diagram. Figure 3 As shown, a stable grinding region is selected, the average value of the resultant force F is calculated, and combined with the corresponding grinding parameters, thus constructing a robot bone grinding dataset.

[0072] Step 102: Based on the constructed dataset and the robot bone grinding dataset, the parameters are optimized using a genetic algorithm, and a bone grinding mechanical model is constructed based on a radial basis function neural network (RBFNN). This process obtains the mathematical representation of the relationship between the three grinding parameters—bone density, spindle speed, and feed rate—and the grinding force. The specific process is as follows:

[0073] Based on the constructed robotic bone grinding dataset, a bone grinding mechanics model was built using a radial basis function neural network (RBFNN). The network structure is as follows: Figure 4 As shown, it consists of three layers: an input layer, a hidden layer, and an output layer. The input layer is composed of input nodes, represented as follows: Each sample data includes three features: bone density, spindle speed, and feed rate, represented as follows: .

[0074] The hidden layer achieves nonlinear transformation through radial basis functions (RBF), using Gaussian functions as the radial basis functions, where the i-th training sample in the input layer... The output to the j-th node in the hidden layer is calculated as follows:

[0075]

[0076] in, and Let represent the cluster center and standard deviation of the j-th Gaussian activation function, respectively. For input samples With the center Euclidean distance.

[0077] Regarding cluster centers, this technical solution uses the K-means clustering algorithm to determine the centers of hidden layer neurons, which can be expressed as:

[0078]

[0079] in Let be the set of samples belonging to the j-th cluster. This represents the number of samples.

[0080] The output layer consists of neurons with linear activation functions. The information from the hidden layer neurons is weighted and summed before being output to obtain the final output of the neural network. The output Y from the hidden layer to the output layer can be expressed as:

[0081]

[0082] in, For the input vector, Let be the output value of the k-th output neuron, m be the number of hidden layer neurons, and j be the index of the hidden layer neuron. For radial basis functions RBF, Let be the weights from the j-th neuron in the hidden layer to the k-th neuron in the output layer. This is the bias of the k-th neuron in the output layer.

[0083] The prediction accuracy of RBFNN is highly dependent on the number of neurons in the hidden layer. and Gaussian function extension parameters The selection of parameters is crucial. Traditional gradient learning methods are prone to getting stuck in local optima when optimizing these parameters, making it difficult to guarantee a globally optimal solution. Therefore, a genetic algorithm (GA) is introduced to globally optimize the key parameters of the RBFNN, achieving joint modeling of GA-RBFNN. The optimization process is as follows: Figure 5 As shown, with the goal of minimizing the root mean square error (RMSE), a global optimal search is achieved through iterative calculation to determine the optimal parameter configuration.

[0084] Based on the GA-RBFNN hybrid model, and optimized using a genetic algorithm, the optimal radial basis expansion parameter of the RBFNN was found to be 1.1, and the optimal number of hidden layers was found to be 25. A grinding force neural network model was then constructed, and its training set data fitting performance is as follows. Figure 6 As shown, its correlation coefficient R 2 =0.992, indicating that the training dataset of the bone grinding mechanical model has a good fitting effect.

[0085] To comprehensively evaluate the grinding force prediction performance of the RBFNN model, a test dataset was constructed based on this invention. The model was trained and then used for inference prediction. The prediction performance on the test set is as follows: Figure 7 As shown, its correlation coefficient R 2=0.987, proving that the mechanical model of bone grinding has a good fitting effect and the mapping relationship between grinding parameters and grinding force is accurately characterized.

[0086] To further evaluate the model's effectiveness, mean absolute error (RMSE), root mean square error (MAE), and coefficient of determination (R²) were used. 2 Statistical standards such as mean absolute percentage error (MAPE) are used to evaluate grinding mechanical models.

[0087] The calculation method for MAPE is as follows:

[0088]

[0089] The method for calculating RMSE is as follows:

[0090]

[0091] The calculation method for MAE is as follows:

[0092]

[0093] Where R 2 The calculation method is as follows:

[0094]

[0095] in, It is a predicted value. It is the actual value. It is the mean of the true values. This is the number of samples in the test set.

[0096] The model evaluation results are shown in Table 3. The RMSE is 0.0501, MAE is 0.0399, MAPE is 0.9491%, and R0 is... 2 The coefficient of determination is 0.9878. Based on the evaluation results, the R-value is... 2 The value of 0.9878 is close to 1, indicating good predictive performance. Low RMSE and MAE values ​​demonstrate high predictive accuracy. A low MAPE value indicates high predictive stability. In conclusion, the constructed model performs significantly well in grinding force prediction tasks, possessing high reliability and practical value.

