A tooth preparation robot trajectory compensation method based on extrusion force prediction and curvature optimization

Abstract

The present application relates to a kind of tooth preparation robot trajectory compensation method based on extrusion force prediction and curvature optimization;The method first imports tooth preparation theoretical trajectory data and carries out smoothing processing, generates smooth theoretical preparation trajectory curve;Then calculate tool contact point curvature and tool contact point distance information, and establish nonlinear extrusion force prediction model, predict each tool contact point extrusion force;Through extrusion force extreme risk point determination, identify the risk point exceeding set threshold and classify;Determine the continuous risk point, identify the continuous high-risk curve;Implement the hierarchical compensation of high-risk curve and high-risk point, respectively using local compensation speed and continuous compensation speed strategy;Finally, tool contact point curvature mutation area additional optimization is carried out, through curvature adjacent difference calculation and nonlinear time compensation mechanism, additional residence time is introduced in curvature mutation area.The present application realizes the geometric and mechanical collaborative optimization of trajectory, effectively suppresses extrusion force peak, improves profile accuracy and surface quality, and gives consideration to machining efficiency and clinical safety.

Description

Technical Field

[0001] This invention patent relates to the field of medical robot and intelligent processing control technology, specifically to a method and implementation system for trajectory compensation of a tooth preparation robot based on extrusion force prediction and curvature optimization. Background Technology

[0002] Existing dental preparation robots mostly execute theoretical trajectories generated by CAD / CAM systems directly, but this presents several problems in actual machining. First, the combined stiffness and compliance of the robot body, end effector, and workpiece can cause pose errors and stress fluctuations, which current trajectory planning often fails to consider. Second, abrupt changes in the geometric curvature and normal of different tooth parts can lead to a local amplification effect of cutting loads, but existing methods are insufficient in handling this effect. Third, fixed or coarse-grained deceleration strategies can easily cause peak extrusion pressure, chatter, and damage in weak tissues or steep curvature areas, while also reducing overall machining efficiency.

[0003] Current commonly used global speed reduction or simple threshold speed regulation strategies struggle to address both isolated high-risk points and continuous high-risk segments, and lack precise time-domain compensation for curvature abrupt change regions. This makes it difficult to simultaneously meet requirements for forming accuracy, surface quality, and safety margin. Therefore, a new trajectory optimization method is urgently needed. This method should integrate geometric and mechanical mechanisms, enabling hierarchical compensation while balancing processing efficiency and forming quality. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a trajectory compensation method for a tooth preparation robot based on extrusion force prediction and curvature optimization. This method enables differentiated feed compensation for isolated high-risk points and continuous high-risk segments, and introduces nonlinear time compensation in curvature abrupt change regions. This suppresses peak extrusion force, improves contour accuracy and surface quality, while simultaneously ensuring processing efficiency and clinical safety.

[0005] A method for trajectory compensation of a tooth preparation robot based on extrusion force prediction and curvature optimization, characterized in that: the specific implementation process of the method is as follows:

[0006] Step 1: Import theoretical trajectory data for tooth preparation:

[0007] Input theoretical preliminary trajectory curve Set of coordinate values ​​of each tool contact point in the base coordinate system , The coordinates of the k-th tool contact point in the base coordinate system are used to prepare the theoretical trajectory; where, To prepare the theoretical trajectory, the x-axis coordinates of the k-th tool contact point in the base coordinate system are... To prepare the theoretical trajectory, the y-axis coordinates of the k-th tool contact point in the base coordinate system are... Preparing the theoretical trajectory The coordinates of each tool contact point in the base coordinate system Axis coordinates;

[0008] Step 2: Smooth the theoretical trajectory:

[0009] Define the element trajectory, which is the theoretical trajectory between two adjacent tool contact points, denoted by the symbol []. ] indicates that, according to the formula and formula For unit trajectories [ Interpolation is performed on the two endpoints of the [], where and For the weighting coefficients related to the interpolation density, calculate the new [ ]insert[ Preliminary smoothing theory-based trajectory curves are formed. ;

[0010] Determine if all tool contact interpolation is complete.

[0011] Specifically:

[0012] like If not, then Proceed to step two;

[0013] like If successful, proceed to step three;

[0014] Step 3: Calculate the curvature and distance information of the tool contact point.

