A curvature segment-based robot-assisted sewing feed trajectory planning method

By using a method based on curvature segmentation and trapezoidal velocity planning, the robot feed trajectory is generated, which solves the problem of fabric deformation or wrinkling in sewing irregular curves with varying curvature, and enables smooth sewing.

CN116695342BActive Publication Date: 2026-07-07ZHEJIANG UNIV

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
ZHEJIANG UNIV
Filing Date
2023-05-26
Publication Date
2026-07-07

AI Technical Summary

Technical Problem

Existing robotic sewing trajectory planning methods cannot effectively handle sewing tasks with irregular curvature changes, which makes the fabric prone to deformation or wrinkles during the sewing process. There is a lack of suitable feed trajectory and speed planning methods.

Method used

The robot feed trajectory is generated by a curvature segmentation method. Combined with the trapezoidal velocity planning method, the mapping relationship between the robot end pose and the sewing curve points is established to generate a trajectory velocity suitable for sewing irregular curves.

Benefits of technology

The robot was able to successfully generate a feed trajectory in sewing tasks with irregular curves of varying curvature, solving the problem of fabric deformation or wrinkles and ensuring the smooth progress of the sewing process.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present application relates to the field of robot trajectory planning, and particularly relates to a robot-assisted sewing feed trajectory planning method based on curvature segmentation, and the specific process is as follows: the contour of a target to-be-sewn bottom plate is extracted based on a Canny operator and converted into a sewing curve; after the target sewing curve is obtained, the pose relationship between the robot end point and the sewing curve point is established according to the motion constraint relationship of the robot and the sewing machine for completing curve sewing, and a robot feed trajectory is generated; the curvature variation trend of the sewing curve is analyzed, and the sewing curve is segmented in combination with the sewing process requirements; finally, the segmented curve is planned for speed based on a trapezoidal speed curve planning method, a trajectory speed suitable for irregular curve sewing is obtained, and the speed planning of robot end assistance sewing is completed. The method of the present application effectively improves the speed fluctuation problem of the robot at the curvature variation when facing a sewing task with a complex curve, and realizes relatively stable sewing of the complex curve.
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Description

Technical Field

[0001] This invention relates to the field of robot trajectory planning, and more particularly to a robot-assisted sewing feed trajectory planning method based on curvature segmentation. Background Technology

[0002] Robotic sewing feed trajectory planning involves generating a robot motion trajectory capable of completing the sewing task based on the contour features of the fabric to be sewn. After the robot sewing feed trajectory is generated, the collaborative planning of the robot trajectory and the sewing machine's sewing speed needs to be considered. On the one hand, existing sewing robot trajectories are mostly composed of simple straight lines and curves. In current mainstream automated sewing systems where the robot feeds the fabric and the sewing machine acts as a peripheral device, only simple curves such as straight line segments and arc segments can be completed. When faced with sewing tasks composed of curves with irregular curvature changes, there is a lack of research on corresponding feed trajectory generation methods. On the other hand, existing sewing robots lack robot trajectory and sewing speed planning. For sewing tasks with regular curvature changes, the robot feed trajectory is also relatively irregular. When the curvature of the sewing curve is irregular or has large curvature changes, the generated robot feed trajectory is also more complex. Current research lacks planning for both robot trajectory and sewing machine sewing speed, which can easily lead to fabric deformation or wrinkles during sewing, making it difficult to complete the sewing of the target curve. Therefore, there is a lack of a method for planning the feed trajectory and speed of robot-assisted sewing when the curvature of the sewing task changes irregularly. Summary of the Invention

[0003] To address the aforementioned technical problems in the existing technology, this invention proposes a robot-assisted sewing feed trajectory planning method based on curvature segmentation, the specific technical solution of which is as follows:

[0004] A robot-assisted sewing feed trajectory planning method based on curvature segmentation is proposed. This method generates a robot feed trajectory capable of sewing the target curve by establishing a mapping relationship between the robot's end-effector pose and the sequence points of the sewing curve under complex sewing curves. Furthermore, it plans the sewing speed based on curvature segmentation and trapezoidal velocity curve planning methods. The specific steps include:

[0005] A robot-assisted sewing feed trajectory planning method based on curvature segmentation specifically includes the following process:

[0006] The outline of the target sewing base plate is extracted based on the Canny operator and converted into a sewing curve;

[0007] After obtaining the target sewing curve, based on the motion constraint relationship between the robot and the sewing machine to complete the curve sewing, the pose relationship between the robot end point and the sewing curve point is established, and the robot feed trajectory is generated.

