A robot pose optimization method based on profile error

Abstract

The present application relates to a kind of robot posture optimization method based on profile error, belong to machining technical field.The method first comprehensively considers the influence of robot stiffness, cutting force, feed direction and surface feature on free-form surface milling process;Then a profile error calculation method is proposed, which can directly represent the milling performance of free-form surface workpiece;Finally, with the profile error as the target, by changing the feed direction and Euler angle of each point on the surface, the optimal machining mode of the point is obtained, and then the optimal robot posture and feed direction of the entire surface are obtained.The robot posture optimization method provided by the present application can comprehensively consider the influence of robot stiffness, cutting force, feed direction and surface feature on milling process, and effectively reduce the influence of cutting force on free-form surface milling quality.

Description

Technical Field

[0001] This invention belongs to the field of machining technology and relates to a robot milling posture optimization method, particularly a robot milling posture optimization method based on surface error planning for freeform surface machining. Background Technology

[0002] During robotic milling, due to the robot's low stiffness, the end effector can shift position under milling forces, reducing milling quality. For planar or relatively regular curved surfaces, robot stiffness can indirectly characterize the end effector shift caused by cutting forces during machining. Therefore, in this case, indirect optimization of robot stiffness can improve the final machining quality. However, for irregular free-form surfaces, indirect optimization of stiffness alone will limit the final optimization results and fail to achieve optimal machining quality. Therefore, finding a method that can directly characterize the errors in robotic milling of free-form surfaces and then establishing an attitude optimization method based on these errors has significant theoretical and engineering application value.

[0003] The paper "Z.-Y.Liao, J.-R.Li, H.-L.Xie, Q.-H.Wang, X.-F.Zhou. Region-based toolpath generation for robotic milling of freeform surfaces with stiffness optimization, Robotics and Computer-Integrated Manufacturing 64(2020)101953" discloses a posture optimization method based on the normal stiffness of a surface. This method optimizes the robot posture with normal stiffness as the target and optimizes the milling feed direction with tangential stiffness as the target. However, stiffness is only an indirect evaluation index of milling quality and is difficult to accurately characterize milling quality. On the other hand, the feed direction is simply specified as the direction with the maximum tangential stiffness, ignoring the influence of feed direction changes on cutting force, and thus also ignoring the influence of feed direction on milling quality.

[0004] The paper "Q.Chen, C.Zhang, T.Hu, Y.Zhou, H.Ni, X.Xue, Posture optimization in robotic machining based on comprehensive deformation index considering spindle weight and cutting force, Robotics and Computer-Integrated Manufacturing 74(2022)102290" discloses a method for simultaneously considering deformation caused by gravity and cutting force, and proposes an evaluation index to characterize the robot stiffness performance at various points along the toolpath. Its shortcomings are: the evaluation index used can only indirectly characterize milling quality, and because it is a study based on a known trajectory on a plane, it does not consider the influence of the feed direction on the milling process, nor does it consider the influence of different surface features at different points on the milling process in curved surface machining.

[0005] The typical characteristics of the aforementioned references are: they use stiffness as an evaluation index to indirectly evaluate the machining quality of robot milling during the calculation process, and they select a trajectory with a given feed direction or simply specify the feed direction. They neglect the influence of cutting force, feed direction, and surface features on the milling process and milling quality, while these influences are particularly significant in free-form surfaces. Ignoring them during the milling of free-form surfaces will lead to a significant decrease in milling quality. Summary of the Invention

[0006] Technical problems to be solved

[0007] To overcome the shortcomings of existing methods that fail to consider the influence of cutting force, feed direction, and surface features, and thus cannot accurately characterize the quality of robot milling, this invention proposes a posture optimization method that comprehensively considers multiple influencing factors in the machining process and directly characterizes milling quality using surface error. This method first comprehensively considers the influence of robot stiffness, cutting force, feed direction, and surface features on freeform surface milling; then, based on this, a method for calculating surface error is proposed; finally, this surface error is used as a direct evaluation index for robot milling quality. By optimizing the robot posture and feed direction with this index as the target, the final machining path and corresponding robot posture are obtained.

[0008] Expected technical effects: The robot posture optimization method provided by this invention can comprehensively consider the influence of robot stiffness, cutting force, feed direction and surface features on the milling process, and effectively reduce the influence of cutting force on the quality of free surface milling.

[0009] Technical solution

[0010] A robot posture optimization method based on surface error, characterized by the following steps:

[0011] Step 1: Calculate the theoretical position of the center point of the freeform ball end mill using the following formula.

