Five-degree-of-freedom hybrid robot ball-end cutter posture planning method and system

Abstract

This invention provides a method and system for planning the attitude of a ball-end milling cutter in a five-DOF hybrid robot, comprising: Step S1: acquiring tool information and surface information of the machining component on the ball-end milling cutter, and establishing a local coordinate system for each tool contact point; Step S2: establishing a global path smoothness performance index and an effective tool diameter performance index for the hybrid robot tool; Step S3: based on the tool information, establishing a constrained optimization model with the weighted sum of the global path smoothness performance index and the effective tool diameter performance index as the optimization objective; generating and simplifying the feasible region of the tool axis direction for each tool contact point according to the constraint conditions; Step S4: optimizing the tool axis direction path according to the constraint model and the feasible region of the tool axis direction for each tool contact point, and outputting the machining path of the five-DOF hybrid robot tool. The method and system provided by this invention can maintain a large effective tool diameter and make the effective tool diameter change smoothly, thereby improving machining efficiency.

Description

Technical Field

[0001] This invention relates to the field of five-axis machining and manufacturing technology, specifically to a method and system for planning the attitude of a ball-end tool for a five-degree-of-freedom hybrid robot. Background Technology

[0002] From a mechanics perspective, robots can be divided into two main categories: serial robots and parallel robots. Serial robots are based on open-loop mechanisms; parallel robots are robots with one or more closed loops whose joint coordinates are interconnected.

[0003] Degrees of freedom (DOF) in a robot refer to the number of degrees of freedom a robot has, or the number of axes of motion it can move along. It is one of the important indicators of a robot, showing the spatial range within which it can perform tasks and the level of complexity required to accomplish these mechanical tasks.

[0004] Hybrid robots are a type of hybrid mechanism consisting of a parallel mechanism and a series mechanism connected in series. They have advantages such as large working space, high stiffness-to-weight ratio, strong reconfigurability, and the ability to achieve closed-loop feedback of end position. They have been widely used in high-speed machining of aircraft structural parts and automotive body panel molds, multi-position pressure assembly of engine cylinder blocks, and various special machining processes such as laser and water jet.

[0005] Five-DOF hybrid robots combine the advantages of serial robots (large workspace) and parallel robots (high rigidity and high dynamic performance), showing great promise for the machining and manufacturing of large and complex parts. Ball end milling is widely used for the finishing of complex curved surfaces. In ball end milling on five-axis machining centers, keeping the tool position point constant allows for adjustments to the tool axis direction, thus avoiding collisions and interference and improving machining accuracy and efficiency.

[0006] Existing research on tool posture optimization in five-axis ball end mill machining mainly focuses on tandem machine tools. Based on the selection of optimization variables, it can be divided into two main categories: methods in the workpiece coordinate system and methods in the machine coordinate system. However, methods in the workpiece coordinate system do not consider the nonlinear mapping between joint motion and end effector motion, and a smooth tool axis path cannot guarantee smooth joint motion. Methods in the machine coordinate system directly optimize the motion of two rotary joints, but since the tool axis direction of a hybrid robot is determined by the motion of three or more joints, related research in machine tool space is not applicable to hybrid robots.

[0007] Chinese patent document CN104238455A discloses a method for milling free-form surfaces using a ball end mill. This method includes measuring the cutting width at any contact point on the surface using a tensor, constructing a second-order tensor field for the cutting width, extracting the three degenerate points from the tensor field, and using these as starting points to search for internal boundary points of the surface, thus dividing the surface machining region. Each region is called a surface machining feature. Several curves are constructed within each surface machining feature, ensuring that the tangent at each point on the curve coincides with the feed direction with the maximum cutting width at that point. The curve with the maximum average cutting width is selected as the initial machining trajectory line within that region. The toolpath for each surface machining feature is calculated by offsetting the initial machining trajectory line, thus obtaining the machining trajectory for the entire surface. However, this method cannot solve the aforementioned problem. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for planning the attitude of a ball-end tool in a five-degree-of-freedom hybrid robot.

[0009] The five-degree-of-freedom hybrid robot ball-end tool attitude planning method provided by the present invention includes:

[0010] Step S1: Collect tool information from the ball end mill and surface information of the machined part, and establish a local coordinate system for each tool contact point;

[0011] Step S2: Establish the global path smoothness performance index and the effective diameter performance index of the five-axis hybrid robot tool;

[0012] Step S3: Based on the tool information, establish a constrained optimization model with the weighted sum of the global path smoothness performance index and the effective tool diameter performance index as the optimization objective; generate and simplify the feasible domain of the tool axis direction for each tool contact point based on the constraint conditions.

[0013] Step S4: Optimize the tool axis direction path based on the constraint model and the feasible region of the tool axis direction at each tool contact point, and output the machining path of the five-DOF hybrid robot tool.

[0014] Preferably, the tool information includes: tool contact point path, tool tilt angle and side tilt angle; the tool tilt angle and side tilt angle represent the tool axis direction and uniquely determine the end effector posture of the five-degree-of-freedom hybrid robot.

[0015] Preferably, step S1 includes the following sub-steps:

[0016] Step S1.1: Generate the local coordinate system {L} for each tool contact point based on the surface information of the machined part. i};

[0017] Where i = 1, ..., n represents the knife contact point number;

[0018] Step S1.2: Based on the tool rake angle λ i and the roll angle ω i Indicates the tool axis direction in the local coordinate system Establish a robot base coordinate system {B} and uniquely determine the tool axis direction within the robot base coordinate system. in Represents {L i The posture of}.

[0019] Preferably, the performance index of the effective diameter of the tool includes: the performance index of the size of the effective diameter of the tool and the performance index of the rate of change of the size of the effective diameter of the tool.

