Cutter shaft synchronous optimization method for fairing track

Abstract

The invention relates to the technical field of motion planning, and particularly discloses a cutter shaft synchronous optimization method for a fairing track, which comprises the following steps of: inserting an Airthoid curve at a corner of a cutter tip as a cutter tip fairing curve corresponding to the corner of the cutter tip, and determining the transition length of the cutter tip fairing curve according to a cutter tip approximate error and a continuity condition; symmetrical Airthoid curves are inserted into the corner of the cutter shaft to serve as a cutter shaft fairing curve corresponding to the corner of the cutter shaft, and the transition length of the cutter shaft fairing curve is determined according to the approximate error of the cutter shaft and the continuity condition; obtaining preliminary interpolation data of the robot which only considers the tool nose constraint; optimizing redundant control vertexes of remaining linear segments of the linear path of the cutter shaft based on a least square method, and realizing optimization of a fairing curve of the cutter shaft; and finally, obtaining final interpolation data of the robot based on a convex optimization time optimal speed planning method. According to the invention, the processing efficiency is improved on the premise of ensuring that the fairing continuity is not damaged and the constraint of each driving shaft is not changed.

Description

Technical Field

[0001] The invention relates to the technical field of motion planning, and in particular to a tool axis synchronization optimization method for a smooth trajectory. Background Art

[0002] In the field of CNC machining, the application of smoothing the discrete linear instructions of tool paths generated by computer-aided manufacturing software is very extensive. Path smoothing methods that need to smooth both the position and posture of robots and then synchronize parameters have also emerged. Through the path smoothing method, the pause at the corner during machining is effectively reduced, which improves machining efficiency and effectively reduces machining vibration.

[0003] Reference 1: He S, Yan C, Deng Y, et al. A tolerance constrained g2continuous path smoothing and interpolation method for industrial scararobots[J]. Robotics and Computer Integrated Manufacturing. 2020, 101907 discloses a method for smoothing the position of a SCARA robot using a B-spline curve in a workpiece coordinate system. First, a pseudo-linear trajectory is obtained by iteration under the approximate error and corner optimal constraints, and then a B-spline curve is used for geometric smoothing to obtain a G2 continuous smooth trajectory. However, due to the nonlinear mapping between the arc length of the B-spline and its parameters, this poses a challenge to the real-time performance of the CNC system.

[0004] Reference 2: JiXiang Y, Abulikemu A, Han D. Real time tool path smoothing of short linear commands for robot manipulator by constructing asymmetrical Pythagoran-hodograph (PH) splines[J]. Science China Technological Sciences, 2023, 66(3): 674-688 discloses a robot smoothing method based on PH splines, which uses PH splines to smooth the pose in the joint coordinate system and achieves parameter synchronization by satisfying a certain ratio of displacement. However, the process of backcalculating the corresponding parameters of PH splines when the displacement value is known cannot be analyzed.

[0005] The above research often focuses on the characteristics of the smoothing curve itself in terms of approximate error control, computational efficiency, and ensuring high-order continuity at the connection points. Although the method of synchronization using parameters can effectively ensure the smoothness of the robot's motion, there is often a sudden change in acceleration when the robot moves to the smooth connection point. This is because the smoothing method based on the parameter synchronization strategy obtains the tool axis result according to the parameters corresponding to the tool tip interpolation point during trajectory planning, and the remaining linear segment tool axis often undergoes a drastic acceleration and deceleration process. Therefore, the synchronized tool axis in robot planning will extend the entire processing time. The optimization of the remaining linear segments on the robot's smooth path is rarely considered, which makes it difficult to improve the robot's processing efficiency. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a tool axis synchronization optimization method with a smooth trajectory, which can effectively improve the robot processing efficiency.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions: A tool axis synchronization optimization method for a smooth trajectory optimizes the remaining linear segments of the robot tool axis linear path while achieving smooth robot posture, specifically including: A symmetrical Airthoid curve is inserted at a tool tip corner composed of adjacent tool tip linear paths as a tool tip smoothing curve corresponding to the tool tip corner, and a transition length of the tool tip smoothing curve is determined according to a tool tip approximation error and a continuity condition; a symmetrical Airthoid curve is inserted at a tool axis corner composed of adjacent tool axis linear paths as a tool axis smoothing curve corresponding to the tool axis corner, and a transition length of the tool axis smoothing curve is determined according to a tool axis approximation error and a continuity condition; the remaining linear segments of the tool tip linear path and the tool axis linear path are both represented by B-spline curves, and continuity is achieved by controlling vertex distribution; A time-optimal velocity planning method based on convex optimization is used to obtain preliminary interpolation data of the robot considering only the tool tip constraint; The redundant control vertices of the remaining linear segments of the tool axis linear path are optimized based on the least square method to achieve tool axis smooth curve optimization; Again, based on the time-optimal speed planning method of convex optimization, the final interpolation data of the robot is obtained.

