Heavy-load forming robot motion planning method based on reduction of joint impact vibration

Abstract

The invention relates to a heavy-load forming robot motion planning method based on reduction of joint impact vibration. The method comprises the following steps: S1, establishing a heavy-load forming robot kinematics model; s2, establishing a heavy-load forming robot dynamic model; s3, determining a dynamic error and a generation mechanism of the heavy-load forming robot; and S4, motion planning of the heavy-load forming robot is carried out. According to the method, the input motion of the robot is planned, and the impact vibration of the robot during working is reduced by reducing the impact speed while ensuring the working efficiency. Dynamic errors of the robot can be reduced, higher motion precision of the robot is achieved, errors of formed parts are reduced, and the method has important application prospects under the heavy load working condition.

Description

Technical Field

[0001] This invention relates to the field of motion planning for heavy-duty forming robots, and more specifically, to a motion planning method for heavy-duty forming robots based on reducing joint impact vibration. Background Technology

[0002] Heavy-duty forming robots are specialized robots used in the production of high-performance metal parts for the aerospace industry. They consist of six chains connecting the machine tool and the moving platform. By controlling the coordinated motion of these six chains, the moving platform performs the desired motion for part forming. Under heavy-duty conditions, collisions at the gaps in the robot's spherical joints, deformation at the links, and the coupling effects between them become more pronounced, generating significant vibration and impact. This leads to increased dynamic errors and reduced forming accuracy. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a motion planning method for heavy-duty forming robots based on reducing joint impact vibration, which can achieve higher motion accuracy of the robot and reduce the error of the formed parts.

[0004] The technical solution adopted by this invention to solve its technical problem is: to construct a motion planning method for a heavy-duty forming robot based on reducing joint impact vibration, comprising the following steps:

[0005] S1. Establish the kinematic model of the heavy-duty forming robot;

[0006] S2. Establish a dynamic model of the heavy-duty forming robot;

[0007] S3. Determine the dynamic error and generation mechanism of the heavy-duty forming robot;

[0008] S4. Perform motion planning for the heavy-duty forming robot.

[0009] According to the above scheme, the heavy-duty forming robot includes six sets of branches connecting the static platform and the moving platform. Each branch is connected in the form of guide rail-slider-ball joint-moving platform. The slider, ball joint-moving platform and the moving platform together form a kinematic model of the heavy-duty forming robot.

[0010] According to the above scheme, in step S2, based on the LN contact model and the discrete mass method, a dynamic model of the heavy-duty robot considering the spherical pair clearance and link deformation is established using the Newton-Euler method.

[0011] According to the above scheme, in step S2, the robot's generalized coordinates are represented as follows:

[0012]

[0013] The generalized coordinates of the slider in the formula are si =[x si ,y si ,0,0,0,0,] T , These represent the positions of the slider's center of mass in the x and y directions, respectively; the generalized coordinates of the upper and lower ends of the connecting rod are respectively represented as... This indicates the change in position of the upper mass block. This indicates the change in the angle of the upper mass block. This indicates the positional change of the lower mass block. This represents the angular change of the lower mass block; the generalized coordinates of the moving platform are p = [x] p ,y p ,z p ,α p ,β p ,γ p ] T x p ,y p ,z p α represents the change in position of the moving platform. p ,β p ,γ p This indicates the change in the angle of the moving platform.

[0014] According to the above scheme, in step S2, based on the positional relationship of each component of the robot, the force analysis of each component is performed individually, and the final overall dynamic equation is obtained as follows:

[0015]

[0016] In the formula, F Mi For the driving force of the slider, The contact force at the ball joint. F is the contact force at the lower ball joint. P External load force on the moving platform. and These are the stiffness matrix and damping matrix of the link, respectively, m S m L m p These represent the masses of the slider, connecting rod, and moving platform, respectively.

[0017] According to the above scheme, in step S3, the dynamic model is solved using the Runge-Kutta method, and the external load force F of the moving platform is... P = [0,0,6]MN, with the position of action r e =r e [sin(πt),cos(πt),0].

[0018] According to the above scheme, in step S3, the driving force curve and velocity curve are obtained by solving the dynamic equation, and both are periodic.

[0019] According to the above scheme, in step S3, based on the comparison of dynamic error and impact force, the moment when the error changes abruptly within a cycle coincides with the moment when the impact force in the driving force occurs. The error generation mechanism under heavy load is that the dynamic error of the moving platform is generated by vibration and impact.

[0020] According to the above scheme, in step S4, since the error changes during robot motion are periodic, motion planning is considered for impact moments when these errors have a significant impact; for heavy-duty forming robots, there is a mapping relationship between the slider input speed and the moving platform output speed, which is represented by the Jacobian matrix.

