A Method for Optimizing Tool Axis Synchronization with a Fairing Trajectory

Abstract

The present invention relates to the technical field of motion planning, and specifically discloses a method for optimizing the synchronization of the tool axis of a fairing trajectory, including: inserting an Airthoid curve at the tool tip corner as the tool tip fairing curve corresponding to the tool tip corner, and determining the transition length of the tool tip fairing curve according to the tool tip approximation error and continuity conditions; inserting symmetric Airthoid curves at the tool axis corner as the tool axis fairing curve corresponding to the tool axis corner, and determining the transition length of the tool axis fairing curve according to the tool axis approximation error and continuity conditions; obtaining the preliminary interpolation data of the robot considering only the tool tip constraints; optimizing the redundant control vertices of the remaining linear segments of the tool axis linear path based on the least squares method to achieve the optimization of the tool axis fairing curve; and again obtaining the final interpolation data of the robot based on the time-optimal speed planning method of convex optimization. The present invention improves the processing efficiency on the premise of ensuring that the fairing continuity is not damaged and the constraints of each drive axis remain unchanged.

Description

Technical Field

[0001] The present invention relates to the technical field of motion planning, and particularly relates to a method for optimizing the synchronization of a cutter axis for a fairing trajectory. Background Art

[0002] In the field of numerical control machining, the application of fairing for discrete linear instructions of tool paths generated by computer-aided manufacturing software is very extensive. A path fairing method that requires simultaneous fairing of position and attitude for robots and then parameter synchronization has also emerged. Through the path fairing method, the pause at the corner during machining is effectively reduced, and while improving the machining efficiency, the machining vibration is also effectively reduced.

[0003] Document 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 fairing the pose in the workpiece coordinate system using B-spline curves in a SCARA robot. First, a pseudo-linear trajectory is iteratively obtained under the approximate error and corner optimal constraints, and then geometric fairing is performed using B-spline curves to obtain a G2 continuous fairing trajectory. Nevertheless, due to the non-linear mapping between the arc length of the B-spline and its parameters, this poses a challenge to the real-time performance of the numerical control system.

[0004] Document 2: JiXiang Y, Abulikemu A, Han D. Real time tool path smoothing ofshort linear commands for robot manipulator by constructing asymmetricalPythagoran-hodograph (PH) splines[J].Science China Technological Sciences,2023,66(3):674-688 discloses a robot fairing method based on PH splines, which uses the pose fairing processing of PH splines in the joint coordinate system to achieve parameter synchronization by satisfying a certain ratio of displacements. However, the process of inverse calculating the corresponding parameters from the known displacement values of PH splines cannot be resolved.

[0005] The above research often focuses on the characteristics of fairing curves themselves in aspects such as approximation error control, computational efficiency, and ensuring high-order continuity at the junction points. Although the method of using parameters for synchronization can effectively ensure the smoothness of robot motion, there is often a sharp change in acceleration when the robot moves to the fairing junction point. This is because when the fairing method based on the parameter synchronization strategy is used for trajectory planning, the tool axis result is obtained according to the parameters corresponding to the tool tip interpolation points, and there is often a violent acceleration and deceleration process in the remaining linear tool axes. Therefore, the synchronized tool axis in robot planning will lead to an extension of the entire processing time. The optimization of the remaining linear segments on the robot fairing path is rarely considered, resulting in difficulty in improving the processing efficiency of the robot. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a method for optimizing the tool axis synchronization of a fairing trajectory, which can effectively improve the processing efficiency of the robot.

