Robot path smoothing and synchronization method based on Airthoid curve

Abstract

The present invention relates to the technical field of motion planning, and discloses a method for robot path smoothing and synchronization based on Airthoid curves, including: determining the transition length of the tool tip smoothing curve according to the tool tip approximation error and the parameter synchronization strategy; determining the preliminary tool axis smoothing curve; calculating the transition length of the tool axis smoothing curve according to the preliminary tool axis smoothing curve and the parameter synchronization strategy to determine the final tool axis smoothing curve; realizing curvature parameter synchronization according to the maximum curvature of the final tool axis smoothing curve and the tool tip smoothing curve; realizing spline parameter synchronization according to the B-spline curves corresponding to the remaining straight line segments of the tool axis smoothing curve and the tool tip smoothing curve. The present invention uses the Airhtoid curve analysis to realize the constraint of the tool axis and the tool tip approximation error, and has high calculation efficiency; realizes the parameter synchronization of the smoothing curve and the remaining straight line segment through the remaining straight line segment B-spline curve, and ensures the C<supgt;3< / supgt> continuity at the connection point between the curve segment and the straight line segment.

Description

Technical Field

[0001] The present invention relates to the technical field of motion planning, and in particular to a robot path smoothing and synchronization method based on Airthoid curves. Background Art

[0002] In the field of CNC machining, the tool paths generated by Computer Aided Manufacturing (CAM) software are usually presented in the form of discrete linear instructions, which can easily lead to tangential discontinuities in the paths at intersections. In order to avoid velocity discontinuities and infinite acceleration at the corners between straight line segments, the robot needs to reduce the speed to zero when reaching these points to avoid large vibrations. However, this approach will sacrifice machining efficiency. Therefore, local smoothing of continuous small line segments in the tool path is of great practical significance for achieving high-speed and high-quality machining of machine tools and robots. Through tool path smoothing, pauses at corners can be reduced, machining efficiency can be improved, and machining quality can be maintained, which is crucial to improving machining accuracy and surface finish.

[0003] Reference 1: Jixiang Yang, Dingwei Li, Congcong Ye, Han Ding, An analytical C3 continuous tool path corner smoothing algorithm for 6R robot manipulator [J]. Robotics and Computer-Integrated Manufacturing, Volume 64, 2020, 101947. This paper discloses a method of using B-spline curve as a smoothing curve on an industrial robot to achieve smoothing of the pose in the joint coordinate system, and at the same time, the parameter synchronization of the entire trajectory is achieved by inserting a straight line represented by the B-spline. However, there is a nonlinear mapping between the arc length and parameters of the B-spline itself, which increases the real-time burden of the CNC system.

[0004] Reference 2: Huang X, Zhao F, Tao T, et al. A Novel Local Smoothing Method for Five-Axis Machining With Time-Synchronization Feedrate Scheduling [J]. IEEE Access, 2020, 889185-89204. A new smoothing curve, the Airthoid curve, is disclosed to achieve path smoothing with controllable continuous small line approximation error under three-axis machine tools. In terms of corner smoothing, the Airthoid curve has the advantages of continuous curvature, controllable approximation error, and analytically calculable displacement.

[0005] The characteristics of the above literature are that different smoothing curves are used to achieve tool path smoothing, and the approximate error analytical control and certain continuity requirements are met in the process. In the field of robotics, there are few technical solutions using Airthoid curves as smoothing curves, and their parameter synchronization strategies need to be improved, which does not give full play to the advantages of analytical control of Airthoid curves such as displacement, curvature and approximate error. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a robot path smoothing and synchronization method based on Airthoid curve, which realizes the smoothing of the tool path by controlling the tool tip position and axis direction of the robot end tool.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A robot path smoothing and synchronization method based on Airthoid curve, the robot controls the tool tip position and tool axis posture simultaneously to achieve path smoothing, specifically including:

[0009] According to the tool tip approximate error and the tool tip smoothing curve transition length determined by the parameter synchronization strategy, the remaining straight line segment of the tool tip linear path is represented by the B-spline curve;

[0010] Determine the preliminary tool axis smoothing curve according to the tool axis approximate error; calculate the transition length of the tool axis smoothing curve according to the preliminary tool axis smoothing curve and parameter synchronization strategy, and determine the final tool axis smoothing curve; use the angular displacement B-spline curve to represent the remaining straight line segment of the tool axis linear path;

[0011] The curvature parameter synchronization is achieved according to the maximum curvature of the final tool axis smoothing curve and the tool tip smoothing curve; the spline parameter synchronization is achieved according to the B-spline curve corresponding to the remaining straight line segments of the final tool axis smoothing curve and the tool tip smoothing curve; and the smoothing of the path corners is achieved.