[0008] In one embodiment, determining the tool tip smoothing curve transition length according to the tool tip approximation error and the continuity condition specifically includes: The Airthoid curve inserted into the tool tip corner needs to meet the set tool tip approximation error The constraint is, then the transition curve length of the tool tip smoothing curve of the kth tool tip corner is The constraints are: ; (1) in, is half of the supplementary angle of the kth tool tip corner; the kth tool tip corner is composed of the adjacent tool tip linear path , constitute; Indicates that the tool tip smoothing curve is The displacement component in the direction, Indicates that the tool tip smoothing curve is The displacement component in the orthogonal direction; the transition curve length of the tool tip smoothing curve of the kth tool tip corner The value of is the maximum value that satisfies formula (1).

[0009] In one embodiment, in order to ensure the existence of the remaining linear segment of the tool tip linear path and meet the distribution requirements of the control vertices, the transition curve length of the tool tip smoothing curve of the kth tool tip corner is On the basis of satisfying the constraints of formula (1), it is necessary to further satisfy: ; (2) in, is the smoothing characteristic parameter corresponding to the kth tool tip corner, Indicates the length of the calculated linear path, the transition curve length of the tool tip smoothing curve of the kth tool tip corner The value of is the maximum value that satisfies both equations (1) and (2).

[0010] In one embodiment, determining the transition length of the tool axis smoothing curve according to the tool axis approximation error and the continuity condition specifically includes: The kth tool axis corner is composed of the adjacent tool axis linear path , Composition, knife axis point , , They are all on the surface of the unit sphere, and the center of the unit sphere is denoted by C; The midpoint of the tool axis smoothing curve corresponding to the kth tool axis corner is recorded as ; The tool axis vector at the point where the tool axis approximation error is the largest corresponding to the kth corner is , The knife axis vector with the kth corner The deviation is recorded as the tool axis approximate error : ; Will The plane is used as the tool axis smoothing plane, and the approximate error of the tool axis smoothing plane is constrained accomplish Constraints are used to determine the preliminary tool axis smoothing curve: ; in, for and The angle of In order to ensure the existence of the remaining linear segment and meet the distribution requirements of the control vertices, the transition length of the tool axis smoothing curve is The constraints are: ; in, is the direction of the tool axis speed at the midpoint of the tool axis smoothing curve at the kth corner and The angle of and They are the linear paths of the tool axis in the tool axis smoothing plane. The corresponding transition length , tool axis linear path The corresponding transition length ; Indicates the starting point of the tool axis smoothing curve corresponding to the kth tool axis corner, is the end point of the tool axis smoothing curve corresponding to the k-1th tool axis corner, Indicates that the tool axis smoothing curve is The displacement component in the direction, Indicates that the tool axis smoothing curve is The displacement components in the orthogonal directions of .

[0011] In one embodiment, the remaining linear segment of the tool tip linear path is represented by a B-spline curve, and continuity is achieved by controlling vertex distribution, specifically including: Control vertices of the B-spline curve of the remaining linear segment of the tool tip linear path to The expression is:

[0012] in, and Tip point and The transition length of the tool tip smooth curve at is the unit direction vector.

[0013] In one embodiment, the remaining linear segments of the tool axis linear path are represented by B-spline curves, and the continuity is achieved by controlling the vertex distribution, specifically including: Control vertices of the B-spline curve of the remaining linear segment of the tool axis linear path to The expression is:

[0014] in, , Indicates The length of the tool axis smoothing curve corresponding to the tool axis corner is Indicates the characteristic parameters of the tool axis smoothing curve. The length of the smoothing start point of the kth tool axis corner , The length of the smoothing end of the k-1th tool axis corner , Indicates the starting point of the tool axis smoothing curve corresponding to the kth tool axis corner, is the end point of the tool axis smoothing curve corresponding to the k-1th tool axis corner. They are , , , , Indicates the linear path of the tool axis The midpoint of .

