Industrial robot flat cutter milling machining posture optimization method and system

Abstract

The present invention provides an industrial robot flat-bottom cutter milling posture optimization method and system, including step S1: reading discrete cutter contact information and design surface information, establishing a cutter axis direction representation corresponding to the discrete cutter contact and a robot posture redundant parameter representation; step S2: establishing a robot path global smoothness performance index; step S3: establishing a constraint optimization model based on the information at the discrete cutter contact and the path global smoothness performance index; step S4: establishing an analytical estimation method for cutting width derivatives; step S5: solving the optimization model; step S6: generating a motion program using the optimal task posture sequence obtained by solving the model. The robot milling processing path generated by the present invention has a smoother joint path and a larger cutting width, and the optimization process has extremely high computational efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial robot processing and manufacturing, and in particular to a method and system for optimizing the milling processing posture of an industrial robot with a flat bottom cutter. Background Art

[0002] The industrial robot flat-bottom cutter milling system has the advantages of large working space, good flexibility, and high processing efficiency, providing a new technical solution for the processing and manufacturing of large and complex parts. In the process of industrial robot flat-bottom cutter processing, in order to generate the robot path, it is necessary to optimize the flat-bottom cutter axis direction and the robot redundant degrees of freedom based on the cutter contact point.

[0003] At present, most of the existing robot flat-bottom cutter machining posture optimization processes are step-by-step solutions to the tool axis direction and redundant degrees of freedom, that is, firstly, the tool axis direction is optimized based on the tool contact point with the goal of maximizing the cutting width, and then the robot redundant degrees of freedom are optimized with the goal of optimizing the robot performance. Since the tool axis direction will also affect the robot configuration, the step-by-step solution framework cannot obtain the optimal robot path. A small number of existing research methods can synchronously optimize the tool axis direction of a spherical milling cutter and the robot's redundant degrees of freedom, but they cannot handle the complex situation of flat-bottom cutter machining. Therefore, the present invention proposes a robot posture optimization method that can synchronously solve the tool axis direction of a flat-bottom cutter and the robot's redundant degrees of freedom, which is of great significance and background for improving the robot milling efficiency and machining surface quality.

[0004] Patent document CN111958611B (application number: CN202010762883.5) discloses a method and device for optimizing the posture of a milling robot considering the minimum contour error. The method includes: S1, simulating the cutting force of the milling process according to the workpiece to be processed and the tool path to obtain the cutting force data at the discrete tool position point; S2, converting the tool position point data in the workpiece coordinate system into the tool position point data in the robot base coordinate system; S3, dividing all tool positions at equal intervals within the feasible range of the tool axis angle; S4, calculating the tool tip point deviation at each tool axis angle; S5, calculating the tool position point contour error of the tool milling process; S6, for a single tool position point, according to the principle of minimum tool position point contour error, searching for the robot posture corresponding to the minimum tool position point contour error in all tool axis angles under given restrictions and constraints, and obtaining the robot posture with the minimum tool position point contour error; S7, repeating S6 for all tool positions to obtain the milling robot posture with the minimum contour error. However, the invention does not adopt the global smoothness index of the robot joint path, and cannot synchronously optimize the robot posture corresponding to all tool contacts. Summary of the invention

[0005] In view of the defects in the prior art, the object of the present invention is to provide a method and system for optimizing the milling posture of an industrial robot with a flat bottom cutter.

[0006] According to the present invention, a method for optimizing the milling posture of an industrial robot flat-bottom cutter includes:

[0007] Step S1: Read the discrete tool contact point information and the design surface information, and establish the tool axis direction representation corresponding to the discrete tool contact point and the robot posture redundant parameter representation;

[0008] Step S2: Establishing the global smoothness performance index of the robot path;

[0009] Step S3: establishing a constrained optimization model based on the information of discrete knife contact points and the global smoothing performance index of the path;

[0010] Step S4: Establishing an analytical estimation method for the cutting width derivative;

[0011] Step S5: solving the optimization model;

[0012] Step S6: Generate a motion program using the optimal task posture sequence obtained by solving the model.

[0013] Preferably, in step S2:

[0014] The numerical differential formula is used to express the first-order derivative and second-order derivative of the robot joint angle with respect to the arc length parameter of the knife contact path:

[0015]

[0016] Where j∈{1,…,6} represents the joint number, i∈{2,…,n-1} represents the knife contact number, and n is the number of knife contacts. represents the angle of joint j corresponding to the i-th knife contact point, Δs i represents the distance between knife contact point i and knife contact point i+1, represents the first-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact path, represents the second-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact point path;

[0017] make

[0018]

[0019] Establish indicators to evaluate the global smoothing performance of the path:

[0020]

[0021] Among them, Φ smoothis the global smoothing performance index of the path, k 1 With k 2 is the weight value.

[0022] Preferably, in step S3:

[0023] The optimization variable is expressed as α = [λ 1 ,ω 1 ,η 1 ,…,λ n ,ω n ,η n ], where λ i is the tool rake angle corresponding to the i-th tool contact point, ω i is the tool tilt angle corresponding to the i-th tool contact point, η i is the redundant parameter of the robot corresponding to the i-th knife contact point;

[0024] Taking the minimization of the global smoothness performance index of the path and the maximization of the minimum cutting width as the optimization objectives, and taking the joint limit and interference avoidance as the constraints, a constrained optimization model is established;

[0025]

[0026] stψ≥-w i

[0027] q i =f -1 (λ i ,ω i ,η i ,CC i )

[0028] q min ≤q i ≤q max

[0029] f i (ω i )≤λ i ≤π / 2

[0030]

[0031] i=1,2,…,n

[0032] Among them, k 3 is the cutting width weight coefficient, ψ is the introduced variable, w i is the cutting width at the i-th knife contact point, f -1 (…) is the inverse kinematics solution function of the robot, CC i is the i-th knife contact point, is the robot joint angle vector corresponding to the i-th knife contact point, q minWith q max are the lower and upper bounds of the robot joint vector, f i (ω i ) is the tilt angle ω at the i-th tool contact point obtained according to the interference avoidance constraint i The corresponding minimum forward tilt angle is and are the lower and upper bounds of the tilt angle at the i-th tool contact point.