[0020] Preferably, step S2 includes the following sub-steps:

[0021] Step S2.1: Based on the tool pose (P) of the i-th tool contact point i O i The corresponding joint angle q is obtained through robot inverse kinematics. i =[q i,1 q i,2 q i,3 q i,4 q i,5 ] T The first, second, and third derivatives of the joint angle with respect to the arc length parameter of the tool position point are obtained through numerical difference formulas, and let... and Let Δs represent the first, second, and third derivatives of the j-th joint variable between the i-th and i+1-th tool points with respect to the path arc length parameter of the tool point, respectively. i This represents the distance between the i-th cutter position and the (i+1)-th cutter position;

[0022] Step S2.2: Establish global path smoothing performance index Φ smooth :

[0023]

[0024] in, These are the weighting coefficients.

[0025] Step S2.3: Establish the performance index Φ for the effective diameter of the cutting tool. DMA The performance index Φ of the rate of change of the effective diameter of the cutting tool DCR :

[0026]

[0027]

[0028] Among them, D i =2rt sin(cos -1 (cosλ i cosω i )) represents the effective diameter of the tool at the i-th tool contact point, r t D is the tool radius. de This is the lower bound of the specified effective tool diameter.

[0029] Preferably, the constraint optimization model in step S3 is established based on the constraints of the hybrid robot and the machining process, with the tool tilt angle λ and side tilt angle ω as optimization variables, and the weighted sum of the global path smoothness performance index and the performance index of the effective diameter of the tool as the optimization objective.

[0030] Preferably, step S3 includes the following sub-steps:

[0031] Step S3.1: Using the tool rake angle λ and side rake angle ω at each tool contact point as optimization variables, construct the optimization variable vector η = [ω1...ω n λ1...λ n ] T Establish a constrained optimization model P1:

[0032]

[0033] stq i =f ikine (P i O i (ω i , λ i ))

[0034] f c,i (ω i ,λ i )≤0

[0035] D i =2r t sin(cos -1 (cosλ i cosω i ))

[0036] i = 1, ..., n;

[0037] Where, k DMA and k DCR f is the weighting coefficient. ikine (·) is the inverse kinematic function, f c,i (ω i ,λ i )≤0 indicates that the constraint condition that the tool axis direction needs to satisfy at the i-th tool contact point;

[0038] Step S3.2: Based on the constraints that need to be satisfied during the machining process of the hybrid robot, including: active and passive joint motion range constraints, kinematic singular constraints, tilt angle constraints, and interference-free constraints, the feasible region {FR} of the tool axis direction for each tool contact point is constructed on the ω-λ plane using a discretization method. i |i=1,...,n};

[0039] Step S3.3: Starting from the initial tool axis direction, progressively search for the boundary of the nearest feasible region along the tool axis direction, and set FR... i Simplified into a rectangular area

[0040] Step S3.4: FR i It remains unchanged during the optimization process, simplifying its form. Corrections are made during the iterative optimization process.

[0041] Preferably, step S4 includes the following sub-steps:

[0042] Step S4.1: Calculate the current q based on the initial value of η. i D i , And obtain the performance index Φ smooth Φ DMA and Φ DCR ;

[0043] Step S4.2: Calculate based on the robot's differential kinematics. Φ can be estimated using the following formula. smooth (η+Δη):

[0044] Φ smooth (η+Δη)=Δη T H smooth Δη+2f smooth T Δη+Φ smooth (η)

[0045]

[0046]

[0047] Step S4.3: Calculation Φ can be estimated using the following formula. DMA (η+Δη):

[0048] Φ DCR (η+Δη)=Δη T H DCR Δη+2f DCR T Δη+Φ DCR (η)

[0049]

[0050]

[0051] Step S4.4: Φ DCR The equivalent representation is:

[0052]

[0053]

[0054] ψ i ≥0, i=1,...,n;

[0055] Step S4.5: Let l represent the current iteration step, η l This represents the initial solution of the l-th iteration, in η l Nearby, the original constrained optimization model P1 is approximately equivalent to P2:

[0056]

[0057]

[0058] ψ i ≥0

[0059]

[0060]

[0061] i = 1, ..., n;

[0062] Among them, H η =H smooth +k DCR H DCR f η =f smooth +k DCR f DCR The maximum iteration step size ζ limits Δη to a small range;

[0063] Step S4.6: In each iteration, solve the above quadratic programming problem to obtain Δη, and update the parameter: η l+1 =η l +Δη;

[0064] Step S4.7: Calculate the updated q i , Computational performance metrics and when If convergence is achieved, stop the iteration and output the optimal solution; otherwise, proceed to step S4.2.

[0065] Step S4.8: Optimize the tool rake angle λ based on each tool contact point. i and the roll angle ω i The direction of the tool axis O at this time is calculated. i The robot motion program is generated based on the obtained tool axis direction path O(u) and the tool position path P(u) determined by the tool contact point and the surface information of the machined part, and the machining path of the hybrid robot tool is controlled.

[0066] The five-degree-of-freedom hybrid robot ball-end tool attitude planning system provided by the present invention includes:

[0067] Module M1: Collects tool information from the ball end mill and surface information of the machined parts, and establishes a local coordinate system for each tool contact point;

[0068] Module M2: Establish global path smoothness performance index and effective tool diameter performance index for the five-axis hybrid robot tool;

[0069] Module M3: Based on tool information, a constrained optimization model is established with the weighted sum of global path smoothness performance index and tool effective diameter performance index as the optimization objective; the feasible domain of tool axis direction for each tool contact point is generated and simplified based on the constraint conditions.

[0070] Module M4: Based on the constraint model and the feasible domain of the tool axis direction at each tool contact point, optimizes the tool axis direction path and outputs the machining path of the five-DOF hybrid robot tool.