[0012] P e =S0+Rw0

[0013] In the formula P e S0 represents the theoretical position of the center point of the ball end mill, R represents the radius of the ball end mill, and w0 represents the normal vector of the freeform surface at the tool contact point.

[0014] Step 2: Calculate the actual position of the ball center of the ball end mill under the milling force using the following formula.

[0015]

[0016]

[0017]

[0018] Δx t =C ft F

[0019] P t =P e +Δx t

[0020] In the formula, J is the Jacobian matrix of the robot in its current posture, and K... θ It is a 6×6 diagonal matrix composed of the stiffnesses of each joint, K θ1 K θ2 K θ3 K θ4 K θ5 K θ6 C represents the stiffness of the six joints respectively. ft It is the force-displacement compliance submatrix, C fr It is the force-rotation compliance submatrix, C mt It is the torque-displacement compliance submatrix, C mr Torque-rotational compliance submatrix, where F is the resultant cutting force. These represent the average components of the cutting force in the x, y, and z directions, respectively. These represent the instantaneous forces in the x, y, and z directions at different rotation angles of the milling cutter. The milling cutter rotation angle, Δx t P represents the offset of the robot's end effector caused by the cutting force, and is also the deviation between the theoretical and actual positions of the ball center point of the ball end mill. tIndicates the actual position of the ball center of the ball end mill;

[0021] Step 3: First, determine the error calculation plane S based on the contact point of the curved surface tool, the actual tool tip point under the cutting force, and the normal vector of the curved surface at the tool contact point using the following formula. p This makes the plane pass through the first two and parallel to the third; then, by solving the system of equations simultaneously, the error calculation is performed to calculate the intersection curve q between the plane and the freeform surface;

[0022]

[0023] q = S p ∩S0

[0024] In the formula S p,x S p,y S p,z Representing plane S respectively p The x, y, and z coordinates of the point P e,x P e,y P e,z S represents the x, y, and z coordinates of the theoretical position of the ball center of the ball end mill, respectively. 0,x S 0,y S 0,z P represents the x, y, and z coordinates of the tool contact point, respectively. t,x P t,y P t,z These represent the x, y, and z coordinates of the actual position of the ball center of the ball end mill;

[0025] Step 4: Calculate the surface error when machining freeform surfaces using the following formula.

[0026]

[0027] d = ER

[0028] In the formula, H is any point on the curve q. P represents t The distance from P to H is E, which represents the distance between P and H. t The profile error between the curve q and the freeform surface is represented by d, which represents the surface error of the freeform surface.

[0029] Step 5: Construct a corresponding local coordinate system x at each freeform surface tool contact point. l y l z l Its origin is located at the corresponding tool contact point, z l The axial direction is the direction of the surface normal, x l Axial direction and z l The axis is perpendicular, and its component in the y-direction of the global coordinate system is 0. l The axial direction is from xl axis, z l The axis direction is determined according to the right-hand rule;

[0030] Step 6: Calculate the constraints that the robot milling trajectory and the poses of each point on the trajectory should satisfy during the optimization process using the following formula:

[0031] α i-1 -ρΔs<α i <α i-1 +ρΔs

[0032]

[0033] θ min ≤θ i ≤θ max

[0034] θ i-1 -δωΔt≤θ i ≤θ i-1 +δωΔt

[0035] ε(J)=||J(θ i )||||J -1 (θ i )||≤ε max

[0036] In the formula CC i Let α represent the i-th tool contact point on the freeform surface. i For CC i The feed direction angle at point X is defined as the angle between the feed direction and the x-axis. l The included angle between the axes, ρ, is used to adjust the maximum allowable change in the feed direction at adjacent tool contact points, and Δs represents the CC. i-1 With CC i The distance between them Indicates the processing of CC i The zyz-type Euler angle of the robot end effector, FA(CC) i ) indicates CC i The region where the tool or robot will not collide is defined, where δ is a constant less than 1, used to constrain the angular velocities of the robot joints, ω represents the maximum angular velocity of each joint, and Δt represents the distance from CC. i-1 Run to CC i The required time, ε(J) represents the Jacobi condition number, used to prevent the robot from reaching a singularity. max θ represents the maximum allowable Jacobian condition number. i =[θ i1 θ i2 θ i3 θ i4 θ i5 θi6 ] T CC i The angles of the robot's six joints, θ i1 θ i2 θ i3 θ i4 θ i5 θ i6 θ represents the angles of the six joints respectively. min With θ max θ represents the minimum and maximum allowable angles for each joint. i The value can be obtained through θ i =IK(T t The calculation is performed using IK(*), where IK(*) represents the inverse kinematics transformation, and T... t The coordinate transformation matrix of the end effector at the tool contact point is represented as:

[0037]

[0038] Among them I 3×3 Represents a 3×3 identity matrix, O 1×3 Represents a 1×3 matrix of zeros;

[0039] Step 7: Based on the constraints in Step 6, adjust the feed direction angle α at each tool contact point. i Euler angles of the end effector Find the combination that minimizes d at that point, and use the simulated annealing algorithm to transform the combination at each point on the freeform surface into the final machining trajectory and the robot posture at each point on the trajectory.