[0097] Table 3 Evaluation of Mechanical Model Indicators

[0098] RMSE MAE MAPE (%) R2 index 0.0501 0.0399 0.9491 0.9878

[0099] Step 103: Based on the constructed bone grinding force model and combined with the theoretical formula of material removal rate, a multi-objective exploratory differential optimization algorithm (MOEDO) is developed to optimize the bone grinding parameters.

[0100] Considering different bone densities during bone grinding The objective function for optimizing bone grinding parameters is constructed using two grinding parameters: spindle speed *n* and feed rate *v*. First, based on RBFNN, a precise mapping between the three grinding parameters (bone density, feed rate, and spindle speed) and the bone grinding force is achieved, and a grinding force prediction model is constructed as the objective function for grinding force. Second, the bone grinding material removal process is analyzed, and a material removal rate model is constructed as the objective function for surgical efficiency. Finally, by integrating the bone grinding force and material removal rate, a bone grinding safety model is established as the objective function for parameter optimization.

[0101] Material removal rate refers to the amount of bone material removed by grinding per unit time, and is one of the key indicators affecting surgical efficiency. According to the definition of material removal rate, its mathematical model is the product of the volume of material removed per unit time during grinding and the drill feed rate, where the material removal area within one rotation cycle of the grinding drill is as follows: Figure 8 As shown. Material removal rate refers to the amount of bone material removed by grinding per unit time, and is one of the key indicators affecting surgical efficiency. According to the definition of material removal rate, its mathematical model can be expressed as:

[0102]

[0103] Where h is the grinding depth, R is the grinding radius, v is the feed rate, and MRR is the material removal rate.

[0104] To address the complex nonlinear coupling and objective conflicts between grinding force and material removal rate in bone grinding process parameter optimization, this invention introduces a multi-objective exploratory differential optimization (MOEDO) algorithm. Based on the differential evolution framework MODE, this algorithm employs a two-stage perturbation strategy and a dynamic Pareto solution set maintenance mechanism, aiming to ensure solution set quality while balancing convergence speed and global search capability.

[0105] In MOEDO, each individual is represented by a position vector. Let represent a candidate solution, where Let be the dimension of the decision variables. To maintain search continuity, each individual maintains a memory vector. Record the location information of its predecessor, that is In each generation, the algorithm updates the position of the individual from the previous generation. In each iteration, the algorithm first selects the mean of the top three dominant individuals based on the non-dominated ranking of the current population as the guiding solution. This guided solution is used to direct individuals to higher quality regions. Simultaneously, local reference points are defined to characterize the individual's local environment. To guide the solution and the midpoint of the memory vector, it can be represented as:

[0106]

[0107] A dynamic perturbation vector is constructed based on this reference point. ,in This indicates element-wise multiplication, which increases the perturbation amplitude as the coordinates of the reference point increase. This allows for a larger step size to accelerate exploration when the point is far from the origin, and a smaller step size to achieve a finer search when the point is close to the origin.

[0108] The core of MOEDO lies in its two-stage perturbation mutation mechanism, which uses probability... Execution development phase (local fine-grained search), with probability Execute the exploration phase (global diversity enhancement). Probability Adaptively adjusting with the number of iterations can be expressed as:

[0109]

[0110] in This represents the current iteration number. For the largest algebra, as well as This allows the algorithm to focus on exploration in its early stages and on development in its later stages.

[0111] During the development phase, the algorithm uses two sub-modes to generate test vectors based on whether the current individual's memory vector is the same as its position. If the memory vector equals the current position (i.e., the individual has not yet made an effective move), then the synergistic effect of memory and guided solution is emphasized, which can be expressed as:

[0112]

[0113] If the memory vector is not equal to the current position (the individual has moved), a nonlinear random perturbation is introduced to enhance the local exploration capability, which can be expressed as:

[0114]

[0115] in For random disturbance factors, logarithmic transformation The generation of negative values ​​with variable amplitude can introduce nonlinear randomness into the search, which helps to escape local extrema.