[0033] Preferably, in step S4:

[0034] At any knife contact CC i For a given tool axis direction, the tool base circle is expressed as C using conformal geometry algebra. BTC =P(p 1 )∧P 2 (p 2 )∧P 3 (p 3 ), where {p i |i=1,2,3} are three different points on the tool bottom circle, and P(…) is the mapping from a point in three-dimensional Euclidean space to a point in conformal space;

[0035] For a given residual height h of the surface machining, suppose two points on the tool bottom circle with a distance h from the design surface are p and a (λ i ,ω i ) and p b (λ i ,ω i ), suppose the distance p on the design surface a With p a The nearest points are q a With q b ; Using conformal geometry, let the center of the circle be q a , a sphere with radius h is expressed as:

[0036] S a =(P(q a )-h 2 e ∞ / 2) *

[0037] Among them, e ∞ is the basis for representing points at infinity in conformal geometric algebra, () * It is the dual operation in conformal geometric algebra; the sphere S is calculated by the following formula a Intersection point with tool bottom circle and

[0038]

[0039] Where ∧ is the outer product operation, satisfy

[0040] Use the same method to calculate q b is the center of the circle, h is the intersection of the sphere with the radius and the bottom circle of the tool and in satisfy

[0041] make

[0042]

[0043] Among them, y i is a unit vector and is related to the knife contact point CC i The feed direction at is perpendicular to the design surface normal vector; use As Analytical estimate of .

[0044] Preferably, in step S5:

[0045] Step S5.1: Establish The nearby quadratic programming subproblem:

[0046]

[0047] Among them, α k is the value of variable α at the kth iteration of the solution algorithm, k is the current iteration number of the solution algorithm, Δψ is the increment of variable ψ, and Δλ i is the angle λ i The increment, Δω i is the angle ω i The increment, Δη i is the angle η i The increment of , ζ is the introduced control coefficient;

[0048]

[0049] Δα=[Δλ 1 ,Δω 1 ,Δη 1 ,…,Δλ n ,Δω n ,Δη n ] is the increment of variable α, is the function f i ()exist The derivative value at w i () is the function of the cutting width at the i-th tool contact point with respect to the variable α;

[0050] Step S5.2: Let k = 0, ζ = 1; calculate the initial joint vector q at the i-th knife contact point i (α 0 ), cutting width w i (α 0 ) and the smoothness index Φ smooth (α 0 ), where i = 1,…,n, is the initial solution of the optimization variable α; let Ψ 0 =Φ smooth (α 0 )+k 3 ψ 0 ;

[0051] Among them, ψ 0 α=α 0 The opposite number of the minimum cutting width at all tool contact points, Ψ 0 α=α 0 The objective function value of the optimization problem;

[0052] Step S5.3: For i=1,…,n,j=1…,6, calculate Solution

[0053] Step S5.4: Solve the quadratic programming subproblem in step S5.1; update α k+1 =α k +Δα; for i=1,…,n, calculate q i (α k+1 ), w i (α k+1 ), Φ smooth (α k+1 );renew Ψ k+1 =Φ smooth (α k+1 )+k 3 ψ k+1 ;

[0054] Among them, ψ k+1 α=α k+1 The opposite number of the minimum cutting width at all tool contact points, Ψ k+1 α=α k+1 The objective function value of the optimization problem;

[0055] Step S5.5: If Ψ k+1 <Ψ k , let k = k + 1, and execute step S5.6; if Ψ k+1 ≥Ψ k, execute step S5.7;

[0056] Step S5.6: If (Ψ k -Ψ k+1 ) / |Ψ k |Greater than the preset threshold τ 2 , execute step S5.3; if (Ψ k -Ψ k+1 ) / |Ψ k |Less than or equal to the preset threshold τ 2 , the output optimal solution is α * =α k ;

[0057] Step S5.7: If ζ is greater than the preset threshold τ 1 , let ζ=0.5ζ, execute step S5.4; if ζ is less than or equal to the preset threshold τ 1 , the output optimal solution is α * =α k .

[0058] An industrial robot flat-bottom cutter milling processing posture optimization system provided by the present invention comprises:

[0059] Module M1: Read the discrete tool contact information and the design surface information, and establish the tool axis direction representation corresponding to the discrete tool contact and the robot posture redundant parameter representation;

[0060] Module M2: Establishing global smoothness performance index of robot path;

[0061] Module M3: Establish a constrained optimization model based on the information of discrete knife contact points and the global smoothing performance index of the path;

[0062] Module M4: Establishing an analytical estimation method for the cutting width derivative;

[0063] Module M5: Solving the optimization model;

[0064] Module M6: Generate motion programs using the optimal task pose sequence obtained by solving the model.

[0065] Preferably, in the module M2:

[0066] The numerical differential formula is used to express the first-order derivative and second-order derivative of the robot joint angle with respect to the arc length parameter of the knife contact path:

[0067]

[0068] Where j∈{1,…,6} represents the joint number, i∈{2,…,n-1} represents the knife contact number, and n is the number of knife contacts. represents the angle of joint j corresponding to the i-th knife contact point, Δs i represents the distance between knife contact point i and knife contact point i+1, represents the first-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact path, represents the second-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact point path;

[0069] make

[0070]

[0071] Establish indicators to evaluate the global smoothing performance of the path:

[0072]

[0073] Among them, Φ smooth is the global smoothing performance index of the path, k 1 With k 2 is the weight value;

[0074] In the module M3:

[0075] The optimization variable is expressed as α = [λ 1 ,ω 1 ,η 1 ,…,λ n ,ω n ,η n ], where λ i is the tool rake angle corresponding to the i-th tool contact point, ω i is the tool tilt angle corresponding to the i-th tool contact point, η i is the redundant parameter of the robot corresponding to the i-th knife contact point;

[0076] Taking the minimization of the global smoothness performance index of the path and the maximization of the minimum cutting width as the optimization objectives, and taking the joint limit and interference avoidance as the constraints, a constrained optimization model is established;

[0077]

[0078] stψ≥-w i

[0079] q i =f -1 (λ i ,ω i ,η i ,CC i )

[0080] q min ≤q i ≤q max

[0081] f i (ω i )≤λ i ≤π / 2

[0082]

[0083] i=1,2,…,n

[0084] Among them, k 3 is the cutting width weight coefficient, ψ is the introduced variable, w i is the cutting width at the i-th knife contact point, f -1 (…) is the inverse kinematics solution function of the robot, CC i is the i-th knife contact point, is the robot joint angle vector corresponding to the i-th knife contact point, q min With q max are the lower and upper bounds of the robot joint vector, f i (ω i ) is the tilt angle ω at the i-th tool contact point obtained according to the interference avoidance constraint i The corresponding minimum forward tilt angle is and are the lower and upper bounds of the tilt angle at the i-th tool contact point.