[0040] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0041] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0042] Beneficial effects

[0043] This invention provides a robot posture optimization method based on surface error. This method first comprehensively considers the influence of robot stiffness, cutting force, feed direction, and surface features on the freeform surface milling process. Then, it proposes a surface error calculation method that can directly characterize the milling performance of freeform surface workpieces. Finally, using surface error as the target, the optimal machining method for each point on the surface is obtained by changing the feed direction and Euler angle, thereby obtaining the optimal robot posture and feed direction for the entire surface. Compared with the given literature, this invention comprehensively considers multiple factors and transforms indirect optimization for stiffness into direct optimization for surface error, effectively improving the milling quality during robot milling of freeform surfaces. Attached Figure Description

[0044] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0045] Figure 1 Photographs of freeform surfaces processed using the methods described in the given literature;

[0046] Figure 2 Photographs of free-form surfaces processed using the method of this invention;

[0047] Figure 3 The results are the error measurements performed on the freeform surfaces obtained by the methods in the given literature and the methods of this invention, respectively. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0049] Example 1

[0050] The experiment used a 10 mm diameter, 75 mm length, 2-tooth ball-end mill with coated carbide end mill to machine freeform surfaces. The robot spindle speed was 3600 rpm, the feed rate was 1.2 mm / s, the axial depth of cut was 1.5 mm, the radial width of cut was 7 mm, the workpiece material was 6061 aluminum alloy, and a 210 kg industrial robot was used to carry out the freeform surface milling experiment.

[0051] Step 1: By applying a load to the robot's end effector, a displacement laser sensor is used to measure the displacement of the robot's end effector caused by the load. After multiple tests, the stiffness K of each joint of the robot is calibrated. θ .

[0052] The calibration results are shown in Table 1.

[0053] Table 1. Stiffness of each joint of the robot (N·mm / rad)

[0054]

[0055] Step 2: Calculate the theoretical position of the center point of the freeform ball end mill using the following formula.

[0056] P e =S0+Rw0

[0057] In the formula P e S0 represents the theoretical position of the center point of the ball end mill, R represents the radius of the ball end mill, and w0 represents the normal vector of the freeform surface at the tool contact point.

[0058] Step 3: Calculate the actual position of the ball center of the ball end mill under the action of the milling force using the following formula.

[0059]

[0060]

[0061]

[0062] Δx t =C ft F

[0063] P t =P e +Δx t

[0064] The Jacobian matrix J of the robot in this posture is derived from the robot's current joint angles and Denavit-Hartenberg (DH) parameters. The joint angles are obtained through inverse kinematic transformation, and the DH parameters are robot properties. The robot DH parameters used in this example are shown in Table 2.

[0065] Table 2 shows the DH parameters of the robot used in the example.

[0066]

[0067]

[0068] K θ It is a 6×6 diagonal matrix composed of the stiffnesses of each joint, K θ1 K θ2 K θ3 K θ4 K θ5 K θ6C represents the stiffness of the six joints respectively. ft It is the force-displacement compliance submatrix, C fr It is the force-rotation compliance submatrix, C mt It is the torque-displacement compliance submatrix, C mr Torque-rotational compliance submatrix, where F is the resultant cutting force. These represent the average components of the cutting force in the x, y, and z directions, respectively. These represent the instantaneous forces in the x, y, and z directions at different rotation angles of the milling cutter. The milling cutter rotation angle, Δx t P represents the offset of the robot's end effector caused by the cutting force, and is also the deviation between the theoretical and actual positions of the ball center point of the ball end mill. t This indicates the actual position of the ball center of the ball end mill.

[0069] Step 4: First, determine the error calculation plane S based on the contact point of the curved surface tool, the actual tool tip point under the cutting force, and the normal vector of the curved surface at the tool contact point using the following formula. p This allows the plane to pass through the first two and be parallel to the third. Then, by solving a system of equations simultaneously, the intersection curve q between the error calculation plane and the freeform surface is calculated.