[0008] Based on the trend of curvature change of the sewing curve, the curvature of the sewing curve is segmented.

[0009] Based on the trapezoidal velocity planning method, the velocity planning of the feed trajectory corresponding to the segmented curve is performed to obtain the trajectory velocity suitable for sewing irregular curves.

[0010] Furthermore, the extraction of the outline of the target base plate to be sewn based on the Canny operator and its conversion into a sewing curve is specifically as follows: the initial outline curve of the base plate to be sewn is obtained based on the Canny operator edge extraction algorithm; considering the safety distance between the sewing machine needle and the edge of the base plate, a safety margin is set and the outline is expanded based on the safety margin to obtain the final sewing outline curve.

[0011] Furthermore, obtaining the initial contour curve specifically includes the following steps:

[0012] Step 1: Based on the original grayscale image, smooth the image using a Gaussian filter;

[0013] Step 2: Obtain the gradient direction and magnitude of the image;

[0014] Step 3: Perform non-maximum suppression on the gradient magnitude;

[0015] Step 4: Perform dual threshold algorithm detection and hysteresis boundary tracking.

[0016] Furthermore, the aforementioned contour expansion based on safety margin involves setting a safety margin for the sewing distance and expanding the initial contour of the base plate outward at equal intervals, specifically including the following process:

[0017] Let P i-1 P i P i+1 Let P be the three adjacent vertices of the contour. i Draw a straight line formed by adjacent points of the contour. Then draw straight lines respectively. Parallel lines, wherein the spacing between the parallel lines is a set safety margin d. i Then Q i-1 Q i Q i+1 For P i-1 P i P i+1 Calculate the value of the expanded vertex Q. i Coordinates, Q i With P i The coordinate relationship is shown in equation (1):

[0018]

[0019] The direction vector of the straight line formed by adjacent points of the contour can be represented by the corresponding unit vector, as shown in equation (2):

[0020]

[0021] The lengths are equal, and the safety margin d is the same. i The relationship between them is shown in equation (3):

[0022]

[0023] In equation (3) θ i For vectors with vector The angle between the vectors can be obtained by the cross product operation:

[0024]

[0025] Substitute equations (2), (3), and (4) into equation (1), and calculate the new vertex coordinates after the contour point expansion process based on the set safety margin. Then, traverse all vertices of the contour to complete the contour expansion process.

[0026] Furthermore, based on the motion constraints between the robot and the sewing machine in completing the curved sewing, the pose relationship between the robot's end point and the sewing curve points is established, and the robot's feed trajectory is generated, specifically as follows:

[0027] Let B represent the origin of the robot's base coordinate system, E represent the robot's end point, C represent the base plate contour point, and T represent the position of the needle.

[0028] Using the coordinate system of the base plate as the tool coordinate system, the contour point where the base plate and the sewing machine needle are closest at a certain moment, i.e., the sewing curve point, is regarded as the working point of the base plate and the tool at that moment. Using the coordinates of the sewing curve point in the tool coordinate system, the position constraint of the tool working point is obtained. In actual sewing processes, the sewing posture of the sewing machine is a chamfering posture, thus obtaining the posture constraint of the tool working point. Combining the position constraint and the posture constraint, the pose transformation matrix of the tool working point in the tool coordinate system at a certain moment is determined. E T C (t);

[0029] Given the sequence of points on the sewing contour curve, the corresponding pose sequence of the robot's end effector in Cartesian space. B T E (t), the contour curve points and the robot end effector points satisfy the pose relationship:

[0030] B T E (t)· E T C(t)= B T T (t) (5)

[0031] In equation (5), t = 1 to N represents the sequence of points on the contour curve; B T T (t) represents the pose matrix of the target point where the sewing machine needle is located in the base coordinate system; when the robot sews, the contour curve points successively reach the position of the sewing machine needle, that is, satisfying the pose transformation relationship represented by equation (5), and the pose matrix of the sewing machine needle in the base coordinate system. B T T It can be represented as:

[0032] B T T =[n T o T a T p T (6)

[0033] In equation (6), p T The sewing machine needle position component is determined by the spatial position of the sewing machine needle in the robot's base coordinate system; [n T o T a T The [] represents the sewing machine needle posture components. The sewing task is completed in a planar state. In the planar state, the sewing machine needle is regarded as a point mass, and the posture components are:

[0034]

[0035] Substituting equations (6) and (7) into equation (5), the robot end-effector trajectory point pose sequence corresponding to the contour point sequence is calculated by determining the contour sewing position constraint and attitude constraint. The end-effector trajectory point sequence is then connected sequentially to generate the robot end-effector feed trajectory.

[0036] Furthermore, the curvature segmentation of the sewing curve is based on the curvature segmentation method, which segments the contour curve of the sewing curve with different curvature segments, wherein the curvature calculation formula is shown in equation (8):

[0037]

[0038] In the formula, Δs represents the value from the current point Q. i The initial arc length, where Δα represents the corresponding tangent angle;

[0039] Then, sequentially traverse each point on the sewn contour curve, calculate the curvature value of each point on the contour, obtain the trend of the change in the curvature of the sewn contour, and divide the contour curve into multiple segments based on the trend of the change in the curvature of the contour.

[0040] Furthermore, the trapezoidal velocity planning method is used to plan the velocity of the feed trajectory corresponding to the segmented curve. The specific steps are as follows:

[0041] Step 101: Divide the robot's movement speed along the feed trajectory into three stages: uniform acceleration, uniform speed, and uniform deceleration. Given the initial speed v0 and the final speed v... e Maximum speed v max acceleration a a deceleration a d and the starting point position x0 and the ending point position x e ; Calculate the maximum achievable speed v under given parameters. lim When there are only acceleration and deceleration phases, the maximum speed can be achieved. The calculation of the limit speed is shown in equation (9):

[0042]

[0043] Step 102: Compare the limiting speed v lim With a given maximum speed v max Determine the velocity v of the uniform segment based on the relative magnitudes. c When the limiting speed is less than the given maximum speed, the system cannot reach the set maximum speed, and in this case, v c =v lim Conversely, the system can meet the set maximum speed requirement, v c =v max ;

[0044] Step 103: Calculate the time and displacement of each segment in the acceleration, constant speed, and deceleration phases, as shown in equation (10):

[0045]

[0046] Step 104: Calculate the displacement, velocity, and acceleration at each moment of the entire curve planning. The displacement q(t) at each moment is shown in Equation (11):

[0047]

[0048] velocity at each moment With acceleration As shown in equation (12):

[0049]

[0050] Step 105: After giving the constraints of sewing time and sewing speed for each contour curve segment, based on the trapezoidal velocity planning method, the sewing position, velocity and acceleration of each contour curve point in the time series are obtained. Then, combined with the generated robot end feed trajectory, the position of the robot end feed trajectory point in the corresponding time series is obtained, and the velocity and acceleration information of the robot feed trajectory point are obtained. Finally, the trajectory velocity of irregular curve sewing is obtained.

[0051] Beneficial effects:

[0052] This invention extracts the sewing contour from the sewing base plate, converts it into a sewing curve, analyzes the curvature change trend of the sewing curve, and segments the curvature of the sewing curve in combination with the sewing process requirements, so that the robot can successfully generate a feed trajectory when facing sewing tasks composed of irregular curves with varying curvature.