[0085] Preferably, in the module M4:

[0086] At any knife contact CC i For a given tool axis direction, the tool base circle is expressed as C using conformal geometry algebra. BTC =P(p 1 )∧P 2 (p 2 )∧P 3 (p 3 ), where {p i |i=1,2,3} are three different points on the tool bottom circle, and P(…) is the mapping from a point in three-dimensional Euclidean space to a point in conformal space;

[0087] For a given residual height h of the surface machining, suppose two points on the tool bottom circle with a distance h from the design surface are p and a (λ i ,ω i ) and p b (λ i ,ω i ), suppose the distance p on the design surface a With p a The nearest points are q a With q b; Using conformal geometry, let the center of the circle be q a , a sphere with radius h is expressed as:

[0088] S a =(P(q a )-h 2 e ∞ / 2) *

[0089] Among them, e ∞ is the basis for representing points at infinity in conformal geometric algebra, () * It is the dual operation in conformal geometric algebra; the sphere S is calculated by the following formula a Intersection point with tool bottom circle and

[0090]

[0091] Where ∧ is the outer product operation, satisfy

[0092] Use the same method to calculate q b is the center of the circle, h is the intersection of the sphere with the radius and the bottom circle of the tool and in satisfy

[0093] make

[0094]

[0095] Among them, y i is a unit vector and is related to the knife contact point CC i The feed direction at is perpendicular to the design surface normal vector; use As Analytical estimate of .

[0096] Preferably, in the module M5:

[0097] Module M5.1: Establishment The nearby quadratic programming subproblem:

[0098]

[0099] Among them, α k is the value of variable α at the kth iteration of the solution algorithm, k is the current iteration number of the solution algorithm, Δψ is the increment of variable ψ, and Δλ i is the angle λ i The increment, Δω i is the angle ω iThe increment, Δη i is the angle η i The increment of , ζ is the introduced control coefficient;

[0100]

[0101] Δα=[Δλ 1 ,Δω 1 ,Δη 1 ,…,Δλ n ,Δω n ,Δη n ] is the increment of variable α, is the function f i ()exist The derivative value at w i () is the function of the cutting width at the i-th tool contact point with respect to the variable α;

[0102] Module M5.2: Let k = 0, ζ = 1; calculate the initial joint vector q at the i-th knife contact point i (α 0 ), cutting width w i (α 0 ) and the smoothness index Φ smooth (α 0 ), where i = 1,…,n, is the initial solution of the optimization variable α; let Ψ 0 =Φ smooth (α 0 )+k 3 ψ 0 ;

[0103] Among them, ψ 0 α=α 0 The opposite number of the minimum cutting width at all tool contact points, Ψ 0 α=α 0 The objective function value of the optimization problem;

[0104] Module M5.3: For i = 1, ..., n, j = 1 ..., 6, calculate Solution

[0105] Module M5.4: Solve the quadratic programming subproblem in Module M5.1; update α k+1 =α k +Δα; for i=1,…,n, calculate q i (α k+1 ), w i (α k+1 ), Φ smooth(α k+1 );renew Ψ k+1 =Φ smooth (α k+1 )+k 3 ψ k+1 ;

[0106] Among them, ψ k+1 α=α k+1 The opposite number of the minimum cutting width at all tool contact points, Ψ k+1 α=α k+1 The objective function value of the optimization problem;

[0107] Module M5.5: If Ψ k+1 <Ψ k , let k = k + 1, execute module M5.6; if Ψ k+1 ≥Ψ k , execution module M5.7;

[0108] Module M5.6: If (Ψ k -Ψ k+1 ) / |Ψ k |Greater than the preset threshold τ 2 , execute module M5.3; if (Ψ k -Ψ k+1 ) / |Ψ k |Less than or equal to the preset threshold τ 2 , the output optimal solution is α * =α k ;

[0109] Module M5.7: If ζ is greater than the preset threshold τ 1 , let ζ=0.5ζ, execute module M5.4; if ζ is less than or equal to the preset threshold τ 1 , the output optimal solution is α * =α k .

[0110] According to a computer-readable storage medium storing a computer program provided by the present invention, when the computer program is executed by a processor, the steps of any one of the methods for optimizing the milling posture of an industrial robot with a flat bottom cutter are implemented.

[0111] Compared with the prior art, the present invention has the following beneficial effects:

[0112] 1. The present invention can synchronously optimize the cutter axis direction of the flat bottom knife and the redundant degrees of freedom of the robot, and has high calculation efficiency;

[0113] 2. The present invention adopts the global smoothness index of the robot joint path to synchronously optimize the robot posture corresponding to all tool contact points;

[0114] 3. The optimized robot flat cutter milling path has a larger cutting width and a smoother joint path;

[0115] 4. The present invention can effectively improve the processing efficiency and processing surface quality of robot milling. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0117] Figure 1 It is a schematic diagram of the process of the present invention;

[0118] Figure 2 It is a schematic diagram of the local coordinate system and tool coordinate system at the end of the flat bottom cutter;

[0119] Figure 3 To design the surface and the knife contact path;

[0120] Figure 4 To optimize the tool cutting width before and after;

[0121] Figure 5 To optimize the paths of the robot's second and fourth joints before and after. DETAILED DESCRIPTION

[0122] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0123] Embodiment 1:

[0124] According to the present invention, an industrial robot flat bottom cutter milling processing posture optimization method is provided. Figure 1-Figure 5 As shown, including:

[0125] Step S1: Read the discrete tool contact point information and the design surface information, and establish the tool axis direction representation corresponding to the discrete tool contact point and the robot posture redundant parameter representation;

[0126] Step S2: Establishing the global smoothness performance index of the robot path;

[0127] Step S3: establishing a constrained optimization model based on the information of discrete knife contact points and the global smoothing performance index of the path;

[0128] Step S4: Establishing an analytical estimation method for the cutting width derivative;

[0129] Step S5: solving the optimization model;

[0130] Step S6: Generate a motion program using the optimal task posture sequence obtained by solving the model.

[0131] Specifically, in step S2:

[0132] The numerical differential formula is used to express the first-order derivative and second-order derivative of the robot joint angle with respect to the arc length parameter of the knife contact path:

[0133]

[0134] Where j∈{1,…,6} represents the joint number, i∈{2,…,n-1} represents the knife contact number, and n is the number of knife contacts. represents the angle of joint j corresponding to the i-th knife contact point, Δs i represents the distance between knife contact point i and knife contact point i+1, represents the first-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact path, represents the second-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact point path;

[0135] make

[0136]

[0137] Establish indicators to evaluate the global smoothing performance of the path:

[0138]

[0139] Among them, Φ smooth is the global smoothing performance index of the path, k 1 With k 2 is the weight value.