[0007] To solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A method for optimizing the tool axis synchronization of a fairing trajectory, while realizing the fairing of the robot pose, optimizing the remaining linear segments of the linear path of the robot tool axis, specifically including:

[0009] Insert symmetric Airthoid curves at the tool tip corners formed by adjacent tool tip linear paths as the tool tip fairing curves corresponding to the tool tip corners, and determine the transition length of the tool tip fairing curves according to the tool tip approximation error and continuity conditions; insert symmetric Airthoid curves at the tool axis corners formed by adjacent tool axis linear paths as the tool axis fairing curves corresponding to the tool axis corners, and determine the transition length of the tool axis fairing curves according to the tool axis approximation error and continuity conditions; 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 through the distribution of control vertices;

[0010] Based on the time-optimal speed planning method of convex optimization, obtain the preliminary interpolation data of the robot considering only the tool tip constraints;

[0011] Optimize the redundant control vertices of the remaining linear segments of the tool axis linear path based on the least squares method to achieve the optimization of the tool axis fairing curves;

[0012] Again, based on the time-optimal speed planning method of convex optimization, obtain the final interpolation data of the robot.

[0013] In one of the embodiments, the determination of the transition length of the tool tip fairing curves according to the tool tip approximation error and continuity conditions specifically includes:

[0014] The Airthoid curves inserted within the tool tip corners need to meet the set tool tip approximation error If under the constraint of, then the transition curve length of the tool tip fairing curve at the k-th tool tip corner The constraint is:

[0015] ; (1)

[0016] Among them, Is half of the supplementary angle of the k-th tool tip corner; the k-th tool tip corner is composed of adjacent tool tip linear paths , Constitute; Indicates the displacement component of the tool tip fairing curve in the Direction, Indicates the displacement component of the tool tip fairing curve in the orthogonal direction of ; The transition curve length of the tool tip fairing curve at the k-th tool tip corner The value of takes the maximum value that satisfies Equation (1).

[0017] 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 fairing curve at the k-th tool tip corner On the basis of satisfying the constraint of Equation (1), it is further necessary to satisfy:

[0018] ; (2)

[0019] Among them, Is the fairing characteristic parameter corresponding to the k-th tool tip corner, Indicates the calculation of the linear path length, and the transition curve length of the tool tip fairing curve at the k-th tool tip corner The value of takes the maximum value that simultaneously satisfies Equation (1) and Equation (2).

[0020] In one embodiment, the method for determining the transition length of the tool axis fairing curve according to the tool axis approximation error and continuity conditions specifically includes:

[0021] The k-th tool axis corner is composed of adjacent tool axis linear paths , Constitute, the tool axis points , , Are all on the spherical surface of the unit sphere, and the center of the unit sphere is denoted as C;

[0022] The midpoint of the tool axis fairing curve corresponding to the k-th tool axis corner is denoted as ; The tool axis vector at the location with the largest tool axis approximation error corresponding to the k-th corner is , The deviation from the tool axis vector Of the k-th corner is denoted as the tool axis approximation error :

[0023] ;

[0024] Taking the plane as the tool axis fairing plane, by constraining the approximation error of the tool axis fairing plane to achieve the constraint and determine the preliminary tool axis fairing curve:

[0025] ;

[0026] Among them, is and the included angle of;

[0027] 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 fairing curve is constrained as:

[0028] ;

[0029] Among them, is the included angle between the tool axis velocity direction at the midpoint of the tool axis fairing curve at the k-th corner and , and are respectively the transition lengths corresponding to the tool axis linear path , the transition length corresponding to the tool axis linear path ; represents the starting point of the tool axis fairing curve corresponding to the k-th tool axis corner, is the end point of the tool axis fairing curve corresponding to the (k - 1)-th tool axis corner, represents the displacement component of the tool axis fairing curve in the direction, represents the displacement component of the tool axis fairing curve in the orthogonal direction of .

[0030] In one embodiment, the remaining linear segment of the tool tip linear path is represented by a B-spline curve, and the continuity is achieved through the distribution of control vertices, specifically including:

[0031] The control vertices to of the B-spline curve of the remaining linear segment of the tool tip linear path are expressed as:

[0032]

[0033] Among them, and are the tool tip points respectively and the transition lengths of the tool tip fairing curves at the positions, is the unit direction vector.

