Robot G3 continuous corner smoothing method based on Bezier curve

Abstract

The invention relates to a robot G3 continuous corner smoothing method based on a Bezier curve. The method comprises the steps that robot small line segment machining tool nose position data is input, six times of Bezier curves are adopted for transfer fairing under a workpiece coordinate system, and control points of the Bezier curves are analyzed and calculated according to the maximum allowable value of tool nose position fairing errors and the condition constraint that G3 at the curve connection position is continuous; secondly, robot small line segment machining cutter axis direction data are input, six times of Bezier curves are adopted in an RPY angle space under a workpiece coordinate system for transfer fairing, and control points of the Bezier curves are analyzed and calculated according to the maximum allowable value of fairing errors in the cutter axis direction and the condition constraint that G3 at the curve connection position is continuous; and finally, parameter synchronization is carried out on the cutter shaft direction and the cutter point position path after switching and smoothing, and a B spline straight line is adopted to replace the remaining linear section. According to the method, continuous and smooth switching of the tool path G3 can be realized analytically, no iterative computation is needed, and the processing real-time performance and stability are improved while the fairing error is controllable.

Description

Technical Field

[0001] The invention belongs to the technical field of robot arm trajectory smoothing, and in particular is a robot G3 continuous corner smoothing method based on Bezier curves. Background Art

[0002] In recent years, robots have been widely used in the processing of complex curved and curved surface parts due to their advantages such as low cost and high flexibility. Due to the complexity of curves and surfaces, robots need to use CAD and CAM software to plan tool paths when processing such parts. Usually, the robot processing path generated by CAM (computer-aided manufacturing software) is composed of a series of discrete small line segments. The tangential discontinuity at the junction of small line segments will cause sudden changes in the speed, acceleration, and jump of the robot's movement, resulting in mechanical vibration, which seriously affects the quality of the processed surface. In order to improve processing efficiency and processing quality, the industry mainly smoothes the small line segment path through the path smoothing algorithm. In addition, in order to avoid the problem of discontinuity in the angular velocity, angular acceleration, and angular jump of the tool axis rotation at the curve cross-segment during the movement of the tool axis direction following the tool tip position path, it is also necessary to synchronize the parameters of the tool axis direction and tool tip position path after the smoothing.

[0003] At present, most robot path smoothing algorithms can only achieve curvature continuity at the path transition points, that is, G2 continuity, but the curvature change rate is discontinuous, which will lead to poor smoothness of the robot's end motion. Secondly, in order to meet the pose smoothing error constraints and pose synchronization requirements, most path smoothing algorithms use an iterative method to calculate the control points of the transition curve, but this will increase the robot's computational burden and seriously affect the real-time performance of processing. Summary of the invention

[0004] To solve the above technical problems, the present invention provides a robot G3 continuous corner smoothing method based on Bezier curves, which can analytically realize the continuous and smooth transition of tool trajectory G3 (curvature differential continuity), thereby improving the real-time and stability of processing.

[0005] The technical solution of the present invention is described as follows in conjunction with the accompanying drawings:

[0006] A robot G3 continuous corner smoothing method based on Bezier curves comprises the following steps:

[0007] Step 1: Input the tool tip position data of the robot for machining small line segments, and use the 6th degree Bezier curve for transfer smoothing in the workpiece coordinate system. According to the maximum allowable value of the tool tip position smoothing error and the G3 continuity condition constraints at the curve connection, the control points of the Bezier curve are analytically calculated. The smoothed path consists of the inserted Bezier curve and the remaining linear segment.

[0008] Step 2: Input the robot's small line segment machining tool axis direction data, use the 6th degree Bezier curve to transfer and smooth in the RPY angle space under the workpiece coordinate system, and calculate the control points of the Bezier curve analytically according to the maximum allowable value of the tool axis direction smoothing error and the G3 continuity condition constraints at the curve connection. The smoothed path consists of the inserted Bezier curve and the remaining linear segment.