[0140] Specifically, in step S3:

[0141] The optimization variable is expressed as α = [λ 1 ,ω 1 ,η 1 ,…,λ n ,ω n ,η n ], where λ i is the tool rake angle corresponding to the i-th tool contact point, ω i is the tool tilt angle corresponding to the i-th tool contact point, η i is the redundant parameter of the robot corresponding to the i-th knife contact point;

[0142] Taking the minimization of the global smoothness performance index of the path and the maximization of the minimum cutting width as the optimization objectives, and taking the joint limit and interference avoidance as the constraints, a constrained optimization model is established;

[0143]

[0144] stψ≥-w i

[0145] q i =f -1 (λ i ,ω i ,η i ,CC i )

[0146] q min ≤q i ≤q max

[0147] f i (ω i )≤λ i ≤π / 2

[0148]

[0149] i=1,2,…,n

[0150] Among them, k 3 is the cutting width weight coefficient, ψ is the introduced variable, w i is the cutting width at the i-th knife contact point, f -1 (…) is the inverse kinematics solution function of the robot, CC i is the i-th knife contact point, is the robot joint angle vector corresponding to the i-th knife contact point, q min With q max are the lower and upper bounds of the robot joint vector, f i (ω i ) is the tilt angle ω at the i-th tool contact point obtained according to the interference avoidance constraint i The corresponding minimum forward tilt angle is and are the lower and upper bounds of the tilt angle at the i-th tool contact point.

[0151] Specifically, in step S4:

[0152] At any knife contact CC i For a given tool axis direction, the tool base circle is expressed as C using conformal geometry algebra. BTC =P(p 1 )∧P 2 (p 2 )∧P3 (p 3 ), where {p i |i=1,2,3} are three different points on the tool bottom circle, and P(…) is the mapping from a point in three-dimensional Euclidean space to a point in conformal space;

[0153] For a given residual height h of the surface machining, suppose two points on the tool bottom circle with a distance h from the design surface are p and a (λ i ,ω i ) and p b (λ i ,ω i ), suppose the distance p on the design surface a With p a The nearest points are q a With q b ; Using conformal geometry, let the center of the circle be q a , a sphere with radius h is expressed as:

[0154] S a =(P(q a )-h 2 e ∞ / 2) *

[0155] Among them, e ∞ is the basis for representing points at infinity in conformal geometric algebra, () * It is the dual operation in conformal geometric algebra; the sphere S is calculated by the following formula a Intersection point with tool bottom circle and

[0156]

[0157] Where ∧ is the outer product operation, satisfy

[0158] Use the same method to calculate q b is the center of the circle, h is the intersection of the sphere with the radius and the bottom circle of the tool and in satisfy

[0159] make

[0160]

[0161] Among them, y i is a unit vector and is related to the knife contact point CC i The feed direction at is perpendicular to the design surface normal vector; use As Analytical estimate of .

[0162] Specifically, in step S5:

[0163] Step S5.1: Establish The nearby quadratic programming subproblem:

[0164]

[0165] Among them, α k is the value of variable α at the kth iteration of the solution algorithm, k is the current iteration number of the solution algorithm, Δψ is the increment of variable ψ, and Δλ i is the angle λ i The increment, Δω i is the angle ω i The increment, Δη i is the angle η i The increment of , ζ is the introduced control coefficient;

[0166]

[0167] Δα=[Δλ 1 ,Δω 1 ,Δη 1 ,…,Δλ n ,Δω n ,Δη n ] is the increment of variable α, is the function f i ()exist The derivative value at w i () is the function of the cutting width at the i-th tool contact point with respect to the variable α;

[0168] Step S5.2: Let k = 0, ζ = 1; calculate the initial joint vector q at the i-th knife contact point i (α 0 ), cutting width w i (α 0 ) and the smoothness index Φ smooth (α 0 ), where i = 1,…,n, is the initial solution of the optimization variable α; let Ψ 0 =Φ smooth (α 0 )+k 3 ψ 0 ;

[0169] Among them, ψ 0 α=α 0The opposite number of the minimum cutting width at all tool contact points, Ψ 0 α=α 0 The objective function value of the optimization problem;

[0170] Step S5.3: For i=1,…,n,j=1…,6, calculate Solution

[0171] Step S5.4: Solve the quadratic programming subproblem in step S5.1; update α k+1 =α k +Δα; for i=1,…,n, calculate q i (α k+1 ), w i (α k+1 ), Φ smooth (α k+1 );renew Ψ k+1 =Φ smooth (α k+1 )+k 3 ψ k+1 ;

[0172] Among them, ψ k+1 α=α k+1 The opposite number of the minimum cutting width at all tool contact points, Ψ k+1 α=α k+1 The objective function value of the optimization problem;

[0173] Step S5.5: If Ψ k+1 <Ψ k , let k = k + 1, and execute step S5.6; if Ψ k+1 ≥Ψ k , execute step S5.7;

[0174] Step S5.6: If (Ψ k -Ψ k+1 ) / |Ψ k |Greater than the preset threshold τ 2 , execute step S5.3; if (Ψ k -Ψ k+1 ) / |Ψ k |Less than or equal to the preset threshold τ 2 , the output optimal solution is α * =α k ;

[0175] Step S5.7: If ζ is greater than the preset threshold τ 1 , let ζ=0.5ζ, execute step S5.4; if ζ is less than or equal to the preset threshold τ 1, the output optimal solution is α * =α k .

[0176] An industrial robot flat-bottom cutter milling processing posture optimization system provided by the present invention comprises:

[0177] Module M1: Read the discrete tool contact information and the design surface information, and establish the tool axis direction representation corresponding to the discrete tool contact and the robot posture redundant parameter representation;

[0178] Module M2: Establishing global smoothness performance index of robot path;

[0179] Module M3: Establish a constrained optimization model based on the information of discrete knife contact points and the global smoothing performance index of the path;

[0180] Module M4: Establishing an analytical estimation method for the cutting width derivative;

[0181] Module M5: Solving the optimization model;

[0182] Module M6: Generate motion programs using the optimal task pose sequence obtained by solving the model.

[0183] Specifically, in the module M2:

[0184] The numerical differential formula is used to express the first-order derivative and second-order derivative of the robot joint angle with respect to the arc length parameter of the knife contact path:

[0185]

[0186] Where j∈{1,…,6} represents the joint number, i∈{2,…,n-1} represents the knife contact number, and n is the number of knife contacts. represents the angle of joint j corresponding to the i-th knife contact point, Δs i represents the distance between knife contact point i and knife contact point i+1, represents the first-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact path, represents the second-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact point path;

[0187] make

[0188]

[0189] Establish indicators to evaluate the global smoothing performance of the path:

[0190]

[0191] Among them, Φ smooth is the global smoothing performance index of the path, k1 With k 2 is the weight value;

[0192] In the module M3:

[0193] The optimization variable is expressed as α = [λ 1 ,ω 1 ,η 1 ,…,λ n ,ω n ,η n ], where λ i is the tool rake angle corresponding to the i-th tool contact point, ω i is the tool tilt angle corresponding to the i-th tool contact point, η i is the redundant parameter of the robot corresponding to the i-th knife contact point;

[0194] Taking the minimization of the global smoothness performance index of the path and the maximization of the minimum cutting width as the optimization objectives, and taking the joint limit and interference avoidance as the constraints, a constrained optimization model is established;

[0195]

[0196] stψ≥-w i

[0197] q i =f -1 (λ i ,ω i ,η i ,CC i )

[0198] q min ≤q i ≤q max

[0199] f i (ω i )≤λ i ≤π / 2

[0200]

[0201] i=1,2,…,n

[0202] Among them, k 3 is the cutting width weight coefficient, ψ is the introduced variable, w i is the cutting width at the i-th knife contact point, f -1 (…) is the inverse kinematics solution function of the robot, CC i is the i-th knife contact point, is the robot joint angle vector corresponding to the i-th knife contact point, q min With q maxare the lower and upper bounds of the robot joint vector, f i (ω i ) is the tilt angle ω at the i-th tool contact point obtained according to the interference avoidance constraint i The corresponding minimum forward tilt angle is and are the lower and upper bounds of the tilt angle at the i-th tool contact point.