[0021] According to the above scheme, in step S4, the piecewise function method is used to plan the speed of the moving platform; the speed planning is divided into three parts: 1. uniform motion at the maximum speed; 2. uniform motion at the minimum speed; 3. transition motion between the maximum speed and the minimum speed. The period of the piecewise speed function is T = 1 / 3s; the final parameterized expression of the speed is shown in equation (2):

[0022]

[0023] The constraints that need to be satisfied are shown in equation (3):

[0024]

[0025] Based on the above objective function and constraints, the optimal speed parameters of the moving platform are determined by solving the problem. The speeds of the slider and the moving platform are optimized using motion planning methods, and the robot's driving force before and after optimization is obtained by solving the problem.

[0026] The motion planning method for heavy-duty forming robots based on reducing joint impact vibration, as described in this invention, has the following beneficial effects:

[0027] 1. The method of this invention plans the input motion of the robot, reducing impact vibration during operation by lowering the speed at impact while ensuring work efficiency. This reduces the robot's dynamic error, achieves higher motion accuracy, and reduces the error of formed parts, showing significant application potential under heavy-duty conditions.

[0028] 2. Based on a dynamic model that considers gaps and deformation, this invention employs a motion planning method for heavy-duty forming robots that reduces joint impact vibration. An aircraft window frame forming experiment was conducted, and the error of the aircraft window frame was reduced by 35%, verifying the effectiveness of the motion planning method. Attached Figure Description

[0029] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0030] Figure 1 It is a kinematic model of a heavy-duty forming robot;

[0031] Figure 2 It is a dynamic model of a heavy-duty forming robot;

[0032] Figure 3 This is a graph showing the changes in driving force and driving speed of a heavy-duty forming robot.

[0033] Figure 4 This is a schematic diagram illustrating the planning of the robot's moving platform speed;

[0034] Figure 5 These are the speed diagrams of each slider on the robot before and after optimization;

[0035] Figure 6 This is a speed graph of the robot's moving platform before and after optimization;

[0036] Figure 7 It shows a comparison of driving force before and after optimization and a reduction rate graph;

[0037] Figure 8 It shows a comparison of impact force before and after optimization, as well as a reduction rate graph.

[0038] Figure 9 It shows a comparison of pose error before and after optimization and a reduction rate graph;

[0039] Figure 10 This is a schematic diagram showing the dimensions of an aircraft window frame component;

[0040] Figure 11 This is a comparison chart of experimental errors in the aircraft window frame before and after optimization. Detailed Implementation

[0041] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0042] The motion planning method for heavy-duty forming robots based on reducing joint impact vibration of the present invention includes the following steps:

[0043] S1. Establish the kinematic model of the heavy-duty forming robot.

[0044] The heavy-duty forming robot has six chains connecting the static and moving platforms. Each chain is connected via a guide rail-slider-ball joint-moving platform configuration. These sliders, ball joints, and moving platforms, totaling 13 components, together form the robot's kinematic model. Figure 1As shown, M1, M2, M3, M4, M5, and M6 are the centers of the ball joints on the sliders and connecting rods, while N1, N2, N3, N4, N5, and N6 are the centers of the ball joints on the lower part of the connecting rod. By coordinating the movement of the six sliders of the heavy-duty forming robot, the moving platform achieves the desired movement for part forming.

[0045] S2. Establish the dynamic model of the heavy-duty forming robot.

[0046] Based on the LN contact model and the discrete mass method, a dynamic model of the heavy-duty robot considering the clearance of the spherical joint and the deformation of the link is established using the Newton-Euler method, such as... Figure 2 As shown. The robot's generalized coordinates can be represented as: The generalized coordinates of the slider are s i =[x si ,y si ,0,0,0,0,] T , These represent the positions of the slider's center of mass in the x and y directions, respectively; the generalized coordinates of the upper and lower ends of the connecting rod are respectively represented as... This indicates the change in position of the upper mass block. This indicates the change in the angle of the upper mass block. This indicates the positional change of the lower mass block. This represents the angular change of the lower mass block; the generalized coordinates of the moving platform are p = [x] p ,y p ,z p ,α p ,β p ,γ p ] T x p ,y p ,z p α represents the change in position of the moving platform. p ,β p ,γ p This represents the angular change of the moving platform. Based on the positional relationships of the robot's components, each component is subjected to individual force analysis, ultimately yielding the overall dynamic equation, expressed as follows:

[0047]

[0048] In the formula, F Mi For the driving force of the slider, The contact force at the ball joint. F is the contact force at the lower ball joint. P External load force on the moving platform. and These are the stiffness matrix and damping matrix of the link, respectively, m S mL m p These represent the masses of the slider, connecting rod, and moving platform, respectively.

