A tooth preparation robot end deformation and material residue collaborative trajectory planning method based on pose compensation

Abstract

The application discloses a kind of based on pose compensation's dental preparation robot end deformation and material residual collaborative trajectory planning method, it relates to dental robot technical field, the present application is aimed at the problem of excessive material residual and the decline of machining accuracy caused by the deformation of robot end in the process of dental preparation, technical points are: calculate the residual volume of the interaction of car needle and tooth in any attitude, and judge different residual modes;Establish the stress deformation model of end effector, solve the comprehensive pose deviation at tool contact point;Construct the multi-objective optimization function of material residual volume and end deformation comprehensive deviation, introduce attitude constraint and penalty function to convert the constrained problem into unconstrained optimization problem;Optimize the pose parameters through multi-objective evolutionary algorithm, output the tool contact position and attitude that meet the accuracy and residual requirements;The present application effectively improves the accuracy and safety of dental preparation by collaborative optimization of end deformation and material residual.

Description

Technical Field

[0001] This invention patent relates to a method for collaborative trajectory planning of end-effector deformation and material residue of a dental preparation robot based on pose compensation, belonging to the field of dental restoration. Background Technology

[0002] Tooth preparation is a crucial step in dental restoration, and its precision directly affects the quality of the restoration and the patient's oral health. Traditional tooth preparation mainly relies on manual operation by dentists, which has problems such as high operational difficulty, unstable precision, and susceptibility to human factors. With the development of robotics technology, dental robots have been gradually introduced into the tooth preparation process to improve the accuracy and consistency of the operation. However, in practical applications, the robot end effector is subjected to complex mechanical forces during the preparation process. In particular, the interaction force between the bur and the tooth can cause elastic deformation of the robot end effector, which in turn causes the deviation between the actual preparation path and the expected path, affecting the preparation accuracy. On the other hand, the complex shape of the tooth makes it easy for the bur to produce material residue during the preparation process, especially in the overlapping area between adjacent cutter contacts. Material residue not only affects the smoothness of the prepared surface, but may also cause the subsequent restoration to not be fully positioned, seriously affecting the restoration effect. Therefore, how to minimize material residue while ensuring cutting accuracy has become a key challenge in tooth preparation robot technology.

[0003] Existing research often focuses on single-aspect optimization, such as considering only path planning or force control, lacking systematic modeling and collaborative optimization of the coupling relationship between end-effector deformation and material residue. Especially in high-precision tooth preparation, the robot's structural flexibility and dynamic loads during the preparation process can lead to end-effector pose deviations, thus affecting the uniformity and integrity of material removal. In addition, changes in robot stiffness under different postures further increase the complexity of control. Therefore, this patent addresses the above problems by proposing a collaborative trajectory planning method for end-effector deformation and material residue of a tooth preparation robot based on pose compensation. The aim is to minimize both material residue and end-effector deformation while ensuring preparation accuracy by establishing a material residue model and an end-effector force deformation model. This algorithm effectively improves the overall performance of the tooth preparation robot through mathematical modeling, multi-objective optimization, and pose compensation strategies, and has significant clinical significance and application value. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a collaborative trajectory planning method for end effector deformation and material residue of a dental preparation robot based on pose compensation. This method aims to simultaneously optimize the end effector deformation and material residue of the dental preparation robot, effectively solve the error coupling problem during the robot's motion, and improve the ability to analyze and optimize the accuracy of the influence of end effector stiffness, thereby achieving precise optimization of the bur pose.

[0005] A method for collaborative trajectory planning of end-effector deformation and material residue in a tooth preparation robot based on pose compensation, the specific implementation process of which is as follows:

[0006] Step 1: Calculation of the intersection parameters of the bur projection profile and the boundary of the preparatory body:

[0007] a) Define the coordinate system and the needle profile, using the robot tool coordinate system. Based on this, the generatrix equation of the needle profile is defined as follows: Its parametric equation is expressed as ,in, The length parameter of the needle generatrix is ​​the length dimension of the effective working section of the needle, and its value range is [value range missing]. , The effective working length of the needle. This is a parameter representing the circumferential rotation angle of the needle, describing the rotation angle of the generatrix around the needle axis. The curvature coefficient of the needle profile generatrix, matching the design specifications of the needle cutting edge; defined Each knife contact point The local tooth coordinate system at that location is With the point of contact of the blade as the origin, the preparatory direction is... coordinate system Positive axis direction The range of values ​​is , This represents the total number of knife contact points;

[0008] b) Calculate the transformed profile, and transform the needle profile equation through a coordinate transformation matrix containing translation and rotation parameters. Transform to knife contact coordinate system at the location The transformed needle profile equation is: ,in, To change the length parameter of the needle profile, compared with the original parameter satisfy The length parameter remains unchanged;

[0009] c) Projection and intersection point finding; defining a preliminary direction vector. Along the local tooth coordinate system of In the positive direction of the axis, establish with Vertical projection plane Parallel to coordinate system The plane will be transformed into the needle profile equation. along Direction projection onto the plane The projection needle profile equation is obtained. , eliminate Axis dimensions, only retain coordinates and Relationship;

[0010] Solve for the intersection of the projected profiles of adjacent tool contact points, taking the same plane. Upper adjacent knife contact and The projection outline of the sewing needle and Through equation Solve for the intersection points The coordinates are used to obtain the corresponding intersection point parameters. and ,in, For the first The intersection length parameter of the projected contours of each blade contact point;

[0011] Solve for the intersection of adjacent tool contact points and the boundary of the pre-work body, and set the projected profile of the bur. The intersection with the upper boundary of the tooth is The intersection point with the lower boundary of the preparatory body is Adjacent knife contacts The corresponding boundary intersection point is and Substituting the intersection points into the projection profile equation yields Solve to obtain the intersection parameters , forming a set of intersection points ;

[0012] d) Loop judgment in intersection set calculation:

[0013] Determine all tool contacts The set of intersections Is the calculation complete?

[0014] Specifically:

[0015] like If established, then... Jump to step 1a), repeat the above process to calculate the first... The set of intersection points of each blade contact point ;

[0016] like If the condition is met, it means that the calculation of the intersection set of all tool contact points has been completed. Then, all intersection set sets are sorted into ordered sets according to the tool contact point index. This serves as the basis for subsequent residual volume calculations; proceed to step two.