[0034] In one embodiment, the remaining linear segment of the tool axis linear path is represented by a B-spline curve, and the continuity is achieved by controlling the vertex distribution, specifically including:

[0035] The control vertices of the B-spline curve of the remaining linear segment of the tool axis linear path to are expressed as:

[0036]

[0037] Among them, , represents the length of the tool axis fairing curve corresponding to the th tool axis corner, represents the tool axis fairing curve characteristic parameter, is the starting length of the fairing at the kth tool axis corner , is the ending length of the fairing at the (k - 1)th tool axis corner , represents the starting point of the tool axis fairing curve corresponding to the kth tool axis corner, is the ending point of the tool axis fairing curve corresponding to the (k - 1)th tool axis corner, and the angles are respectively , , , , represents the midpoint of the tool axis linear path .

[0038] In one embodiment, the time-optimal speed planning method based on convex optimization obtains the preliminary interpolation data of the robot considering only the tool tip constraints, specifically including:

[0039] For the hybrid path composed of B-spline curves and Airthoid curves, the time-optimal speed planning method based on convex optimization is adopted to obtain the preliminary interpolation data of the robot; among them, the tangential constraint of the end pose of the robot is constructed:

[0040] ;

[0041] Among them, is the robot joint angle, are the first derivative, second derivative, and third derivative of the robot joint angle with respect to the tool tip displacement, is expressed as the tool tip displacement, They are the cutting-edge tangential velocity, cutting-edge tangential acceleration, and cutting-edge tangential jerk respectively. They are the joint angular velocity, joint angular acceleration, and joint angular jerk respectively;

[0042] The robot velocity planning model is:

[0043] ;

[0044] ;

[0045] Among them, represents maximization, is the cutting-edge tangential velocity constraint, is the cutting-edge tangential acceleration constraint, is the cutting-edge tangential jerk constraint, is the joint velocity constraint, is the joint acceleration constraint, is the joint angular jerk constraint, is the total displacement of the cutting-edge fairing path composed of the cutting-edge fairing curve and the remaining straight line segment; the preliminary interpolation data is obtained through the robot velocity planning model.

[0046] In one embodiment, it further includes: in order to ensure that the kinematics of the hybrid path does not exceed the limit, when selecting sampling points through the robot velocity planning model, the starting point, midpoint, and ending point of the cutting-edge fairing curve and the tool axis fairing curve in the hybrid path are fixedly selected, and the knot vector of the velocity spline obtained through the robot velocity planning model is determined as:

[0047] ;

[0048] Among them, is the total number of sampling points, is the displacement of the jth sampling point.

[0049] In one embodiment, the redundant control vertices of the remaining linear segment of the tool axis linear path are optimized based on the least squares method to realize the optimization of the tool axis fairing curve, specifically including:

[0050] According to the preliminary interpolation data and the parameter synchronization strategy, the relationship between the tool axis angular velocity and the tool axis angular acceleration at the same time can be determined as:

[0051] ;

[0052] Among them, are the cutting-edge tangential velocity and cutting-edge tangential acceleration respectively, is the tool axis angular displacement, 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;

[0053] Select the remaining linear segments in the tool axis linear path. observation points, at each observation point, the objective function is established with the goal of minimizing the angular acceleration of the remaining linear segment of the tool axis linear path, and the least squares method is used for constraints:

[0054] ;

[0055] in, is a constant matrix, represents the spline parameters of the ith 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;

[0056] The least square method constraints are simplified and combined with the angular velocity constraints to achieve tool axis smooth curve optimization.

[0057] In one embodiment, simplifying the least squares constraint and combining it with the angular velocity constraint specifically includes:

[0058] ;

[0059] ;

[0060] 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.

[0061] Compared with the prior art, the beneficial technical effects of the present invention are:

[0062] The present invention utilizes the constrained tool axis and the approximate error of the tool tip analyzed by the Airhtoid curve, and at the same time realizes parameter synchronization through the remaining B-spline of the linear segment, achieving the smoothing of the robot path; optimizes the tool axis vector of the remaining linear segment of the tool axis based on the least square method; and improves the machining efficiency on the premise of ensuring that the smoothing continuity is not damaged and the constraints of each driving axis remain unchanged. The present invention has the advantages of high calculation efficiency and flexible motion ability, and is more suitable for the online application of the robot trajectory speed planning algorithm. Description of the Drawings

[0063] In order to more clearly illustrate the technical solutions in the specific embodiments of the present invention, the drawings required for use in the specific embodiments will be briefly introduced below. Obviously, the drawings described below are only the drawings of some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0064] Figure 1 is the flowchart of the method in the embodiment of the present invention.