[0071] Preferably, the tool information includes: tool contact point path, tool tilt angle and side tilt angle; the tool tilt angle and side tilt angle represent the tool axis direction and uniquely determine the end effector posture of the five-degree-of-freedom hybrid robot.

[0072] Preferably, module M1 includes the following sub-modules:

[0073] Module M1.1: Generates the local coordinate system {L} for each tool contact point based on the surface information of the machined part. i};

[0074] Where i = 1, ..., n represents the knife contact point number;

[0075] Module M1.2: Based on the tool rake angle λ i and the roll angle ω i Indicates the tool axis direction in the local coordinate system Establish a robot base coordinate system {B} and uniquely determine the tool axis direction within the robot base coordinate system. in Represents {L iThe posture of}.

[0076] Preferably, the performance index of the effective diameter of the tool includes: the performance index of the size of the effective diameter of the tool and the performance index of the rate of change of the size of the effective diameter of the tool.

[0077] Preferably, module M2 includes the following sub-modules:

[0078] Module M2.1: Based on the tool pose (P) of the i-th tool contact point i O i The corresponding joint angle q is obtained through robot inverse kinematics. i =[q i,1 q i,2 q i,3 q i,4 q i,5 ] T The first, second, and third derivatives of the joint angle with respect to the arc length parameter of the tool position point are obtained through numerical difference formulas, and let... and Let Δs represent the first, second, and third derivatives of the j-th joint variable between the i-th and i+1-th tool points with respect to the path arc length parameter of the tool point, respectively. i This represents the distance between the i-th cutter position and the (i+1)-th cutter position;

[0079] Module M2.2: Establish global path smoothing performance index Φ smooth :

[0080]

[0081] in, These are the weighting coefficients.

[0082] Module M2.3: Establishes the performance index Φ for the effective diameter of the cutting tool. DMA The performance index Φ of the rate of change of the effective diameter of the cutting tool DCR :

[0083]

[0084]

[0085] Among them, D i =2r t sin(cos -1 (cosλ i cosω i )) represents the effective diameter of the tool at the i-th tool contact point, r t D is the tool radius. de This is the lower bound of the specified effective tool diameter.

[0086] Preferably, the constraint optimization model of module M3 is established based on the constraints of the hybrid robot and the machining process, with the tool tilt angle λ and side tilt angle ω as optimization variables, and the weighted sum of the global path smoothness performance index and the performance index of the effective diameter of the tool as the optimization objective.

[0087] Preferably, module M3 includes the following sub-modules:

[0088] Module M3.1: Using the tool rake angle λ and side rake angle ω at each tool contact point as optimization variables, construct the optimization variable vector η=[ω1...ω n λ1...λ n ] T Establish a constrained optimization model P1:

[0089]

[0090] stq i =f ikine (P i O i (ω i ,λ i ))

[0091] f c,i (ω i ,λ i )≤0

[0092] D i =2r t sin(cos -1 (cosλ i cosω i ))

[0093] i = 1, ..., n;

[0094] Where, k DMA and k DCR f is the weighting coefficient. ikine (·) is the inverse kinematic function, f c,i (ω i ,λ i )≤0 indicates that the constraint condition that the tool axis direction needs to satisfy at the i-th tool contact point;

[0095] Module M3.2: Based on the constraints of active and passive joint motion range, kinematic singularity, tilt angle, and interference-free constraints that need to be satisfied during the machining process of the hybrid robot, the feasible region {FR} of the tool axis direction for each tool contact point is constructed on the ω-λ plane using a discretization method. i |i=1,…,n};

[0096] Module M3.3: Starting from the initial tool axis direction, progressively search the boundary of the nearest feasible region for the tool axis direction, and set FR... i Simplified into a rectangular area

[0097] Module M3.4: FR i It remains unchanged during the optimization process, simplifying its form. Corrections are made during the iterative optimization process.

[0098] Preferably, module M4 includes the following sub-modules:

[0099] Module M4.1: Calculates the current q based on the initial value of η. i D i , And obtain the performance index Φ smooth Φ DMA and Φ DCR ;

[0100] Module M4.2: Calculates based on the robot's differential kinematics. Φ can be estimated using the following formula. smooth (η+Δη):

[0101] Φ smooth (η+Δη)=Δη T H smooth Δη+2f smooth T Δη+Φ smooth (η)

[0102]

[0103]

[0104] Module M4.3: Calculation Φ can be estimated using the following formula. DMA (η+Δη):

[0105] Φ DCR (η+Δη)=Δη T H DCR Δη+2f DCR T Δη+Φ DCR (η)

[0106]

[0107]

[0108] Module M4.4: Φ DCR The equivalent representation is:

[0109]

[0110]

[0111] ψ i ≥0, i=1,…,n;

[0112] Module M4.5: Let l represent the current iteration step, η l This represents the initial solution of the l-th iteration, in η l Nearby, the original constrained optimization model P1 is approximately equivalent to P2:

[0113]

[0114]

[0115] ψ i ≥0

[0116]

[0117]

[0118] i = 1, ..., n;

[0119] Among them, H η =H smooth +k DCR H DCR f η =f smooth +k DCR f DCR The maximum iteration step size ζ limits Δη to a small range;

[0120] Module M4.6: In each iteration, solve the above quadratic programming problem to obtain Δη, and update the parameter η. l+1 =η l +Δη;

[0121] Module M4.7: Calculates the updated q i , Computational performance metrics and when If convergence is achieved, stop the iteration and output the optimal solution; otherwise, proceed to step S4.2.

[0122] Module M4.8: Optimized tool rake angle λ based on each tool contact point. i and the roll angle ω i The direction of the tool axis O at this time is calculated. iThe robot motion program is generated based on the obtained tool axis direction path O(u) and the tool position path P(u) determined by the tool contact point and the surface information of the machined part, and the machining path of the hybrid robot tool is controlled.