[0015] In one embodiment, the time-optimal velocity planning method based on convex optimization obtains preliminary interpolation data of the robot considering only the tool tip constraint, specifically comprising: For the hybrid path composed of B-spline curves and Airthoid curves, the time-optimal speed planning method based on convex optimization is used to obtain the preliminary interpolation data of the robot; among them, the tangential constraint of the robot end position is constructed: ; in, is the robot joint angle, are the first-order derivative, second-order derivative, and third-order derivative of the robot joint angle with respect to the tool tip displacement, Expressed as tool tip displacement, are respectively the tool tip tangential velocity, tool tip tangential acceleration, and tool tip tangential jerk, They are joint angular velocity, joint angular acceleration, and joint angular jerk respectively; The robot speed planning model is: ; ; in, represents maximization, is the tool tip tangential velocity constraint, is the tool tip tangential acceleration constraint, is the tool tip tangential acceleration constraint, is the joint velocity constraint, is the joint acceleration constraint, is the joint jerk constraint, It is the total displacement of the tool tip smooth path composed of the tool tip smooth curve and the remaining straight line segment; the preliminary interpolation data is obtained through the robot speed planning model.

[0016] In one of the embodiments, the invention further includes: in order to ensure that the kinematics of the hybrid path does not exceed the limit, when selecting the sampling point through the robot speed planning model, the starting point, the midpoint and the end point of the tool tip smoothing curve and the tool axis smoothing curve in the hybrid path are fixedly selected, and the node vector of the speed spline obtained through the robot speed planning model is determined. for: ; in, is the total number of sampling points, is the displacement of the jth sampling point.

[0017] In one embodiment, the method of optimizing the redundant control vertices of the remaining linear segments of the tool axis linear path based on the least square method to achieve tool axis smoothing curve optimization specifically includes: According to the preliminary interpolation data and parameter synchronization strategy, the angular velocity of the tool axis at the same time can be determined and tool axis angular acceleration The relationship is: ; in, are the tool tip tangential velocity and tool tip tangential acceleration, respectively. is the angular displacement of the tool axis, are respectively the tool axis angular displacement with respect to the spline parameters The first and second derivatives of are respectively the tool tip parameter curve with respect to the spline parameters The first and second derivatives of represents the inner product; Select the remaining linear segments in the tool axis linear path. observation points, at each observation point, the objective function is established with the minimum angular acceleration of the remaining linear segment of the tool axis linear path as the goal, and the least squares method is used for constraints: ; in, is a constant matrix, represents the spline parameters of the i-th observation point, , is the tool tip tangential acceleration, represents the tangential velocity of the tool tip, They represent the first-order derivative and second-order derivative of the B-spline curve basis function of the remaining linear segment angular displacement of the tool axis linear path, The control vertices of the B-spline curve representing the angular displacement of the remaining linear segment of the tool axis linear path; The least square method constraints are simplified and combined with the angular velocity constraints to achieve tool axis smooth curve optimization.

[0018] In one embodiment, simplifying the least squares constraint and combining it with the angular velocity constraint specifically includes: ; ; in, are the redundant control vertices of the remaining linear segments, The constant matrix, is the two-norm, Indicates the maximum angular velocity of the tool axis. It is expressed as the tangential velocity of the tool tip at the i-th observation point.

[0019] Compared with the prior art, the beneficial technical effects of the present invention are: The present invention utilizes the constrained tool axis and tool tip approximate errors analyzed by the Airhtoid curve, and realizes parameter synchronization through the linear segment residual B-spline, thereby realizing the smoothing of the robot path; the tool axis vector optimization of the residual linear segment of the tool axis is realized based on the least squares method; and the processing efficiency is improved under the premise of ensuring that the smoothing continuity is not destroyed and the constraints of each driving axis remain unchanged. The present invention has the advantages of high computational efficiency and flexible motion ability, and is more suitable for the online application of the robot trajectory speed planning algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the specific implementation of the present invention, the following briefly introduces the drawings required for use in the specific implementation. Obviously, the drawings described below are only drawings of some implementations of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0021] Figure 1 is a flow chart of a method in an embodiment of the present invention.