[0009] Step 3: Synchronize the parameters of the tool axis direction and tool tip position path after the smoothing process. Replace the remaining linear segments with B-spline lines to ensure the continuity of the third-order derivative of the tool axis direction relative to the tool tip position path arc length at the cross-segment, and then analytically synchronize the pose parameters. Finally, generate a G3 continuous and parameter-synchronized robot path through the control points solved above.

[0010] Furthermore, the specific method of step one is as follows:

[0011] 11) The tool tip position data of the robot for processing small line segments refers to the position data P = [x, y, z] relative to the workpiece coordinate system. Let the three consecutive tool tip points in the original tool tip point position path be P i-1 , P i , P i+1 At the corner formed by these three points, a 6th-order Bezier curve is used as the transition curve; the curve expression is as follows:

[0012]

[0013] Where P i (u) is the angle at the corner point P i The tool tip position transfer curve inserted at B j,i represents the inserted sixth degree Bezier curve P i (u), where i is the number of the transition curve, j is the number of the control point, and the number of control points is 7; u∈[0,1] is the curve parameter; is the number of combinations;

[0014] 12) Set conditions:

[0015]

[0016] In the formula, When u=0, P i Point to P i-1 The unit tangent vector of ; When u=1, P i Point to P i+1 The unit tangent vector of the tool tip; s is the arc length of the tool tip position path;

[0017] To satisfy Insert the first three control points B of the 6th degree Bezier curve 0,i , B 1,i , B 2,i Should be located at the tool tip position path P i-1 P i On the segment, the last three control points B 4,i , B 5,i , B 6,i Should be located at the tool tip position path P i P i+1 on; to make Established, the following conditions are met:

[0018] Right now:

[0019]

[0020] In the formula, B j,i is the Bezier curve P of the tool tip position i (u), where i is the transfer curve number and j is the control point number; according to the above formula, the length relationship between the control points is as follows:

[0021] To maintain symmetry, let ||B 2,i B 3,i ||=||B 3,i B 4,i ||=l p,i ;

[0022] 13) Set the smoothing parameters of the transfer p,i Requirements:

[0023]

[0024] In the formula, ε pos,max It is the maximum allowable value of the tool tip position smoothing error, and it is generally believed in the industry that the deviation between the midpoint of the inserted curve segment and the original path is the largest;

[0025] 14) Determine the control point, the formula is as follows:

[0026]

[0027] Furthermore, the specific method of step 2 is as follows:

[0028] 21) The robot small line segment processing tool axis direction data refers to the RPY angle data of the tool axis relative to the workpiece coordinate system φ = [α, β, γ], assuming that the three sequentially connected direction points in the original tool axis direction path are φ i-1 ,φ i ,φ i+1At the corner formed by these three points, a 6th-order Bezier curve is used as the transition curve; the curve expression is as follows:

[0029]

[0030] In the formula, φ i (u) is the angle at the corner point φ i The tool axis direction transition curve inserted at j,i is the inserted sixth degree Bezier curve φ i (u), where i is the number of the transition curve, j is the number of the control point, and the number of control points is 7; u∈[0,1] is the curve parameter; is the number of combinations;

[0031] 22) Set conditions:

[0032]

[0033] In the formula, When u=0, φ i Pointing to φ i-1 The unit tangent vector of ; When u=1, φ i Pointing to φ i+1 The unit tangent vector of the tool; s is the arc length of the path in the tool axis direction;

[0034] To satisfy Insert the first three control points Q of the 6th degree Bezier curve 0,i , Q 1,i , Q 2,i Should be located in the tool axis direction path φ i-1 φ i On the segment, the last three control points Q 0,i , Q 1,i , Q 2,i Should be located in the tool axis direction path φ i φ i+1 paragraph; in order to To be established, the following conditions must be met:

[0035] Right now:

[0036]

[0037] In the formula, Q j,i is the Bezier curve φ in the tool axis direction i (u), where i is the transfer curve number and j is the control point number; according to the above formula, the length relationship between the control points is as follows:

[0038] To maintain symmetry, let ||Q 2,i Q 3,i ||=||Q 3,i Q 4,i ||=l o,i ;

[0039] 23) Set the smoothing parameters of the transfer o,i The following conditions are met:

[0040]

[0041] In the formula, ε ori,max is the maximum allowable value of the smoothing error in the tool axis direction, and is used to limit the smoothing error ΔO of the tool axis direction vector within the allowable value. J o is the Jacobian matrix in the tool axis direction, specifically:

[0042]

[0043] In the formula, S α , S β , S γ They are the abbreviations of sin(α), sin(β), and sin(γ), respectively. α , C β , C γ They are the abbreviations of cos(α), cos(β), and cos(γ), respectively; α, β, and γ are the RPY angles of the tool axis relative to the workpiece coordinate system;

[0044] 24) Determine the control point, the formula is as follows:

[0045]

[0046] Furthermore, the specific method of step three is as follows:

[0047] 31) The remaining linear segments in the tool tip position path and tool axis direction path after smoothing are replaced by B-spline fitting, where the degree of B-spline is selected as 5, the number of control points is selected as 9, and the node vector is: U = [0,0,0,0,0,0,0.5,0.5,0.5,1,1,1,1,1,1];

[0048] 32) In order to achieve third-order parameter synchronization, the tool axis direction at the cross-segment should be continuous with respect to the third-order derivative of the tool tip position path arc length, and finally a G3 continuous and parameter synchronized robot path is generated by solving the control points.

[0049] Furthermore, the method for constructing the straight line of the B-spline fitting is as follows:

[0050] 311) The constructed spline line should meet the following conditions:

[0051] a. The straight line constructed by B-spline should maintain the same continuity as the original remaining straight line, the control point should be on the original remaining straight line, and it also needs to satisfy:

[0052]

[0053] b. To ensure the synchronization of parameter analysis, it is necessary to ensure that the first, second, and third order differentials of the tool axis direction relative to the arc length of the tool tip position path are continuous at the span, that is:

[0054]

[0055] 312) Solve the control points and perform B-spline fitting based on the control points to generate a G3 continuous and parameter-synchronized robot path.

[0056] The beneficial effects of the present invention are:

[0057] 1) The present invention adopts the technical solution of G3 continuous local corner smoothing by using the sixth-order Bezier curve, which can improve the low-cost continuity at the connection of the linear path, realize the differential continuity of the motion path curvature, and help avoid sudden changes in the robot speed, acceleration and acceleration direction;

[0058] 2) The present invention realizes parameter synchronization by replacing the remaining straight line segments with B-splines, which can avoid iterative calculations, improve calculation efficiency, and help improve the real-time and stability of robot processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0060] Figure 1 It is a flowchart of the present invention;

[0061] Figure 2 It is the tool tip position path smoothing diagram of the present invention;

[0062] Figure 3 It is the path smoothing diagram of the tool axis direction of the present invention;

[0063] Figure 4 It is the posture synchronization diagram of the present invention;

[0064] Figure 5 It is a curvature comparison diagram of the method of the present invention and the existing method;

[0065] Figure 6It is a comparison chart of the running time of the method of the present invention and the existing method;

[0066] Figure 7 The figure is a comparison diagram of joint acceleration between the method of the present invention and the existing method. DETAILED DESCRIPTION

[0067] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0068] Embodiment 1

[0069] See also Figure 1 This embodiment provides a robot G3 continuous corner smoothing method based on Bezier curve, comprising the following steps:

[0070] Step 1: Input the tool tip position data of the robot for machining small line segments, and use the 6th degree Bezier curve for transfer smoothing in the workpiece coordinate system. According to the maximum allowable value of the tool tip position smoothing error and the G3 continuity (curvature differential continuity) condition constraints at the curve connection, the control points of the Bezier curve are analytically calculated. The smoothed path consists of the inserted Bezier curve and the remaining linear segments, as follows:

[0071] 11) The robot small line segment machining tool tip position data refers to the position data P = [x, y, z] relative to the workpiece coordinate system (WCS), such as Figure 2 As shown in the figure, let the three consecutive tool tip points in the original tool tip position path be P i-1 , P i , P i+1 At the corner formed by these three points, a 6th-order Bezier curve is used as the transition curve; the curve expression is as follows:

[0072]

[0073] Where P i (u) is the angle at the corner point P i The tool tip position transfer curve inserted at B j,i represents the inserted sixth degree Bezier curve P i (u), where i is the number of the transition curve, j is the number of the control point, and the number of control points is 7; u∈[0,1] is the curve parameter; is the number of combinations;

[0074] 12) In order to make the transition curve G3 continuous (curvature differential continuous) at the path connection point of the tool tip point, the following conditions must be met:

[0075]

[0076] like Figure 2 As shown, in the formula, When u=0, P i Point to P i-1 The unit tangent vector of ; When u=1, P i Point to P i+1 The unit tangent vector of the tool tip; s is the arc length of the tool tip position path;

[0077] To satisfy Insert the first three control points B of the 6th degree Bezier curve 0,i , B 1,i , B 2,i Should be located at the tool tip position path P i-1 P i On the segment, the last three control points B 4,i , B 5,i , B 6,i Should be located at the tool tip position path P i P i+1 on; to make Established, the following conditions are met:

[0078] Right now:

[0079]

[0080] In the formula, B j,i is the Bezier curve P of the tool tip position i (u), where i is the transfer curve number and j is the control point number; according to the above formula, the length relationship between the control points is as follows:

[0081] To maintain symmetry, let ||B 2,i B 3,i ||=||B 3,i B 4,i ||=l p,i ;

[0082] 13) In order to avoid overlapping and intersecting of the constructed transfer curves and ensure that the smoothing error is within the maximum allowable value of the tool tip position smoothing error, and at the same time retain a certain residual segment to adjust the tool axis direction and tool tip position synchronization, the transfer smoothing parameter l p,i The following conditions need to be met:

[0083]

[0084] In the formula, ε pos,max is the maximum allowable value of the tool tip position smoothing error, and the industry generally believes that the deviation between the midpoint of the inserted curve segment and the original path is the largest, such as Figure 2 As shown;

[0085] 14) According to the transfer smoothing parameter l p,i And the above geometric relationship determines the control point, the formula is as follows:

[0086]

[0087] Step 2: Input the robot's small line segment machining tool axis direction data, and use the 6th degree Bezier curve to smooth the transition in the RPY angle space under the workpiece coordinate system. According to the maximum allowable value of the tool axis direction smoothing error and the G3 continuity condition constraints at the curve connection, the control points of the Bezier curve are analytically calculated. The smoothed path consists of the inserted Bezier curve and the remaining linear segment, as follows:

[0088] 21) The robot small line segment machining tool axis direction data refers to the RPY angle data φ = [α, β, γ] of the tool axis relative to the workpiece coordinate system (WCS), such as Figure 3 As shown, let the three sequentially connected direction points in the original tool axis direction path be φ i-1 ,φ i ,φ i+1 At the corner formed by these three points, a 6th-order Bezier curve is used as the transition curve; the curve expression is as follows:

[0089]

[0090] In the formula, φ i (u) is the angle at the corner point φ i The tool axis direction transition curve inserted at j,i is the inserted sixth degree Bezier curve φ i (u), where i is the number of the transition curve, j is the number of the control point, and the number of control points is 7; u∈[0,1] is the curve parameter; is the number of combinations;

[0091] 22) In order to make the transition curve G3 continuous (curvature differential continuous) at the path connection point in the tool axis direction, the following conditions must be met:

[0092]

[0093] like Figure 3 As shown, in the formula, When u=0, φ i Pointing to φi-1 The unit tangent vector of ; When u=1, φ i Pointing to φ i+1 The unit tangent vector of the tool; s is the arc length of the path in the tool axis direction;