[0017] Step 2: Determining different residual patterns of bur-tooth interaction under arbitrary postures:

[0018] Based on the result obtained in step one The length parameter of the intersection point of the projected profile of the tool contact point and the upper boundary of the tooth. and the The length parameter of the intersection point of the projected contours of each tool contact point and the adjacent tool contact point By analyzing the size relationship between the two, the residual pattern of the interaction between the bur and the tooth is determined, with a key distinction being whether overcutting occurs and the location of the intersection point, thereby calculating the adjacent tool contact points. and Residual area between and residual volume The specific process is as follows:

[0019] Scenario 1: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect below the upper boundary. The calculation process needs to consider the influence of the overcut area on the residual area. The calculation method is as follows:

[0020]

[0021] Scenario 2: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect at the upper boundary. The calculation process needs to consider the influence of the overcut area on the residual area. The calculation method is the same as in case 1:

[0022]

[0023] Scenario 3: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect on the upper boundary. Considering the influence of the overcut area on the residual area, the residual area... The calculation method is as follows:

[0024]

[0025] in, and For the residual area The two diagonals of the approximate rhombus The angle between the two diagonals is the value; similarly, the residual area of ​​the material when there is no over-cut area can be calculated. By calculating adjacent tool contacts and The straight-line distance between them, combined with the residual area mentioned above, is calculated using the formula... Calculate the residual volume of the material, where, The distance projection of the two intersection points onto the preparatory direction, and the distance projection onto the preparatory direction vector from step one. In the same direction; finally, collect all adjacent tool contact pairs that can form residual volumes to obtain the set of material residual volumes. The total number of residual volumes that can be formed by adjacent knife contacts is , This represents the total number of contact points in step one.

[0026] Residual volume calculation loop judgment:

[0027] Determine the residual volume between any two adjacent tool contacts. Is the calculation complete?

[0028] Specifically:

[0029] like If true, meaning not all adjacent tool contact pairs of the target have been calculated, then let Return to step two a) and continue calculating the first step. and Residual volume of adjacent knife contacts ;

[0030] like Once the residual volume calculation for all adjacent tool contact pairs of the target is completed, the residual volumes will be set together. Organize the serial numbers of adjacent tool contacts into ordered data, which will be used as input for subsequent end deformation calculation and optimization. Proceed to step three.

[0031] Step 3: Expression of the comprehensive deviation of the end effector under stress and deformation:

[0032] Based on the material residual volume set obtained in step two Combining the force characteristics of the end effector of the tooth preparation robot with the deformation law of the system, the comprehensive force deviation at each tool contact point is solved through modeling, matrix calculation and deviation synthesis. The specific process is as follows:

[0033] a) End-effector deformation modeling: During tooth preparation, the bur is subjected to linear force and torque, causing overall deformation of the series system. The core force relationship is expressed as follows: ,in, The linear force acting on the robot's end effector, oriented by a unit vector. The decision is made in the opposite direction to the prepared direction, and its magnitude is... , For torsional moment, This refers to the lever arm, which is the distance from the point of application of the needle to the axis. linear force With lever arm The included angle is determined by the cutting posture of the bur; considering the preparatory parameters and the material removal performance of the actual bur used, the force calculation for the bur during its advance is as follows: ,in, The diameter of the needle. It is a material constant that matches the tooth material, bur geometry, and preparation conditions. The material removal rate is determined by the residual volume in step two. The volume of material removed can be calculated. , , The speed at which the needle travels forward;

[0034] b) Calculation of Jacobian matrix, compliance matrix, and deformation, given the terminal velocity and Jacobian matrix. The relationship between them is Calculate the Jacobian matrix of the robot in the current pose. ,in The terminal linear velocity, Let be the joint angular velocity; the formula for the Jacobian matrix under any tool contact posture is: ,in, The coordinates of the end position, For joint angle parameters; calculate system flexibility and deformation based on the Jacobian matrix. Calculate the system compliance under arbitrary attitudes ,in The stiffness coefficient matrix in the robot's Cartesian coordinate system is determined by the robot's body parameters; the compliance matrix... Divided into four Submatrix, through the relationship between robot deformation and forces. Calculate the deformation, where, Indicates linear displacement deformation. Indicates angular displacement deformation. The force-linear displacement compliance matrix is ​​related to the linear stiffness of the tooth preparation robot system. The coupling compliance submatrix describes the coupling relationship between force and angular displacement, and torque and linear displacement. The torque-angular displacement compliance matrix is ​​related to the torsional stiffness of the system; considering the combined deformation of the robot's end effector caused by linear force and torque, the linear displacement deformation is derived. and angular displacement deformation The formula is expressed as Combined with the force expression of the needle during its forward movement The linear displacement deformation of the end effector needle of the robot can be derived. and angular displacement deformation The formula is expressed as ;

[0035] c) Overall stress deviation, based on the linear displacement deformation of the needle. and angular displacement deformation Solve the first... Each knife contact point The overall force deviation at the point is ,in, Let be the relative position vector between the needle and the robot end effector, defined in the robot tool coordinate system, and remain unchanged during preparation. yes Calculate the relative position vector from the antisymmetric matrix. , and The three-dimensional components of the position vector of the constructed tooth preparation robot system are used to collect the combined force deviations of all tool contacts, forming a set. ;

[0036] d) Comprehensive deviation calculation and iterative judgment:

[0037] Determine whether the overall force deviation at all tool contact points has been calculated.

[0038] Specifically:

[0039] like This is not valid; not all tool contact points have been calculated. Therefore, let... Return to step 3b) and continue calculating the... Overall force deviation at each tool contact point ;

[0040] like Once the calculation of all tool contact point deviations is completed, the deviation set will be... Sort the input data in ascending order by the tool contact number to form an ordered input data, then proceed to step four.