[0012] In one embodiment, the tool tip smoothing curve transition length determined according to the tool tip approximation error and parameter synchronization strategy specifically includes:

[0013] A pair of symmetrical Airthoid curves are inserted into the corner formed by two adjacent tool tip linear paths as the tool tip smoothing curve of the current corner. The transition length of the tool tip smoothing curve is calculated according to the parameter synchronization strategy, the transition length of the tool tip smoothing curve corresponding to the tool tip approximation error, the remaining straight line segment length of the tool tip linear path and the tool tip linear path length.

[0014] In one embodiment, the calculating the transition length of the tool tip smoothing curve according to the parameter synchronization strategy, the tool tip smoothing curve transition length corresponding to the tool tip approximation error, the remaining straight line segment length of the tool tip linear path and the tool tip linear path length specifically includes:

[0015] Transition length of the tool tip smoothing curve corresponding to the i-th corner for:

[0016]

[0017] in, and are the two adjacent tool tip linear paths that constitute the i-th corner; i is the corner index of the current corner, i.e., the i-th corner, in the continuous tool tip linear path; Represents the operation of finding the path length; represents the tool tip approximation error given for the i-th corner The corresponding tool tip smoothing curve transition length, is the remaining straight line segment length of the tool tip linear path corresponding to the i-th corner, is the total number of corners in the continuous linear path of the tool tip.

[0018] In one embodiment, the tool tip approximation error given for the i-th corner is The corresponding tool tip smoothing curve transition length , calculated as:

[0019] ;

[0020] in, is the tool tip approximation error given for the i-th corner The corresponding velocity direction at the midpoint of the tool tip smoothing curve and the tool tip linear path The angle of 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 .

[0021] In one embodiment, the method of using a B-spline curve to represent the remaining straight line segment of the tool tip linear path specifically includes:

[0022] The node vector and control vertex of the B-spline curve are designed. The derivative value of the B-spline curve endpoint is changed by changing the control vertex to achieve the continuity of the B-spline curve and the tool tip smooth curve within the set order range at the endpoint; in order to avoid the intersection of adjacent tool tip smooth curves, the length of the remaining straight line segment of the tool tip linear path corresponding to the i-th corner is Transition length to the smooth curve of the tool tip Need to meet:

[0023] ;

[0024] ;

[0025] in, is the tool tip approximation error given for the i-th corner The corresponding velocity direction at the midpoint of the tool tip smoothing curve and the tool tip linear path The angle of is the characteristic parameter of the tool tip smoothing curve corresponding to the i-th corner.

[0026] In one embodiment, determining a preliminary tool axis smoothing curve according to the tool axis approximation error specifically includes:

[0027] , The two adjacent tool axis linear paths that form the i-th corner, the tool axis point , , are all on the unit sphere, and the center of the unit sphere is recorded as ;exist A pair of symmetrical Airthoid curves are used in the plane As the tool axis plane smoothing curve, the tool axis linear path corresponding to the i-th corner is smoothed, and the tool axis plane smoothing curve is mapped to the unit sphere to form the tool axis smoothing curve. , are the starting and ending points of the tool axis smoothing curve. is the midpoint of the tool axis smoothing curve corresponding to the i-th corner; is the tool axis vector at the point where the tool axis approximation error corresponding to the i-th corner is the largest, The tool axis vector with the i-th corner The deviation is recorded as ;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:

[0028] ;

[0029] in, for and Angle.

[0030] In one embodiment, calculating the transition length of the tool axis smoothing curve according to the preliminary tool axis smoothing curve and the parameter synchronization strategy to determine the final tool axis smoothing curve specifically includes:

[0031] Combined with the tool axis smoothing plane approximation error , while ensuring that the minimum length of the remaining straight line segment of the tool axis linear path meets the parameter synchronization requirements, calculate the transition length of the tool axis smoothing curve at the i-th corner :

[0032] ;

[0033] in, is the tool axis speed direction and tool axis linear path at the midpoint of the tool axis smoothing curve at the i-th corner The angle of is the approximate error of the tool axis smoothing plane, and They are the linear paths of the tool axis in the tool axis smoothing plane. and The corresponding transition length , ; Indicates the tool axis smoothing curve on the tool axis linear path The displacement component in the direction, Indicates the tool axis smoothing curve on the tool axis linear path The displacement components in the orthogonal directions of ; ; Represents the integral variable, representing 0 to A continuously changing angle value between .