[0022] Figure 2 It is a schematic diagram of using the Airthoid curve to smooth the tool tip in an embodiment of the present invention.

[0023] Figure 3a and Figure 3b It is a schematic diagram of using the Airthoid curve to smooth the tool axis in an embodiment of the present invention.

[0024] Figure 4 This is a comparison diagram of the tool axis accelerations obtained by the method of the present invention and the non-optimized method.

[0025] Figure 5This is a comparison chart of tool tip speeds obtained by the method of the present invention and a non-optimized method. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0027] like Figure 1 As shown, the present invention discloses a tool axis synchronization optimization method for a smooth trajectory, which optimizes the remaining linear segments of the robot tool axis linear path while achieving robot posture smoothness, and specifically includes the following steps: S1, inserting a symmetrical Airthoid curve at a tool tip corner composed of adjacent tool tip linear paths as a tool tip smoothing curve corresponding to the tool tip corner, and determining a tool tip smoothing curve transition length according to a tool tip approximation error and a continuity condition; inserting a symmetrical Airthoid curve at a tool axis corner composed of adjacent tool axis linear paths as a tool axis smoothing curve corresponding to the tool axis corner, and determining a tool axis smoothing curve transition length according to a tool axis approximation error and a continuity condition; the remaining linear segments of the tool tip linear path and the tool axis linear path are both represented by B-spline curves, and continuity is achieved by controlling vertex distribution; S2, a time-optimal velocity planning method based on convex optimization is used to obtain preliminary interpolation data of the robot considering only the tool tip constraint; S3, based on the least square method, the redundant control vertices of the remaining linear segments of the tool axis linear path are optimized to achieve tool axis smoothing curve optimization; S4, again based on the time-optimal speed planning method of convex optimization, obtains the final interpolation data of the robot.

[0028] The interpolation data is the robot's joint angles, parameters, and tool tip displacements at each interpolation cycle. For B-spline curves, the parameters are the spline parameters, and for Airthoid curves, the parameters are the Airthoid parameters. The interpolation cycle is the minimum time unit for the CNC system to perform interpolation calculations and position control.

[0029] In one embodiment, determining the tool tip smoothing curve transition length according to the tool tip approximation error and the continuity condition in step S1 specifically includes: Inserting the Airthoid curve into the tool tip corner needs to meet the tool tip approximation error set by the user The constraint is, then the transition curve length of the tool tip smoothing curve of the kth tool tip corner is The constraints are: ; (1) in, is half of the supplementary angle of the kth tool tip corner; the kth tool tip corner is composed of the adjacent tool tip linear path , constitute; Indicates that the tool tip smoothing curve is The displacement component in the direction, Indicates that the tool tip smoothing curve is The displacement component in the orthogonal direction of ; ; ; Represents the integral variable, representing 0 to A continuously changing angle value between; the transition curve length of the tool tip smoothing curve of the kth tool tip corner The value of is the maximum value that satisfies formula (1).

[0030] In one embodiment, the method further includes: in order to ensure the existence of the remaining linear segment of the tool tip linear path and to meet the distribution requirements of the control vertices, the transition curve length of the tool tip smoothing curve of the kth tool tip corner is On the basis of satisfying the constraints of formula (1), it is necessary to further satisfy: ; (2) in, is the smoothing characteristic parameter corresponding to the kth tool tip corner, Indicates the length of the calculated linear path, the transition curve length of the tool tip smoothing curve of the kth tool tip corner The value of is the maximum value that satisfies both equations (1) and (2).