[0065] Figure 2 is a schematic diagram of tool tip smoothing using the Airthoid curve in the embodiment of the present invention.

[0066] Figure 3a and Figure 3b is a schematic diagram of tool axis smoothing using the Airthoid curve in the embodiment of the present invention.

[0067] Figure 4 is a comparison chart of tool axis acceleration obtained by using the method of the present invention and the unoptimized method.

[0068] Figure 5 is a comparison chart of tool tip speed obtained by using the method of the present invention and the unoptimized method. Detailed Embodiments

[0069] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0070] As Figure 1 shown, the present invention discloses a method for synchronously optimizing the tool axis of a smoothed trajectory, which optimizes the remaining linear segment of the linear path of the robot tool axis while realizing the smoothing of the robot pose, and specifically includes the following steps:

[0071] S1. Insert symmetric Airthoid curves at the tool tip corners formed by adjacent linear tool tip paths as the tool tip fairing curves corresponding to the tool tip corners, and determine the transition length of the tool tip fairing curves according to the tool tip approximation error and continuity conditions; insert symmetric Airthoid curves at the tool axis corners formed by adjacent linear tool axis paths as the tool axis fairing curves corresponding to the tool axis corners, and determine the transition length of the tool axis fairing curves according to the tool axis approximation error and continuity conditions; the remaining linear segments of the tool tip linear paths and tool axis linear paths are represented by B-spline curves, and continuity is achieved by controlling the vertex distribution.

[0072] S2. Based on the time-optimal speed planning method of convex optimization, obtain the preliminary interpolation data of the robot considering only the tool tip constraints.

[0073] S3. Optimize the redundant control vertices of the remaining linear segments of the tool axis linear paths based on the least squares method to achieve the optimization of the tool axis fairing curves.

[0074] S4. Again, based on the time-optimal speed planning method of convex optimization, obtain the final interpolation data of the robot.

[0075] The interpolation data are the joint angles, parameters, and tool tip displacements of the robot at each interpolation period; for B-spline curves, the parameter is the spline parameter, and for Airthoid curves, the parameter is the Airthoid parameter. The interpolation period is the minimum time unit for the numerical control system to perform interpolation calculations and position control.

[0076] In one embodiment, determining the transition length of the tool tip fairing curves according to the tool tip approximation error and continuity conditions in step S1 specifically includes:

[0077] Inserting an Airthoid curve within the tool tip corner needs to satisfy the constraint of the tool tip approximation error set by the user. Then, the transition curve length of the tool tip fairing curve of the k-th tool tip corner is subject to the following constraint:

[0078] ; (1)

[0079] where is half of the supplementary angle of the k-th tool tip corner; the k-th tool tip corner is formed by adjacent tool tip linear paths , ; represents the displacement component of the tool tip fairing curve in the direction, and represents the displacement component of the tool tip fairing curve in the orthogonal direction of ; ; ; represents the integration variable, representing a continuously varying angular value between 0 and ; the transition curve length of the tool nose fairing curve of the k-th tool nose corner takes the maximum value that satisfies Equation (1).

[0080] In one of the embodiments, it further includes: in order to ensure the existence of the remaining linear segment of the tool axis linear path and meet the distribution requirements of the control vertices, the transition curve length of the tool nose fairing curve of the k-th tool nose corner On the basis of satisfying the constraints of Equation (1), it is further required to satisfy:

[0081] ; (2)

[0082] where is the fairing characteristic parameter corresponding to the k-th tool nose corner, represents the calculation of the linear path length, and the transition curve length of the tool nose fairing curve of the k-th tool nose corner takes the maximum value that simultaneously satisfies Equation (1) and Equation (2).