[0041] Step 4: Establishing the optimization function for material residue and pre-accuracy:

[0042] Based on the material residual volume set obtained in step two and the set of combined force deviations obtained in step three To address the conflicting optimization approaches, a comprehensive constraint optimization function is established, clearly defining attitude restrictions and penalty mechanisms. The specific process is as follows:

[0043] a) Establishing a dual-objective model and solving the attitude matrix: The residual material volume and the end-effector force are negatively correlated; the larger the residual volume, the smaller the removed volume and the smaller the end-effector force. The optimization objective is to obtain a smaller end-effector deformation while minimizing the residual material. This requires comprehensive constraints on both objectives. Input the tool contact point position information determined in step one. Including coordinates and initial pose parameters, a local coordinate system is constructed based on this information, maintaining consistency with step one. The coordinate system reference is consistent, and the supplementary axis directions are defined to satisfy orthogonality. The origin is consistent with the local tooth coordinate system in step one. Consistency, i.e., knife contact point , The positive direction of the axis is aligned with the direction in step one as the preparatory direction. The axis is the direction of needle travel, and... The axis is perpendicular. The axis is determined by the right-hand rule. shaft and The cross product of the axes is obtained All knife contacts The pose matrix at each location is integrated into a set. , of which The formula for the pose matrix of each blade contact point is defined as follows: To prevent excessive deviation from the correct posture and interference with adjacent teeth and healthy tissue, axial constraints on the bur are set. The threshold is represented by the constraint formula defined as follows: ,in, The direction of the needle axis. The direction of the normal to the tool contact point. The cosine of the angle between the bur and the normal of the current tool contact point. Set a preset threshold; set a preliminary accuracy error index. The objective function is ,in, Weighting factors for residual material volume and overall stress deviation. The normalization coefficient is... The 2-norm of the set of residual volumes of materials. The maximum residual volume comes from the set in step two. The 2-norm of the set of combined force deviations. The maximum value of the overall deviation comes from the set in step three; constraint transformation and objective function correction, setting a penalty function. ,in By using the interior point method, the constrained problem is transformed into an unconstrained problem, and the corrected objective function is: The solution range of this function is the feasible region of the needle posture, ensuring that it does not interfere with adjacent teeth and healthy tissues during the optimization process;

[0044] b) Clarify the role of the penalty function. The core function is to impose a significant penalty on tool contact points that exceed attitude constraints, forcing the trowel attitude to fall within the safe and feasible region during the optimization process. This transforms a constrained problem into an unconstrained one, providing a solvable objective function for the multi-objective optimization in step five. At this point, the optimization function for material residue and pre-accuracy is complete, and the corrected objective function and related parameters are... As input data, proceed to step five for multi-objective optimization of pose parameters;

[0045] Step 5: Multi-objective optimization of tooth preparation pose parameters based on the collaborative trajectory planning method of end deformation and material residue:

[0046] The material residual volume collection in step two Step 3: Set of Comprehensive Force Deviations The core optimization object is the modified objective function constructed in step four. Given the attitude constraints, the optimal tool contact point pose parameters are solved using a multi-objective optimization algorithm. The specific process is as follows:

[0047] a) The core execution flow of the optimization algorithm is as follows:

[0048] Initialize the population, set the population size, based on the knife contact point location information from step one. Generate an initial population of individuals, each individual corresponding to a set of knife-point pose parameters. ,in, Based on the local coordinate system of step one The coordinate range is generated. Based on the orthogonal coordinate system corrected in step four Axis generation, setting angle range Ensure the initial pose falls within the safe and feasible region; population evaluation involves substituting the pose parameters of each individual in the population into the corrected objective function from step four to calculate the corresponding fitness value. A smaller fitness value indicates better individual pose parameters; fitness sorting involves ranking the population by fitness value from smallest to largest, selecting the current best individual with the smallest fitness value, and recording its pose parameters and fitness value; during the learning phase, learning operators are executed based on the current best individual to learn the pose parameters of other individuals in the population. The angle is fine-tuned, and then boundary constraints are applied. If the adjusted pose parameters exceed the feasible pose region of step four, i.e. If the parameters are not within the feasible region boundary, then the parameters are corrected to the boundary of the feasible region. In the reflection phase, the reflection operator is executed on the individual after the learning phase to map the individual pose parameters to the neighborhood of the optimal solution of the objective function. If the parameters exceed the preset range... Beyond the boundary of the preparatory body, Exceeding If the value is within the range, it is corrected by symmetric reflection. After correction, the boundary constraints are executed again to ensure that the individual meets the attitude restriction conditions.

[0049] b) Iterative judgment and result output, setting... The current iteration number, initial value , This represents the maximum number of iterations.

[0050] The loop condition logic is as follows:

[0051] like If true, but the maximum number of iterations has not been reached, then let... Return to step 5a) and repeat the population assessment, sorting, learning, and reflection operations to continuously iterate and optimize;

[0052] like If the maximum number of iterations is reached, the iteration stops, and the pose parameters of the individual with the smallest fitness value in the current population are output, along with the optimal pose of all tool contacts. This parameter simultaneously meets the dual-objective optimization requirements of minimizing residual material volume and minimizing end bur deformation, without interfering with adjacent teeth and healthy tissue.

[0053] The beneficial effects of this invention are as follows:

[0054] 1. This invention establishes a material residue model and an end-force deformation model, and sets a multi-objective optimization function. The algorithm can minimize robot end-effector deformation while reducing material residue, thereby significantly improving the geometric accuracy and surface quality of tooth preparation, avoiding overcutting or excessive material residue, and ensuring that the preparation results meet clinical requirements.

[0055] 2. This invention analyzes the linear and angular displacement deformation of the end effector under stress conditions and uses the Jacobian matrix and compliance matrix for real-time compensation. The algorithm enhances the dynamic stability of the robot in complex operations, reduces the pose deviation caused by external forces, and improves the robustness and controllability of the overall system.

[0056] 3. The collaborative trajectory planning method of the present invention uses the combined deviation of residual material volume and end deformation as multi-objective optimization parameters. Through steps such as initializing the population, fitness ranking and iterative learning, it automatically outputs the optimal tool contact pose, thereby reducing manual intervention while ensuring preparation accuracy and improving the automation level and efficiency of the tooth preparation process. Attached Figure Description

[0057] For ease of explanation, the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.

[0058] Figure 1 This is a schematic diagram of the method;

[0059] Figure 2 A schematic diagram showing the different intersection points between the projected outline of the sewing needle and the boundary outline of the pre-trajectory;

[0060] Figure 3 A schematic diagram showing the different intersection points between the projected outline of the sewing needle and the boundary outline of the pre-trajectory;

[0061] Figure 4 Diagram of the experimental setup;

[0062] Figure 5Simulation experiment diagram for optimizing material residual volume;

[0063] Figure 6 Optimize the line graph for residual material volume;

[0064] Figure 7 Scanning results for different pre-existing bodies;

[0065] Figure 8 This is a schematic diagram of the ultra-depth-of-field scanning results;

[0066] Figure 9 Index curves set at different cross-sections of the preparatory body;

[0067] Figure 10 Simulation experimental diagram for material deformation optimization;

[0068] Figure 11 Optimize the line graph for material deformation;

[0069] Figure 12 This is a comparison chart of the preliminary trajectories before and after optimization;

[0070] Figure 13 To prepare for tooth comparison; Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention patent clearer, the invention patent is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of this invention patent. Furthermore, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concepts of this invention patent.