[0123] Compared with the prior art, the present invention has the following beneficial effects:

[0124] 1. The ball end mill posture planning method for a five-degree-of-freedom hybrid robot provided by this invention can solve the problem of tool axis direction planning in ball end milling of a five-degree-of-freedom hybrid robot. The generated robot ball end milling path can maintain a large and stable effective tool diameter, which helps to maintain good machining quality; it can improve the smoothness of the joint path of the hybrid robot and improve machining efficiency.

[0125] 2. The five-degree-of-freedom hybrid robot ball end tool posture planning method provided by the present invention simplifies the complex geometric and mechanical constraints of the hybrid robot into linear constraints in each iteration, and dynamically updates the linear constraint conditions during the iteration process, thereby taking into account both computational efficiency and optimization effect. This method has a wide range of applications in the field of five-axis machining and manufacturing technology.

[0126] 3. The five-degree-of-freedom hybrid robot ball-end tool attitude planning system provided by this invention has low cost and is easy to mass-produce.

[0127] Other beneficial effects of the present invention will be explained in detail through the introduction of specific technical features and technical solutions in specific embodiments. Those skilled in the art should be able to understand the beneficial technical effects brought about by these technical features and technical solutions through the introduction of these technical features and technical solutions. Attached Figure Description

[0128] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0129] Figure 1 This is a flowchart of an embodiment of the present invention.

[0130] Figure 2 This is a schematic diagram of the path between the surface of the part to be processed and the tool contact point in an embodiment of the present invention.

[0131] Figure 3 This is a schematic diagram of the structure of a hybrid processing robot according to an embodiment of the present invention.

[0132] Figure 4 This is a schematic diagram of the joint motion of the tool before and after optimization in the first path segment of the embodiment of the present invention.

[0133] Figure 5 This is a comparison chart of machining time before and after toolpath optimization in an embodiment of the present invention.

[0134] Figure 6 This is a comparison chart of performance indicators before and after toolpath optimization in an embodiment of the present invention. Detailed Implementation

[0135] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0136] This invention provides a method for attitude planning of a ball-end tool in a five-degree-of-freedom hybrid robot, characterized by comprising:

[0137] Step S1: Collect tool information from the ball end mill and surface information of the machined part, and establish a local coordinate system {L} for each tool contact point. i}, where i = 1, ..., n represent the tool contact point number, the x-axis of the coordinate system is along the feed direction, the z-axis is along the normal direction of the surface of the machined part, and the y-axis is determined by the right-hand rule.

[0138] Tool information includes: tool contact path, tool rake angle, and tool tilt angle.

[0139] Based on the tool tilt angle λ i and the roll angle ω i Indicates the tool axis direction in the local coordinate system Establish a robot base coordinate system {B} and uniquely determine the tool axis direction within the robot base coordinate system. in Represents {L i The posture of}.

[0140] Step S2: Based on the tool pose (P) of the i-th tool contact point i O i The corresponding joint angle q is obtained through robot inverse kinematics. i =[q i,1 q i,2 q i,3 q i,4 q i,5 ] T The first, second, and third derivatives of the joint angle with respect to the arc length parameter of the tool position point are obtained through numerical difference formulas, and let... and Let Δs represent the first, second, and third derivatives of the j-th joint variable between the i-th and i+1-th tool points with respect to the path arc length parameter of the tool point, respectively. i This represents the distance between the i-th and (i+1)-th knife positions.

[0141] First, establish the global path smoothing performance index Φ smooth :

[0142]

[0143] in, These are the weighting coefficients.

[0144] Next, the performance index Φ for the effective diameter of the cutting tool is established. DMA The performance index Φ of the rate of change of the effective diameter of the cutting tool DCR :

[0145]

[0146]

[0147] Among them, D i =2r t sin(cos -1 (cosλ i cosω i )) represents the effective diameter of the tool at the i-th tool contact point, r t D is the tool radius. de This is the lower bound of the specified effective tool diameter.

[0148] Step S3: Using the tool tilt angle λ and the side tilt angle ω as optimization variables, construct the optimization variable vector η = [ω1...ω2]. n λ1...λ n ] T Using the weighted sum of the global path smoothness performance index and the effective tool diameter performance index as the optimization objective, a constrained optimization model P1 is established:

[0149]

[0150] stq i =f ikine (P i O i (ω i ,λ i ))

[0151] f c,i (ω i ,λ i )≤0

[0152] D i =2r t sin(cos -1 (cosλ i cosω i ))

[0153] i = 1, ..., n;

[0154] Where, k DMA and k DCR f is the weighting coefficient. ikine (·) is the inverse kinematic function, f c,i (ω i ,λ i )≤0 indicates that the constraint condition that the tool axis direction needs to satisfy at the i-th tool contact point is .

[0155] Based on the constraints that need to be satisfied during the machining process of the hybrid robot, including: active and passive joint motion range constraints, kinematic singular constraints, tilt angle constraints, and interference-free constraints, a feasible region {FR} for the tool axis direction of each tool contact point is constructed on the ω-λ plane using a discretization method. i |i=1,...,n};Starting from the initial tool axis direction, progressively search the boundary of the nearest feasible region of the tool axis direction, and set FR i Simplified into a rectangular area

[0156] FR i It remains unchanged during the optimization process, simplifying its form. Corrections are made during the iterative optimization process.

[0157] Step S4: Calculate the current q based on the initial value of η. i D i , And obtain the performance index Φ smooth Φ DMA and Φ DCR Based on the robot's differential kinematics, calculate... Φ can be estimated using the following formula. smooth (η+Δη):

[0158] Φ smooth (η+Δη)=Δη T H smooth Δη+2f smooth T Δη+Φ smooth (η)

[0159]

[0160]

[0161] calculate Φ can be estimated using the following formula. DMA (η+Δη):

[0162] Φ DCR(η+Δη)=Δη T H DCR Δη+2f DCR T Δη+Φ DCR (η)

[0163]

[0164]

[0165] Φ DCR The equivalent representation is:

[0166]

[0167]

[0168] ψ i ≥0, i=1,...,n.

