Metal plate bending robot path optimization method, system and equipment based on five-order Bezier curve
By optimizing the sheet metal bending robot path using fifth-order Bézier curves, the vibration and energy consumption problems in traditional fifth-order polynomial trajectory planning are solved, resulting in a smoother and more efficient sheet metal bending process and improving the flexibility and accuracy of robot path planning.
Patent Information
- Application Number
- CN202511984597.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-26
- Publication Date
- 2026-02-24
AI Technical Summary
Traditional quintic polynomial trajectory planning methods suffer from problems such as vibration caused by sudden acceleration changes, increased energy consumption, and insufficient planning flexibility in high-precision and high-stability sheet metal bending tasks.
Fifth-order Bézier curves are used for trajectory planning. By generating intermediate control points with an asymmetric layout, the velocity and acceleration in the initial and final stages are ensured to approach zero, and the peak acceleration during the motion process is reduced. Combined with multi-coordinate system environment modeling and inverse kinematics solution, the robot path is optimized.
It significantly improves trajectory smoothness, suppresses mechanical vibration, reduces energy consumption, and enhances the flexibility and accuracy of complex path planning, extends equipment life, and strengthens the adaptability of robot operations.
Smart Images
Figure CN121552368A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of robot path optimization technology, and more specifically to a method, system and equipment for optimizing the path of a sheet metal bending robot based on a fifth-order Bézier curve. Background Technology
[0002] Currently, with the increasing maturity of robotics technology, higher and higher requirements are being placed on the control precision and stability of robots. It is not only necessary to enable robots to complete simple trajectory formation, but also in some high-precision fields, robots are required to achieve smaller errors, lower energy consumption, and more stable operation. This requires robots to further optimize trajectories at the trajectory planning level.
[0003] However, in practical applications, especially for sheet metal bending tasks requiring high precision and stability, the traditional fifth-order polynomial trajectory planning method still has significant limitations. First, under complex paths or dynamic constraints, this method is prone to sudden acceleration changes, leading to severe vibrations in the robotic arm. This vibration not only affects the bending accuracy of the sheet metal parts, causing a decrease in workpiece surface quality, but also impacts the robot body and bending dies, shortening equipment lifespan. Second, sudden acceleration changes mean that the joint motors need to output larger peak torques, leading to increased energy consumption. Furthermore, the flexibility of the fifth-order polynomial trajectory is limited. When faced with complex bending processes requiring real-time adjustment of tool posture or obstacle avoidance, its adjustment capability is insufficient, often necessitating the division of the entire trajectory into multiple sub-segments for planning, increasing control complexity.
[0004] Therefore, how to provide a new method for robot path planning that can further optimize trajectory smoothness, effectively suppress vibration, reduce energy consumption, and have greater planning flexibility is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0005] In view of this, the present invention provides a method, system and equipment for optimizing the path of sheet metal bending robots based on fifth-order Bézier curves, in order to meet the higher requirements of modern intelligent manufacturing for sheet metal bending processes.
[0006] To achieve the above objectives, the present invention adopts the following technical solution: A path optimization method for sheet metal bending robots based on fifth-order Bézier curves includes: S1: Based on the working environment of sheet metal bending tasks, establish a multi-coordinate system environment model including tool coordinate system and multiple user coordinate systems, and determine multiple key path points that the robot needs to pass through when performing bending tasks. S2: Based on the pose of the key path points, the joint angles corresponding to each key path point are obtained by using the inverse kinematics equations of the robot. S3: For a path segment formed by two adjacent critical path points, a fifth-order Bézier curve is used for trajectory planning in the joint space based on the joint angle; wherein, the start and end control points of the fifth-order Bézier curve are determined by the joint angle of the two adjacent critical path points. S4: According to the preset asymmetric layout rules, generate the intermediate control points of the fifth-order Bézier curve, so that the robot has a speed and acceleration that tend to be zero at the beginning and end of the path segment, and reduce the peak acceleration during the motion process. S5: Calculate the motion trajectory of each joint of the robot based on the generated fifth-order Bézier curve, and drive the robot to move along the motion trajectory.
[0007] Furthermore, in S3, the beginning and end control points are:
[0008] In the formula, j represents the trajectory of the j-th joint, and the first and last control points are respectively... and .
[0009] Furthermore, in S4, intermediate control points are generated according to the following rules:
[0010]
[0011]
[0012]
[0013] Velocity and acceleration approach zero at the boundaries of motion:
[0014] In the formula, Indicates intermediate control points, where, and Closer to the start and finish lines, This represents the coordinate increment from the start point to the end point of the j-th joint. , and These are the coordinates of the starting point and the ending point, respectively.