[0116] During the exploration phase, the algorithm employs the mutation concept of classic differential evolution, using the population mean and random individuals to generate a global perturbation. First, the mean vector of the current population is calculated, and then two distinct individuals are randomly selected. Define two intermediate vectors, which can be represented as:

[0117]

[0118] in Can be understood as an individual Overlaid The new position obtained after offset from the mean. Similarly, both reflect the offset direction guided by the population mean from a symmetrical perspective, forming a pair of complementary perturbation bases. Therefore, the formula for generating the experimental vector can be expressed as:

[0119]

[0120] in For adaptive parameters. This design enhances global exploration capability through two complementary perturbation directions: when When the range changes, it can be flexibly combined. and This information generates a rich variety of perturbation patterns; simultaneously, the mean vector is subtracted. This helps maintain the overall central stability of the population and prevents systematic drift of individuals during iteration. It can be proven that this expression is equivalent to the variation form of classical differential evolution. This reflects the inherent connection with the standard difference evolution framework, and this design enhances the intuitiveness and controllability of the implementation while maintaining equivalence by explicitly introducing the mean vector.

[0121] The adaptive parameter in the above formula It changes dynamically with iteration. Define the current iteration progress. And introduce random factors (obey If the distribution is uniform, then the parameter settings can be expressed as:

[0122]

[0123] in By compressing random perturbations with high powers, making them close to 0 in most cases and occasionally producing large values, the randomness of local and global searches is balanced. Combined with schedule factors This allows the exploration intensity to gradually increase with iteration, which aligns with the basic strategy of the algorithm: explore first and then develop.

[0124] The generated new solution After boundary constraint processing to ensure that each component lies within the feasible region, it can be represented as:

[0125]

[0126] in, The solution vector is the first The components of the dimension, and These are the upper and lower bounds of the dimension, respectively. This refers to the number of variables in the optimization problem. This step ensures that all candidate solutions lie within the feasible search space. After mutating all individuals, the memory vector is updated with the new solution. Meanwhile, the new generation of the population was directly set as the experimental vector: This complete replacement strategy, combined with the subsequent Pareto archiving mechanism, can effectively preserve outstanding individuals.

[0127] To maintain the quality and diversity of the solution set, MOEDO employs a dynamic Pareto solution set maintenance mechanism. The algorithm maintains an external archive. Used to store data up to the [number]th [year]. All non-dominated solutions discovered in each generation. A population of offspring is generated in each generation. Then, merge it with the current archive to obtain a mixed population. .right Performing a fast nondominated sort yields several Pareto fronts. Take the first frontier All individuals as a new generation of external archives , can be represented as:

[0128]

[0129] in and To solve for points in the search space, the dominance relation , For the first One objective function, The target number (in this invention) ).

[0130]

[0131] If the external archive size Exceeding the preset limit Then calculate The crowding distance of each individual is calculated and sorted in descending order of distance, retaining the top [number]. Individual. Crowding distance measures the density of an individual within the target space relative to its neighbors; a larger distance indicates a sparser surrounding environment. Prioritizing the preservation of sparse individuals helps maintain a uniform distribution of the Pareto front. Through this mechanism, MOED can continuously retain high-quality solutions during evolution while ensuring the diversity of the solution set, providing decision-makers with a rich pool of candidate solutions.

[0132] Regarding the construction of the objective function, firstly, using the RBFNN grinding force prediction model established earlier, the grinding resultant force corresponding to different combinations of process parameters is predicted under a given bone density, and the predicted grinding force is used as the first optimization objective. Secondly, based on the theoretical calculation model of bone grinding material removal rate, the material removal rate is calculated using feed rate, grinding depth, and grinding drill geometry parameters as inputs, and this is used as the second optimization objective. Since multi-objective optimization algorithms usually adopt a unified minimization form, this invention transforms the material removal rate objective into its negative form, thereby constructing a bi-objective optimization model, which can be expressed as:

[0133]

[0134] in, as well as .

[0135] Based on this, the aforementioned objective function is embedded into the MOEDO multi-objective optimization algorithm framework. A global exploration of the process parameter space is achieved through population iterative search, and a Pareto solution set is constructed by combining non-dominated sorting and crowding distance mechanisms. This yields the optimal combination of process parameters that balances minimizing grinding force with maximizing material removal rate. The overall optimization process is as follows: Figure 9 .

[0136] Based on the constructed grinding force model and material removal rate theoretical formula, with the objectives of minimizing grinding force and maximizing material removal rate, a MOEDO optimization algorithm was constructed to achieve the optimal parameter combination of feed rate and spindle speed at bone mineral density of 800 kg / m³ and 1640 kg / m³. Through iterative selection, the Pareto front of MOEDO multi-objective parameter optimization at bone mineral density of 800 kg / m³ and 1640 kg / m³ was obtained. Figure 10 As shown.