[0015] Define the curvature of the knife contact point using the symbol The formula for calculating the curvature of the tool contact point is as follows: Define the tool contact distance as the straight-line distance between two adjacent tool contacts, denoted by the symbol... If we express this as follows, then the distance between the k-th and (k+1)-th knife contact points is expressed as: ;

[0016] Step 4: Establish a nonlinear extrusion pressure prediction model:

[0017] Define the cutting edge pressure as the pressure exerted on the tip of the needle when the needle moves from the k-th cutting edge to the (k+1)-th cutting edge. Let the symbol be the cutting edge pressure exerted on the needle when it moves from the k-th cutting edge to the (k+1)-th cutting edge. The pressure exerted at the knife contact point is expressed as: ;in, Let the system stiffness of the robotic arm be defined in the base coordinate system. The straight-line distance between the k-th and (k+1)-th knife contact points. For the set feed rate, For exercise time, For the area to be removed from the material, Material removal rate;

[0018] Step 5: Determining the extreme risk point of extrusion pressure:

[0019] Define the maximum compressive force F at the knife contact point max It is the threshold of compressive force that the tooth can withstand; set the risk point set U of the compressive force at the knife contact point; calculate the first... The extrusion force of each blade contact point;

[0020] a) Determine whether the compressive force between all tool contacts has been calculated.

[0021] Specifically:

[0022] like If not, then Proceed to step five;

[0023] like If successful, proceed to step six a);

[0024] b) Determine the pressure at the tool contact point Greater than the maximum compressive force F at the knife contact point max Whether it is valid,

[0025] Specifically:

[0026] like If this is not the case, then the knife contact point is the safe point for knife contact pressure, and proceed to step five (b).

[0027] like If it is established, then the knife contact point is a knife contact pressure risk point. Put the kth knife contact point into the knife contact pressure risk point set U, and jump to step five (b).

[0028] c) Determine whether the extrusion pressure at the n tool contact points of the prepared trajectory has been evaluated.

[0029] judge Whether it is valid,

[0030] Specifically:

[0031] like The establishment of this rule indicates that not all potential risks related to pressure at the tool contact points have been fully assessed. Proceed to step five (b);

[0032] like If the condition is not met, then the assessment of all knife contact point pressure risk points is complete, and proceed to step six;

[0033] Step Six: Determining the High-Risk Curve:

[0034] a) If there are risk points in U If the continuous extrusion pressure risk points are considered as continuous tool contact points, then the continuous line segment formed by these continuous extrusion pressure risk points constitutes a high-risk curve. ;calculate and The length of the high-risk curve between them is expressed as: Set the set of curves to be compensated. ,in Let t be the curve to be compensated; set a threshold for the length of high-risk curves. Determine the length of the high-risk curve. Less than the high-risk curve length threshold Is it valid?

[0035] Specifically:

[0036] like If so, the high-risk point curve does not require compensation, and proceed to step six (b).

[0037] like If the high-risk curve needs compensation, then the high-risk curve should be added to the set of curves to be compensated. Proceed to step six (b);

[0038] b) Determine whether all high-risk curves have been assessed.

[0039] judge Whether it is valid,

[0040] Specifically:

[0041] like The establishment of this statement indicates that not all high-risk curves have been fully assessed, thus... Proceed to step six a);

[0042] like If the condition is not met, then all high-risk curve assessments are complete, and proceed to step seven.

[0043] Step 7: Tiered compensation for high-risk curves and high-risk points:

[0044] Define local compensation speed as the speed after compensating for isolated high-risk tool contacts, denoted by the symbol. The local compensation velocity is expressed as: ,in The compensation coefficient is defined as follows: The continuous compensation rate is defined as the rate at which the high-risk curve is compensated, denoted by the symbol... The continuous compensation speed is expressed as: The average knife contact pressure is defined as follows: ,in, This is the adjustment coefficient;

[0045] a) Determine the trajectory compensation method.

[0046] Specifically:

[0047] If the knife contact point k belongs to set U but not set C, then perform local velocity compensation and jump to step seven (b).

[0048] If the knife contact point k belongs to both set U and set C, then perform continuous velocity compensation and jump to step seven (b).

[0049] b) Determine whether the compensation method has been determined.

[0050] judge Whether it is valid,

[0051] Specifically:

[0052] like If the condition is met, it means that the knife contact point has not been fully evaluated. Therefore, let k = k + 1 and jump to step six (a).