[0070]

[0071] q = S p ∩S0

[0072] In the formula S p,x S p,y S p,z Representing plane S respectively p The x, y, and z coordinates of the point P e,x P e,y P e,z S represents the x, y, and z coordinates of the theoretical position of the ball center of the ball end mill, respectively. 0,x S 0,y S 0,z P represents the x, y, and z coordinates of the tool contact point, respectively. t,x P t,y P t,z These represent the x, y, and z coordinates of the actual position of the ball center of the ball end mill.

[0073] Step 5: Calculate the surface error when machining freeform surfaces using the following formula.

[0074]

[0075] d = ER

[0076] In the formula, H is any point on the curve q. P represents t The distance from P to H is E, which represents the distance between P and H. t The profile error between curve q and curve q, where d represents the surface error of the freeform surface.

[0077] Step 6: Construct a corresponding local coordinate system x at each freeform surface tool contact point. l y l z l Its origin is located at the corresponding tool contact point, z l The axial direction is the direction of the surface normal, x l Axial direction and z l The axis is perpendicular, and its component in the y-direction of the global coordinate system is 0. l The axial direction is from x l axis, z l The direction of the axis is determined according to the right-hand rule.

[0078] Step 7: Calculate the constraints that the robot milling trajectory and the posture of each point on the trajectory should satisfy during the optimization process using the following formula.

[0079] α i-1 -ρΔs<a i <a i-1 +ρΔs

[0080]

[0081] θ min ≤θ i ≤θ max

[0082] θ i-1 -δωΔt≤θ i ≤θ i-1 +δωΔt

[0083] ε(J)=||J(θ i )||||J -1 (θ i )||≤ε max

[0084] In the formula CC i Let α represent the i-th tool contact point on the freeform surface. i For CC i The feed direction angle at point X is defined as the angle between the feed direction and the x-axis. l The included angle between axes, ρ, is used to adjust the maximum allowable change in the feed direction at adjacent tool contact points; in this example, it is specified as 1. Δs represents CC. i-1 With CC i The distance between them Indicates the processing of CCi The zyz-type Euler angle of the robot end effector, FA(CC) i ) indicates CC i The region where the tool or robot will not collide is defined. δ is a constant less than 1, specified as 0.5 in this example, used to constrain the angular velocities of the robot joints. ω represents the maximum angular velocity of each joint. The maximum angular velocities of each joint of the robot used in this example are shown in Table 3. Δt represents the distance from CC... i-1 Run to CC i The required time, ε(J) represents the Jacobi condition number, used to prevent the robot from reaching a singularity. max This represents the maximum allowable Jacobian condition number during processing; in this example, it is set to 1.5. θ i =[θ i1 θ i2 θ i3 θ i4 θ i5 θ i6 ] T CC i The angles of the robot's six joints, θ i1 to θ i6 θ represents the angles of the six joints respectively. min With θ max The minimum and maximum allowable angles for each joint are shown in Table 3, with values ​​as shown in Table 3. i The value can be obtained through θ i =IK(T t The calculation is performed using IK(*), where IK(*) represents the inverse kinematics transformation, and T... t The coordinate transformation matrix representing the end effector at the tool contact point can be expressed as:

[0085]

[0086] Among them I 3×3 Represents a 3×3 identity matrix, O 1×3 This represents a 1×3 matrix of zeros.

[0087] Table 3 shows the maximum angular velocities of each joint of the robot used in this example.

[0088]

[0089] Step 8: Based on the constraints in the previous step, adjust the feed direction angle α at each tool contact point. i Euler angles of the end effector Find the combination that minimizes d at that point, and use the simulated annealing algorithm to transform the combination at each point on the freeform surface into the final machining trajectory and the robot posture at each point on the trajectory.

[0090] Through append Figure 1 , Figure 2 It can be seen that the workpiece surface quality processed using the method of the present invention is better, through the attachment Figure 3 It can be seen that by using the method of the present invention, not only is the average surface error of each tool contact point reduced, but the fluctuation of the surface error is also reduced, proving that the workpiece processed by this method has achieved higher precision.

[0091] This demonstrates that by comprehensively considering the combined effects of robot stiffness, cutting force, feed direction, and surface features on the freeform surface milling process, and by transforming indirect optimization into direct optimization, the method of this invention significantly improves both the surface quality and machining accuracy of the workpiece compared to the methods in the literature. These results prove that, compared to the methods in the literature, this invention can effectively improve milling quality.