[0169] Let l represent the current iteration step, η l This represents the initial solution of the l-th iteration, in η l Nearby, the original constrained optimization model P1 is approximately equivalent to P2:

[0170]

[0171]

[0172] ψ i ≥0

[0173]

[0174]

[0175] i = 1, ..., n;

[0176] Among them, H η =H smooth +k DCR H DCR f η =f smooth +k DCR f DCR The maximum iteration step size ζ limits Δη to a small range;

[0177] In each iteration, the above quadratic programming problem is solved to obtain Δη, and the parameter η is updated. l+1 =η l +Δη, then calculate the updated q i , Computational performance metrics and when When convergence is achieved, stop the iteration and output the optimal solution; otherwise, recalculate. Φ can be estimated using the following formula. smooth (η+Δη):

[0178] Φ smooth (η+Δη)=Δη T H smooth Δη+2f smooth T Δη+Φ smooth (η)

[0179]

[0180]

[0181] The optimized tool rake angle λ based on each tool contact point i and the roll angle ω i The direction of the tool axis O at this time is calculated. i The robot motion program is generated based on the obtained tool axis direction path O(u) and the tool position path P(u) determined by the tool contact point and the surface information of the machined part, and the machining path of the hybrid robot tool is controlled.

[0182] The above are basic embodiments of the present invention. The technical solution of the present invention will be further described below through a preferred embodiment:

[0183] Reference Figure 1 As shown, this invention provides a method for attitude planning of a ball-end tool in a five-DOF hybrid robot, comprising:

[0184] Step S1: Collect tool information from the ball end mill and surface information of the machined part, and establish a local coordinate system for each tool contact point;

[0185] Step S2: Establish the global path smoothness performance index and the effective diameter performance index of the hybrid robot tool;

[0186] Step S3: Based on the tool information, establish a constrained optimization model with the weighted sum of the global path smoothness performance index and the effective tool diameter performance index as the optimization objective; generate and simplify the feasible domain of the tool axis direction for each tool contact point based on the constraint conditions.

[0187] Step S4: Optimize the tool axis direction path based on the constraint model and the feasible region of the tool axis direction at each tool contact point, and output the machining path of the five-DOF hybrid robot tool.

[0188] Specifically, step S1 includes: referring to Figure 2As shown, the surface information S(u,v) of the part to be processed is obtained. It is a bicubic Bezier surface, and its control points are represented in the workpiece coordinate system as follows:

[0189]

[0190] The unit is mm; the tool contact path of the curved surface is a zigzag toolpath containing 53 long path segments. The tool contact path is represented as P. c (u), which includes a series of discrete knife contact points {P c,i |i=1,...,n};

[0191] Collect tool information from the ball end mill and surface information of the machined parts, and establish a local coordinate system {L} for each tool contact point. i}, where i = 1, ..., n represent the tool contact point numbers, the x-axis of the coordinate system is along the feed direction, the z-axis is along the normal direction of the surface of the machined part, and the y-axis is determined by the right-hand rule.

[0192] Tool information includes: tool contact path, tool rake angle, and tool tilt angle.

[0193] Based on the tool tilt angle λ i and the roll angle ω i Indicates the tool axis direction in the local coordinate system Establish a robot base coordinate system {B} and uniquely determine the tool axis direction within the robot base coordinate system. in Represents {L i The orientation of the tool; the tool tilt angle range is set to [λ]. min ,λ max ] = [π / 72, π / 3] and [ω min ,ω max ] = [-15π / 36, 15π / 36], sampling interval set to Δλ s =π / 72 and Δω s =π / 72. Optimize the tool axis direction path for each of the 53 long path segments, while keeping the tool axis direction unchanged at both ends of the tool contact point during the optimization process, referencing the feed rate f. ref The speed is set to 10 mm / s, the maximum iteration step size ζ is initialized to 0.04, and the thresholds γ1 and γ2 are set to 10. -5 .

[0194] Reference Figure 3 As shown, the drive joints of this hybrid robot have five translational axes, using the generalized coordinate vector x = [xy z α β]. T Indicates the end-effector posture:

[0195]

[0196] Where, P = [xyz] T Let be the cutter position, α and β be the rotation angles, and the cutter axis direction be O = [sinαcosβ -sinβcosαcosβ]. T According to the robot's closed-loop constraint condition f(x,q)=0 5×1 A linear mapping can be established from the tool position point and tool axis direction to the motion of the active joint:

[0197]

[0198] Furthermore, the local linear mapping from the tool tilt angle change Δλ and Δω to Δq is obtained:

[0199]

[0200] Joint kinematic performance constraints are set as follows:

[0201] V j,max =20mm / s,A j,max =100mm / s 2 J j,max =2000mm / s 3 ,j=1,...,5.

[0202] Reference Figure 4 As shown, specifically, step S2 includes: based on the tool pose (P) of the i-th tool contact point. i O i The corresponding joint angle q is obtained through robot inverse kinematics. i =[q i,1 q i,2 q i,3 q i,4 q i,5 ] T The first, second, and third derivatives of the joint angle with respect to the arc length parameter of the tool position point are obtained through numerical difference formulas, and let... and Let the first, second, and third derivatives of the j-th joint variable between the i-th and i+1-th tool points be represented, respectively, with respect to the path arc length parameter of the tool point:

[0203]

[0204]

[0205]

[0206] Among them, S i,j =Δs i Δs i+1 (Δs i +Δs i+1 ), Qi,j =Δs i+1 q i,j -(Δs i +Δs i+1 )q i+1,j +Δs i q i+2,j Δs i This represents the distance between the i-th and (i+1)-th knife positions.