[0053] This invention uses a trapezoidal speed planning method to perform speed planning on segmented curves, thereby obtaining a trajectory speed variation law suitable for sewing irregular curves. This solves the problem of fabric wrinkles that occur when sewing irregular curves with irregular curvature due to the lack of sewing speed planning. Attached Figure Description

[0054] Figure 1 This is a flowchart of a robot-assisted sewing feed trajectory planning method based on curvature segmentation according to the present invention.

[0055] Figure 2 This is a schematic diagram of the outline expansion process of the present invention;

[0056] Figure 3 This is a schematic diagram of trajectory coordinate transformation according to the present invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0058] like Figure 1 As shown, the present invention provides a robot-assisted sewing feed trajectory planning method based on curvature segmentation, which specifically includes the following process:

[0059] The outline of the target base plate to be sewn is extracted based on the Canny operator and converted into a sewing curve;

[0060] After obtaining the target sewing curve, based on the motion constraint relationship between the robot and the sewing machine to complete the curve sewing, the pose relationship between the robot end point and the sewing curve point is established, and the robot feed trajectory is generated.

[0061] Analyze the trend of curvature change of the sewing curve, and divide the curvature of the sewing curve into segments according to the sewing process requirements;

[0062] Based on the trapezoidal speed planning method, the speed of the feed trajectory corresponding to the segmented curve is planned to obtain the trajectory speed suitable for sewing irregular curves, thus completing the speed planning of robot end-effector assisted sewing.

[0063] Specifically, the extraction of the outline of the target base plate to be sewn based on the Canny operator and its conversion into a sewing curve involves: obtaining the initial outline curve of the base plate to be sewn based on the Canny operator edge extraction algorithm; considering the safety distance between the sewing machine needle and the edge of the base plate; setting a safety margin; and expanding the outline based on the safety margin to obtain the final sewing outline curve.

[0064] Obtaining the initial contour curve specifically includes the following steps:

[0065] Step 1: Based on the original grayscale image, smooth the image using a Gaussian filter;

[0066] Step 2: Obtain the gradient direction and magnitude of the image;

[0067] Step 3: Perform non-maximum suppression on the gradient magnitude;

[0068] Step 4: Perform dual threshold algorithm detection and hysteresis boundary tracking.

[0069] The aforementioned contour expansion based on a safety margin specifically involves the following steps: During the sewing process, the robot drives the sewing base plate to move around the sewing machine needle, and the sewing machine overlocks the fabric according to the contour shape of the base plate. Considering the relative positional relationship between the edge of the base plate and the sewing machine needle, if the overlocking is performed exactly along the edge of the base plate, collisions may occur between the edge of the base plate and the sewing machine needle due to robot motion errors, leading to safety issues. Therefore, a safety margin for the sewing distance is set, and the initial contour of the base plate is expanded outward at equal intervals to obtain the final sewing curve.

[0070] like Figure 2 As shown, P i-1 P i P i+1 Let P be the three adjacent vertices of the contour. i Draw a straight line formed by adjacent points of the contour. Then draw straight lines respectively. Parallel lines, wherein the spacing between the parallel lines is a set safety margin d. i Then Q i-1 Q i Q i+1 For P i-1 P i P i+1 Calculate the value of the expanded vertex Q. i Coordinates, Q i With Pi The coordinate relationship is shown in equation (1):

[0071]

[0072] The direction vector of the straight line formed by adjacent points of the contour can be represented by the corresponding unit vector, as shown in equation (2):

[0073]

[0074] The lengths are equal, and the safety margin d is the same. i The relationship between them is shown in equation (3):

[0075]

[0076] In equation (3) θ i For vectors with vector The angle between the vectors can be obtained by the cross product operation:

[0077]

[0078] Substitute equations (2), (3), and (4) into equation (1), and calculate the new vertex coordinates after the contour point expansion process based on the set safety margin. Then, traverse all vertices of the contour to complete the contour expansion process.