[0034] In one embodiment, the method of using the angular displacement B-spline curve to represent the remaining straight line segment of the tool axis linear path specifically includes:

[0035] The B-spline curves corresponding to the remaining straight line segments of the tool axis linear path and the tool tip linear path have the same node vector. The tool axis linear path direction and the angular displacement B-spline curve represent the remaining straight line segments of the tool axis linear path, and set the corresponding control vertices.

[0036] In one embodiment, the curvature parameter synchronization is achieved according to the maximum curvature of the final tool axis smoothing curve and the tool tip smoothing curve, specifically including:

[0037] Curvature parameters are shared in equal proportion to achieve synchronization of curvature parameters of the tool axis smooth curve and the tool tip smooth curve; the curvature parameter synchronization means that the curvature of a certain point on the tool tip smooth curve corresponds to the curvature of the only point on the tool axis smooth curve;

[0038] The curvature value of the tool axis plane smoothing curve corresponding to the tool axis linear path It is expressed as:

[0039] ;

[0040] in, is the curvature extreme value of the tool tip smoothing curve, is the curvature extreme value of the smooth curve on the tool axis plane, is the curvature extreme value of the tool axis smoothing curve, is the characteristic parameter of the tool tip smoothing curve; is the arc length of the smooth curve of the tool tip;

[0041] Arc length of smooth curve on tool axis plane for:

[0042] ;

[0043] in, is the characteristic parameter of the smoothing curve on the tool axis plane.

[0044] In one embodiment, the B-spline curve corresponding to the remaining straight line segments of the final tool axis smoothing curve and the tool tip smoothing curve realizes spline parameter synchronization, specifically including:

[0045] According to the parameters of the tool axis smoothing curve and the tool tip smoothing curve, the expression of the control vertices of the B-spline curve corresponding to the remaining straight line segments of the tool tip linear path and the tool axis linear path is determined:

[0046] Control vertices of the B-spline curve corresponding to the remaining straight line segment of the tool tip linear path to They are:

[0047]

[0048] in, is the unit direction vector, and are the two adjacent tool tip linear paths that constitute the i-th corner, represents the operation of finding the path length, and Tip point and The length of the tool tip smooth curve at ;

[0049] Control vertices of the B-spline curve corresponding to the remaining straight line segment of the tool axis linear path to They are:

[0050] in, , , represents the length of the smoothing curve of the tool axis plane corresponding to the i-th corner, The length of the smoothing start point of the i+1th corner ; Represents the tool axis point on the tool axis linear path that constitutes the i-th corner , , The center of the unit sphere where Indicates the starting point of the tool axis smoothing curve at the i+1th corner; is the length of the smoothing end of the i-th corner , Indicates the end point of the tool axis smoothing curve at the i-th corner; , , , They are , , , ; Indicates the linear path of the tool axis The midpoint of

[0051] By analyzing the control vertices of the B-spline curves corresponding to the remaining straight line segments of the tool axis linear path and the tool tip linear path, the spline parameter correspondence of the remaining straight line segments of the linear path is achieved.

[0052] Compared with the prior art, the beneficial technical effects of the present invention are:

[0053] First, the present invention uses Airhtoid curve analysis to realize the constraint of tool axis and tool tip approximate error, and the calculation efficiency is high. Secondly, the present invention realizes the parameter synchronization of the smooth curve and the remaining straight line segment through the remaining straight line segment B-spline curve, ensuring that the C 3The invention is suitable for the online application of robot trajectory planning algorithm and has important significance in the occasions where both processing efficiency and contour accuracy are important. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] 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.