[0072] Example 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 , Figure 13 As shown, this specific embodiment adopts the following technical solution: a method for collaborative trajectory planning of end-effector deformation and material residue of a tooth preparation robot based on pose compensation, the specific implementation process of which is as follows:

[0073] Step 1: Calculation of the intersection parameters of the bur projection profile and the boundary of the preparatory body:

[0074] a) Define the coordinate system and the needle profile, using the robot tool coordinate system. Based on this, the generatrix equation of the needle profile is defined as follows: Its parametric equation is expressed as ,in, The length parameter of the needle generatrix is ​​the length dimension of the effective working section of the needle, and its value range is [value range missing]. , The effective working length of the needle. This is a parameter representing the circumferential rotation angle of the needle, describing the rotation angle of the generatrix around the needle axis. The curvature coefficient of the needle profile generatrix, matching the design specifications of the needle cutting edge; defined Each knife contact point The local tooth coordinate system at that location is With the point of contact of the blade as the origin, the preparatory direction is... coordinate system Positive axis direction The range of values ​​is , This represents the total number of knife contact points;

[0075] b) Calculate the transformed profile, and transform the needle profile equation through a coordinate transformation matrix containing translation and rotation parameters. Transform to knife contact coordinate system at the location The transformed needle profile equation is: ,in, To change the length parameter of the needle profile, compared with the original parameter satisfy The length parameter remains unchanged;

[0076] c) Projection and intersection point finding; defining a preliminary direction vector. Along the local tooth coordinate system of In the positive direction of the axis, establish with Vertical projection plane parallel to coordinate system The plane will be transformed into the needle profile equation. along Direction projection onto the plane The projection needle profile equation is obtained. , eliminate Axis dimensions, only retain coordinates and Relationship;

[0077] Solve for the intersection of the projected profiles of adjacent tool contact points, taking the same plane. Upper adjacent knife contact and The projection outline of the sewing needle and Through equation Solve for the intersection points The coordinates are used to obtain the corresponding intersection point parameters. and ,in, For the first The intersection length parameter of the projected contours of each blade contact point;

[0078] Solve for the intersection of adjacent tool contact points and the boundary of the pre-work body, and set the projected profile of the bur. The intersection with the upper boundary of the tooth is The intersection point with the lower boundary of the preparatory body is Adjacent knife contacts The corresponding boundary intersection point is and Substituting the intersection points into the projection profile equation yields Solve to obtain the intersection parameters , forming a set of intersection points ;

[0079] d) Loop judgment in intersection set calculation:

[0080] Determine all tool contacts The set of intersections Is the calculation complete?

[0081] Specifically:

[0082] like If established, then... Jump to step 1a), repeat the above process to calculate the first... The set of intersection points of each blade contact point ;

[0083] like If the condition is met, it means that the calculation of the intersection set of all tool contact points has been completed. Then, all intersection set sets are sorted into ordered sets according to the tool contact point index. This serves as the basis for subsequent residual volume calculations; proceed to step two.

[0084] Step 2: Determining different residual patterns of the interaction between the bur and the tooth in any posture:

[0085] Based on the result obtained in step one The length parameter of the intersection point of the projected profile of the tool contact point and the upper boundary of the tooth. and the The length parameter of the intersection point of the projected contours of each tool contact point and the adjacent tool contact point By analyzing the size relationship between the two, the residual pattern of the interaction between the bur and the tooth is determined, with a key distinction being whether overcutting occurs and the location of the intersection point, thereby calculating the adjacent tool contact points. and Residual area between and residual volume The specific process is as follows:

[0086] Scenario 1: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect below the upper boundary. The calculation process needs to consider the influence of the overcut area on the residual area. The calculation method is as follows:

[0087]

[0088] Scenario 2: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect at the upper boundary. The calculation process needs to consider the influence of the overcut area on the residual area. The calculation method is the same as in case 1:

[0089]

[0090] Scenario 3: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect on the upper boundary. Considering the influence of the overcut area on the residual area, the residual area... The calculation method is as follows:

[0091]

[0092] in, and For the residual area The two diagonals of the approximate rhombus The angle between the two diagonals is the value; similarly, the residual area of ​​the material when there is no over-cut area can be calculated. By calculating adjacent tool contacts and The straight-line distance between them, combined with the residual area mentioned above, is calculated using the formula... Calculate the residual volume of the material, where, The distance projection of the two intersection points onto the preparatory direction, and the distance projection onto the preparatory direction vector from step one. In the same direction; finally, collect all adjacent tool contact pairs that can form residual volumes to obtain the set of material residual volumes. The total number of residual volumes that can be formed by adjacent knife contacts is , This represents the total number of contact points in step one;

[0093] Residual volume calculation loop judgment:

[0094] Determine the residual volume between any two adjacent tool contacts. Is the calculation complete?

[0095] Specifically:

[0096] like If true, meaning not all adjacent tool contact pairs of the target have been calculated, then let Return to step two a) and continue calculating the first step. and Residual volume of adjacent knife contacts ;

[0097] like Once the residual volume calculation for all adjacent tool contact pairs of the target is completed, the residual volumes will be set together. Organize the serial numbers of adjacent tool contacts into ordered data, which will be used as input for subsequent end deformation calculation and optimization. Proceed to step three.