[0092] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A robot posture optimization method based on surface error, characterized in that... The steps are as follows: Step 1: Calculate the theoretical position of the center point of the freeform ball end mill using the following formula. P e =S0+Rw0 In the formula P e S0 represents the theoretical position of the center point of the ball end mill, R represents the radius of the ball end mill, and w0 represents the normal vector of the freeform surface at the tool contact point. Step 2: Calculate the actual position of the ball center of the ball end mill under the milling force using the following formula. Δx t =C ft F P t =P e +Δx t In the formula, J is the Jacobian matrix of the robot in its current posture, and K... θ It is a 6×6 diagonal matrix composed of the stiffnesses of each joint, K θ1 K θ2 K θ3 K θ4 K θ5 K θ6 C represents the stiffness of the six joints respectively. ft It is the force-displacement compliance submatrix, C fr It is the force-rotation compliance submatrix, C mt It is the torque-displacement compliance submatrix, C mr Torque-rotational compliance submatrix, where F is the resultant cutting force. These represent the average components of the cutting force in the x, y, and z directions, respectively. These represent the instantaneous forces in the x, y, and z directions at different rotation angles of the milling cutter. The milling cutter rotation angle, Δx t P represents the offset of the robot's end effector caused by the cutting force, and is also the deviation between the theoretical and actual positions of the ball center point of the ball end mill. t Indicates the actual position of the ball center of the ball end mill; Step 3: First, determine the error calculation plane S based on the contact point of the curved surface tool, the actual tool tip point under the cutting force, and the normal vector of the curved surface at the tool contact point using the following formula. p This makes the plane pass through the first two and parallel to the third; then, by solving the system of equations simultaneously, the error calculation is performed to calculate the intersection curve q between the plane and the freeform surface; q=S p ∩S0 In the formula S p,x S p,y S p,z Representing plane S respectively p The x, y, and z coordinates of the point P e,x P e,y P e,z S represents the x, y, and z coordinates of the theoretical position of the ball center of the ball end mill, respectively. 0,x S 0,y S 0,z P represents the x, y, and z coordinates of the tool contact point, respectively. t,x P t,y P t,z These represent the x, y, and z coordinates of the actual position of the ball center of the ball end mill; Step 4: Calculate the surface error when machining freeform surfaces using the following formula. d = ER In the formula, H is any point on the curve q. P represents t The distance from P to H is E, which represents the distance between P and H. t The profile error between the curve q and the freeform surface is represented by d, which represents the surface error of the freeform surface. Step 5: Construct a corresponding local coordinate system x at each freeform surface tool contact point. l y1z l Its origin is located at the corresponding tool contact point, z l The axial direction is the direction of the surface normal, x l Axial direction and z l The y-axis is perpendicular to the x-axis and has a component of 0 in the y-direction of the global coordinate system. The y1-axis direction is from x... l The directions of the z1 and z2 axes are determined according to the right-hand rule. Step 6: Calculate the constraints that the robot milling trajectory and the poses of each point on the trajectory should satisfy during the optimization process using the following formula: a i-1 -ρΔs<α i <a i-1 +ρΔs i min ≤θ i ≤θ max i i-1 -δωΔt≤θ i ≤θ i-1 +dωΔt ε(J)=||J(θ i )||||J -1 (i i )||e max In the formula CC i Let α represent the i-th tool contact point on the freeform surface. i For CC i The feed direction angle at point X1 is defined as the angle between the feed direction and the x1 axis. ρ is used to adjust the maximum allowable change in feed direction at adjacent tool contact points. Δs represents the CC angle. i-1 With CC i The distance between them Indicates the processing of CC i The zyz-type Euler angle of the robot end effector, FA(CC) i ) indicates CC i The region where the tool or robot will not collide is defined, where δ is a constant less than 1, used to constrain the angular velocities of the robot joints, ω represents the maximum angular velocity of each joint, and Δt represents the distance from CC. i-1 Run to CC i The required time, ε(J) represents the Jacobi condition number, used to prevent the robot from reaching a singularity. max θ represents the maximum allowable Jacobian condition number. i =[θ i1 θ i2 θ i3 θ i4 θ i5 θ i6 ] T CC i The angles of the robot's six joints, θ i1 θ i2 θ i3 θ i4 θ i5 θ i6 θ represents the angles of the six joints respectively. min With θ max θ represents the minimum and maximum allowable angles for each joint. i The value can be obtained through θ i =IK(T t The calculation is performed using IK(*), where IK(*) represents the inverse kinematics transformation, and T... t The coordinate transformation matrix of the end effector at the tool contact point is represented as: Where I 3×3 Represents a 3×3 identity matrix, O 1×3 This represents a 1×3 matrix of zeros. Step 7: Based on the constraints in Step 6, adjust the feed direction angle α at each tool contact point. i Euler angles of the end effector Find the combination that minimizes d at that point, and use the simulated annealing algorithm to transform the combination at each point on the freeform surface into the final machining trajectory and the robot posture at each point on the trajectory.

2. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

3. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

Images