[0055] Figure 1 is a flow chart of a method in an embodiment of the present invention;

[0056] Figure 2 It is a schematic diagram of using Airthoid curve to smooth the robot tool tip path in an embodiment of the present invention;

[0057] Figure 3 It is a schematic diagram of using Airthoid curve to smooth the robot tool axis path in an embodiment of the present invention;

[0058] Figure 4 This is a schematic diagram of the straight line segments remaining on the robot tool axis path after path smoothing in an embodiment of the present invention;

[0059] Figure 5 Schematic diagram of the robot tool axis acceleration without parameter synchronization in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0061] like Figure 1 As shown, the robot path smoothing and synchronization method based on Airthoid curve in the present invention includes the following steps:

[0062] Initialize the index of the current corner i=1;

[0063] S1, based on the tool tip approximation error and the tool tip smoothing curve transition length determined by the parameter synchronization strategy, the remaining straight line segment of the tool tip linear path is represented by a B-spline curve.

[0064] S2, determine the preliminary tool axis smoothing curve based on the tool axis approximate error.

[0065] S3, calculate the transition length of the tool axis smoothing curve according to the preliminary tool axis smoothing curve and parameter synchronization strategy, and determine the final tool axis smoothing curve; use the angular displacement B-spline curve to represent the remaining straight line segment of the tool axis linear path.

[0066] S4, realizes the curvature parameter synchronization according to the maximum curvature of the final tool axis smoothing curve and the tool tip smoothing curve.

[0067] S5, realizing spline parameter synchronization according to the B-spline curve corresponding to the remaining straight line segments of the final tool axis smoothing curve and the tool tip smoothing curve; realizing smoothing of the path corners.

[0068] S6, i=i+1, repeat steps S1 to S5 until the smooth curve transition lengths of all corners on the robot's linear path and the expressions of the inserted B-spline curves are determined.

[0069] The present invention solves the contradiction between efficiency, accuracy and stability in robot path smoothing through Airthoid curve analytical control and dual-level parameter synchronization strategy (curvature + spline). The robot can simultaneously ensure path accuracy (tool tip), posture stability (tool axis) and motion efficiency (parameter synchronization) during high-speed machining, avoiding performance bottlenecks caused by a single factor.

[0070] In one embodiment, the tool tip smoothing curve transition length determined according to the tool tip approximation error and the parameter synchronization strategy in step S1 specifically includes:

[0071] A pair of symmetrical Airthoid curves are inserted into the corner formed by two adjacent tool tip linear paths as the tool tip smoothing curve of the current corner. The transition length of the tool tip smoothing curve is calculated according to the parameter synchronization strategy, the transition length of the tool tip smoothing curve corresponding to the tool tip approximation error, the remaining straight line segment length of the tool tip linear path and the tool tip linear path length.

[0072] In one embodiment, the transition length of the tool tip smoothing curve is calculated according to the parameter synchronization strategy, the transition length of the tool tip smoothing curve corresponding to the tool tip approximation error, the remaining straight line segment length of the tool tip linear path, and the tool tip linear path length, specifically including:

[0073] Transition length of the tool tip smoothing curve corresponding to the i-th corner for:

[0074] ;

[0075] in, and are the two adjacent tool tip linear paths that constitute the i-th corner; i is the corner index of the current corner, i.e., the i-th corner, in the continuous tool tip linear path; Represents the operation of finding the path length; represents the tool tip approximation error given for the i-th corner The corresponding tool tip smoothing curve transition length, is the remaining straight line segment length of the tool tip linear path corresponding to the i-th corner, is the total number of corners in the continuous linear path of the tool tip.

[0076] In one embodiment, the tool tip approximation error given for the i-th corner is The corresponding tool tip smoothing curve transition length The calculation method is:

[0077] ;

[0078] in, is the tool tip approximation error given for the i-th corner The corresponding velocity direction at the midpoint of the tool tip smoothing curve and the tool tip linear path The angle of ; .

[0079] After inserting the Airthoid smoothing curve at the corner of the original linear path, the original path segment not covered by the smoothing curve is called the remaining straight line segment. It is located at both ends of the smoothing curve and connects the smoothing segment with the adjacent unprocessed linear path. For example, at the corner of the path, the smoothing curve replaces the center area of ​​the corner, and the original straight line segments are retained at both ends.