[0137] Figure 10 This indicates that minimizing grinding force and maximizing material removal rate are conflicting. The Pareto front in the figure can help select a suitable combination of grinding parameters. For example, if the drill is close to an important anatomical structure, the constraints on grinding force are extremely stringent, and a possible solution near point A should be selected to maximize control over the grinding force. Alternatively, if the grinding force can be increased without damaging bone tissue to maximize material removal rate, a possible solution near point C can be selected. When grinding force and material removal rate are equally important, a feasible solution near point B can be chosen. Examples of grinding parameter solution sets near points A, B, and C at bone mineral density of 800 kg / m³ and 1640 kg / m³ are shown in Tables 4 and 5, respectively.

[0138] Table 4. Optimal Solution Case for ρ=800 kg / m³

[0139]

[0140] Table 5. Optimal Solution Case for ρ=1640 kg / m³

[0141]

[0142] Compared to other optimization algorithms, the MOEDO multi-objective optimization algorithm employed can more comprehensively and uniformly solve for the Pareto front optimal solution set, such as... Figure 11 As shown, this provides a richer selection of Pareto optimal options for process parameter decisions. In summary, the technical solution provided by this invention effectively achieves high-precision prediction of grinding force and multi-objective optimization of grinding parameters, improving process efficiency while providing reliable support for autonomous parameter decision-making in actual manufacturing.

[0143] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0144] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A multi-objective optimization method for robot bone grinding parameters, characterized in that, include: Based on real experimental measurement data of milling artificial bone blocks of different densities, a robot bone grinding dataset was constructed through signal processing. Based on the robot bone grinding dataset, the parameters were optimized by a genetic algorithm, and a bone grinding mechanical model was constructed based on a radial basis function neural network (RBFNN) to obtain the mathematical representation of the relationship between the three grinding parameters—bone density, spindle speed, and feed rate—and the grinding force. Based on the constructed bone grinding force model and combined with the theoretical formula of material removal rate, a multi-objective exploratory differential optimization algorithm (MOEDO) was developed to optimize bone grinding parameters.

2. The method according to claim 1, characterized in that, Based on real experimental measurement data of milling artificial bone blocks of different densities, a robot bone grinding dataset was constructed through signal processing. The specific process is as follows: Based on the UR10 robotic arm with a repeatability of 0.1mm, a six-dimensional force sensor was added, and a 5mm diameter spherical drill was selected for... 1640 SAWBONES solid rigid polyurethane foam of these three densities simulated cancellous bone and cortical bone for bone grinding experiments. The design of full factorial experimental design (DOE) was used to design the parameters for bone grinding experiments. All combinations of grinding parameters were arranged into a test matrix, and grinding experiments were carried out accordingly. The robot moved the milling unit perpendicular to the bone block surface along a straight path at a fixed linear speed, maintaining a consistent grinding depth during the process, and recording the data from the six-dimensional force sensor as the raw signal. Based on each sampling time, obtain Fx, Fy, and Fz from the original signal, and obtain the resultant force F as: Based on the resultant force signal of the sampling points, high-frequency noise is removed using a Butterworth low-pass filter and the signal is smoothed using a moving average. The average value of the resultant force F is then calculated. Combined with the corresponding grinding parameters, a robot bone grinding dataset is constructed.

3. The method according to claim 1, characterized in that, Based on the robot bone grinding dataset, parameters were optimized using a genetic algorithm, and a bone grinding mechanical model was constructed using a radial basis function neural network (RBFNN). This model obtained mathematical representations of the relationship between three grinding parameters—bone density, spindle speed, and feed rate—and grinding force. The specific process is as follows: Based on the constructed robotic bone grinding dataset, a bone grinding mechanical model is built using a radial basis function neural network (RBFNN), which can be represented as follows: Where m is the number of radial basis function units in the hidden layer, and each unit maps the input to a high-dimensional space using a Gaussian function. For the input vector, For the first The output value of each output neuron For the hidden layer The nth neuron to the output layer The weights of each neuron, For radial basis functions RBF, For the output layer Bias of each neuron; To obtain the best data fitting effect of the bone grinding mechanical model, this paper uses a genetic algorithm to optimize two key parameters in RBFNN: the expansion parameter of the radial basis function and the number of hidden layers. With the goal of minimizing the root mean square error (RMSE), the global optimal search is achieved through iterative calculation to determine the optimal parameter configuration. Based on the optimal grinding parameter configuration obtained through training, an RBFNN grinding force model is constructed. The input bone grinding data is mapped to a high-dimensional space, and the average grinding force is fitted by nonlinear transformation regression. This achieves a mathematical representation of the relationship between the three grinding parameters—bone density, spindle speed, and feed rate—and the grinding force.