[0031] In one embodiment, determining the tool axis smoothing curve transition length according to the tool axis approximation error and the continuity condition in step S1 specifically includes: See also Figure 3a and Figure 3b , the kth corner is composed of the adjacent tool axis linear path , Composition, knife axis point , , They are all on the surface of the unit sphere, and the center of the unit sphere is denoted by C; The midpoint of the tool axis smoothing curve corresponding to the kth tool axis corner is recorded as ; The tool axis vector at the point where the tool axis approximation error is the largest corresponding to the kth corner is , The knife axis vector with the kth corner The deviation is recorded as the tool axis approximate error : ; Will The plane is used as the tool axis smoothing plane, and the approximate error of the tool axis smoothing plane is constrained accomplish Constraints are used to determine the preliminary tool axis smoothing curve: ; in, for and The angle of In order to ensure the existence of the remaining linear segment and meet the distribution requirements of the control vertices, the transition length of the tool axis smoothing curve is The constraints are: ; in, is the direction of the tool axis speed at the midpoint of the tool axis smoothing curve at the kth corner and The angle of and They are the linear paths of the tool axis in the tool axis smoothing plane. The corresponding transition length , tool axis linear path The corresponding transition length ; Indicates the starting point of the tool axis smoothing curve corresponding to the kth tool axis corner, is the end point of the tool axis smoothing curve corresponding to the k-1th tool axis corner, Indicates that the tool axis smoothing curve is The displacement component in the direction, Indicates that the tool axis smoothing curve is The displacement components in the orthogonal directions of ; ; Represents the integral variable, representing 0 to A continuously changing angle value between .

[0032] The final tool axis smooth transition length is determined thereby, and the tool axis smooth curve is determined.

[0033] In one embodiment, the remaining linear segment of the tool tip linear path is represented by a B-spline curve, and continuity is achieved by controlling vertex distribution, specifically including: Control vertices of the B-spline curve of the remaining linear segment of the tool tip linear path to The expression is:

[0034] in, and Tip point and The transition length of the tool tip smooth curve at is the unit direction vector.

[0035] In a preferred embodiment, based on the parameter synchronization strategy, in order to ensure the high-order parameter continuity of the tool tip smoothing path composed of the remaining linear segment of the tool tip linear path and the Airthoid curve, a 5th-order B-spline curve is used to represent the remaining linear segment, and the node vector is designed to be: [0,0,0,0,0, 0,0.2,0.4,0.6,0.8,1,1,1,1,1,1], and the control vertex is set to to , a total of 10, see Figure 2 ; Figure 2 The linear NURNS in represents the interpolated B-spline curve, which in this embodiment represents a straight line.

[0036] In one embodiment, the remaining linear segments of the tool axis linear path are represented by B-spline curves, and the continuity is achieved by controlling the vertex distribution, specifically including: Control vertices of the B-spline curve of the remaining linear segment of the tool axis linear path to The expression is:

[0037] in, , Indicates the length of the tool axis smoothing curve corresponding to the kth corner, Indicates the characteristic parameters of the tool axis smoothing curve. The length of the smoothing start point of the kth tool axis corner , The length of the smoothing end of the k-1th tool axis corner , Indicates the starting point of the tool axis smoothing curve corresponding to the kth tool axis corner, is the end point of the tool axis smoothing curve corresponding to the k-1th tool axis corner. They are , , , , Indicates the linear path of the tool axis The midpoint of .

[0038] In a preferred embodiment, based on the parameter synchronization strategy, in order to ensure the high-order parameter continuity of the tool axis smoothing path composed of the remaining linear segments of the tool axis linear path and the Airthoid curve, the 5th-order B-spline curve is used to represent the remaining linear segments, and the node vector is designed to be: [0,0,0,0,0,0,0.2,0.4,0.6,0.8,1,1,1,1,1,1], and the control vertex is set to to , a total of 10. Among them, the control vertices of the tool axis spline curve It is only a preliminary determination and needs further optimization.

[0039] In one embodiment, the time-optimal velocity planning method based on convex optimization obtains preliminary interpolation data of the robot considering only the tool tip constraint, specifically comprising: For the hybrid path composed of B-spline curves and Airthoid curves, the time-optimal speed planning method based on convex optimization is used to obtain the preliminary interpolation data of the robot; among them, the tangential constraint of the robot end position is constructed: ; in, is the robot joint angle, are the first-order derivative, second-order derivative, and third-order derivative of the robot joint angle with respect to the tool tip displacement, Expressed as tool tip displacement, are respectively the tool tip tangential velocity, tool tip tangential acceleration, and tool tip tangential jerk, They are joint angular velocity, joint angular acceleration, and joint angular jerk respectively; The robot speed planning model is: ; ; in, represents maximization, is the tool tip tangential velocity constraint, is the tool tip tangential acceleration constraint, is the tool tip tangential acceleration constraint, is the joint velocity constraint, is the joint acceleration constraint, is the joint jerk constraint, It is the total displacement of the tool tip smooth path composed of the tool tip smooth curve and the remaining straight line segment; the preliminary interpolation data is obtained through the robot speed planning model.