[0094] To satisfy like Figure 3 As shown, insert the first three control points Q of the 6th degree Bezier curve 0,i , Q 1,i , Q 2,i Should be located in the tool axis direction path φ i-1 φ i On the segment, the last three control points Q 0,i , Q 1,i , Q 2,i Should be located in the tool axis direction path φ i φ i+1 paragraph; in order to To be established, the following conditions must be met:

[0095] Right now:

[0096]

[0097] In the formula, Q j,i is the Bezier curve φ in the tool axis direction i (u), where i is the transfer curve number and j is the control point number; according to the above formula, the length relationship between the control points is as follows:

[0098] To maintain symmetry, let ||Q 2,i Q 3,i ||=||Q 3,i Q 4,i ||=l o,i ;

[0099] 23) In order to avoid overlapping and intersecting of the constructed transfer curves and ensure that the smoothing error is within the maximum allowable value of the smoothing error in the tool axis direction, and to reserve a certain residual segment to adjust the tool axis direction and tool tip position synchronization, the transfer smoothing parameter l o,i The following conditions need to be met:

[0100]

[0101] In the formula, ε ori,max is the maximum allowable value of the smoothing error in the tool axis direction, and is used to limit the smoothing error ΔO of the tool axis direction vector within the allowable value. J o is the Jacobian matrix in the tool axis direction, specifically:

[0102]

[0103] In the formula, S α , S β , S γ They are the abbreviations of sin(α), sin(β), and sin(γ), respectively. α , C β , C γ They are the abbreviations of cos(α), cos(β), and cos(γ), respectively; α, β, and γ are the RPY angles of the tool axis relative to the workpiece coordinate system;

[0104] 24) According to the transfer smoothing parameter l o,i And the above geometric relationship determines the control point, the formula is as follows:

[0105]

[0106] Step 3: Synchronize the parameters of the tool axis direction and tool tip position path after the smoothing. Replace the remaining linear segment with a B-spline line to ensure that the third-order derivative of the tool axis direction relative to the tool tip position path arc length at the cross-segment is continuous, and then analytically synchronize the pose parameters. Finally, a G3 continuous and parameter-synchronized robot path is generated through the control points solved above. The purpose of replacing the remaining linear segment is to analytically synchronize the parameters. The control points obtained through the above three steps are fitted with a B-spline to obtain the path, as follows:

[0107] 31) The remaining linear segments in the tool tip position path and tool axis direction path after smoothing are replaced by B-spline fitting, where the degree of B-spline is selected as 5, the number of control points is selected as 9, and the node vector is: U = [0,0,0,0,0,0,0.5,0.5,0.5,1,1,1,1,1,1];

[0108] The method for constructing the straight line of the B-spline fitting is as follows:

[0109] 311) The constructed spline line should meet the following conditions:

[0110] a. The straight line constructed by B-spline should maintain the same continuity as the original remaining straight line, the control point should be on the original remaining straight line, and it also needs to satisfy:

[0111]

[0112] b. Ensure that the first, second, and third order differentials of the tool axis direction relative to the arc length of the tool tip position path are continuous at the span, that is:

[0113]

[0114] 312) Solve the control points and then obtain the straight line of B-spline fitting to achieve analytical synchronization of posture parameters.

[0115] 32) Perform B-spline fitting based on the required control points to generate a G3 continuous and parameter-synchronized robot path.

[0116] In summary, through the above three steps, a high-order continuous motion path can be generated, and parameter synchronization does not require iterative calculation; the present invention adopts the technical solution of 6th-order Bezier curve for G3 continuous local corner smoothing, which can improve the low-cost continuity at the connection of linear paths and realize the differential continuity of the curvature of the motion path, which is beneficial to avoid sudden changes in the robot speed, acceleration and acceleration direction. In addition, by using B-spline to replace the remaining straight line segments to achieve parameter synchronization, iterative calculation can be avoided, the calculation efficiency is improved, and it is beneficial to improve the real-time and stability of robot processing.