[0080] In one embodiment, the step S1 of using a B-spline curve to represent the remaining straight line segment of the tool tip linear path specifically includes:

[0081] The node vector and control vertex of the B-spline curve are designed. The derivative value of its endpoint is changed by changing the control vertex to achieve the continuity of the B-spline curve and the tool tip smooth curve within the set order range at the endpoint; in order to avoid the intersection of adjacent tool tip smooth curves, the length of the remaining straight line segment of the tool tip linear path corresponding to the i-th corner is Transition length to the smooth curve of the tool tip Need to meet:

[0082] ;

[0083] ;

[0084] in, is the tool tip approximation error given for the i-th corner The corresponding velocity direction at the midpoint of the tool tip smoothing curve and the tool tip linear path The angle of is the characteristic parameter of the tool tip smoothing curve corresponding to the i-th corner.

[0085] In order to achieve parameter synchronization, the present invention uses B-spline curves to represent the remaining straight line segments of the linear path, designs the node vector U=[0,0,0,0, 0, 0.5,0.5, 1,1,1,1,1,1], and controls the vertex distribution as follows: , a total of 8, such as Figure 2 As shown. In particular, by inserting the B-spline curve, the derivative value of its endpoint can be effectively changed by changing the control vertex, so as to achieve high-order continuity of the endpoint. At the same time, in order to ensure that adjacent smooth curves do not intersect, the linear path has a remaining straight line segment length of The corresponding relationship with the smooth transition length is thus determined to determine the final robot tool tip smooth curve transition length, thereby achieving the determination of the tool tip smooth curve and the high-order continuity of the tool tip path. Figure 2 middle, represents the i-th tool tip point, and linear NURNS represents the inserted B-spline curve, which represents a straight line in this embodiment.

[0086] In one embodiment, determining a preliminary tool axis smoothing curve according to the tool axis approximation error in step S2 specifically includes:

[0087] , The two adjacent tool axis linear paths that form the i-th corner, the tool axis point , , are all on the unit sphere, and the center of the unit sphere is recorded as ;exist A pair of symmetrical Airthoid curves are used in the plane As the tool axis plane smoothing curve, the tool axis linear path corresponding to the i-th corner is smoothed, and the tool axis plane smoothing curve is mapped to the unit sphere to form the tool axis smoothing curve. , are the starting and ending points of the tool axis smoothing curve. is the midpoint of the tool axis smoothing curve corresponding to the i-th corner; is the tool axis vector at the point where the tool axis approximation error corresponding to the i-th corner is the largest, The tool axis vector with the i-th corner The deviation is recorded as ;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:

[0088] ;

[0089] in, for and Angle.

[0090] The tool axis plane smoothing curve is similar to the tool tip smoothing curve, which is used to smooth the corner composed of three points. However, the tool axis plane smoothing curve needs to be mapped back to the unit sphere to be the final tool axis smoothing curve. The tool axis plane smoothing curve can be understood as the smoothing result that is not on the sphere, and the tool axis smoothing curve is on the unit sphere.

[0091] like Figure 3 As shown in the figure, in order to achieve robot tool axis smoothing in the workpiece coordinate system, the linear path smoothing of the tool axis uses a pair of Airthoid curves to perform high-order continuous smoothing on the tool axis smoothing plane formed by discrete tool postures, and then obtains the tool axis vector according to the unit vector normalization strategy. A pair of symmetrical Airthoid curves are used in the plane Smooth the corners. The constraint can be constrained by constraining the tool axis smoothing plane approximation error Achieve. The constraint method is the same as step S1.

[0092] In one embodiment, the step S3 calculates the transition length of the tool axis smoothing curve according to the preliminary tool axis smoothing curve and the parameter synchronization strategy to determine the final tool axis smoothing curve, specifically including:

[0093] Combined with the tool axis smoothing plane approximation error , while ensuring that the minimum length of the remaining straight line segment of the tool axis linear path meets the parameter synchronization requirements, calculate the transition length of the tool axis smoothing curve at the i-th corner :

[0094] ;

[0095] in, is the tool axis speed direction and linear path at the midpoint of the tool axis smoothing curve at the i-th corner The angle of is the approximate error of the tool axis smoothing plane, and They are the linear paths of the tool axis in the tool axis smoothing plane. and The corresponding transition length and ; The remaining straight line length for the tool axis; ; .

[0096] In particular It can be solved by a quartic equation, where , for half of; Can be obtained similarly:

[0097] ;

[0098] .