[0040] In one of the embodiments, the invention further includes: in order to ensure that the kinematics of the hybrid path does not exceed the limit, when selecting the sampling point through the robot speed planning model, the starting point, the midpoint and the end point of the tool tip smoothing curve and the tool axis smoothing curve in the hybrid path are fixedly selected, and the node vector of the speed spline obtained through the robot speed planning model is determined. for: ; in, is the total number of sampling points, is the displacement of the jth sampling point.

[0041] In one embodiment, the method of optimizing the redundant control vertices of the remaining linear segments of the tool axis linear path based on the least square method to achieve tool axis smoothing curve optimization specifically includes: According to the preliminary interpolation data and parameter synchronization strategy, the angular velocity of the tool axis at the same time can be determined and tool axis angular acceleration The relationship is: ; in, are the tool tip tangential velocity and tool tip tangential acceleration, respectively. is the angular displacement of the tool axis, are respectively the tool axis angular displacement with respect to the spline parameters The first and second derivatives of are respectively the tool tip parameter curve with respect to the spline parameters The first and second derivatives of represents the inner product; Select the remaining linear segments in the tool axis linear path. Observation points , the objective function is established with the minimum angular acceleration of the remaining linear segment of the tool axis linear path at each observation point, and the least squares method is used for constraints: ; in, is a constant matrix, represents the spline parameters of the i-th observation point, is the tool tip tangential acceleration, represents the tangential velocity of the tool tip, They represent the first-order derivative and second-order derivative of the B-spline curve basis function of the remaining linear segment angular displacement of the tool axis linear path, The control vertices of the B-spline curve representing the angular displacement of the remaining linear segment of the tool axis linear path; Simplify the least squares constraint and combine it with the angular velocity constraint: ; ; in, are the redundant control vertices of the remaining linear segments, The constant matrix, is the two-norm, Indicates the maximum angular velocity of the tool axis. It is expressed as the tangential velocity of the tool tip at the i-th observation point.

[0042] The position of the tool axis is determined by the tool tip parameters: in the smooth curve segment, the movement synchronization of the tool axis and the tool tip is achieved by the proportional linear increase of the extreme values ​​of their trajectory curvature; in the straight line motion stage, the angular displacement of the tool axis is described by a quintic B-spline curve and changes synchronously with the tool tip displacement increment, while ensuring the C3 continuity of the tool axis at the connection between the straight line segment and the smooth segment.

[0043] like Figure 4 As shown, the present invention can firstly effectively realize the smoothness of the robot at the discrete path and the kinematic continuity at the connection point, thereby improving the processing efficiency. Furthermore, the method of the present invention can optimize the robot's tool axis acceleration that changes sharply near the connection point, effectively reduce the tool axis peak acceleration, and ensure smooth motion. At the same time, in this embodiment, the tool axis is close to the North Pole, demonstrating the robustness of the method of the present invention.

[0044] like Figure 5 As shown, the present invention can firstly effectively realize the smoothness of the robot at the discrete path and the speed continuity at the connection point, thereby improving the processing efficiency. Furthermore, the method of the present invention can realize the optimization of the linear segment of the tool axis with a long path, further improve the movement efficiency and reduce frequent and drastic acceleration and deceleration while ensuring that various constraints are not exceeded.

[0045] It should be understood that, although the steps in the flowcharts of the accompanying drawings of the specification are displayed in sequence as indicated by the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts of the accompanying drawings of the specification may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0046] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.