[0098] Step 3: Expression of the comprehensive deviation of the end effector under stress and deformation:

[0099] Based on the material residual volume set obtained in step two Combining the force characteristics of the end effector of the tooth preparation robot with the deformation law of the system, the comprehensive force deviation at each tool contact point is solved through modeling, matrix calculation and deviation synthesis. The specific process is as follows:

[0100] a) End-effector deformation modeling: During tooth preparation, the bur is subjected to linear force and torque, causing overall deformation of the series system. The core force relationship is expressed as follows: ,in, The linear force acting on the robot's end effector, oriented by a unit vector. The decision is made in the opposite direction to the prepared direction, and its magnitude is... , For torsional moment, This refers to the lever arm, which is the distance from the point of application of the needle to the axis. linear force With lever arm The included angle is determined by the cutting posture of the bur; considering the preparatory parameters and the material removal performance of the actual bur used, the force calculation for the bur during its advance is as follows: ,in, The diameter of the needle. It is a material constant that matches the tooth material, bur geometry, and preparation conditions. The material removal rate is determined by the residual volume in step two. The volume of material removed can be calculated. , , The speed at which the needle travels forward;

[0101] b) Calculation of Jacobian matrix, compliance matrix, and deformation, given the terminal velocity and Jacobian matrix. The relationship between them is Calculate the Jacobian matrix of the robot in the current pose. ,in, The terminal linear velocity, Let be the joint angular velocity; the formula for the Jacobian matrix under any tool contact posture is: ,in, The coordinates of the end position, For joint angle parameters; calculate system flexibility and deformation based on the Jacobian matrix. Calculate the system compliance under arbitrary attitudes ,in The stiffness coefficient matrix in the robot's Cartesian coordinate system is determined by the robot's body parameters; the compliance matrix... Divided into four Submatrix, through the relationship between robot deformation and forces. Calculate the deformation, where, Indicates linear displacement deformation. Indicates angular displacement deformation. The force-to-linear-displacement compliance matrix is ​​related to the linear stiffness of the tooth preparation robot system. The coupling compliance submatrix describes the coupling relationship between force and angular displacement, and torque and linear displacement. The torque-angular displacement compliance matrix is ​​related to the torsional stiffness of the system; considering the combined deformation of the robot's end effector caused by linear force and torque, the linear displacement deformation is derived. and angular displacement deformation The formula is expressed as Combined with the force expression of the needle during its forward movement The linear displacement deformation of the end effector needle of the robot can be derived. and angular displacement deformation The formula is expressed as ;

[0102] c) Overall stress deviation, based on the linear displacement deformation of the needle. and angular displacement deformation Solve the first... Each knife contact point The overall force deviation at the point is ,in, Let be the relative position vector between the needle and the robot end effector, defined in the robot tool coordinate system, and remain unchanged during preparation. yes Calculate the relative position vector from the antisymmetric matrix. , and The three-dimensional components of the position vector of the constructed tooth preparation robot system are used to collect the combined force deviations of all tool contacts, forming a set. ;

[0103] d) Comprehensive deviation calculation and iterative judgment:

[0104] Determine whether the overall force deviation at all tool contact points has been calculated.

[0105] Specifically:

[0106] like This is not valid; not all tool contact points have been calculated. Therefore, let... Return to step 3b) and continue calculating the... Overall force deviation at each tool contact point ;

[0107] like Once the calculation of all tool contact point deviations is completed, the deviation set will be... Sort the input data in ascending order by the tool contact number to form an ordered input data, then proceed to step four.

[0108] Step 4: Establishing the optimization function for material residue and pre-accuracy:

[0109] Based on the material residual volume set obtained in step two and the set of combined force deviations obtained in step three To address the conflicting optimization approaches, a comprehensive constraint optimization function is established, clearly defining attitude restrictions and penalty mechanisms. The specific process is as follows:

[0110] a) Establishing a dual-objective model and solving the attitude matrix: The residual material volume and the end-effector force are negatively correlated; the larger the residual volume, the smaller the removed volume and the smaller the end-effector force. The optimization objective is to obtain a smaller end-effector deformation while minimizing the residual material. This requires comprehensive constraints on both objectives. Input the tool contact point position information determined in step one. Including coordinates and initial pose parameters, a local coordinate system is constructed based on this information, maintaining consistency with step one. The coordinate system reference is consistent, and the supplementary axis directions are defined to satisfy orthogonality. The origin is consistent with the local tooth coordinate system in step one. Consistency, i.e., knife contact point , The positive direction of the axis is aligned with the direction in step one as the preparatory direction. The axis is the direction of needle travel, and... The axis is perpendicular. The axis is determined by the right-hand rule. shaft and The cross product of the axes is obtained All knife contacts The pose matrix at each location is integrated into a set. , of which The formula for the pose matrix of each blade contact point is defined as follows: To prevent excessive deviation from the correct posture and interference with adjacent teeth and healthy tissue, axial constraints on the bur are set. The threshold is represented by the constraint formula defined as follows: ,in, The direction of the needle axis. The direction of the normal to the tool contact point. The cosine of the angle between the bur and the normal of the current tool contact point. Set a preset threshold; set a preliminary accuracy error index. The objective function is ,in, Weighting factors for residual material volume and overall stress deviation. The normalization coefficient is... The 2-norm of the set of residual volumes of materials. The maximum residual volume comes from the set in step two. The 2-norm of the set of combined force deviations. The maximum value of the overall deviation comes from the set in step three; constraint transformation and objective function correction, setting a penalty function. ,in By using the interior point method, the constrained problem is transformed into an unconstrained problem, and the corrected objective function is: The solution range of this function is the feasible region of the needle posture, ensuring that it does not interfere with adjacent teeth and healthy tissues during the optimization process;

[0111] b) Clarify the role of the penalty function. The core function is to impose a significant penalty on tool contact points that exceed attitude constraints, forcing the trowel attitude to fall within the safe and feasible region during the optimization process. This transforms a constrained problem into an unconstrained one, providing a solvable objective function for the multi-objective optimization in step five. At this point, the optimization function for material residue and pre-accuracy is complete, and the corrected objective function and related parameters are... As input data, proceed to step five for multi-objective optimization of pose parameters;

[0112] Step 5: Multi-objective optimization of tooth preparation pose parameters based on the collaborative trajectory planning method of end deformation and material residue:

[0113] The material residual volume collection in step two Step 3: Set of Comprehensive Force Deviations The core optimization object is the modified objective function constructed in step four. Given the attitude constraints, the optimal tool contact point pose parameters are solved using a multi-objective optimization algorithm. The specific process is as follows:

[0114] a) The core execution flow of the optimization algorithm is as follows:

[0115] Initialize the population, set the population size, based on the knife contact point location information from step one. Generate an initial population of individuals, each individual corresponding to a set of knife-point pose parameters. ,in, Based on the local coordinate system of step one The coordinate range is generated. Based on the orthogonal coordinate system corrected in step four Axis generation, setting angle range Ensure the initial pose falls within the safe and feasible region; population evaluation involves substituting the pose parameters of each individual in the population into the corrected objective function from step four to calculate the corresponding fitness value. A smaller fitness value indicates better individual pose parameters; fitness sorting involves ranking the population by fitness value from smallest to largest, selecting the current best individual with the smallest fitness value, and recording its pose parameters and fitness value; during the learning phase, learning operators are executed based on the current best individual to learn the pose parameters of other individuals in the population. The angle is fine-tuned, and then boundary constraints are applied. If the adjusted pose parameters exceed the feasible pose region of step four, i.e. If the parameters are not within the feasible region boundary, then the parameters are corrected to the boundary of the feasible region. In the reflection phase, the reflection operator is executed on the individual after the learning phase to map the individual pose parameters to the neighborhood of the optimal solution of the objective function. If the parameters exceed the preset range... Beyond the boundary of the preparatory body, Exceeding If the value is within the range, it is corrected by symmetric reflection. After correction, the boundary constraints are executed again to ensure that the individual meets the attitude restriction conditions.

[0116] b) Iterative judgment and result output, setting... The current iteration number, initial value , This represents the maximum number of iterations.

[0117] The loop condition logic is as follows:

[0118] like If true, but the maximum number of iterations has not been reached, then let... Return to step 5a) and repeat the population assessment, sorting, learning, and reflection operations to continuously iterate and optimize;

[0119] like If the maximum number of iterations is reached, the iteration stops, and the pose parameters of the individual with the smallest fitness value in the current population are output, along with the optimal pose of all tool contacts. This parameter simultaneously meets the dual-objective optimization requirements of minimizing residual material volume and minimizing end bur deformation, without interfering with adjacent teeth and healthy tissue.

[0120] Example 2: This example focuses on tooth preparation for a posterior porcelain crown restoration. It employs 21 machining paths, each containing 21 tool contacts, totaling... Each blade contact point The range of values ​​is The core preset parameters are as follows: effective working length of the needle. Length parameter Range of values curvature coefficient needle diameter Dental material constants needle forward speed Preparation time Material residual factors and normalization coefficient ,satisfy Attitude limiting threshold Population size Maximum number of iterations First, perform step one: calculate the intersection parameters of the projected profile of the sewing needle and the boundary of the preparatory body. a) Define the coordinate system and the sewing needle profile, with the generatrix equation as follows: , Range of values b) Through coordinate transformation matrix Preset translation amount Rotation angle Transform the needle profile to each coordinate system, to obtain c) Define the preparatory direction vector Projection plane Parallel to coordinate system Plane, after projection Solve for the intersection of the projected profiles of adjacent tool contact points. , with the first Taking a single tool contact point as an example, calculate the intersection parameters. Boundary intersection , Corresponding parameters , This forms the corresponding set of intersection points. d) According to the loop judgment logic, when At this point, the set of all intersection points of the tool contacts has been calculated and organized into an ordered set. Proceed to step two to determine the different residual patterns of the bur interacting with the tooth in any orientation, based on the first... Taking a single blade contact point as an example, because At this point, the projection profile equations of the two needles at adjacent tool contacts intersect below the upper boundary. Considering the influence of the overcut area on the residual area, the residual area... The calculation method is as follows: Calculate the residual area The residual area of ​​a single group of adjacent knife contacts was calculated. The straight-line distance between adjacent knife contacts is Residual volume according to formula ,in ,have to Adjacent knife contact pairs that can form residual volume Residual volume set ,average value maximum value Loop judgment, when hour, Established, proceed to step three, calculate the comprehensive deviation of the end effector's stress deformation, a) material removal rate Find ,Depend on , Torsional torque is b) Calculate the matrix and its transformations, with the first... Taking a single blade contact point as an example, solve for the Jacobian matrix. System stiffness coefficient matrix Take diagonal elements Flexibility matrix After splitting, we get , , Substituting into the transformed formula, we get c) Combined bias, antisymmetric matrix According to the formula ,have to d) Perform a loop check, when At that time, all tool contact point deviations have been calculated, and the deviation set is complete. maximum value Proceed to step four, establish the material residue and pre-accuracy optimization function, a) pose matrix and constraint settings, construct the local coordinate system, pose matrix Constraint formula Ensure the angle between the normal of the needle and the tool contact point. ,Depend on The corrected objective function is ,in, Calculate the penalty function Verified The tool contacts satisfy the constraints, with only 8 tool contacts. Taking the third over-constraint tool contact as an example, its penalty function The remaining knife contact points b) Apply a maximum penalty to over-constrained tool contacts, forcing them to correct their posture during optimization, and then proceed to step five. For non-over-constrained tool contacts, the penalty is ineffective, and the process proceeds to step five to perform multi-objective optimization of tooth preparation pose parameters. a) Optimization execution: Initialize the population. Range of values Substitute the values ​​into the objective function to calculate the fitness value, and fine-tune the step size during the learning phase. The attitude parameters of the over-constrained tool contact are corrected first, and those exceeding the range will be corrected during the reflection phase. Angle, the largest is Corrected to within; b) Iterative judgment, when When the iteration stops, the fitness is selected. The optimal individual with the smallest value is output as the optimal pose of all tool contacts. Among them, the over-constraint tool contact was optimized. , The mean is Maximum residual volume after optimization Compared to before optimization, it has reduced To meet clinical residual volume requirements Requirements, end deformation, maximum comprehensive deviation Compared to before optimization, it has reduced Suitable for tooth preparation The accuracy standards and attitude constraints are met by all tool contacts. There was no interference from adjacent teeth or gingival tissue, and the prepared tooth morphology fit the restoration well. In summary, this embodiment... Under the specified parameter settings, the algorithm described in the claims achieved a balanced optimization of material residue and end deformation, verifying the feasibility and clinical applicability of the algorithm in a dual-objective weight balance scenario.