[0099] In one embodiment, the step S3 of using the angular displacement B-spline curve to represent the remaining straight line segment of the tool axis linear path specifically includes:

[0100] The B-spline curves corresponding to the remaining straight line segments of the tool axis linear path and the tool tip linear path have the same node vector. The remaining straight line segments of the tool axis linear path are represented by the known straight line segment (tool axis linear path) direction and angular displacement B-spline curve, and the corresponding control vertices are set.

[0101] Different from the B-spline inserted during tool tip smoothing to represent the position of the remaining straight line segment of the tool tip, tool axis smoothing uses B-spline to represent the angular displacement of the remaining straight line segment of the tool axis, and both use the same node vector. The tool axis B-spline control vertex distribution is determined by the tool axis smoothing transition length and parameter synchronization strategy.

[0102] In one embodiment, the step S4 of synchronizing the curvature parameters according to the maximum curvature of the final tool axis smoothing curve and the tool tip smoothing curve specifically includes:

[0103] Curvature parameters are shared in equal proportion to achieve synchronization of curvature parameters of the tool axis smooth curve and the tool tip smooth curve; the curvature parameter synchronization means that the curvature of a certain point on the tool tip smooth curve corresponds to the curvature of the only point on the tool axis smooth curve;

[0104] Curvature value of the smooth curve on the tool axis plane It is expressed as:

[0105] ;

[0106] in, is the curvature extreme value of the tool tip smoothing curve, is the curvature extreme value of the smooth curve on the tool axis plane, is the curvature extreme value of the tool axis smoothing curve, is the characteristic parameter of the tool tip smoothing curve; is the arc length of the smooth curve of the tool tip;

[0107] Arc length of smooth curve on tool axis plane for:

[0108] ;

[0109] in, is the characteristic parameter of the smoothing curve on the tool axis plane.

[0110] For the parameter synchronization of the smooth curve part, the curvature parameter is proportionally shared, that is, when the curvature of a certain point on the robot tool tip smooth curve corresponds to the only point on the tool axis smooth curve, the parameter correspondence is achieved. Make full use of the robot tool axis trajectory curvature information to coordinate the tool axis and tool tip movement and speed reduction, avoid the tool axis curvature factor becoming the bottleneck of the robot transfer speed, and enable the robot to maintain a high transfer speed during the transfer smooth motion, thereby improving the processing efficiency.

[0111] In one embodiment, the B-spline curve corresponding to the remaining straight line segments of the final tool axis smoothing curve and the tool tip smoothing curve in step S5 realizes spline parameter synchronization, specifically including:

[0112] According to the parameters of the tool axis smoothing curve and the tool tip smoothing curve, the expression of the control vertices of the B-spline curve corresponding to the remaining straight line segments of the tool tip linear path and the tool axis linear path is determined:

[0113] Control vertices of the B-spline curve corresponding to the remaining straight line segment of the tool tip linear path to They are:

[0114]

[0115] in, is the unit direction vector, and are the two adjacent tool tip linear paths that constitute the i-th corner, represents the operation of finding the path length, and Tip point and Length of tool tip smoothing curve at:

[0116] ; .

[0117] like Figure 4 As shown in the figure, the control vertices of the B-spline curve corresponding to the remaining straight line segment of the tool axis linear path to They are:

[0118]

[0119] in, , , represents the length of the smoothing curve of the tool axis plane corresponding to the i-th corner, The length of the smoothing start point of the i+1th corner ; Represents the tool axis point on the tool axis linear path that constitutes the i-th corner , , The center of the unit sphere where Indicates the starting point of the tool axis smoothing curve at the i+1th corner; is the length of the smoothing end of the i-th corner , Indicates the end point of the tool axis smoothing curve at the i-th corner; , , , They are , , , ; Indicates the linear path of the tool axis The midpoint of .

[0120] By analyzing the control vertices of the B-spline curves corresponding to the remaining straight line segments of the tool axis linear path and the tool tip linear path, the two share the same spline parameters, thereby achieving the corresponding spline parameters of the remaining straight line segments of the linear path.

[0121] For B-splines, the same node vector means the same spline parameter range. On this basis, each parameter corresponds to a result in the B-spline expression for the tool axis and tool tip, so the tool axis and tool tip position correspond one to one and synchronization is achieved.