[0047] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A tool axis synchronization optimization method for a smooth trajectory, characterized in that: While achieving smoothing of the robot's posture, optimize the remaining linear segments of the robot's tool axis linear path, including: A symmetrical Airthoid curve is inserted at a tool tip corner composed of adjacent tool tip linear paths as a tool tip smoothing curve corresponding to the tool tip corner, and a transition length of the tool tip smoothing curve is determined according to a tool tip approximation error and a continuity condition; a symmetrical Airthoid curve is inserted at a tool axis corner composed of adjacent tool axis linear paths as a tool axis smoothing curve corresponding to the tool axis corner, and a transition length of the tool axis smoothing curve is determined according to a tool axis approximation error and a continuity condition; the remaining linear segments of the tool tip linear path and the tool axis linear path are both represented by B-spline curves, and continuity is achieved by controlling vertex distribution; A time-optimal velocity planning method based on convex optimization is used to obtain preliminary interpolation data of the robot considering only the tool tip constraint; The redundant control vertices of the remaining linear segments of the tool axis linear path are optimized based on the least square method to achieve tool axis smooth curve optimization; Again, based on the time-optimal speed planning method of convex optimization, the final interpolation data of the robot is obtained.

2. The tool axis synchronization optimization method for a smooth trajectory according to claim 1 is characterized in that: Determining the transition length of the tool tip smoothing curve according to the tool tip approximate error and the continuity condition specifically includes: The Airthoid curve inserted into the tool tip corner needs to meet the set tool tip approximation error The constraint is, then the transition curve length of the tool tip smoothing curve of the kth tool tip corner is The constraints are: ；（1） in, is half of the supplementary angle of the kth tool tip corner; the kth tool tip corner is composed of the adjacent tool tip linear path , constitute; Indicates that the tool tip smoothing curve is The displacement component in the direction, Indicates that the tool tip smoothing curve is The displacement component in the orthogonal direction; the transition curve length of the tool tip smoothing curve of the kth tool tip corner The value of is the maximum value that satisfies formula (1).

3. The tool axis synchronization optimization method for a smooth trajectory according to claim 2, characterized in that: In order to ensure the existence of the remaining linear segment of the tool tip linear path and meet the distribution requirements of the control vertices, the transition curve length of the tool tip smoothing curve of the kth tool tip corner is On the basis of satisfying the constraints of formula (1), it is necessary to further satisfy: ；（2） in, is the smoothing characteristic parameter corresponding to the kth tool tip corner, Indicates the length of the calculated linear path, the transition curve length of the tool tip smoothing curve of the kth tool tip corner The value of is the maximum value that satisfies both equations (1) and (2).

4. The tool axis synchronization optimization method for a smooth trajectory according to claim 1 is characterized in that: Determining the transition length of the tool axis smoothing curve according to the tool axis approximate error and the continuity condition specifically includes: The kth tool axis corner is composed of the adjacent tool axis linear path , Composition, knife axis point , , They are all on the surface of the unit sphere, and the center of the unit sphere is denoted by C; The midpoint of the tool axis smoothing curve corresponding to the kth tool axis corner is recorded as ; The tool axis vector at the point where the tool axis approximation error is the largest corresponding to the kth corner is , The knife axis vector with the kth corner The deviation is recorded as the tool axis approximate error : ； Will The plane is used as the tool axis smoothing plane, and the approximate error of the tool axis smoothing plane is constrained accomplish Constraints are used to determine the preliminary tool axis smoothing curve: ； in, for and The angle of In order to ensure the existence of the remaining linear segment and meet the distribution requirements of the control vertices, the transition length of the tool axis smoothing curve is The constraints are: ； in, is the direction of the tool axis speed at the midpoint of the tool axis smoothing curve at the kth corner and The angle of and They are the linear paths of the tool axis in the tool axis smoothing plane. The corresponding transition length , tool axis linear path The corresponding transition length ; Indicates the starting point of the tool axis smoothing curve corresponding to the kth tool axis corner, is the end point of the tool axis smoothing curve corresponding to the k-1th tool axis corner, Indicates that the tool axis smoothing curve is The displacement component in the direction, Indicates that the tool axis smoothing curve is The displacement components in the orthogonal directions of .

5. The tool axis synchronization optimization method for a smooth trajectory according to claim 4 is characterized in that: The remaining linear segments of the tool tip linear path are represented by B-spline curves, and continuity is achieved by controlling vertex distribution, including: Control vertices of the B-spline curve of the remaining linear segment of the tool tip linear path to The expression is: in, and Tip point and The transition length of the tool tip smooth curve at is the unit direction vector.