[0083] In one of the embodiments, determining the transition length of the tool axis fairing curve according to the tool axis approximation error and continuity conditions in step S1 specifically includes:

[0084] Referring to Figure 3a and Figure 3b , the k-th corner is composed of adjacent tool axis linear paths , , the tool axis points , , are all on the spherical surface of the unit sphere, and the center of the unit sphere is denoted as C;

[0085] The midpoint of the tool axis fairing curve corresponding to the k-th tool axis corner is denoted as ; the tool axis vector at the maximum tool axis approximation error corresponding to the k-th corner is , The deviation between and the tool axis vector of the k-th corner is denoted as the tool axis approximation error

[0086] ;

[0087] Taking the plane as the tool axis fairing plane, by constraining the tool axis fairing plane approximation error to achieve constraint, determining the preliminary tool axis fairing curve:

[0088] ;

[0089] Among them, is and the included angle of;

[0090] 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 fairing curve is constrained to:

[0091] ;

[0092] Among them, is the included angle between the tool axis velocity direction at the midpoint of the tool axis fairing curve at the k-th corner and , and are respectively the transition lengths corresponding to the tool axis linear path , the transition length corresponding to the tool axis linear path ; represents the starting point of the tool axis fairing curve corresponding to the k-th tool axis corner, is the end point of the tool axis fairing curve corresponding to the (k - 1)-th tool axis corner, represents the displacement component of the tool axis fairing curve in the direction, represents the displacement component of the tool axis fairing curve in the orthogonal direction of , ; ; represents the integration variable, representing a continuously changing angular value between 0 and .

[0093] Thus, the final transition length of the tool axis fairing is determined to realize the determination of the tool axis fairing curve.

[0094] In one of the embodiments, the remaining linear segment of the tool tip linear path is represented by a B-spline curve and the continuity is achieved through the distribution of control vertices, specifically including:

[0095] The control vertices to of the B-spline curve of the remaining linear segment of the tool tip linear path are expressed as:

[0096]

[0097] Among them, and are respectively the transition lengths of the tool tip fairing curves at the tool tip points and , is the unit direction vector.

[0098] In a preferred embodiment, based on the parameter synchronization strategy, in order to ensure the high-order parameter continuity of the tool tip fairing path composed of the remaining linear segment of the tool tip linear path and the Airthoid curve, a 5th-degree B-spline curve is used to represent the remaining linear segment, and the knot vector is designed as: [0, 0, 0, 0, 0, 0, 0.2, 0.4, 0.6, 0.8, 1, 1, 1, 1, 1, 1], and the control vertices are set as to , a total of 10, see Figure 2 ; Figure 2 The linear NURNS in

[0099] represents the inserted B-spline curve, which represents a straight line in this embodiment.

[0100] In one embodiment, the remaining linear segment of the tool axis linear path is represented by a B-spline curve, and the continuity is achieved through the distribution of control vertices, specifically including: to The expression of the control vertices of the B-spline curve of the remaining linear segment of the tool axis linear path is:

[0101]

[0102] wherein, , represents the length of the tool axis fairing curve corresponding to the kth corner, represents the characteristic parameter of the tool axis fairing curve, is the length at the fairing start of the kth tool axis corner , is the length at the fairing end of the (k - 1)th tool axis corner , represents the starting point of the tool axis fairing curve corresponding to the kth tool axis corner, is the end point of the tool axis fairing curve corresponding to the (k - 1)th tool axis corner, and the angles are respectively , , , , represents the midpoint of the tool axis linear path .

[0103] In a preferred embodiment, based on the parameter synchronization strategy, in order to ensure the high-order parameter continuity of the tool axis fairing path composed of the remaining linear segment of the tool axis linear path and the Airthoid curve, a 5th-degree B-spline curve is used to represent the remaining linear segment, and the knot vector is designed as: [0, 0, 0, 0, 0, 0, 0.2, 0.4, 0.6, 0.8, 1, 1, 1, 1, 1, 1], and the control vertices are set as to , a total of 10. Among them, the control vertices of the tool axis spline curve are only preliminarily determined and need to be further optimized.