[0079] The aforementioned method establishes the pose relationship between the robot's end point and the sewing curve points based on the motion constraints between the robot and the sewing machine to complete the curve sewing, and generates the robot's feed trajectory. Specifically, in the scenario where the robot drags the base plate to perform contour sewing, the contour point where the base plate is closest to the sewing machine needle at a certain moment is regarded as the base plate's working point at that moment, i.e., the tool working point. As the robot drags the base plate to feed the fabric, the tool working point changes with the robot's movement at different moments. Considering the characteristics of the robot's sewing motion, and combining the sewing contour position constraints and sewing posture constraints, the pose relationship between the robot's end point and the base plate's working point is established based on the homogeneous transformation method, and the robot's end point feed trajectory is generated.

[0080] like Figure 3As shown, Base represents the origin of the robot's base coordinate system, Ele represents the robot's end effector point, Con represents the base plate contour point, and Tar represents the needle's position. The sewing base plate is the robot's end effector tool, and the base plate coordinate system is the tool coordinate system. Using the coordinates of a contour curve point in the tool coordinate system, the position constraint of the tool's working point is obtained. In actual sewing processes, the sewing posture is a tangent posture, meaning the current point is the contour tangent point, thus obtaining the posture constraint of the tool's working point. Combining the position and posture constraints, the pose transformation matrix of the tool's working point in the tool coordinate system at a given moment is determined. E T C (t).

[0081] Determining the feed trajectory of the robot's end effector is equivalent to determining the pose sequence of the robot's end effector in Cartesian space corresponding to the sequence of points on the sewing contour curve. B T E (t), the sewing task is completed, and the pose relationship between the contour curve points and the robot end point is satisfied:

[0082] B T E (t)· E T C (t)= B T T (t) (5)

[0083] In equation (5), t = 1 to N represents the sequence of points on the contour curve; B T T (t) represents the pose matrix of the target point where the sewing machine needle is located in the base coordinate system; when the robot sews, the contour curve points successively reach the position of the sewing machine needle, that is, satisfying the pose transformation relationship represented by equation (5), and the pose matrix of the sewing machine needle in the base coordinate system. B T T It can be represented as:

[0084] B T T =[n T o T a T p T (6)

[0085] In equation (6), p T The sewing machine needle position component is determined by the spatial position of the sewing machine needle in the robot's base coordinate system; [n T o T a T The [] represents the sewing machine needle posture components. The sewing task is completed in a planar state. In the planar state, the sewing machine needle is regarded as a point mass, and the posture components are:

[0086]

[0087] Substituting equations (6) and (7) into equation (5), the robot end-effector trajectory point pose sequence corresponding to the contour point sequence is calculated by determining the contour sewing position constraint and attitude constraint. The end-effector trajectory point sequence is then connected sequentially to generate the robot end-effector feed trajectory.

[0088] The curvature segmentation of the sewing curve is based on the curvature segmentation method, which segments the contour curve of different curvature segments. The curvature calculation formula is shown in Equation (8):

[0089]

[0090] In the formula, Δs represents the value from the current point Q. i The initial arc length, where Δα represents the corresponding tangent angle;

[0091] Then, sequentially traverse each point on the contour curve, calculate the curvature value of each point on the contour, obtain the trend of the change in the curvature of the sewing contour, and divide the contour curve into multiple segments based on the trend of the change in the curvature of the contour.

[0092] The trapezoidal velocity planning method is used to plan the velocity of the feed trajectory corresponding to the segmented curve. Specifically:

[0093] This invention divides the velocity of the entire motion process into three stages: uniform acceleration, uniform speed, and uniform deceleration, given an initial velocity v0 and an ending velocity v e Maximum speed v max acceleration a a deceleration a d and the starting point position x0 and the ending point position x e The specific steps of the trapezoidal velocity planning method are as follows:

[0094] Step 101: Calculate the achievable maximum speed v under the set parameters. lim When there are only acceleration and deceleration phases, the maximum speed can be achieved. The calculation of the maximum speed is shown in equation (9):

[0095]