[0203] Specifically, in the module M4:

[0204] At any knife contact CC i For a given tool axis direction, the tool base circle is expressed as C using conformal geometry algebra. BTC =P(p 1 )∧P 2 (p 2 )∧P 3 (p 3 ), where {p i |i=1,2,3} are three different points on the tool bottom circle, and P(…) is the mapping from a point in three-dimensional Euclidean space to a point in conformal space;

[0205] For a given residual height h of the surface machining, suppose two points on the tool bottom circle with a distance h from the design surface are p and a (λ i ,ω i ) and p b (λ i ,ω i ), suppose the distance p on the design surface a With p a The nearest points are q a With q b ; Using conformal geometry, let the center of the circle be q a , a sphere with radius h is expressed as:

[0206] S a =(P(q a )-h 2 e ∞ / 2) *

[0207] Among them, e ∞ is the basis for representing points at infinity in conformal geometric algebra, () * It is the dual operation in conformal geometric algebra; the sphere S is calculated by the following formula a Intersection point with tool bottom circle and

[0208]

[0209] Where ∧ is the outer product operation, satisfy

[0210] Use the same method to calculate q b is the center of the circle, h is the intersection of the sphere with the radius and the bottom circle of the tool and in satisfy

[0211] make

[0212]

[0213] Among them, y i is a unit vector and is related to the knife contact point CC i The feed direction at is perpendicular to the design surface normal vector; use As Analytical estimate of .

[0214] Specifically, in the module M5:

[0215] Module M5.1: Establishment The nearby quadratic programming subproblem:

[0216]

[0217] Among them, α k is the value of variable α at the kth iteration of the solution algorithm, k is the current iteration number of the solution algorithm, Δψ is the increment of variable ψ, and Δλ i is the angle λ i The increment, Δω i is the angle ω i The increment, Δη i is the angle η i The increment of , ζ is the introduced control coefficient;

[0218]

[0219] Δα=[Δλ 1 ,Δω 1 ,Δη 1 ,…,Δλ n ,Δω n ,Δη n ] is the increment of variable α, is the function f i ()exist The derivative value at w i () is the function of the cutting width at the i-th tool contact point with respect to the variable α;

[0220] Module M5.2: Let k = 0, ζ = 1; calculate the initial joint vector q at the i-th knife contact point i (α 0 ), cutting width w i (α 0 ) and the smoothness index Φ smooth (α 0 ), where i = 1,…,n, is the initial solution of the optimization variable α; let Ψ 0 =Φ smooth (α 0 )+k 3 ψ 0 ;

[0221] Among them, ψ 0 α=α 0 The opposite number of the minimum cutting width at all tool contact points, Ψ 0 α=α 0 The objective function value of the optimization problem;

[0222] Module M5.3: For i = 1, ..., n, j = 1 ..., 6, calculate Solution

[0223] Module M5.4: Solve the quadratic programming subproblem in Module M5.1; update α k+1 =α k +Δα; for i=1,…,n, calculate q i (α k+1 ), w i (α k+1 ), Φ smooth (α k+1 );renew Ψ k+1 =Φ smooth (α k+1 )+k 3 ψ k+1 ;

[0224] Among them, ψ k+1 α=α k+1 The opposite number of the minimum cutting width at all tool contact points, Ψ k+1 α=α k+1 The objective function value of the optimization problem;

[0225] Module M5.5: If Ψ k+1 <Ψ k , let k = k + 1, execute module M5.6; if Ψ k+1 ≥Ψ k , execution module M5.7;

[0226] Module M5.6: If (Ψ k -Ψ k+1 ) / |Ψ k |Greater than the preset threshold τ 2 , execute module M5.3; if (Ψ k -Ψ k+1 ) / |Ψ k |Less than or equal to the preset threshold τ 2 , the output optimal solution is α * =α k ;

[0227] Module M5.7: If ζ is greater than the preset threshold τ 1 , let ζ=0.5ζ, execute module M5.4; if ζ is less than or equal to the preset threshold τ 1 , the output optimal solution is α * =α k .

[0228] According to a computer-readable storage medium storing a computer program provided by the present invention, when the computer program is executed by a processor, the steps of any one of the methods for optimizing the milling posture of an industrial robot with a flat bottom cutter are implemented.

[0229] Embodiment 2:

[0230] Embodiment 2 is a preferred example of Embodiment 1, and is used to illustrate the present invention in more detail.

[0231] This embodiment provides an industrial robot flat cutter milling processing posture optimization method, such as Figure 1 shown.

[0232] This embodiment specifically includes the following steps:

[0233] Step 1: Read the discrete tool contact point information and the design surface information, use the rake angle and the roll angle to represent the tool axis direction corresponding to the discrete tool contact point, and establish the robot posture redundant parameter representation corresponding to the discrete tool contact point;

[0234] Step 2: Establish the global smoothness performance index of the path in the robot joint space;

[0235] Step 3: Take the rake angle, side rake angle and redundant parameters at the discrete tool contact point as optimization variables, minimize the global smoothness performance index of the path and maximize the minimum cutting width as optimization goals, and take joint limit and interference avoidance as constraints to establish a constrained optimization model;

[0236] Step 4: Establish an analytical estimation method for the cutting width derivative;

[0237] Step 5: Use the sequential quadratic programming algorithm to solve the optimization model;

[0238] Step 6: Use the obtained optimal robot task pose sequence to generate a robot motion program according to the specific robot system.

[0239] Specifically, in step 1:

[0240] Read the tool contact sequence {CC} on the design surface represented in the workpiece coordinate system {WCS} i |i=1,2,…,n}.