[0049] S3. Determine the dynamic error and generation mechanism of the heavy-duty forming robot.

[0050] The number of robot dynamics equations equals the number of unknown variables, and the system of equations is solvable. The dynamics model is solved using the Runge-Kutta method, considering the external load F on the moving platform. P = [0,0,6]MN, with the position of action r e =r e Given [sin(πt),cos(πt),0], with a spherical pair clearance of 0.1mm, the calculation is performed over a 2-second period with a step size of 0.001 seconds. Based on this setting, the dynamic error of the robot's moving platform is obtained. It is found that the dynamic error changes significantly at certain moments, exhibiting 12 abrupt changes within a 2-second period, demonstrating a certain periodicity.

[0051] Solving the dynamic equations yields the changes in driving force and driving speed, such as... Figure 3 As shown, both the red driving force curve and the blue velocity curve are periodic, with a period of 2 seconds. At certain moments, the driving force curve changes significantly, with all six branches undergoing abrupt changes at the same time, but with varying magnitudes. There are 12 abrupt changes within one driving force cycle.

[0052] By comparing the dynamic error and the impact force, it can be found that a total of 12 abrupt changes in error and impact force occurred within one cycle. Furthermore, the timing of the abrupt error changes coincides with the timing of the impact force in the driving force. This reveals the error generation mechanism under heavy load, namely, that the dynamic error of the moving platform is mainly generated by vibration and impact.

[0053] S4. Perform motion planning for the heavy-duty forming robot.

[0054] Because the errors in robot motion are periodic, motion planning is considered for impact moments where these errors have a significant impact. For heavy-duty forming robots, there is a mapping relationship between the slider input velocity and the moving platform output velocity, which can be represented by a Jacobian matrix. To achieve the ideal trajectory of the moving platform, the motion of each slider must be determined through inverse kinematics. Therefore, the problem is transformed into a velocity planning problem for the moving platform. The moving platform must meet the following conditions: 1. The stroke cycle must remain at 2 seconds per revolution. 2. The speed must not exceed the maximum speed provided by the motor. 3. The acceleration must not exceed the maximum acceleration provided by the motor. 4. The velocity curve must remain continuous. 5. The acceleration curve must remain continuous.

[0055] Given the relatively short time interval between impact points (0.12 seconds), to avoid frequent velocity changes, velocity planning involves maintaining a constant velocity within these time intervals. A piecewise function method is used to plan the velocity of the moving platform. The velocity planning consists of three parts: 1. Uniform motion at maximum speed, 2. Uniform motion at minimum speed, and 3. Transitional motion between maximum and minimum speeds, which can be expressed as follows: Figure 4 As shown. The period of the piecewise velocity function is T = 1 / 3 s. To ensure the continuity of velocity and acceleration during the transition phase, a cosine function is chosen as the transition velocity curve. The final parameterized expression of the velocity is shown in equation (2).

[0056]

[0057] In the expression, the parameters are t1, T3, T4, T5, π+v1, π-v2, among which there are six different variables. Since the moving platform completes a 2-second cycle of rotation with six such piecewise functions, there are a total of 36 variable parameters. The constraints that need to be satisfied are shown in equation (3).

[0058]

[0059] Based on the objective function and constraints described above, the optimal velocity parameters of the moving platform are determined, as shown in Table 1. The velocities of the slider and the moving platform optimized using the motion planning method are as follows: Figure 5 , Figure 6 As shown. The comparison of the robot's driving force before and after optimization is obtained by solving the problem. Figure 7 As shown in the figure, the comparison of the impact force on the robot joints before and after optimization is as follows: Figure 8 As shown in the figure. After optimization, the driving force and joint impact force of the six sliders were reduced, with better results and greater reductions in areas with higher forces. The pose errors before and after optimization are shown in the figure. Figure 9 As shown, the reduction rates in the x, y, z, α, β, and γ directions are 38.04%, 44.37%, 46.05%, 29.45%, 26.53%, and 48.47%, respectively.

[0060] Based on a dynamic model considering clearance and deformation under heavy-load conditions, a motion planning method for heavy-load robots is proposed to reduce joint impact vibration and improve robot motion accuracy. Using the proposed motion planning method, a forming experiment of an aircraft window frame is conducted on the heavy-load robot. The required steps include mounting the designed mold onto the robot and placing the machined blank onto the mold. After the required forming process, a coordinate measuring machine (CMM) is used to measure the various dimensional parameters of the aircraft window frame. The dimensional parameters of the aircraft window frame include the outer thickness and the inner thickness, such as... Figure 10As shown. The experiment was repeated multiple times, and the average of the repeated experimental data was taken as the final experimental result. The root mean square error of the aircraft window frame size between the unoptimized and optimized versions was compared, as shown. Figure 11 As shown, the outer thickness error was reduced by 36.53%, and the inner thickness error was reduced by 33.65%, indicating that the proposed motion planning method is feasible in improving robot accuracy.