[0096] Step 102: Compare the limiting speed v lim With a given maximum speed v max Determine the velocity v of the uniform segment based on the relative magnitudes. c When the limiting speed is less than the given maximum speed, the system consisting of the auxiliary robot and the sewing machine cannot reach the set maximum speed; in this case, v c =v lim Conversely, the system can meet the set maximum speed requirement, v c =v max ;

[0097] Step 103: Calculate the time and displacement of each segment in the acceleration, constant speed, and deceleration phases, as shown in equation (10):

[0098]

[0099] Step 104: Calculate the displacement, velocity, and acceleration at each moment of the entire curve planning. The displacement q(t) at each moment is shown in Equation (11):

[0100]

[0101] velocity at each moment With acceleration As shown in equation (12):

[0102]

[0103] Step 105: Given the constraints such as sewing time and sewing speed of each contour curve segment, based on trapezoidal velocity planning, the sewing position, speed and acceleration of each contour curve point in the time series are obtained. Combined with the method for determining the robot end feed trajectory described above, the position of the robot end feed trajectory point in the corresponding time series is obtained, and then the speed, acceleration and other information of the robot feed trajectory point are obtained, and finally the trajectory speed suitable for sewing irregular curves is obtained.

[0104] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the implementation process of the present invention has been described in detail above, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robot-assisted sewing feed trajectory planning method based on curvature segmentation, characterized in that, Specifically, the process includes the following: The outline of the target sewing base plate is extracted based on the Canny operator and converted into a sewing curve; After obtaining the target sewing curve, based on the motion constraints between the robot and the sewing machine in completing the curve sewing, the pose relationship between the robot's end point and the sewing curve points is established, and the robot's feed trajectory is generated; specifically: Let B represent the origin of the robot's base coordinate system, E represent the robot's end point, C represent the base plate contour point, and T represent the position of the needle. Using the coordinate system of the base plate as the tool coordinate system, the contour point where the base plate and the sewing machine needle are closest at a certain moment, i.e., the sewing curve point, is regarded as the working point of the base plate and the tool at that moment. Using the coordinates of the sewing curve point in the tool coordinate system, the position constraint of the tool working point is obtained. In actual sewing processes, the sewing posture of the sewing machine is a chamfering posture, thus obtaining the posture constraint of the tool working point. Combining the position constraint and the posture constraint, the pose transformation matrix of the tool working point in the tool coordinate system at a certain moment is determined. ; Given the sequence of points on the sewing contour curve, the corresponding pose sequence of the robot's end effector in Cartesian space. The contour curve points and the robot end effector points satisfy the pose relationship: (5) In equation (5), , representing the sequence of points on the contour curve; Let represent the pose matrix of the target point where the sewing machine needle is located in the base coordinate system; when the robot sews, the contour curve points successively reach the position of the sewing machine needle, that is, satisfy the pose transformation relationship expressed by equation (5), and the pose matrix of the sewing machine needle in the base coordinate system. It can be represented as: (6) In formula (6) The component representing the position of the sewing machine needle is determined by the spatial position of the sewing machine needle in the robot's base coordinate system; This represents the posture components of the sewing machine needle. The sewing task is completed in a planar state. In the planar state, the sewing machine needle is regarded as a point mass, and the posture components are: (7) Substituting equations (6) and (7) into equation (5), the robot end trajectory point pose sequence corresponding to the contour point sequence is calculated by determining the contour sewing position constraint and posture constraint. The end trajectory point sequence is then connected sequentially to generate the robot end feed trajectory. Based on the trend of curvature change of the sewing curve, the curvature of the sewing curve is segmented. Based on the trapezoidal velocity planning method, the velocity planning of the feed trajectory corresponding to the segmented curve is performed to obtain the trajectory velocity suitable for sewing irregular curves.

2. The robot-assisted sewing feed trajectory planning method based on curvature segmentation as described in claim 1, characterized in that, The process of extracting the outline of the target base plate to be sewn based on the Canny operator and converting it into a sewing curve is as follows: the initial outline curve of the base plate to be sewn is obtained based on the Canny operator edge extraction algorithm; the safety margin is set considering the safety distance between the sewing machine needle and the edge of the base plate; and the outline is expanded based on the safety margin to obtain the final sewing outline curve.