[0053] like If not, then all tool contact point evaluations are complete, proceed to step eight;

[0054] Step 8: Additional optimization of the curvature abrupt change region at the knife contact point:

[0055] Define curvature adjacency as the absolute value of the difference between the curvatures of adjacent elements, denoted by the symbol... The adjacency difference of the k-th curvature is expressed as: Define curvature dwell time, which is the additional dwell time at the tool contact point for abrupt curvature changes, denoted by the symbol [symbol missing]. The curvature dwell time is expressed as: ,in, For time-compensated intensity, The average curvature of the entire trajectory, It is a non-linear adjustment index. These are the upper and lower thresholds for the additional stay time, respectively.

[0056] a) Determine the adjacent difference of curvature Is it greater than the adjacent difference of the maximum curvature? Further optimizations will be performed.

[0057] Specifically:

[0058] If the curvature is adjacent difference Greater than the adjacent difference of the maximum curvature If true, the curve is in a region of sudden curvature change, and we proceed to step eight (b).

[0059] If the curvature is adjacent difference Greater than the adjacent difference of the maximum curvature If this is not true, then the curve is a normal curve, and we will proceed to step eight (b).

[0060] b) Determine whether the curvature abrupt change curve has been further optimized;

[0061] judge Whether it is valid,

[0062] Specifically:

[0063] like If this holds true, it means that the curvature of all curves has not yet been evaluated, so let... Jump to 8a);

[0064] like If this condition is not met, then all curvature evaluations are complete.

[0065] The beneficial effects of this invention are as follows:

[0066] 1. This invention proposes differentiated compensation strategies for isolated high-risk points and continuous high-risk segments. For isolated high-risk points, local feed rate compensation is used to quickly reduce the instantaneous load; for continuous high-risk segments, full-segment speed compensation is implemented, and an adjustment coefficient based on average extrusion pressure is introduced to achieve smooth load reduction. This hierarchical compensation mechanism avoids the efficiency loss caused by global speed reduction and can accurately address the mechanical challenges of different risk types. Simultaneously, through extrusion pressure prediction models and threshold judgments, the system can identify risks in advance and intervene, significantly suppressing peak extrusion pressure and mechanical vibration during the cutting process. This enhances the operational stability and reliability of the robot system under variable loads, ensuring the safety and controllability of the surgical procedure.

[0067] 2. This invention endows the system with intelligent response capabilities to geometrical abrupt changes through curvature adjacency difference calculation and nonlinear time compensation. In areas with drastic curvature changes, the dwell time is increased to ensure that the bur cuts sufficiently without overload. Combined with speed compensation at pressure risk points, this method can effectively handle local high-risk conditions without significantly reducing the overall feed rate, achieving a balance between processing efficiency and clinical safety. This characteristic makes this invention particularly suitable for the restoration of posterior teeth with complex morphology and delicate structure, expanding the clinical application scope of robots in full dentition preparation.

[0068] 3. This invention constructs a complete mathematical model for predicting extrusion force, encompassing multiple factors such as robot system stiffness, motion parameters, and material removal characteristics, achieving feedforward prediction of cutting force. By setting explicit extrusion force thresholds, curvature adjacency thresholds, and continuous segment length thresholds, a quantitative risk assessment and compensation triggering standard is established. Furthermore, the coefficients in the compensation strategy can be adjusted according to the actual system and working conditions, giving the method good scalability and adaptability. This model-based quantitative method not only improves the transparency and repeatability of the trajectory optimization process but also lays a solid theoretical foundation for subsequent iterative optimization of the algorithm and its application on different dental robot platforms.

[0069] 4. Compared with the invention patent "A Method for Optimizing the Trajectory of a Tooth Preparation Robot Based on End-Finger Stiffness Perception" filed on the same day by the inventor, although both methods are used for the control and optimization of robot tooth preparation trajectories with high precision requirements, the method mentioned in "A Method for Optimizing the Trajectory of a Tooth Preparation Robot Based on End-Finger Stiffness Perception" is based on the premise that multi-directional cutting forces can easily cause deformation of the robot arm end-effector, thus affecting accuracy. Therefore, it uses the method of calculating the end-effector stiffness and compliance matrix to evaluate the spatial force state, and then selects the stiffness-dominant direction as the optimized preparation direction. This method, on the other hand, uses the method of establishing a nonlinear extrusion force prediction model to determine high-risk processing areas, and then performs differentiated feed speed and nonlinear time compensation for different risk areas. The two methods are applied to different categories of control dimensions and operation stages when optimizing robot tooth preparation trajectories. Therefore, the proposed method and the other method complement each other, thus improving a series of methods for intelligent control and optimization of robot automated tooth preparation trajectories. Attached Figure Description

[0070] For ease of explanation, the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.