[0241] With any knife contact CC i As the center, establish Figure 2 The local coordinate system {LCS i}, the x-axis is the tool feed direction, the z-axis is the design surface normal vector, and the y-axis is determined by the right-hand rule. Establish a coordinate system {TCS0}, whose origin is the center of the tool bottom circle, and the x-axis points to CC i , the z-axis is along the tool axis, and the y-axis is determined by the right-hand rule. Figure 2 The forward tilt angle λ i With the roll angle ω i Definition, where the rake angle is the tool radius around {LCS i The y-axis rotation angle is the angle of rotation of the tool around {LCS i}The angle of rotation of the z-axis in the coordinate system {LCS i The relationship between} and the coordinate system {TCS0} is

[0242]

[0243] Where r is the radius of the tool bottom circle, T x Represents the homogeneous transformation matrix for translation along the x-axis, R z With R y They represent rotations around the z-axis and around the y-axis respectively.

[0244] The robot's redundant degrees of freedom are defined as the tool's rotation angle η around the tool axis. i The tool posture is represented by the coordinate system {TCS}, and the coordinate system {LCS i The relationship between {TCS} and {TCS} is

[0245]

[0246] Assume the robot base coordinate system is {BCS}, and express the kinematic model of the robot milling system as

[0247]

[0248] in represents the transformation from the coordinate system {BCS} to the robot flange coordinate system {FCS}, is the joint vector of the robot, is the transformation from {FCS} to {TCS}, is the transformation from {BCS} to {WCS}, From {WCS} to {LCS i}Transformation.

[0249] Specifically, in step 2:

[0250] Use the numerical differential formula to express the first-order and second-order derivatives of the robot joint angle with respect to the arc length parameter of the knife contact path:

[0251]

[0252]

[0253] Where j∈{1,…,6} represents the joint number, i∈{2,…,n-1} represents the knife contact number, and n is the number of knife contacts. represents the angle of joint j corresponding to the i-th knife contact point, Δs i represents the distance between knife contact point i and knife contact point i+1, represents the first-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact path, Represents the second-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact point path.

[0254] make

[0255]

[0256] Establish indicators to evaluate the global smoothing performance of the path:

[0257]

[0258] Among them, Φ smooth is the global smoothing performance index of the path, k 1 With k 2 is the weight value.

[0259] Specifically, in step 3:

[0260] The optimization variable is expressed as α = [λ 1 ,ω 1 ,η 1 ,…,λ n ,ω n ,η n ], where λ i is the tool rake angle corresponding to the i-th tool contact point, ωi is the tool tilt angle corresponding to the i-th tool contact point, η i is the redundant parameter of the robot corresponding to the i-th tool contact point.

[0261] Taking the minimization of the global smoothness performance index of the path and the maximization of the minimum cutting width as the optimization objectives, and taking the joint limit and interference avoidance as the constraints, a constrained optimization model is established;

[0262]

[0263] stψ≥-w i

[0264] q i =f -1 (λ i ,ω i ,η i ,CC i )

[0265] q min ≤q i ≤q max

[0266] f i (ω i )≤λ i ≤π / 2

[0267]

[0268] i=1,2,…,n

[0269] where k 3 is the cutting width weight coefficient, ψ is the introduced variable, w i is the cutting width at the i-th knife contact point, f -1 (…) is the inverse kinematics solution function of the robot, q min With q max are the lower and upper bounds of the robot joint vector, f i (ω i ) is the tilt angle ω at the i-th tool contact point obtained according to the interference avoidance constraint i The corresponding minimum rake angle can be calculated by multi-point processing method, rolling ball method, etc. and are the lower and upper bounds of the tilt angle at the i-th tool contact point.

[0270] Specifically, in step 4:

[0271] At any knife contact CC i For a given tool axis direction, the tool base circle is expressed as C using conformal geometry algebra. BTC =P(p1 )∧P 2 (p 2 )∧P 3 (p 3 ), where {p i |i=1,2,3} are three different points on the tool bottom circle, and P(…) is the mapping from a point in three-dimensional Euclidean space to a point in conformal space.

[0272] For a given residual height h of the surface machining, suppose two points on the tool bottom circle with a distance h from the design surface are p and a (λ i ,ω i ) and p b (λ i ,ω i ), suppose the distance p on the design surface a With p a The nearest points are q a With q b Using conformal geometry, we can set the center of the circle to q. a , the sphere with radius h is expressed as

[0273] S a =(P(q a )-h 2 e ∞ / 2) *

[0274] where e ∞ is a basis for representing points at infinity in conformal geometric algebra, (…) * It is a dual operation in conformal geometric algebra.

[0275] The spherical surface S is calculated by the following formula a Intersection point with tool bottom circle and

[0276]

[0277] Where ∧ is the outer product operation, satisfy

[0278] Use the same method to calculate q b is the center of the circle, h is the intersection of the sphere with the radius and the bottom circle of the tool and in satisfy

[0279] make where y i is a unit vector and is related to the knife contact point CC iThe feed direction at is perpendicular to the design surface normal vector. As Analytical estimate of .

[0280] Specifically, in step 5:

[0281] Step 5.1: Build The nearby quadratic programming subproblem:

[0282]

[0283] in

[0284]

[0285] Δα=[Δλ 1 ,Δω 1 ,Δη 1 ,…,Δλ n ,Δω n ,Δη n ] is the increment of variable α, is the function f i (…)exist The derivative value at .

[0286] Step 5.2: Let k = 0, ζ = 1; calculate the initial joint vector q at the i-th knife contact point i (α 0 ), cutting width w i (α 0 ) and the smoothness index Φ smooth (α 0 ), where i = 1,…,n, is the initial solution of the optimization variable α; let Ψ 0 =Φ smooth (α 0 )+k 3 ψ 0 .

[0287] Step 5.3: For i = 1, ..., n, j = 1 ..., 6, calculate By deriving the kinematic model of the robot milling system in step 1, we can calculate Use the method proposed in step 4 to estimate

[0288] Step 5.4: Solve the quadratic programming subproblem in step 5.1; update α k+1 =α k +Δα; for i=1,…,n, calculate q i (α k+1 ), w i (αk+1 ), Φ smooth (α k+1 );renew Ψ k+1 =Φ smooth (α k+1 )+k 3 ψ k+1 .

[0289] Step 5.5: If Ψ k+1 <Ψ k , let k=k+1, and execute step 5.6; otherwise, execute step 5.7.

[0290] Step 5.6: If (Ψ k -Ψ k+1 ) / |Ψ k | is greater than a given threshold τ 2 , execute step 5.3; otherwise, output the optimal solution as α * =α k .

[0291] Step 5.7: If ζ is greater than a given threshold τ 1 , let ζ=0.5ζ, and execute step 5.4; otherwise, the output optimal solution is α * =α k .