[0122] like Figure 5 As shown, the method of the present invention can effectively avoid the frequent start and stop of the robot at the discrete path, and effectively improve the motion efficiency. At the same time, the parameter synchronization method of the present invention effectively avoids the acceleration mutation of the robot's tool axis motion at the connection point of the Airthoid curve and the original path, and improves the motion stability.

[0123] 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.

[0124] 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 robot path smoothing and synchronization method based on Airthoid curve, characterized in that: The robot controls the tool tip position and tool axis posture simultaneously to achieve path smoothing, including: According to the tool tip approximate error and the tool tip smoothing curve transition length determined by the parameter synchronization strategy, the remaining straight line segment of the tool tip linear path is represented by the B-spline curve; Determine the preliminary tool axis smoothing curve according to the tool axis approximate error; calculate the transition length of the tool axis smoothing curve according to the preliminary tool axis smoothing curve and parameter synchronization strategy, and determine the final tool axis smoothing curve; use the angular displacement B-spline curve to represent the remaining straight line segment of the tool axis linear path; The curvature parameter synchronization is realized according to the maximum curvature of the final tool axis smoothing curve and the tool tip smoothing curve: specifically, the curvature parameter is shared proportionally to realize the curvature parameter synchronization of the tool axis smoothing curve and the tool tip smoothing curve; the curvature parameter synchronization refers to the curvature of a certain point on the tool tip smoothing curve corresponding to the curvature of the only point on the tool axis smoothing curve; the curvature value of the tool axis plane smoothing curve corresponding to the tool axis linear path It is expressed as: ;in, is the curvature extreme value of the tool tip smoothing curve, is the curvature extreme value of the smooth curve on the tool axis plane, is the curvature extreme value of the tool axis smoothing curve, is the characteristic parameter of the tool tip smoothing curve; is the arc length of the tool tip smooth curve; the arc length of the tool axis plane smooth curve for: ;in, is the characteristic parameter of the smoothing curve on the tool axis plane; The spline parameters are synchronized according to the B-spline curves corresponding to the remaining straight line segments of the final tool axis smoothing curve and the tool tip smoothing curve; and the smoothing of the path corners is achieved.

2. The robot path smoothing and synchronization method based on Airthoid curve according to claim 1, characterized in that: The tool tip smoothing curve transition length determined according to the tool tip approximate error and parameter synchronization strategy specifically includes: A pair of symmetrical Airthoid curves are inserted into the corner formed by two adjacent tool tip linear paths as the tool tip smoothing curve of the current corner. The transition length of the tool tip smoothing curve is calculated according to the parameter synchronization strategy, the transition length of the tool tip smoothing curve corresponding to the tool tip approximation error, the remaining straight line segment length of the tool tip linear path and the tool tip linear path length.

3. The robot path smoothing and synchronization method based on Airthoid curve according to claim 2, characterized in that: The method of calculating the transition length of the tool tip smooth curve according to the parameter synchronization strategy, the transition length of the tool tip smooth curve corresponding to the tool tip approximation error, the remaining straight line segment length of the tool tip linear path and the tool tip linear path length specifically includes: Transition length of the tool tip smoothing curve corresponding to the i-th corner for: in, and are the two adjacent tool tip linear paths that constitute the i-th corner; i is the corner index of the current corner, i.e., the i-th corner, in the continuous tool tip linear path; Represents the operation of finding the path length; represents the tool tip approximation error given for the i-th corner The corresponding tool tip smoothing curve transition length, is the remaining straight line segment length of the tool tip linear path corresponding to the i-th corner, is the total number of corners in the continuous linear path of the tool tip.

4. The robot path smoothing and synchronization method based on Airthoid curve according to claim 3 is characterized in that: The tool tip approximation error given for the i-th corner is The corresponding tool tip smoothing curve transition length , calculated as: ； in, is the tool tip approximation error given for the i-th corner The corresponding velocity direction at the midpoint of the tool tip smoothing curve and the tool tip linear path The angle of 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 .

5. The robot path smoothing and synchronization method based on Airthoid curve according to claim 3, characterized in that: The method of using a B-spline curve to represent the remaining straight line segment of the tool tip linear path specifically includes: The node vector and control vertex of the B-spline curve are designed. The derivative value of the B-spline curve endpoint is changed by changing the control vertex to achieve the continuity of the B-spline curve and the tool tip smooth curve within the set order range at the endpoint; in order to avoid the intersection of adjacent tool tip smooth curves, the length of the remaining straight line segment of the tool tip linear path corresponding to the i-th corner is Transition length to the smooth curve of the tool tip Need to meet: ； ； in, is the tool tip approximation error given for the i-th corner The corresponding velocity direction at the midpoint of the tool tip smoothing curve and the tool tip linear path The angle of is the characteristic parameter of the tool tip smoothing curve corresponding to the i-th corner.