[0015] Furthermore, the parameterized equation of the fifth-order Bézier curve is:
[0016] in, Let t be the number of combinations, and t be the normalized time parameter; Each control point P iThe degree of influence on the curve is determined by the Bernstein basis functions. Decide.
[0017] Furthermore, the motion velocity, acceleration, and jerk of the robot joints are calculated using the first, second, and third derivatives of the fifth-order Bézier curve, respectively, with the following expressions:
[0018]
[0019]
[0020] In the formula, t is the normalized time parameter. These are the coordinates of the three-dimensional control points.
[0021] Furthermore, in step S3, the fifth-order Bézier curve is extended to a three-dimensional Cartesian space to plan the motion path of the robot end effector in three-dimensional space.
[0022] Furthermore, the expression for extending the fifth-order Bézier curve to three-dimensional Cartesian space is as follows:
[0023] Where P i = (x i ,y i ,z i () represents the coordinates of the three-dimensional control point.
[0024] A path optimization system for sheet metal bending robots based on fifth-order Bézier curves, comprising: The environment modeling module is used to establish the multi-coordinate system environment model and determine the key path points; The inverse kinematics solution module is used to calculate the joint angles of each joint of the robot based on the pose of the key path points. The trajectory planning module is used to generate smooth motion trajectories of each joint of the robot based on the joint angle using a fifth-order Bézier curve. The trajectory planning module has a built-in control point generation unit, which is used to execute the asymmetric layout rules to generate intermediate control points. A motion control module is used to drive the robot to move according to the smooth motion trajectory.
[0025] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a path optimization method for sheet metal bending robots based on fifth-order Bézier curves.
[0026] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method, system, and device for optimizing the path of a sheet metal bending robot based on a fifth-order Bézier curve, which can significantly improve trajectory smoothness, effectively suppress mechanical vibration, reduce energy consumption, and improve the flexibility of complex bending path planning. It has the following beneficial effects: (1) This invention uses a fifth-order Bézier curve for trajectory planning, which ensures the continuity of position, velocity, acceleration, and even jerk. Through simulation verification, compared with the traditional fifth-order polynomial, the trajectory planned by this invention has a smoother acceleration curve without abrupt changes. This effectively suppresses the mechanical vibration of the robot during the movement process, which not only improves the forming accuracy and surface quality of sheet metal bending, but also reduces the impact on the robot body and extends the service life of the equipment.
[0027] (2) By generating intermediate control points through specific asymmetric layout rules, this invention can optimize the trajectory shape, thereby significantly reducing the peak joint velocity and acceleration of the robot during movement. The reduction in peak load directly means a reduction in the output torque required by the joint motors, thus reducing the overall energy consumption of the machine, which is in line with the development concept of green manufacturing.
[0028] (3) The fifth-order Bézier curve has multiple intermediate control points. By adjusting the position of these control points, the shape of the entire trajectory can be flexibly adjusted without changing the start and end points. This feature enables the present invention to easily handle complex bending tasks, such as flexibly adjusting the posture of the end effector to avoid interference from the bending machine mold, or generating different optimized paths for multiple bends of the same sheet metal part, which greatly enhances the robot's operational adaptability and intelligence level.
[0029] (4) This invention is not an isolated algorithm, but rather a complete technical solution that integrates multi-coordinate system environment modeling, inverse kinematics calculation of critical path points, and Bézier curve optimization planning. This system systematically combines path optimization algorithms with the robot's kinematic model and working environment, forming an effective engineering solution that is easy to integrate into existing industrial robot control systems and has high practical value and promising prospects for promotion. Attached Figure Description
[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0031] Figure 1 This is a schematic diagram of the method flow provided by the present invention; Figure 2 This is a schematic diagram of the system structure provided by the present invention; Figure 3(a) is a schematic diagram of the first bending process; Figure 3(b) is a schematic diagram of the second bending process; Figure 3(c) is a schematic diagram of the third bending process; Figure 4 The figure shows the simulation results of the fifth-order polynomial provided in Embodiment 2 of the present invention; Figure 5 A comparison diagram of the trajectory of a fifth-order polynomial and a Bézier curve provided in Embodiment 2 of the present invention; Figure 6 This is a comparison diagram of the velocity acceleration of a fifth-order polynomial and a Bézier curve provided in Embodiment 2 of the present invention; Figure 7 This is a comparison chart of maximum speed and acceleration provided for Embodiment 2 of the present invention. Detailed Implementation
[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0033] See Figure 1 Embodiment 1 of this invention discloses a path optimization method for sheet metal bending robots based on fifth-order Bézier curves, comprising: S1: Based on the working environment of sheet metal bending tasks, establish a multi-coordinate system environment model including tool coordinate system and multiple user coordinate systems, and determine multiple key path points that the robot needs to pass through when performing bending tasks. S2: Based on the pose of the key path points, the joint angles corresponding to each key path point are obtained by using the inverse kinematics equations of the robot. S3: For a path segment formed by two adjacent critical path points, a fifth-order Bézier curve is used for trajectory planning in the joint space based on the joint angle; wherein, the start and end control points of the fifth-order Bézier curve are determined by the joint angle of the two adjacent critical path points. S4: According to the preset asymmetric layout rules, generate the intermediate control points of the fifth-order Bézier curve, so that the robot has a speed and acceleration that tend to be zero at the beginning and end of the path segment, and reduce the peak acceleration during the motion process. S5: Calculate the motion trajectory of each joint of the robot based on the generated fifth-order Bézier curve, and drive the robot to move along the motion trajectory.