[0292] The specific embodiments of the present invention are described below in conjunction with specific processing examples. Figure 3 As shown, the example machining design surface is a cubic Bezier surface, and the control points of the surface are

[0293]

[0294] The industrial robot model used is ABB IRB4600-60. The knife contact path is as follows Figure 3 As shown, the number of tool contact points n = 114, the tool feed direction is the direction of minimum curvature of the designed surface, and the distance between the tool contact points Δs i About 2mm. The radius of the flat bottom knife is 3.5mm. Set the robot command feed speed to 200mm / min, and the three weight systems are k 1 =k 2 =10 -4 , k 3 = 1. The two thresholds are set to τ 1 =τ 2 =10 -5 .

[0295] Substitute the known parameters into steps 1 to 6 in the Summary of the Invention.

[0296] The results obtained using the sequential quadratic programming algorithm are as follows Figure 4-5 As shown, Figure 4 To optimize the cutting width before and after, Figure 5 The results show that for the robot posture obtained by the present invention, the minimum cutting width is significantly increased, the joint path is smoother, and the processing efficiency and processing surface quality can be improved.

[0297] Those skilled in the art know that, in addition to implementing the system, device and its various modules provided by the present invention in a purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, the system, device and its various modules provided by the present invention can be considered as a hardware component, and the modules included therein for implementing various programs can also be considered as structures within the hardware component; the modules for implementing various functions can also be considered as both software programs for implementing the method and structures within the hardware component.

[0298] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for optimizing the milling posture of an industrial robot flat-bottom cutter, characterized in that: include: Step S1: Read the discrete tool contact point information and the design surface information, and establish the tool axis direction representation corresponding to the discrete tool contact point and the robot posture redundant parameter representation; Step S2: Establishing the global smoothness performance index of the robot path; Step S3: establishing a constrained optimization model based on the information of discrete knife contact points and the global smoothing performance index of the path; Step S4: Establishing an analytical estimation method for the cutting width derivative; Step S5: solving the optimization model; Step S6: Generate a motion program using the optimal task posture sequence obtained by solving the model; In step S2: The numerical differential formula is used to express the first-order derivative and second-order derivative of the robot joint angle with respect to the arc length parameter of the knife contact path: Where j∈{1,…,6} represents the joint number, i∈{2,…,n-1} represents the knife contact number, and n is the number of knife contacts. represents the angle of joint j corresponding to the i-th knife contact point, Δs i represents the distance between knife contact point i and knife contact point i+1, represents the first-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact path, represents the second-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact point path; make Establish indicators to evaluate the global smoothing performance of the path: Among them, Φ smooth is the global smoothing performance index of the path, k1 and k2 are weight values; In step S3: The optimization variables are expressed as α = [λ1, ω1, η1, …, λ n ,ω n ,η n ], where λ i is the tool rake angle corresponding to the i-th tool contact point, ω i is the tool tilt angle corresponding to the i-th tool contact point, η i is the redundant parameter of the robot corresponding to the i-th knife contact point; Taking the minimization of the global smoothness performance index of the path and the maximization of the minimum cutting width as the optimization objectives, and taking the joint limit and interference avoidance as the constraints, a constrained optimization model is established; s.t.ψ≥-w i q i =f -1 (l i ,oh i ,or i ,CC i ) q min ≤q i ≤q max f i (oh i )≤λ i ≤π / 2 i=1,2,…,n Among them, k3 is the cutting width weight coefficient, ψ is the introduced variable, and w i is the cutting width at the i-th knife contact point, f -1 (…) is the inverse kinematics solution function of the robot, CC i is the i-th knife contact point, is the robot joint angle vector corresponding to the i-th knife contact point, q min With q max are the lower and upper bounds of the robot joint vector, f i (ω i ) is the tilt angle ω at the i-th tool contact point obtained according to the interference avoidance constraint i The corresponding minimum forward tilt angle is and are the lower and upper bounds of the tilt angle at the i-th knife contact point; In step S4: At any knife contact CC i For a given tool axis direction, the tool base circle is expressed as C using conformal geometry algebra. BTC =P(p1)∧P2(p2)∧P3(p3), where {p i |i=1,2,3} are three different points on the tool bottom circle, and P(…) is the mapping from a point in three-dimensional Euclidean space to a point in conformal space; For a given residual height h of the surface machining, suppose two points on the tool bottom circle with a distance h from the design surface are p and a (λ i ,ω i ) and p b (λ i ,ω i ), suppose the distance p on the design surface a With p a The nearest points are q a With q b ; Using conformal geometry, let q be the center of the circle a , a sphere with radius h is expressed as: S a =(P(q a )-h 2 e ∞ / 2) * Among them, e ∞ is the basis for representing points at infinity in conformal geometric algebra, () * It is the dual operation in conformal geometric algebra; The spherical surface S is calculated by the following formula a Intersection point with tool bottom circle and Where ∧ is the outer product operation, satisfy Use the same method to calculate q b is the center of the circle, h is the intersection of the sphere with the radius and the bottom circle of the tool and in satisfy make Among them, y i is a unit vector and is related to the knife contact point CC i The feed direction at is perpendicular to the design surface normal vector; use As Analytical estimate of ; In step S5: Step S5.1: Establish The nearby quadratic programming subproblem: i=1,2,…,n Among them, α k is the value of variable α at the kth iteration of the solution algorithm, k is the current iteration number of the solution algorithm, Δψ is the increment of variable ψ, and Δλ i is the angle λ i The increment, Δω i is the angle ω i The increment, Δη i is the angle η i The increment of , ζ is the introduced control coefficient; Δα=[Δλ1,Δω1,Δη1,…,Δλ n ,Δω n ,Δη n ] is the increment of variable α, is the function f i ()exist The derivative value at w i () is the function of the cutting width at the i-th tool contact point with respect to the variable α; Step S5.2: Let k = 0, ζ = 1; calculate the initial joint vector q at the i-th knife contact point i (α0), cutting width w i (α0) and the smoothness index Φ smooth (α0), where i = 1,…,n, is the initial solution of the optimization variable α; let Ψ0=Φ smooth (α0)+k3ψ0; Among them, ψ0 is the inverse of the minimum cutting width at all tool contact points when α=α0, and Ψ0 is the objective function value of the optimization problem when α=α0; Step S5.3: For i=1,…,n,j=1…,6, calculate Solution Step S5.4: Solve the quadratic programming subproblem in step S5.1; update α k+1 =α k +Δα; for i=1,…,n, calculate q i (α k+1 ), w i (α k+1 ), Φ smooth (α k+1 );renew Ψ k+1 =Φ smooth (α k+1 )+k3ψ k+1 ; Among them, ψ k+1 α=α k+1 The opposite number of the minimum cutting width at all tool contact points, Ψ k+1 α=α k+1 The objective function value of the optimization problem; Step S5.5: If Ψ k+1 <Ψ k , let k = k + 1, and execute step S5.6; if Ψ k+1 ≥Ψ k , execute step S5.7; Step S5.6: If (Ψ k -Ψ k+1 ) / |Ψ k | is greater than the preset threshold τ2, execute step S5.3; if (Ψ k -Ψ k+1 ) / |Ψ k | is less than or equal to the preset threshold τ2, and the output optimal solution is α * =α k ; Step S5.7: If ζ is greater than the preset threshold τ1, set ζ = 0.5ζ and execute step S5.4; if ζ is less than or equal to the preset threshold τ1, output the optimal solution as α * =α k .