[0207] First, establish the global path smoothing performance index Φ smooth :

[0208]

[0209] in, These are the weighting coefficients. Assume the reference feed rate is f ref Then the weighting coefficient can be set as follows:

[0210]

[0211]

[0212]

[0213] Among them, V j,max A j,max and J j,max These are the maximum velocity, acceleration, and jump of joint j, respectively.

[0214] Next, the performance index Φ for the effective diameter of the cutting tool is established. DMA The performance index Φ of the rate of change of the effective diameter of the cutting tool DCR :

[0215]

[0216]

[0217] Among them, D i =2r t sin(cos -1 (cosλ i cosω i )) represents the effective diameter of the tool at the i-th tool contact point, r t D is the tool radius. de This is the lower bound of the specified effective tool diameter.

[0218] Specifically, step S3 includes: constructing an optimization variable vector η = [ω1...ω2] using the tool tilt angle λ and the side tilt angle ω as optimization variables. n λ1...λn ] T Using the weighted sum of the global path smoothness performance index and the effective tool diameter performance index as the optimization objective, a constrained optimization model P1 is established:

[0219]

[0220] stq i =f ikine (P i O i (ω i ,λ i ))

[0221] f c,i (ω i ,λ i )≤0

[0222] D i =2r t sin(cos -1 (cosλ i cosω i ))

[0223] i = 1, ..., n;

[0224] Where, k DMA and k DCR f is the weighting coefficient. ikine (·) is the inverse kinematic function, f c,i (ω i ,λ i )≤0 indicates that the constraint condition that the tool axis direction needs to satisfy at the i-th tool contact point is .

[0225] Then, the constraints that need to be satisfied during the processing of the hybrid robot, such as the active and passive joint motion range constraints, kinematic singular constraints, tool tilt angle constraints, and interference-free constraints, are projected onto the ω-λ plane.

[0226] With sampling interval Δω s and Δλ s For the interval [ω min ,ω max ]×[λ min ,λ max Discretize the data to obtain a series of sampling points. Construct the feasible region {FR} of the tool axis direction for each tool contact point. i |i=1,...,n},FR i Represented as the union of a series of rectangular grids; from the initial tool axis direction (ω) i,ini ,λ i,ini ) beginning, in and The process involves progressively searching for the boundary of the nearest feasible region in the tool axis direction, and then defining FR. i Simplified into a rectangular area FR i It remains unchanged during the optimization process, while its simplified form remains unchanged. This requires correction during the iterative optimization process.

[0227] Specifically, step S4 includes: calculating the current q based on the initial value of η. i D i , And obtain the performance index Φ smooth Φ DMA and Φ DCR Based on the robot's differential kinematics, calculate... Φ can be estimated using the following formula. smooth (η+Δη):

[0228] Φ smooth (η+Δη)=Δη T H smooth Δη+2f smooth T Δη+Φ smooth (η)

[0229]

[0230]

[0231] calculate Φ can be estimated using the following formula. DMA (η+Δη):

[0232] Φ DCR (η+Δη)=Δη T H DCR Δη+2f DCR T Δη+Φ DCR (η)

[0233]

[0234]

[0235] Φ DCR The equivalent representation is:

[0236]

[0237]

[0238] ψ i≥0, i=1,...,n.

[0239] Let l represent the current iteration step, η l This represents the initial solution of the l-th iteration, in η l Nearby, the original constrained optimization model P1 is approximately equivalent to P2:

[0240]

[0241]

[0242] ψ i ≥0

[0243]

[0244]

[0245] i = 1, ..., n;

[0246] Among them, H η =H smooth +k DCR H DCR f η =f smooth +k DCR f DCR The maximum iteration step size ζ limits Δη to a small range;

[0247] In each iteration, the above quadratic programming problem is solved to obtain Δη, and the parameter η is updated. l+1 =η l +Δη, then calculate the updated q i , Computational performance metrics and The convergence criterion is set as follows:

[0248]

[0249] Where γ1 and γ2 are threshold coefficients, convergence occurs when both of the above two conditions are met; otherwise, the maximum iteration step size ζ is modified.

[0250] ζ = 0.5max(|Δη|)

[0251] when When convergence is achieved, stop iterating and output the optimal solution; otherwise, calculate... Estimate Φ smooth (η+Δη).

[0252] Reference Figure 5 and Figure 6As shown, the optimized tool rake angle λ based on each tool contact point i and the roll angle ω i The direction of the tool axis O at this time is calculated. i The robot motion program is generated based on the obtained tool axis direction path O(u) and the tool position path P(u) determined by the tool contact point and the surface information of the machined part, and the machining path of the hybrid robot tool is controlled.

[0253] The present invention also provides a five-degree-of-freedom hybrid robot ball end tool attitude planning system. The five-degree-of-freedom hybrid robot ball end tool attitude planning system can be implemented by executing the process steps of the five-degree-of-freedom hybrid robot ball end tool attitude planning method. That is, those skilled in the art can understand the five-degree-of-freedom hybrid robot ball end tool attitude planning method as a preferred embodiment of the five-degree-of-freedom hybrid robot ball end tool attitude planning system.

[0254] Specifically, a five-degree-of-freedom hybrid robot ball-end tool attitude planning system is characterized by comprising:

[0255] Module M1: Collects tool information from the ball end mill and surface information of the machined part, and establishes a local coordinate system {L} for each tool contact point. i}, where i = 1, ..., n represent the tool contact point numbers, the x-axis of the coordinate system is along the feed direction, the z-axis is along the normal direction of the surface of the machined part, and the y-axis is determined by the right-hand rule.