[0117] Embodiment 2

[0118] In order to verify the effectiveness and superiority of the method proposed in the invention, an existing method was selected to compare and verify the present invention;

[0119] Depend on Figure 5 It can be seen that in terms of curvature, the robot G3 continuous corner smoothing method based on Bezier curve proposed in the present invention has a smaller curvature extreme value, which means that the motion path constructed by the present invention is more continuous and smoother, which is beneficial to improving the robot processing stability.

[0120] Depend on Figure 6 It can be seen that in terms of running time, the robot G3 continuous corner smoothing method based on Bezier curve proposed in the present invention has a relatively short running time and high running efficiency, which can improve the real-time performance and efficiency of robot processing.

[0121] Depend on Figure 7 It can be seen that in terms of joint acceleration, the robot G3 continuous corner smoothing method based on Bezier curve proposed in the present invention has relatively smaller fluctuations and mutations in joint jerk, which further verifies that the method of the present invention can improve the robot's motion performance.

[0122] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A robot G3 continuous corner smoothing method based on Bezier curve, characterized in that: The following steps are involved: Step 1: Input the tool tip position data of the robot for machining small line segments, and use the 6th degree Bezier curve for transfer smoothing in the workpiece coordinate system. According to the maximum allowable value of the tool tip position smoothing error and the G3 continuity condition constraints at the curve connection, the control points of the Bezier curve are analytically calculated. The smoothed path consists of the inserted Bezier curve and the remaining linear segment. Step 2: Input the robot's small line segment machining tool axis direction data, use the 6th degree Bezier curve to transfer and smooth in the RPY angle space under the workpiece coordinate system, and calculate the control points of the Bezier curve analytically according to the maximum allowable value of the tool axis direction smoothing error and the G3 continuity condition constraints at the curve connection. The smoothed path consists of the inserted Bezier curve and the remaining linear segment. Step 3: Synchronize the parameters of the tool axis direction and tool tip position path after the smoothing process. Replace the remaining linear segments with B-spline lines to ensure the continuity of the third-order derivative of the tool axis direction relative to the tool tip position path arc length at the cross-segment, and then analytically synchronize the pose parameters. Finally, generate a G3 continuous and parameter-synchronized robot path through the control points solved above.

2. A robot G3 continuous corner smoothing method based on Bezier curve according to claim 1, characterized in that: The specific method of step one is as follows: 11) The tool tip position data of the robot for processing small line segments refers to the position data P = [x, y, z] relative to the workpiece coordinate system. Let the three consecutive tool tip points in the original tool tip point position path be P i-1 , P i , P i+1 At the corner formed by these three points, a 6th-order Bezier curve is used as the transition curve; the curve expression is as follows: Where P i (u) is the angle at the corner point P i The tool tip position transfer curve inserted at B j,i represents the inserted sixth degree Bezier curve P i (u) is the control point of the transition curve, where i is the number of the transition curve, j is the number of the control point, and the number of control points is 7; u∈[0,1] is the curve parameter; is the number of combinations; 12) Set conditions: In the formula, When u=0, P i Point to P i-1 The unit tangent vector of ; When u=1, P i Point to P i+1 The unit tangent vector of the tool tip; s is the arc length of the tool tip position path; To satisfy Insert the first three control points B of the 6th degree Bezier curve 0,i , B 1,i , B 2,i Should be located at the tool tip position path P i-1 P i On the segment, the last three control points B 4,i , B 5,i , B 6,i Should be located at the tool tip position path P i P i+1 on; to make Established, the following conditions are met: Right now: In the formula, B j,i is the Bezier curve P of the tool tip position i (u), where i is the transfer curve number and j is the control point number; according to the above formula, the length relationship between the control points is as follows: To maintain symmetry, let ||B 2,i B3,i||=||B 3,i B4,i||=l p,i ; 13) Set the smoothing parameters of the transfer p,i Requirements: In the formula, ε pos,max It is the maximum allowable value of the tool tip position smoothing error, and it is generally believed in the industry that the deviation between the midpoint of the inserted curve segment and the original path is the largest; 14) Determine the control point, the formula is as follows:

3. The robot G3 continuous corner smoothing method based on Bezier curve according to claim 1, characterized in that: The specific method of step 2 is as follows: 21) The robot small line segment processing tool axis direction data refers to the RPY angle data of the tool axis relative to the workpiece coordinate system φ = [α, β, γ], assuming that the three sequentially connected direction points in the original tool axis direction path are φ i-1 ,φ i ,φ i+1 At the corner formed by these three points, a 6th-order Bezier curve is used as the transition curve; The curve expression is as follows: In the formula, φ i (u) is the angle at the corner point φ i The tool axis direction transition curve inserted at j,i is the inserted sixth degree Bezier curve φ i (u) is the control point of the transition curve, where i is the number of the transition curve, j is the number of the control point, and the number of control points is 7; u∈[0,1] is the curve parameter; is the number of combinations; 22) Set conditions: In the formula, When u=0, φ i Pointing to φ i-1 The unit tangent vector of ; When u=1, φ i Pointing to φ i+1 The unit tangent vector of ; s is the arc length of the path in the tool axis direction; To satisfy Insert the first three control points Q of the 6th degree Bezier curve 0,i , Q 1,i , Q 2,i Should be located in the tool axis direction path φ i-1 φ i On the segment, the last three control points Q 0,i , Q 1,i , Q 2,i Should be located in the tool axis direction path φ i φ i+1 paragraph; in order to To be established, the following conditions must be met: Right now: In the formula, Q j,i is the Bezier curve φ in the tool axis direction i (u), where i is the transfer curve number and j is the control point number; according to the above formula, the length relationship between the control points is as follows: To maintain symmetry, let ||Q 2,i Q 3,i ||=||Q 3,i Q 4,i ||=l o,i ; 23) Set the smoothing parameters of the transfer o,i The following conditions are met: In the formula, ε ori,max is the maximum allowable value of the smoothing error in the tool axis direction, and is used to limit the smoothing error ΔO of the tool axis direction vector within the allowable value. J o is the Jacobian matrix in the tool axis direction, specifically: In the formula, S α , S β , S γ They are the abbreviations of sin(α), sin(β), and sin(γ), respectively. α , C β , C γ They are the abbreviations of cos(α), cos(β), and cos(γ), respectively; α, β, and γ are the RPY angles of the tool axis relative to the workpiece coordinate system; 24) Determine the control point, the formula is as follows:

4. The robot G3 continuous corner smoothing method based on Bezier curve according to claim 1, characterized in that: The specific method of step three is as follows: 31) The remaining linear segments in the tool tip position path and tool axis direction path after smoothing are replaced by B-spline fitting, where the degree of B-spline is selected as 5, the number of control points is selected as 9, and the node vector is: U = [0,0,0,0,0,0,0.5,0.5,0.5,1,1,1,1,1,1]; 32) In order to achieve third-order parameter synchronization, the tool axis direction at the cross-segment should be continuous with respect to the third-order derivative of the tool tip position path arc length, and finally a G3 continuous and parameter synchronized robot path is generated by solving the control points.

5. The robot G3 continuous corner smoothing method based on Bezier curve according to claim 1, characterized in that: The method for constructing the straight line of the B-spline fitting is as follows: 311) The constructed spline line should meet the following conditions: a. The straight line constructed by B-spline should maintain the same continuity as the original remaining straight line, the control point should be on the original remaining straight line, and it also needs to satisfy: b. Ensure that the first, second, and third order differentials of the tool axis direction relative to the arc length of the tool tip position are continuous at the span, that is: 312) Solve the control points and obtain the straight line of B-spline fitting.

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