[0071] Figure 1 This is a trajectory compensation method for a tooth preparation robot based on extrusion force prediction and curvature optimization;

[0072] Figure 2 This is a schematic diagram of an implementation example 1 of a tooth preparation robot trajectory compensation method based on extrusion force prediction and curvature optimization;

[0073] Figure 3 This is a schematic diagram of an implementation example 2 of a tooth preparation robot trajectory compensation method based on extrusion force prediction and curvature optimization;

[0074] Figure 4 , Figure 5 A schematic diagram showing the area removed and the area remaining after tooth preparation material is used.

[0075] Figure 6 The simulation results show the surface roughness of the prepared teeth;

[0076] Figure 7 Prepare an experimental platform for the dental structure;

[0077] Figure 8 Results of tooth preparation experiments; Detailed Implementation

[0078] 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.

[0079] Example 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 As shown, this specific embodiment adopts the following technical solution: a tooth preparation robot trajectory compensation method based on extrusion force prediction and curvature optimization, the specific implementation process of the method is as follows:

[0080] Step 1: Import theoretical trajectory data for tooth preparation:

[0081] Input theoretical preliminary trajectory curve Set of coordinate values ​​of each tool contact point in the base coordinate system , The coordinates of the k-th tool contact point in the base coordinate system are used to prepare the theoretical trajectory; where, To prepare the theoretical trajectory, the x-axis coordinates of the k-th tool contact point in the base coordinate system are... To prepare the theoretical trajectory, the y-axis coordinates of the k-th tool contact point in the base coordinate system are... Preparing the theoretical trajectory The coordinates of each tool contact point in the base coordinate system Axis coordinates;

[0082] Step 2: Smooth the theoretical trajectory:

[0083] Define the element trajectory, which is the theoretical trajectory between two adjacent tool contact points, denoted by the symbol []. ] indicates that, according to the formula and formula For unit trajectories [ Interpolation is performed on the two endpoints of the [], where and For the weighting coefficients related to the interpolation density, calculate the new [ ]insert[ Preliminary smoothing theory-based trajectory curves are formed. ;

[0084] Determine if all tool contact interpolation is complete.

[0085] Specifically:

[0086] like If not, then Proceed to step two;

[0087] like If successful, proceed to step three;

[0088] Step 3: Calculate the curvature and distance information of the tool contact point.

[0089] Define the curvature of the knife contact point using the symbol The formula for calculating the curvature of the tool contact point is as follows: Define the tool contact distance as the straight-line distance between two adjacent tool contacts, denoted by the symbol... If we express this as follows, then the distance between the k-th and (k+1)-th knife contact points is expressed as: ;

[0090] Step 4: Establish a nonlinear extrusion pressure prediction model:

[0091] Define the cutting edge pressure as the pressure exerted on the tip of the needle when the needle moves from the k-th cutting edge to the (k+1)-th cutting edge. Let the symbol be the cutting edge pressure exerted on the needle when it moves from the k-th cutting edge to the (k+1)-th cutting edge. The pressure exerted at the knife contact point is expressed as: ;in, Let the system stiffness of the robotic arm be defined in the base coordinate system. The straight-line distance between the k-th and (k+1)-th knife contact points. For the set feed rate, For exercise time, For the area to be removed from the material, Material removal rate;

[0092] Step 5: Determining the extreme risk point of extrusion pressure:

[0093] Define the maximum compressive force F at the knife contact point max It is the threshold of compressive force that the tooth can withstand; set the risk point set U of the compressive force at the knife contact point; calculate the first... The extrusion force of each blade contact point;

[0094] a) Determine whether the compressive force between all tool contacts has been calculated.

[0095] Specifically:

[0096] like If not, then Proceed to step five;

[0097] like If successful, proceed to step six a);

[0098] b) Determine the pressure at the tool contact point Greater than the maximum compressive force F at the knife contact point max Whether it is valid,

[0099] Specifically:

[0100] like If this is not the case, then the knife contact point is the safe point for knife contact pressure, and proceed to step five (b).

[0101] like If it is established, then the knife contact point is a knife contact pressure risk point. Put the kth knife contact point into the knife contact pressure risk point set U, and jump to step five (b).