[0256] Tool information includes: tool contact path, tool rake angle, and tool tilt angle.

[0257] Based on the tool tilt angle λ i and the roll angle ω i Indicates the tool axis direction in the local coordinate system Establish a robot base coordinate system {B} and uniquely determine the tool axis direction within the robot base coordinate system. in Represents {L i The posture of}.

[0258] Module M2: Based on the tool pose (P) of the i-th tool contact point i O i The corresponding joint angle q is obtained through robot inverse kinematics. i =[q i,1 q i,2 q i,3 q i,4 q i,5 ] T The first, second, and third derivatives of the joint angle with respect to the arc length parameter of the tool position point are obtained through numerical difference formulas, and let... and Let Δs represent the first, second, and third derivatives of the j-th joint variable between the i-th and i+1-th tool points with respect to the path arc length parameter of the tool point, respectively. i This represents the distance between the i-th and (i+1)-th knife positions.

[0259] First, establish the global path smoothing performance index Φ smooth :

[0260]

[0261] in, These are the weighting coefficients.

[0262] Next, the performance index Φ for the effective diameter of the cutting tool is established. DMA The performance index Φ of the rate of change of the effective diameter of the cutting tool DCR :

[0263]

[0264]

[0265] Among them, D i =2r t sin(cos -1 (cosλ i cosω i )) represents the effective diameter of the tool at the i-th tool contact point, r t D is the tool radius. de This is the lower bound of the specified effective tool diameter.

[0266] Module M3: Using the tool rake angle λ and side rake angle ω as optimization variables, construct the optimization variable vector η = [ω1...ω n λ1...λ n ] T Using the weighted sum of the global path smoothness performance index and the effective tool diameter performance index as the optimization objective, a constrained optimization model P1 is established:

[0267]

[0268] stq i =f ikine (P i O i (ω i ,λ i ))

[0269] f c,i (ω i ,λ i )≤0

[0270] Di =2r t sin(cos -1 (cosλ i cosω i ))

[0271] i = 1, ..., n;

[0272] Where, k DMA and k DCR f is the weighting coefficient. ikine (·) is the inverse kinematic function, f c,i (ω i ,λ i )≤0 indicates that the constraint condition that the tool axis direction needs to satisfy at the i-th tool contact point is .

[0273] Based on the constraints that need to be satisfied during the machining process of the hybrid robot, including: active and passive joint motion range constraints, kinematic singular constraints, tilt angle constraints, and interference-free constraints, a feasible region {FR} for the tool axis direction of each tool contact point is constructed on the ω-λ plane using a discretization method. i |i=1,...,n};Starting from the initial tool axis direction, progressively search the boundary of the nearest feasible region of the tool axis direction, and set FR i Simplified into a rectangular area

[0274] FR i It remains unchanged during the optimization process, simplifying its form. Corrections are made during the iterative optimization process.

[0275] Module M4: Calculates the current q based on the initial value of η. i D i , And obtain the performance index Φ smooth Φ DMA and Φ DCR Based on the robot's differential kinematics, calculate... Φ can be estimated using the following formula. smooth (η+Δη):

[0276] Φ smooth (η+Δη)=Δη T H smooth Δη+2f smooth T Δη+Φ smooth (η)

[0277]

[0278]

[0279] calculate Φ can be estimated using the following formula. DMA (η+Δη):

[0280] Φ DCR (η+Δη)=Δη T H DCR Δη+2f DCR T Δη+Φ DCR (η)

[0281]

[0282]

[0283] Φ DCR The equivalent representation is:

[0284]

[0285]

[0286] ψ i ≥0, i=1,...,n.

[0287] Let l represent the current iteration step, η l This represents the initial solution of the l-th iteration, in η l Nearby, the original constrained optimization model P1 is approximately equivalent to P2:

[0288]

[0289]

[0290] ψ i ≥0

[0291]

[0292]

[0293] i = 1, ..., n;

[0294] Among them, H η =H smooth +k DCR H DCR f η =f smooth +k DCR f DCR The maximum iteration step size ζ limits Δη to a small range;

[0295] In each iteration, the above quadratic programming problem is solved to obtain Δη, and the parameter η is updated.l+1 =η l +Δη, then calculate the updated q i , Computational performance metrics and when When convergence is achieved, stop the iteration and output the optimal solution; otherwise, recalculate. Φ can be estimated using the following formula. smooth (η+Δη):

[0296] Φ smooth (η+Δη)=Δη T H smooth Δη+2f smooth T Δη+Φ smooth (η)

[0297]

[0298]

[0299] The optimized tool rake angle λ based on each tool contact point i and the roll angle ω i The direction of the tool axis O at this time is calculated. i The robot motion program is generated based on the obtained tool axis direction path O(u) and the tool position path P(u) determined by the tool contact point and the surface information of the machined part, and the machining path of the hybrid robot tool is controlled.

[0300] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for attitude planning of a ball-end cutting tool in a five-degree-of-freedom hybrid robot, characterized in that, include: Step S1: Collect tool information from the ball end mill and surface information of the machined part, and establish a local coordinate system for each tool contact point; Step S2: Establish the global path smoothness performance index and the effective diameter performance index of the five-axis hybrid robot tool; Establish performance indicators for the effective diameter of the cutting tool. Performance indicators of the rate of change of the effective diameter of the cutting tool : ； in, For the first The effective diameter of the tool at each tool contact point For the tool radius, This is the lower bound of the specified effective tool diameter; Indicates the first The first and second knife positions and the The distance between each knife point ; The tool tilt angle, The tool tilt angle; Step S3: Based on the tool information, establish a constrained optimization model with the weighted sum of the global path smoothness performance index and the effective tool diameter performance index as the optimization objective; generate and simplify the feasible domain of the tool axis direction for each tool contact point based on the constraint conditions. Step S4: Optimize the tool axis direction path based on the constraint model and the feasible region of the tool axis direction at each tool contact point, and output the machining path of the five-DOF hybrid robot tool.