2. An industrial robot flat-bottom cutter milling processing posture optimization system, characterized in that: include: Module M1: Read the discrete tool contact information and the design surface information, and establish the tool axis direction representation corresponding to the discrete tool contact and the robot posture redundant parameter representation; Module M2: Establishing global smoothness performance index of robot path; Module M3: Establish a constrained optimization model based on the information of discrete knife contact points and the global smoothing performance index of the path; Module M4: Establishing an analytical estimation method for the cutting width derivative; Module M5: Solving the optimization model; Module M6: Generate motion program using the optimal task pose sequence obtained by solving the model; In the module M2: The numerical differential formula is used to express the first-order derivative and second-order derivative of the robot joint angle with respect to the arc length parameter of the knife contact path: Where j∈{1,…,6} represents the joint number, i∈{2,…,n-1} represents the knife contact number, n is the number of knife contacts, θ j i represents the angle of joint j corresponding to the i-th knife contact point, Δs i represents the distance between knife contact point i and knife contact point i+1, represents the first-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact path, represents the second-order derivative of the angle of joint j corresponding to the i-th knife contact point with respect to the arc length parameter of the knife contact point path; make Establish indicators to evaluate the global smoothing performance of the path: Among them, Φ smooth is the global smoothing performance index of the path, k1 and k2 are weight values; In the module M3: The optimization variables are expressed as α = [λ1, ω1, η1, …, λ n ,ω n ,η n ], where λ i is the tool rake angle corresponding to the i-th tool contact point, ω i is the tool tilt angle corresponding to the i-th tool contact point, η i is the redundant parameter of the robot corresponding to the i-th knife contact point; Taking the minimization of the global smoothness performance index of the path and the maximization of the minimum cutting width as the optimization objectives, and taking the joint limit and interference avoidance as the constraints, a constrained optimization model is established; s.t.ψ≥-w i q i =f -1 (l i ,oh i ,or i ,CC i ) q min ≤q i ≤q max f i (oh i )≤λ i ≤π / 2 i=1,2,…,n Among them, k3 is the cutting width weight coefficient, ψ is the introduced variable, and w i is the cutting width at the i-th knife contact point, f -1 (…) is the inverse kinematics solution function of the robot, CC i is the i-th knife contact point, is the robot joint angle vector corresponding to the i-th knife contact point, q min With q max are the lower and upper bounds of the robot joint vector, f i (ω i ) is the tilt angle ω at the i-th tool contact point obtained according to the interference avoidance constraint i The corresponding minimum forward tilt angle is and are the lower and upper bounds of the tilt angle at the i-th knife contact point; In the module M4: At any knife contact CC i For a given tool axis direction, the tool base circle is expressed as C using conformal geometry algebra. BTC =P(p1)∧P2(p2)∧P3(p3), where {p i |i=1,2,3} are three different points on the tool bottom circle, and P(…) is the mapping from a point in three-dimensional Euclidean space to a point in conformal space; For a given residual height h of the surface machining, suppose two points on the tool bottom circle with a distance h from the design surface are p and a (λ i ,ω i ) and p b (λ i ,ω i ), suppose the distance p on the design surface a With p a The nearest points are q a With q b ; Using conformal geometry, let q be the center of the circle a , a sphere with radius h is expressed as: S a =(P(q a )-h 2 e ∞ / 2) * Among them, e ∞ is the basis for representing points at infinity in conformal geometric algebra, () * It is the dual operation in conformal geometric algebra; The spherical surface S is calculated by the following formula a Intersection point with tool bottom circle and Where ∧ is the outer product operation, satisfy Use the same method to calculate q b is the center of the circle, h is the intersection of the sphere with the radius and the bottom circle of the tool and in satisfy make Among them, y i is a unit vector and is related to the knife contact point CC i The feed direction at is perpendicular to the design surface normal vector; use As Analytical estimate of ; In the module M5: Module M5.1: Establishment The nearby quadratic programming subproblem: i=1,2,…,n Among them, α k is the value of variable α at the kth iteration of the solution algorithm, k is the current iteration number of the solution algorithm, Δψ is the increment of variable ψ, and Δλ i is the angle λ i The increment, Δω i is the angle ω i The increment, Δη i is the angle η i The increment of , ζ is the introduced control coefficient; Δα=[Δλ1,Δω1,Δη1,…,Δλ n ,Δω n ,Δη n ] is the increment of variable α, f i ′(ω i k ) is the function f i ()exist The derivative value at w i () is the function of the cutting width at the i-th tool contact point with respect to the variable α; Module M5.2: Let k = 0, ζ = 1; calculate the initial joint vector q at the i-th knife contact point i (α0), cutting width w i (α0) and the smoothness index Φ smooth (α0), where i = 1,…,n, is the initial solution of the optimization variable α; let Ψ0=Φ smooth (α0)+k3ψ0; Among them, ψ0 is the inverse of the minimum cutting width at all tool contact points when α=α0, and Ψ0 is the objective function value of the optimization problem when α=α0; Module M5.3: For i = 1, ..., n, j = 1 ..., 6, calculate Solution Module M5.4: Solve the quadratic programming subproblem in Module M5.1; update α k+1 =α k +Δα; for i=1,…,n, calculate q i (α k+1 ), w i (α k+1 ), Φ smooth (α k+1 );renew Ψ k+1 =Φ smooth (α k+1 )+k3ψ k+1 ; Among them, ψ k+1 α=α k+1 The opposite number of the minimum cutting width at all tool contact points, Ψ k+1 α=α k+1 The objective function value of the optimization problem; Module M5.5: If Ψ k+1 <Ψ k , let k = k + 1, execute module M5.6; if Ψ k+1 ≥Ψ k , execution module M5.7; Module M5.6: If (Ψ k -Ψ k+1 ) / |Ψ k | is greater than the preset threshold τ2, execute module M5.3; if (Ψ k -Ψ k+1 ) / |Ψ k | is less than or equal to the preset threshold τ2, and the output optimal solution is α * =α k ; Module M5.7: If ζ is greater than the preset threshold τ1, set ζ = 0.5ζ and execute module M5.4; if ζ is less than or equal to the preset threshold τ1, output the optimal solution as α * =α k .

3. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the industrial robot flat-bottom cutter milling processing posture optimization method described in claim 1 are implemented.

Images