[0104] In one embodiment, the time-optimal velocity planning method based on convex optimization obtains the preliminary interpolation data of the robot considering only the tool tip constraints, specifically including:

[0105] For the hybrid path composed of B-spline curve and Airthoid curve, the time-optimal velocity planning method based on convex optimization is used to obtain the preliminary interpolation data of the robot; among them, the tangential constraint of the end pose of the robot is constructed:

[0106] ;

[0107] Among them, is the robot joint angle, are the first, second, and third derivatives of the robot joint angle with respect to the tool tip displacement, represents the tool tip displacement, are the tool tip tangential velocity, tool tip tangential acceleration, and tool tip tangential jerk respectively, are the joint angular velocity, joint angular acceleration, and joint angular jerk respectively;

[0108] The robot velocity planning model is:

[0109] ;

[0110] ;

[0111] Among them, represents maximization, is the tool tip tangential velocity constraint, is the tool tip tangential acceleration constraint, is the tool tip tangential jerk constraint, is the joint velocity constraint, is the joint acceleration constraint, is the joint jerk constraint, is the total displacement of the tool tip fairing path composed of the tool tip fairing curve and the remaining straight line segment; the preliminary interpolation data is obtained through the robot velocity planning model.

[0112] In one embodiment, it further includes: in order to ensure that the kinematics of the hybrid path does not exceed the limit, when selecting sampling points through the robot velocity planning model, the starting point, midpoint, and end point of the tool tip fairing curve and the tool axis fairing curve in the hybrid path are fixedly selected, and the knot vector of the velocity spline obtained through the robot velocity planning model is determined as:

[0113] ;

[0114] in, is the total number of sampling points, is the displacement of the jth sampling point.

[0115] 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:

[0116] 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:

[0117] ;

[0118] 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;

[0119] 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:

[0120] ;

[0121] in, is a constant matrix, represents the spline parameters of the ith 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;

[0122] Simplify the least squares constraint and combine it with the angular velocity constraint:

[0123] ;

[0124] ;

[0125] Among them, is the redundant control vertex of the remaining linear segment, constant matrix, is the two-norm, represents the maximum angular velocity of the tool axis, represents the tangential velocity of the tool tip at the i-th observation point.

[0126] The tool axis position is determined by the tool tip parameters: in the fairing curve segment, the movement of the tool axis and the tool tip is synchronized and achieved by the linear increase of the equal ratio of the extreme values of its trajectory curvature; in the linear motion stage, the angular displacement of the tool axis is described by a fifth-order B-spline curve and changes synchronously with the displacement increment of the tool tip, while ensuring the C3 continuity of the tool axis at the connection between the linear segment and the fairing segment.

[0127] As Figure 4 shown, the present invention can first effectively achieve the fairing of the robot at the discrete path and the kinematic continuity at the connection point, improving the processing efficiency. Further, the method of the present invention can optimize the tool axis linear segment of the long path, and further improve the motion efficiency and reduce the frequent and drastic acceleration and deceleration on the premise of ensuring that all constraints are not exceeded.

[0128] As Figure 5 shown, the present invention can first effectively achieve the fairing of the robot at the discrete path and the velocity continuity at the connection point, improving the processing efficiency. Further, the method of the present invention can optimize the tool axis linear segment of the long path, and further improve the motion efficiency and reduce the frequent and drastic acceleration and deceleration on the premise of ensuring that all constraints are not exceeded.

[0129] It should be understood that although the steps in the flowchart of the accompanying drawings of the specification are shown sequentially according to the indication of the arrows, these steps are not necessarily executed sequentially according to the order indicated by the arrows. Unless there is a clear indication in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowchart 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 alternately or alternately with at least a part of other steps or steps or stages in other steps.

[0130] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above-described exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention, and any reference signs in the claims should not be regarded as limiting the claims involved.

[0131] In addition, it should be understood that although this specification is described in terms of embodiments, not every embodiment only contains an independent technical solution. This narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments 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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