Claims

1. A method for collaborative trajectory planning of end-effector deformation and material residue in a tooth preparation robot based on pose compensation, characterized in that: The specific implementation process of the method is as follows: Step 1: Calculation of the intersection parameters of the bur projection profile and the boundary of the preparatory body: a) Define the coordinate system and the needle profile, using the robot tool coordinate system. Based on this, the generatrix equation of the needle profile is defined as follows: Its parametric equation is expressed as ,in, The length parameter of the needle generatrix is ​​the length dimension of the effective working section of the needle, and its value range is [value range missing]. , The effective working length of the needle. This is a parameter representing the circumferential rotation angle of the needle, describing the rotation angle of the generatrix around the needle axis. The curvature coefficient of the needle profile generatrix, matching the design specifications of the needle cutting edge; defined Each knife contact point The local tooth coordinate system at that location is With the point of contact of the blade as the origin, the preparatory direction is... coordinate system Positive axis direction The range of values ​​is , This represents the total number of knife contact points; b) Calculate the transformed profile, and transform the needle profile equation through a coordinate transformation matrix containing translation and rotation parameters. Transform to knife contact coordinate system at the location The transformed needle profile equation is: ,in, To change the length parameter of the needle profile, compared with the original parameter satisfy The length parameter remains unchanged; c) Projection and intersection point finding; defining a preliminary direction vector. Along the local tooth coordinate system of In the positive direction of the axis, establish with Vertical projection plane parallel to coordinate system The plane will be transformed into the needle profile equation. along Direction projection onto the plane The projection needle profile equation is obtained. , eliminate Axis dimensions, only retain coordinates and Relationship; Solve for the intersection of the projected profiles of adjacent tool contact points, taking the same plane. Upper adjacent knife contact and The projection outline of the sewing needle and Through equation Solve for the intersection points The coordinates are used to obtain the corresponding intersection point parameters. and ,in, For the first The intersection length parameter of the projected contours of each blade contact point; Solve for the intersection of adjacent tool contact points and the boundary of the pre-work body, and set the projected profile of the bur. The intersection with the upper boundary of the tooth is The intersection point with the lower boundary of the preparatory body is Adjacent knife contacts The corresponding boundary intersection point is and Substituting the intersection points into the projection profile equation yields Solve to obtain the intersection parameters , forming a set of intersection points ; d) Loop judgment in intersection set calculation: Determine all tool contacts The set of intersections Is the calculation complete? Specifically: like If established, then... Jump to step 1a), repeat the above process to calculate the first... The set of intersection points of each blade contact point ; like If the condition is met, it means that the calculation of the intersection set of all tool contact points has been completed. Then, all intersection set sets are sorted into ordered sets according to the tool contact point index. This serves as the basis for subsequent residual volume calculations; proceed to step two. Step 2: Determining different residual patterns of the interaction between the bur and the tooth in any posture: Based on the result obtained in step one The length parameter of the intersection point of the projected profile of the tool contact point and the upper boundary of the tooth. and the The length parameter of the intersection point of the projected contours of each tool contact point and the adjacent tool contact point By analyzing the size relationship between the two, the residual pattern of the interaction between the bur and the tooth is determined, with a key distinction being whether overcutting occurs and the location of the intersection point, thereby calculating the adjacent tool contact points. and Residual area between and residual volume The specific process is as follows: Scenario 1: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect below the upper boundary. The calculation process needs to consider the influence of the overcut area on the residual area. The calculation method is as follows: Scenario 2: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect at the upper boundary. The calculation process needs to consider the influence of the overcut area on the residual area. The calculation method is the same as in case 1: Scenario 3: When At this point, the projection profile equations of the two needles at adjacent tool contacts intersect on the upper boundary. Considering the influence of the overcut area on the residual area, the residual area... The calculation method is as follows: in, and For the residual area The two diagonals of the approximate rhombus The angle between the two diagonals is the value; similarly, the residual area of ​​the material when there is no overcutting area can be calculated. By calculating adjacent tool contacts and The straight-line distance between them, combined with the residual area mentioned above, is calculated using the formula... Calculate the residual volume of the material, where, The distance projection of the two intersection points onto the preparatory direction, and the distance projection onto the preparatory direction vector from step one. In the same direction; finally, collect all adjacent tool contact pairs that can form residual volumes to obtain the set of material residual volumes. The total number of residual volumes that can be formed by adjacent knife contacts is , This represents the total number of contact points in step one; Residual volume calculation loop judgment: Determine the residual volume between any two adjacent tool contacts. Is the calculation complete? Specifically: like If true, meaning not all adjacent tool contact pairs of the target have been calculated, then let Return to step two a) and continue calculating the first step. and Residual volume of adjacent knife contacts ; like Once the residual volume calculation for all adjacent tool contact pairs of the target is completed, the residual volumes will be set together. Organize the serial numbers of adjacent tool contacts into ordered data, which will be used as input for subsequent end deformation calculation and optimization. Proceed to step three. Step 3: Expression of the comprehensive deviation of the end effector under stress and deformation: Based on the material residual volume set obtained in step two Combining the force characteristics of the end effector of the tooth preparation robot with the deformation law of the system, the comprehensive force deviation at each tool contact point is solved through modeling, matrix calculation and deviation synthesis. The specific process is as follows: a) End-effector deformation modeling: During tooth preparation, the bur is subjected to linear force and torque, causing overall deformation of the series system. The core force relationship is expressed as follows: ,in, The linear force acting on the robot's end effector, oriented by a unit vector. The decision is made in the opposite direction to the prepared direction, and its magnitude is... , For torsional moment, This refers to the lever arm, which is the distance from the point of application of the needle to the axis. linear force With lever arm The included angle is determined by the cutting posture of the bur; considering the preparatory parameters and the material removal performance of the actual bur used, the force calculation for the bur during its advance is as follows: ,in, The diameter of the needle. It is a material constant that matches the tooth material, bur geometry, and preparation conditions. The material removal rate is determined by the residual volume in step two. The volume of material removed can be calculated. , , The speed at which the needle travels forward; b) Calculation of Jacobian matrix, compliance matrix, and deformation, given the terminal velocity and Jacobian matrix. The relationship between them is Calculate the Jacobian matrix of the robot in the current pose. ,in The terminal linear velocity, Let be the joint angular velocity; the formula for the Jacobian matrix under any tool contact posture is: ,in, The coordinates of the end position, For joint angle parameters; calculate system flexibility and deformation based on the Jacobian matrix. Calculate the system compliance under arbitrary attitudes ,in The stiffness coefficient matrix in the robot's Cartesian coordinate system is determined by the robot's body parameters; the compliance matrix... Divided into four Submatrix, through the relationship between robot deformation and