6. The robot path smoothing and synchronization method based on Airthoid curve according to claim 1, characterized in that: Determining a preliminary tool axis smoothing curve according to the tool axis approximate error specifically includes: , The two adjacent tool axis linear paths that form the i-th corner, the tool axis point , , are all on the unit sphere, and the center of the unit sphere is ;exist A pair of symmetrical Airthoid curves are used in the plane As the tool axis plane smoothing curve, the tool axis linear path corresponding to the i-th corner is smoothed, and the tool axis plane smoothing curve is mapped to the unit sphere to form the tool axis smoothing curve. , are the starting and ending points of the tool axis smoothing curve, is the midpoint of the tool axis smoothing curve corresponding to the i-th corner; is the tool axis vector at the point where the tool axis approximation error corresponding to the i-th corner is the largest, The tool axis vector with the i-th corner The deviation is recorded as ;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 Angle.

7. The robot path smoothing and synchronization method based on Airthoid curve according to claim 6, characterized in that: The method of calculating the transition length of the tool axis smoothing curve according to the preliminary tool axis smoothing curve and the parameter synchronization strategy and determining the final tool axis smoothing curve specifically includes: Combined with the tool axis smoothing plane approximation error , while ensuring that the minimum length of the remaining straight line segment of the tool axis linear path meets the parameter synchronization requirements, calculate the transition length of the tool axis smoothing curve at the i-th corner : ； in, is the tool axis speed direction and tool axis linear path at the midpoint of the tool axis smoothing curve at the i-th corner The angle of is the approximate error of the tool axis smoothing plane, and They are the linear paths of the tool axis in the tool axis smoothing plane. and The corresponding transition length , ; Indicates the tool axis smoothing curve on the tool axis linear path The displacement component in the direction, Indicates the tool axis smoothing curve on the tool axis linear path The displacement component in the orthogonal direction of ; ; Represents the integral variable, representing 0 to A continuously changing angle value between .

8. The robot path smoothing and synchronization method based on Airthoid curve according to claim 1, characterized in that: The method of using the angular displacement B-spline curve to represent the remaining straight line segment of the tool axis linear path specifically includes: The B-spline curves corresponding to the remaining straight line segments of the tool axis linear path and the tool tip linear path have the same node vector. The tool axis linear path direction and the angular displacement B-spline curve represent the remaining straight line segments of the tool axis linear path, and set the corresponding control vertices.

9. The robot path smoothing and synchronization method based on Airthoid curve according to claim 1, characterized in that: The B-spline curve corresponding to the remaining straight line segment of the final tool axis smoothing curve and the tool tip smoothing curve realizes spline parameter synchronization, specifically including: According to the parameters of the tool axis smoothing curve and the tool tip smoothing curve, the expression of the control vertices of the B-spline curve corresponding to the remaining straight line segments of the tool tip linear path and the tool axis linear path is determined: Control vertices of the B-spline curve corresponding to the remaining straight line segment of the tool tip linear path to They are: in, is the unit direction vector, and are the two adjacent tool tip linear paths that constitute the i-th corner, represents the operation of finding the path length, and Tip point and The length of the tool tip smooth curve at ; Control vertices of the B-spline curve corresponding to the remaining straight line segment of the tool axis linear path to They are: in, , , represents the length of the smoothing curve of the tool axis plane corresponding to the i-th corner, The length of the smoothing start point of the i+1th corner ; Represents the tool axis point on the tool axis linear path that constitutes the i-th corner , , The center of the unit sphere where Indicates the starting point of the tool axis smoothing curve at the i+1th corner; is the length of the smoothing end of the i-th corner , Indicates the end point of the tool axis smoothing curve at the i-th corner; , , , They are , , , ; Indicates the linear path of the tool axis The midpoint of By analyzing the control vertices of the B-spline curves corresponding to the remaining straight line segments of the tool axis linear path and the tool tip linear path, the spline parameter correspondence of the remaining straight line segments of the linear path is achieved.

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