[0102] c) Determine whether the extrusion pressure at the n tool contact points of the prepared trajectory has been evaluated.

[0103] judge Whether it is valid,

[0104] Specifically:

[0105] like The establishment of this rule indicates that not all potential risks related to pressure at the tool contact points have been fully assessed. Proceed to step five (b);

[0106] like If the condition is not met, then the assessment of all knife contact point pressure risk points is complete, and proceed to step six;

[0107] Step Six: Determining the High-Risk Curve:

[0108] a) If there are risk points in U If the continuous extrusion pressure risk points are considered as continuous tool contact points, then the continuous line segment formed by these continuous extrusion pressure risk points constitutes a high-risk curve. ;calculate and The length of the high-risk curve between them is expressed as: Set the set of curves to be compensated. ,in Let t be the curve to be compensated; set a threshold for the length of high-risk curves. Determine the length of the high-risk curve. Less than the high-risk curve length threshold Is it valid?

[0109] Specifically:

[0110] like If so, the high-risk point curve does not require compensation, and proceed to step six (b).

[0111] like If the high-risk curve needs compensation, then the high-risk curve should be added to the set of curves to be compensated. Proceed to step six (b);

[0112] b) Determine whether all high-risk curves have been assessed.

[0113] judge Whether it is valid,

[0114] Specifically:

[0115] like The establishment of this statement indicates that not all high-risk curves have been fully assessed, thus... Proceed to step six a);

[0116] like If the condition is not met, then all high-risk curve assessments are complete, and proceed to step seven.

[0117] Step 7: Tiered compensation for high-risk curves and high-risk points:

[0118] Define local compensation speed as the speed after compensating for isolated high-risk tool contacts, denoted by the symbol. The local compensation velocity is expressed as: ,in The compensation coefficient is defined as follows: The continuous compensation rate is defined as the rate at which the high-risk curve is compensated, denoted by the symbol... The continuous compensation speed is expressed as: The average knife contact pressure is defined as follows: ,in, This is the adjustment coefficient;

[0119] a) Determine the trajectory compensation method.

[0120] Specifically:

[0121] If the knife contact point k belongs to set U but not set C, then perform local velocity compensation and jump to step seven (b).

[0122] If the knife contact point k belongs to both set U and set C, then perform continuous velocity compensation and jump to step seven (b).

[0123] b) Determine whether the compensation method has been determined.

[0124] judge Whether it is valid,

[0125] Specifically:

[0126] like If the condition is met, it means that the knife contact point has not been fully evaluated. Therefore, let k = k + 1 and jump to step six (a).

[0127] like If not, then all tool contact point evaluations are complete, proceed to step eight;

[0128] Step 8: Additional optimization of the curvature abrupt change region at the knife contact point:

[0129] Define curvature adjacency as the absolute value of the difference between the curvatures of adjacent elements, denoted by the symbol... The adjacency difference of the k-th curvature is expressed as: Define curvature dwell time, which is the additional dwell time at the tool contact point for abrupt curvature changes, denoted by the symbol [symbol missing]. The curvature dwell time is expressed as: ,in, For time-compensated intensity, The average curvature of the entire trajectory, It is a non-linear adjustment index. These are the upper and lower thresholds for the additional stay time, respectively.

[0130] a) Determine the adjacent difference of curvature Is it greater than the adjacent difference of the maximum curvature? Further optimizations will be performed.

[0131] Specifically:

[0132] If the curvature is adjacent difference Greater than the adjacent difference of the maximum curvature If true, the curve is in a region of sudden curvature change, and we proceed to step eight (b).

[0133] If the curvature is adjacent difference Greater than the adjacent difference of the maximum curvature If this is not true, then the curve is a normal curve, and we will proceed to step eight (b).

[0134] b) Determine whether the curvature abrupt change curve has been further optimized;

[0135] judge Whether it is valid,

[0136] Specifically:

[0137] like If this holds true, it means that the curvature of all curves has not yet been evaluated, so let... Jump to 8a);

[0138] like If this condition is not met, then all curvature evaluations are complete.