forces. Calculate the deformation, where, Indicates linear displacement deformation. Indicates angular displacement deformation. The force-to-linear-displacement compliance matrix is ​​related to the linear stiffness of the tooth preparation robot system. The coupling compliance submatrix describes the coupling relationship between force and angular displacement, and torque and linear displacement. The torque-angular displacement compliance matrix is ​​related to the torsional stiffness of the system; considering the combined deformation of the robot's end effector caused by linear force and torque, the linear displacement deformation is derived. and angular displacement deformation The formula is expressed as Combined with the force expression of the needle during its forward movement The linear displacement deformation of the end effector needle of the robot can be derived. and angular displacement deformation The formula is expressed as ; c) Overall stress deviation, based on the linear displacement deformation of the needle. and angular displacement deformation Solve the first... Each knife contact point The overall force deviation at the point is ,in, Let be the relative position vector between the needle and the robot end effector, defined in the robot tool coordinate system, and remain unchanged during preparation. yes Calculate the relative position vector from the antisymmetric matrix. , and The three-dimensional components of the position vector of the constructed tooth preparation robot system are used to collect the combined force deviations of all tool contacts, forming a set. ; d) Comprehensive deviation calculation and iterative judgment: Determine whether the overall force deviation at all tool contact points has been calculated. Specifically: like This is not valid; not all tool contact points have been calculated. Therefore, let... Return to step 3b) and continue calculating the... Overall force deviation at each tool contact point ; like Once the calculation of all tool contact point deviations is completed, the deviation set will be... Sort the input data in ascending order by the tool contact number to form an ordered input data, then proceed to step four. Step 4: Establishing the optimization function for material residue and pre-accuracy: Based on the material residual volume set obtained in step two and the set of combined force deviations obtained in step three To address the conflicting optimization approaches, a comprehensive constraint optimization function is established, clearly defining attitude restrictions and penalty mechanisms. The specific process is as follows: a) Establishing a dual-objective model and solving the attitude matrix: The residual material volume and the end-effector force are negatively correlated; the larger the residual volume, the smaller the removed volume and the smaller the end-effector force. The optimization objective is to obtain a smaller end-effector deformation while minimizing the residual material. This requires comprehensive constraints on both objectives. Input the tool contact point position information determined in step one. Including coordinates and initial pose parameters, a local coordinate system is constructed based on this information, maintaining consistency with step one. The coordinate system reference is consistent, and the supplementary axis directions are defined to satisfy orthogonality. The origin is consistent with the local tooth coordinate system in step one. Consistency, i.e., knife contact point , The positive direction of the axis is aligned with the direction in step one as the preparatory direction. The axis is the direction of needle travel, and... The axis is perpendicular. The axis is determined by the right-hand rule. shaft and The cross product of the axes is obtained All knife contacts The pose matrix at each location is integrated into a set. , of which The formula for the pose matrix of each blade contact point is defined as follows: To prevent excessive deviation from the correct posture and interference with adjacent teeth and healthy tissue, axial constraints on the bur are set. The threshold is represented by the constraint formula defined as follows: ,in, The direction of the needle axis. The direction of the normal to the tool contact point. The cosine of the angle between the bur and the normal of the current tool contact point. Set a preset threshold; set a preliminary accuracy error index. The objective function is ,in, Weighting factors for residual material volume and overall stress deviation. The normalization coefficient is... The 2-norm of the set of residual volumes of materials. The maximum residual volume comes from the set in step two. The 2-norm of the set of combined force deviations. The maximum value of the overall deviation comes from the set in step three; constraint transformation and objective function correction, setting a penalty function. ,in By using the interior point method, the constrained problem is transformed into an unconstrained problem, and the corrected objective function is: The solution range of this function is the feasible region of the needle posture, ensuring that it does not interfere with adjacent teeth and healthy tissues during the optimization process; b) Clarify the role of the penalty function. The core function is to impose a significant penalty on tool contact points that exceed attitude constraints, forcing the trowel attitude to fall within the safe and feasible region during the optimization process. This transforms a constrained problem into an unconstrained one, providing a solvable objective function for the multi-objective optimization in step five. At this point, the optimization function for material residue and pre-accuracy is complete, and the corrected objective function and related parameters are... As input data, proceed to step five for multi-objective optimization of pose parameters; Step 5: Multi-objective optimization of tooth preparation pose parameters based on a collaborative optimization algorithm for end deformation and material residue: The material residual volume collection in step two Step 3: Comprehensive set of force deviations The core optimization object is the modified objective function constructed in step four. Given the attitude constraints, the optimal tool contact point pose parameters are solved using a multi-objective optimization algorithm. The specific process is as follows: a) The core execution flow of the optimization algorithm is as follows: Initialize the population, set the population size, based on the knife contact point location information from step one. Generate an initial population of individuals, each individual corresponding to a set of knife-point pose parameters. ,in, Based on the local coordinate system of step one The coordinate range is generated. Based on the orthogonal coordinate system corrected in step four Axis generation, setting angle range Ensure the initial pose falls within the safe and feasible region; population evaluation involves substituting the pose parameters of each individual in the population into the corrected objective function from step four to calculate the corresponding fitness value. A smaller fitness value indicates better individual pose parameters; fitness sorting involves ranking the population by fitness value from smallest to largest, selecting the current best individual with the smallest fitness value, and recording its pose parameters and fitness value; during the learning phase, learning operators are executed based on the current best individual to learn the pose parameters of other individuals in the population. The angle is fine-tuned, and then boundary constraints are applied. If the adjusted pose parameters exceed the feasible pose region of step four, i.e. If the parameters are not within the feasible region boundary, then the parameters are corrected to the boundary of the feasible region. In the reflection phase, the reflection operator is executed on the individual after the learning phase to map the individual pose parameters to the neighborhood of the optimal solution of the objective function. If the parameters exceed the preset range... Beyond the boundary of the preparatory body, Exceeding If the value is within the range, it is corrected by symmetric reflection. After correction, the boundary constraints are executed again to ensure that the individual meets the attitude restriction conditions. b) Iterative judgment and result output, setting... The current iteration number, initial value , This represents the maximum number of iterations. The loop condition logic is as follows: like If true, but the maximum number of iterations has not been reached, then let... Return to step 5a) and repeat the population assessment, sorting, learning, and reflection operations to continuously iterate and optimize; like If the maximum number of iterations is reached, the iteration stops, and the pose parameters of the individual with the smallest fitness value in the current population are output, along with the optimal pose of all tool contacts. This parameter simultaneously meets the dual-objective optimization requirements of minimizing residual material volume and minimizing end bur deformation, without interfering with adjacent teeth and healthy tissue.

Images