4. The method according to claim 1, characterized in that, Based on the constructed bone grinding force model and combined with the theoretical formula for material removal rate, a multi-objective exploratory differential optimization algorithm (MOEDO) was developed to optimize the bone grinding parameters. The specific process is as follows: Material removal rate refers to the amount of bone material removed by grinding per unit time, which can be expressed as: in, For grinding depth, The radius of the drill bit. For feed rate, Material removal rate; To address the complex nonlinear coupling and objective conflict between grinding force and material removal rate in bone grinding process parameter optimization, this invention introduces a multi-objective exploratory differential optimization (MOEDO) algorithm. Based on the classic multi-objective differential evolution framework MODE, this algorithm designs a two-stage perturbation strategy and a dynamic Pareto solution set maintenance mechanism, aiming to ensure solution set quality while taking into account convergence speed and global search capability. In MOEDO, each individual is represented by a position vector. Let represent a candidate solution, where To determine the dimension of the decision variables, and to maintain search continuity, each individual maintains a memory vector. It records the position information of its previous generation. In each iteration, the algorithm first selects the mean of the top three individuals as the guiding solution based on the non-dominated ranking results of the current population. It is used to guide individuals to high-quality areas and define local reference points to characterize the individual's local environment. To guide the solution and the midpoint of the memory vector, it can be represented as: A dynamic perturbation vector is constructed based on this reference point. ,in This indicates element-wise multiplication, which increases the disturbance amplitude as the reference point coordinates increase, thus achieving adaptive step size adjustment; The core of MOEDO lies in its two-stage perturbation mutation mechanism, which uses probability... Execution development phase (local fine-grained search), with probability The exploration phase is executed (global diversity enhancement), in which probability... Adaptive adjustment based on the number of iterations; During the development phase, two sub-modes are used to generate test vectors based on whether the memory vector equals the current position. If the memory equals the current position (the individual has not moved effectively), then the synergistic effect of memory and the guided solution is emphasized, which can be expressed as: If the memory vector is not equal to the current position (the individual has moved), a nonlinear random perturbation is introduced to enhance the local exploration capability, which can be expressed as: in As a random perturbation factor, the logarithmic transformation produces a negative value with variable amplitude, enhancing local exploration capabilities; In the exploration phase, the classic differential mutation approach is adopted: two distinct individuals are randomly selected. Construct the difference vector Then the test vector is: scaling factor , by adaptive parameters The decision made To balance population diversity and convergence, the adaptive parameters in the above formula... The current iteration progress changes dynamically with each iteration. And introduce random factors (obey (uniform distribution) The generated new solution After boundary constraint processing to ensure that each component lies within the feasible region, it can be represented as: in, The solution vector is the first The components of the dimension, and These are the upper and lower bounds of the dimension, respectively. This is the number of variable dimensions in the optimization problem. This step ensures that all candidate solutions are within the feasible search space. MOEDO employs a dynamic Pareto solution set maintenance mechanism, effectively reducing computational overhead while ensuring solution set quality through non-dominated solution selection and elite retention strategies. New individuals are merged with their parent population after generation. Let the... The Pareto solution set is The offspring population is Mixed population construction The new generation of Pareto solutions, selected through non-dominated sorting, can be represented as: in, yes The set of all non-dominated solutions, the dominance relation can be defined as: in, and To find the point in the search space, It is the first With the above update mechanism, MOEDO can achieve multi-objective optimization of bone grinding process parameters while maintaining high-quality non-dominated solutions and taking into account the diversity of solution sets. Based on the grinding force model and material removal rate theoretical formula constructed above, and with the objectives of minimizing grinding force and maximizing material removal rate, a MOEDO optimization algorithm is constructed for bone mineral density of 800. and 1640 The feed rate and spindle speed under two working conditions are iteratively optimized to obtain the optimal front edge under the corresponding bone density. This Pareto front edge can provide the selection basis for the optimal parameter combination for different grinding scenarios and provide key reference parameters for subsequent controller design.

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