[0139] Implementation Example 2: Based on step one, select 10 tool contact points from the theoretical preparatory trajectory, taking 4 of them as an example: Continue until the 10th blade contact point; jump to step two, smooth the theoretical trajectory, and generate new points for each edge, where... Take 0.75, Taking 0.25, the new smooth trajectory coordinates are: , , , , , , , Obtain the smoothed coordinate set Proceed to step three to calculate the curvature and distance information of the tool contact point, and calculate the curvature of each point in the smooth trajectory to obtain: , , , , ; Calculate the distance between the tool contact points to obtain: , , , , , , Proceed to step four to calculate the pressure at the tool contact point, and obtain: , , , , , , Proceed to step five, set the maximum allowable compressive force threshold to 15N, then... Five high-risk points are added to the risk point set U; proceed to step six, set the continuous risk segment threshold to 0.3mm, define the five high-risk points as continuous high-risk points, and ensure that the continuous segment length (0.53mm) is greater than the continuous risk segment threshold; then, place the corresponding curve... Place it in the high-risk curve set C; according to step seven, determine the risk compensation strategy, knife contact point. It belongs to both set U and set C, and a continuous compensation strategy is adopted; the feed rate is set to 0.5 mm / s, and the compensation coefficient is... The continuous compensation speed is calculated as follows: Therefore, in In step eight, the feed rate is reduced from 0.5 mm / s to 0.35 mm / s; proceed to step eight and set the curvature adjacency threshold. With a nonlinear adjustment index of 2 and a time compensation intensity of 0.1, the curvature adjacency difference is calculated as follows: , , , , The results show that ,determination For the curvature abrupt change section, the additional curvature compensation time is calculated as follows: In trajectory testing involving regions of abrupt curvature change, traditional fixed-speed reduction or global speed adjustment strategies still easily result in peak extrusion pressure exceeding the safety threshold of tooth tissue. However, by employing the extrusion pressure prediction and curvature optimization method of this invention, the system performs precise nonlinear time compensation and differentiated feed adjustment for high-risk points and segments. Experiments show that the peak extrusion pressure is significantly reduced by 40%, remaining below the safety threshold throughout the entire process, and the surface roughness of the formed surface is improved by 25%. This method deeply integrates geometric curvature characteristics with the extrusion pressure prediction model, achieving hierarchical compensation from global to local levels. In particular, the introduction of nonlinear time-domain compensation for curvature abrupt change regions not only precisely suppresses peak extrusion pressure in weak tissue areas and prevents medical damage, but also maintains a high processing speed in conventional areas, perfectly balancing cutting efficiency, forming quality, and clinical safety.