3. The robot-assisted sewing feed trajectory planning method based on curvature segmentation as described in claim 2, characterized in that, Obtaining the initial contour curve specifically includes the following steps: Step 1: Based on the original grayscale image, smooth the image using a Gaussian filter; Step 2: Obtain the gradient direction and magnitude of the image; Step 3: Perform non-maximum suppression on the gradient magnitude; Step 4: Perform dual threshold algorithm detection and hysteresis boundary tracking.

4. The robot-assisted sewing feed trajectory planning method based on curvature segmentation as described in claim 2, characterized in that, The aforementioned contour expansion based on safety margin refers to setting a safety margin for the sewing distance and expanding the initial contour of the base plate outward at equal intervals. Includes the following processes: set up For the three adjacent vertices of the contour, pass through the point Draw a straight line formed by adjacent points of the contour. Then draw straight lines respectively. Parallel lines, wherein the spacing between the parallel lines is a set safety margin. ,but for Calculate the corresponding vertices after expansion. coordinate, and The coordinate relationship is shown in equation (1): (1) The direction vector of the line formed by adjacent points of the contour can be represented by the corresponding unit vector, as shown in equation (2): (2) The lengths are equal, and the safety margin is... The relationship between them is shown in equation (3): (3) In formula (3) For vectors with vector The angle between the vectors can be obtained by the cross product operation: (4) Substitute equations (2), (3), and (4) into equation (1), and calculate the new vertex coordinates after the contour point expansion process based on the set safety margin. Then, traverse all vertices of the contour to complete the contour expansion process.

5. The robot-assisted sewing feed trajectory planning method based on curvature segmentation as described in claim 1, characterized in that, The curvature segmentation of the sewing curve is based on the curvature segmentation method, which segments the contour curve of the sewing curve with different curvature segments. The curvature calculation formula is shown in equation (8): (8) In the formula Indicates from the current point The initial arc length, Indicates the corresponding tangent angle; Then, sequentially traverse each point on the sewn contour curve, calculate the curvature value of each point on the contour, obtain the trend of the change in the curvature of the sewn contour, and divide the contour curve into multiple segments based on the trend of the change in the curvature of the contour.

6. The robot-assisted sewing feed trajectory planning method based on curvature segmentation as described in claim 5, characterized in that, The trapezoidal velocity planning method is used to plan the velocity of the feed trajectory corresponding to the segmented curve. The specific steps are as follows: Step 101: Divide the robot's movement speed along the feed trajectory into three stages: uniform acceleration, uniform speed, and uniform deceleration, and give an initial speed. Termination speed Maximum speed acceleration deceleration and starting point position and the location of the termination point ; Calculate the achievable maximum speed under given parameters. When there are only acceleration and deceleration phases, the maximum speed can be achieved. The calculation of the limit speed is shown in equation (9): (9) Step 102: Compare the ultimate speeds With a given maximum speed Determine the velocity of the uniform segment based on the relative magnitudes. When the limit speed is less than the given maximum speed, the system cannot reach the set maximum speed. Conversely, the system can meet the set maximum speed requirement. ; Step 103: Calculate the time and displacement of each segment in the acceleration, constant speed, and deceleration phases, as shown in equation (10): (10) Step 104: Calculate the displacement, velocity, and acceleration at each moment in the entire curve planning process, and the displacement at each moment. As shown in equation (11): (11) velocity at each moment With acceleration As shown in equation (12): (12); Step 105: After giving the constraints of sewing time and sewing speed for each contour curve segment, based on the trapezoidal velocity planning method, the sewing position, velocity and acceleration of each contour curve point in the time series are obtained. Then, combined with the generated robot end feed trajectory, the position of the robot end feed trajectory point in the corresponding time series is obtained, and the velocity and acceleration information of the robot feed trajectory point are obtained. Finally, the trajectory velocity of irregular curve sewing is obtained.