6. The tool axis synchronization optimization method for a smooth trajectory according to claim 4 is characterized in that: The remaining linear segments of the tool axis linear path are represented by B-spline curves, and continuity is achieved by controlling the vertex distribution, including: Control vertices of the B-spline curve of the remaining linear segment of the tool axis linear path to The expression is: in, , Indicates The length of the tool axis smoothing curve corresponding to the tool axis corner is Indicates the characteristic parameters of the tool axis smoothing curve. The length of the smoothing start point of the kth tool axis corner , The length of the smoothing end of the k-1th tool axis corner , Indicates the starting point of the tool axis smoothing curve corresponding to the kth tool axis corner, is the end point of the tool axis smoothing curve corresponding to the k-1th tool axis corner. They are , , , , Indicates the linear path of the tool axis The midpoint of .

7. The tool axis synchronization optimization method for a smooth trajectory according to claim 1 is characterized in that: The time-optimal speed planning method based on convex optimization obtains preliminary interpolation data of the robot considering only the tool tip constraint, specifically including: For the hybrid path composed of B-spline curves and Airthoid curves, the time-optimal speed planning method based on convex optimization is used to obtain the preliminary interpolation data of the robot; among them, the tangential constraint of the robot end position is constructed: ； in, is the robot joint angle, are the first-order derivative, second-order derivative, and third-order derivative of the robot joint angle with respect to the tool tip displacement, Expressed as tool tip displacement, are respectively the tool tip tangential velocity, tool tip tangential acceleration, and tool tip tangential jerk, They are joint angular velocity, joint angular acceleration, and joint angular jerk respectively; The robot speed planning model is: ； ； in, represents maximization, is the tool tip tangential velocity constraint, is the tool tip tangential acceleration constraint, is the tool tip tangential acceleration constraint, is the joint velocity constraint, is the joint acceleration constraint, is the joint jerk constraint, It is the total displacement of the tool tip smooth path composed of the tool tip smooth curve and the remaining straight line segment; the preliminary interpolation data is obtained through the robot speed planning model.

8. The tool axis synchronization optimization method for a smooth trajectory according to claim 7, characterized in that: Also includes: In order to ensure that the kinematics of the hybrid path does not exceed the limit, when selecting the sampling point through the robot speed planning model, the starting point, midpoint and end point of the tool tip smoothing curve and the tool axis smoothing curve in the hybrid path are fixedly selected, and the node vector of the speed spline obtained by the robot speed planning model is determined. for: ； in, is the total number of sampling points, is the displacement of the jth sampling point.

9. The tool axis synchronization optimization method for a smooth trajectory according to claim 1, characterized in that: The method of optimizing the redundant control vertices of the remaining linear segments of the tool axis linear path based on the least square method to achieve tool axis smoothing curve optimization specifically includes: According to the preliminary interpolation data and parameter synchronization strategy, the angular velocity of the tool axis at the same time can be determined and tool axis angular acceleration The relationship is: ； in, are the tool tip tangential velocity and tool tip tangential acceleration, respectively. is the angular displacement of the tool axis, are respectively the tool axis angular displacement with respect to the spline parameters The first and second derivatives of are respectively the tool tip parameter curve with respect to the spline parameters The first and second derivatives of represents the inner product; Select the remaining linear segments in the tool axis linear path. observation points, at each observation point, the objective function is established with the minimum angular acceleration of the remaining linear segment of the tool axis linear path as the goal, and the least squares method is used for constraints: ； in, is a constant matrix, represents the spline parameters of the i-th observation point, , represents the tangential acceleration of the tool tip, represents the tangential velocity of the tool tip, They represent the first-order derivative and second-order derivative of the B-spline curve basis function of the remaining linear segment angular displacement of the tool axis linear path, The control vertices of the B-spline curve representing the angular displacement of the remaining linear segment of the tool axis linear path; The least square method constraints are simplified and combined with the angular velocity constraints to achieve tool axis smooth curve optimization.

10. The tool axis synchronization optimization method for a smooth trajectory according to claim 9, characterized in that: The least square method constraint is simplified and combined with the angular velocity constraint, specifically including: ； ； in, are the redundant control vertices of the remaining linear segments, The constant matrix, is the two-norm, Indicates the maximum angular velocity of the tool axis. It is expressed as the tangential velocity of the tool tip at the i-th observation point.

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