Claims

1. A method for trajectory compensation of a tooth preparation robot based on extrusion force prediction and curvature optimization, characterized in that: The specific implementation process of the method is as follows: Step 1: Import theoretical trajectory data for tooth preparation: Input theoretical preliminary trajectory curve Set of coordinate values ​​of each tool contact point in the base coordinate system , Preparing the theoretical trajectory The coordinate values ​​of each tool contact point in the base coordinate system; where... Preparing the theoretical trajectory The x-axis coordinates of each tool contact point in the base coordinate system. Preparing the theoretical trajectory The coordinates of each tool contact point in the base coordinate system Axis coordinates Preparing the theoretical trajectory The coordinates of each tool contact point in the base coordinate system Axis coordinates; Step 2: Smooth the theoretical trajectory: Define the element trajectory, which is the theoretical trajectory between two adjacent tool contact points, denoted by the symbol []. ] indicates that, according to the formula and formula For unit trajectory [ Interpolation is performed on the two endpoints of the [], where and For the weighting coefficients related to the interpolation density, calculate the new [ ]insert[ Preliminary smoothing theory-prepared trajectory curves are formed. ; Determine if all tool contact interpolation is complete. Specifically: like If not, then Proceed to step two; like If successful, proceed to step three; Step 3: Calculate the curvature and distance information of the tool contact point. Define the curvature of the knife contact point using the symbol The formula for calculating the curvature of the knife contact point is as follows: Define the tool contact distance as the straight-line distance between two adjacent tool contacts, denoted by the symbol... If we express this as follows, then the distance between the k-th and (k+1)-th knife contact points is expressed as: ; Step 4: Establish a nonlinear extrusion pressure prediction model: Define the extrusion force at the knife contact point; the extrusion force at the knife contact point is the first... The first blade contact point moves to the... The compressive force exerted on the tip of the nib at the first contact point, let the nib be at the first contact point. The first blade contact point moves to the... The compressive force experienced at each contact point is represented by the symbol. The pressure applied at the knife contact point is expressed as: ;in, Let the system stiffness of the robotic arm be defined in the base coordinate system. The straight-line distance between the k-th and (k+1)-th knife contact points. For the set feed rate, For exercise time, For the area to be removed from the material, Material removal rate; Step 5: Determining the extreme risk point of extrusion pressure: Define the maximum compressive force at the blade contact point. It is the threshold of compressive force that the tooth can withstand; set the risk point set U of the compressive force at the knife contact point; calculate the first... The extrusion force of each blade contact point; a) Determine whether the compressive force between all tool contacts has been calculated. Specifically: like If not, then Proceed to step five; like If successful, proceed to step six a); b) Determine the pressure at the tool contact point Greater than the maximum compressive force of the knife contact point Whether it is valid, Specifically: like If this is not the case, then the knife contact point is the safe point for knife contact pressure, and proceed to step five (b). like If it is established, then the knife contact point is a knife contact pressure risk point. Put the kth knife contact point into the knife contact pressure risk point set U, and jump to step five (b). c) Determine the preliminary trajectory Has the pressure exerted on each blade contact point been assessed? judge Whether it is valid, Specifically: like The establishment of this rule indicates that not all potential risks related to pressure at the tool contact points have been fully assessed. Proceed to step five (b); like If the condition is not met, then the assessment of all knife contact point pressure risk points is complete, and proceed to step six; Step Six: Determining the High-Risk Curve: a) If there are risk points in U If the continuous extrusion pressure risk points are considered as continuous tool contact points, then the continuous line segment formed by these continuous extrusion pressure risk points constitutes a high-risk curve. ;calculate and The length of the high-risk curve between them is expressed as: Set the set of curves to be compensated. ,in Let t be the curve to be compensated; set a threshold for the length of high-risk curves. Determine the length of the high-risk curve. Less than the high-risk curve length threshold Is it valid? Specifically: like If the high-risk point curve does not require compensation, proceed to step six (b). like If the high-risk curve needs compensation, then the high-risk curve should be added to the set of curves to be compensated. Proceed to step six (b); b) Determine whether the high-risk curve has been fully assessed. judge Whether it is valid, Specifically: like The establishment of this statement indicates that not all high-risk curves have been fully assessed, thus... Proceed to step six a); like If the condition is not met, then all high-risk curve assessments are complete, and proceed to step seven. Step 7: Tiered compensation for high-risk curves and high-risk points: Define local compensation speed as the speed after compensating for isolated high-risk tool contacts, denoted by the symbol. The local compensation velocity is expressed as: ,in The compensation coefficient is defined as follows: The continuous compensation rate is defined as the rate at which the high-risk curve is compensated, denoted by the symbol... The continuous compensation speed is expressed as: The average knife contact pressure is defined as follows: ,in, This is the adjustment coefficient; a) Determine the trajectory compensation method. Specifically: If the knife contact point If the value belongs to set U but not set C, then perform local velocity compensation and jump to step 7b). If the knife contact point If a value belongs to both set U and set C, then perform continuous velocity compensation and jump to step 7b). b) Determine whether the compensation method has been determined. judge Whether it is valid, Specifically: like If this is established, it means the knife contact point has not yet been fully evaluated, then... Jump to step six (a); like If not, then all tool contact point evaluations are complete, proceed to step eight; Step 8: Additional optimization of the curvature abrupt change region at the knife contact point: Define curvature adjacency as the absolute value of the difference between the curvatures of adjacent elements, denoted by the symbol... It means that the first Each curvature adjacent difference is represented as: Define curvature dwell time, which is the additional dwell time at the tool contact point for abrupt curvature changes, denoted by the symbol [symbol missing]. The curvature dwell time is expressed as: ,in, For time-compensated intensity, The average curvature of the entire trajectory, It is a non-linear adjustment index. These are the upper and lower thresholds for the additional stay time, respectively. a) Determine the adjacent difference of curvature Is it greater than the adjacent difference of the maximum curvature? Further optimizations will be performed. Specifically: If the curvature is adjacent difference Greater than the nearest neighbor difference of the maximum curvature If true, the curve is in a region of sudden curvature change, and we proceed to step eight (b). If the curvature is adjacent difference Greater than the nearest neighbor difference of the maximum curvature If this is not true, then the curve is a normal curve, and we will proceed to step eight (b). b) Determine whether the curvature abrupt change curve has been further optimized; judge Whether it is valid, Specifically: like If this holds true, it means that the curvature of all curves has not yet been evaluated, so let... Jump to 8a); like If this condition is not met, then all curvature evaluations are complete.

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