[0061] Table 1. Optimized speed parameters of the moving platform

[0062]

[0063] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A motion planning method for heavy-duty forming robots based on reducing joint impact vibration, characterized in that, Includes the following steps: S1. Establish the kinematic model of the heavy-duty forming robot; S2. Establish a dynamic model of the heavy-duty forming robot; S3. Determine the dynamic error and generation mechanism of the heavy-duty forming robot; S4. Perform motion planning for the heavy-duty forming robot.

2. The motion planning method for heavy-duty forming robots based on reducing joint impact vibration according to claim 1, characterized in that, The heavy-duty forming robot includes six sets of branches connecting the static platform and the moving platform. Each branch is connected by a guide rail-slider-ball joint-moving platform. The slider, ball joint, and moving platform together form thirteen components, which constitute the kinematic model of the heavy-duty forming robot.

3. The motion planning method for heavy-duty forming robots based on reducing joint impact vibration according to claim 2, characterized in that, In step S2, based on the LN contact model and the discrete mass method, a dynamic model of the heavy-duty robot considering the spherical joint clearance and link deformation is established using the Newton-Euler method.

4. The motion planning method for heavy-duty forming robots based on reducing joint impact vibration according to claim 3, characterized in that, In step S2, the robot's generalized coordinates are represented as: The generalized coordinates of the slider in the formula are s i =[x si ,y si ,0,0,0,0,] T , These represent the positions of the slider's center of mass in the x and y directions, respectively; the generalized coordinates of the upper and lower ends of the connecting rod are respectively represented as... This indicates the change in position of the upper mass block. This indicates the change in the angle of the upper mass block. This indicates the positional change of the lower mass block. This represents the angular change of the lower mass block; the generalized coordinates of the moving platform are p = [x] p ,y p ,z p ,α p ,β p ,γ p ] T x p ,y p ,z p α represents the positional change of the moving platform. p ,β p ,γ p This indicates the change in the angle of the moving platform.

5. The motion planning method for heavy-duty forming robots based on reducing joint impact vibration according to claim 4, characterized in that, In step S2, based on the positional relationships of the robot's components, each component is subjected to individual force analysis, and the final overall dynamic equation is obtained as follows: In the formula, F Mi For the driving force of the slider, The contact force at the ball joint. F is the contact force at the lower ball joint. P External load force on the moving platform. and These are the stiffness matrix and damping matrix of the link, respectively, m S m L m p These represent the masses of the slider, connecting rod, and moving platform, respectively.

6. The motion planning method for heavy-duty forming robots based on reducing joint impact vibration according to claim 5, characterized in that, In step S3, the dynamic model is solved using the Runge-Kutta method, and the external load force F of the moving platform is determined. P = [0,0,6]MN, with the position of action r e =r e [sin(πt),cos(πt),0].

7. The motion planning method for heavy-duty forming robot based on reducing joint impact vibration according to claim 6, characterized in that, In step S3, the driving force curve and velocity curve are obtained by solving the dynamic equation, and both are periodic.

8. The motion planning method for heavy-duty forming robots based on reducing joint impact vibration according to claim 6, characterized in that, In step S3, based on the comparison between dynamic error and impact force, the moment when the error changes abruptly within a cycle coincides with the moment when the impact force in the driving force occurs. The error generation mechanism under heavy load is that the dynamic error of the moving platform is generated by vibration and impact.

9. The motion planning method for heavy-duty forming robots based on reducing joint impact vibration according to claim 8, characterized in that, In step S4, since the error changes during robot motion are periodic, motion planning is considered for impact moments when these errors have a significant impact. For heavy-duty forming robots, there is a mapping relationship between the slider input speed and the moving platform output speed, which is represented by the Jacobian matrix.

10. The motion planning method for heavy-duty forming robots based on reducing joint impact vibration according to claim 8, characterized in that, In step S4, the piecewise function method is used to plan the velocity of the moving platform; the velocity planning is divided into three parts:

1. uniform motion at maximum speed; 2. uniform motion at minimum speed; 3. The transition motion between the maximum and minimum speeds has a period of T = 1 / 3 s for the piecewise velocity function; the final parameterized expression of the velocity is shown in equation (2): The constraints that need to be satisfied are shown in equation (3): Based on the above objective function and constraints, the optimal speed parameters of the moving platform are determined by solving the problem. The speeds of the slider and the moving platform are optimized using motion planning methods, and the robot's driving force before and after optimization is obtained by solving the problem.

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