2. The five-degree-of-freedom hybrid robot ball-end tool attitude planning method according to claim 1, characterized in that, The tool information includes: tool contact path, tool tilt angle and tilt angle; the tool tilt angle and tilt angle represent the tool axis direction and uniquely determine the end effector posture of the five-degree-of-freedom hybrid robot.

3. The method for attitude planning of a ball-end tool in a five-degree-of-freedom hybrid robot according to claim 2, characterized in that, Step S1 includes the following sub-steps: Step S1.1: Generate the local coordinate system of each tool contact point based on the surface information of the machined part. ; in, Indicates the knife contact number; Step S1.2: Based on the tool rake angle and roll angle Indicates the tool axis direction in the local coordinate system Establish robot base coordinate system And uniquely determine the direction of the tool axis in the robot's base coordinate system. ,in express The posture.

4. The five-degree-of-freedom hybrid robot ball-end tool attitude planning method according to claim 3, characterized in that, Step S2 includes the following sub-steps: Step S2.1: According to the first Tool position at each contact point The corresponding joint angles are obtained through robot inverse kinematics. The first, second, and third derivatives of the joint angle with respect to the arc length parameter of the tool position point are obtained through numerical difference formulas, and let... , and They represent the first and The interval between the first and second knife points The first, second, and third derivatives of each joint variable with respect to the arc length parameter of the tool position path. Indicates the first The first and second knife positions and the The distance between each cutter point; Step S2.2: Establish global path smoothing performance indicators : ； in, These are the weighting coefficients. .

5. The method for attitude planning of a ball-end tool in a five-degree-of-freedom hybrid robot according to claim 1, characterized in that, The constraint optimization model in step S3 uses the tool rake angle and roll angle To optimize the variables, the weighted sum of the global path smoothness performance index and the effective diameter of the tool is used as the optimization objective, based on the constraints of the hybrid robot and the machining process.

6. The method for attitude planning of a ball-end tool in a five-degree-of-freedom hybrid robot according to claim 4, characterized in that, Step S3 includes the following sub-steps: Step S3.1: Adjust the tool inclination angle at each tool contact point. and roll angle As optimization variables, construct the optimization variable vector. Establish a constrained optimization model P1: ； in, and These are the weighting coefficients. It is the inverse kinematic function. Indicates the direction of the tool axis at the 1st The constraints that need to be satisfied at each tool contact point; Step S3.2: Based on the constraints that need to be met during the processing of the hybrid robot, including: active and passive joint motion range constraints, kinematic singular constraints, tilt angle constraints, and interference-free constraints, the discretization method is used to... Feasible region for constructing tool axis directions at each tool contact point on a plane ; Step S3.3: Starting from the initial tool axis direction, progressively search the boundary of the nearest feasible region along the tool axis direction, and... Simplified into a rectangular area ; Step S3.4: It remains unchanged during the optimization process, simplifying its form. Corrections are made during the iterative optimization process.

7. The method for attitude planning of a ball-end tool in a five-degree-of-freedom hybrid robot according to claim 6, characterized in that, Step S4 includes the following sub-steps: Step S4.1: According to The initial value is used to calculate the current value. , , , , , , And obtain performance indicators , and ; Step S4.2: Calculate based on the robot's differential kinematics. , , , Estimate using the following formula : ； Step S4.3: Calculation Estimate using the following formula : ； Step S4.4: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require The equivalent representation is: ； Step S4.5: Let Indicates the current iteration step. Indicates the first The initial solution of the first iteration, in Nearby, the original constrained optimization model P1 is approximately equivalent to P2: ； in, , Maximum iteration step size Will Limited to a smaller scope; Step S4.6: In each iteration, solve the above quadratic programming problem to obtain... And update the parameters: ; Step S4.7: Calculate the updated... , , , , , ; Computational performance indicators , and ;when If convergence is achieved, stop the iteration and output the optimal solution; otherwise, proceed to step S4.

2. Step S4.8: Optimize the tool rake angle based on each tool contact point. and roll angle The direction of the tool axis at this time is calculated. Based on the obtained tool axis direction path and the tool position path determined by the tool contact point and the surface information of the machined part. Generate robot motion programs to control the machining path of the hybrid robot's cutting tools.

8. A five-degree-of-freedom hybrid robot ball-end tool attitude planning system, characterized in that, include: Module M1: Collects tool information from the ball end mill and surface information of the machined parts, and establishes a local coordinate system for each tool contact point; Module M2: Establish global path smoothness performance index and effective tool diameter performance index for the five-axis hybrid robot tool; Establish performance indicators for the effective diameter of the cutting tool. Performance indicators of the rate of change of the effective diameter of the cutting tool : ； in, For the first The effective diameter of the tool at each tool contact point For the tool radius, This is the lower bound of the specified effective tool diameter; Indicates the first The first and second knife positions and the The distance between each knife point ; The tool tilt angle, The tool tilt angle; Module M3: Based on tool information, a constrained optimization model is established with the weighted sum of global path smoothness performance index and tool effective diameter performance index as the optimization objective; the feasible domain of tool axis direction for each tool contact point is generated and simplified based on the constraint conditions. Module M4: Based on the constraint model and the feasible domain of the tool axis direction at each tool contact point, optimizes the tool axis direction path and outputs the machining path of the five-DOF hybrid robot tool.

9. The five-degree-of-freedom hybrid robot ball-end tool attitude planning system according to claim 8, characterized in that, The tool information includes: tool contact point path, tool tilt angle and side tilt angle; the tool tilt angle and side tilt angle represent the tool axis direction and uniquely determine the end effector posture of the five-degree-of-freedom hybrid robot.

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