[0034] Specifically, a fifth-order Bézier curve has six control points. If the starting and ending points are fixed, trajectory planning in complex environments can be achieved by adjusting the intermediate control points. Therefore, it has a greater advantage in spatial path planning for six-axis robots. Moreover, the fifth-order Bézier curve has a higher degree, and by adjusting the control points, third-order continuity of position, velocity, and acceleration can be achieved, thereby achieving the stability of the robot during operation.
[0035] Specifically, a fifth-order Bézier curve is defined by six control points, and its parameterized equation is:
[0036] in, Let t be the number of combinations, and t be the normalized time parameter.
[0037] Each control point P i The degree of influence on the curve is determined by the Bernstein basis functions. Decide.
[0038] The characteristic of this weighting function is that when t is close to 0, only P0 has the largest weight; when t is close to 1, only P5 has the largest weight; and the weights of the intermediate control points P1-P4 reach their peak at a specific t value.
[0039] The expressions for the horizontal and vertical coordinate components need to be developed in detail, and their continuity and smoothness need to be analyzed. Curvature smoothness refers to the continuous change of curvature of the fifth-order curve, which avoids the abrupt changes of lower-order curves and is suitable for the robot's requirements for steering stability. The influence of control points refers to the fact that intermediate control points (P1, P2, P3, P4) adjust the curve shape through weights to achieve path obstacle avoidance and trajectory optimization.
[0040] Specifically, the velocity, acceleration, and jerk of a fifth-order Bézier curve can be obtained by successive differentiation:
[0041]
[0042]
[0043] The fifth-order curve can ensure continuous acceleration and significantly reduce the risk of mechanical vibration.
[0044] For robot path planning in Cartesian space, the Bézier curve needs to be extended to three dimensions:
[0045] Where P i = (x i ,y i ,z i() represents the coordinates of the three-dimensional control point.
[0046] Specifically, initial control points are set according to the sheet metal bending process path (key points such as gripping, centering, and bending). Now we will discuss the first segment of the sheet metal bending process, from the gripping preparation point to the centering table unloading point.
[0047] For the trajectory of the j-th joint, first define
[0048] The beginning and end control points are:
[0049] Intermediate control points are generated according to the following rules:
[0050]
[0051]
[0052]
[0053] This design places P1 and P4 close to the start and end points, limiting the amplitude of motion in the initial and final phases, and ensuring that velocity and acceleration approach zero at the motion boundaries.
[0054] The P2 and P3 points in the middle are set far from the boundary points, allowing for a larger range of motion in the middle stage. This asymmetrical layout can reduce the peak maximum acceleration by about 30-40% and avoid the abrupt change of the fifth polynomial in the middle.
[0055] Furthermore, the shape of the Bézier curve can be controlled by adjusting the scaling factor to achieve more different motion trajectories, and the position of the control point can be adjusted to achieve more complex motions.
[0056] Specifically, path planning and design include: First, based on the sheet metal bending process, key path points are identified using feature extraction algorithms, including the coordinates of important positions such as gripping points, centering points, and bending points. These key points constitute the basic framework of robot motion, laying the foundation for subsequent trajectory planning. The coordinates of these path points are transformed into a unified expression through a homogeneous transformation matrix to obtain the homogeneous matrix of the corresponding end effector. Then, inverse kinematics is used to solve for the joint angles of each joint at the corresponding path point.
[0057] Specifically, the robot used in this embodiment is the ER80-2600 robot. The coordinates of the path points are obtained through the defined coordinate system transformation rules, including: The DH parameters of the ER80-2600 robot are shown in Table 1.
[0058] Table 1. Parameters of ER80-2600 Robot DH
[0059] Table 1 shows the robot's link parameters and joint angles. The relationship between adjacent links is described using a homogeneous transformation matrix. Using the coordinate position of link i relative to the coordinate position of link i-1, we can obtain... The general formula for transformation is as follows:
[0060] The transformation matrices between the links of the robot are obtained as follows:
[0061]
[0062]
[0063] By multiplying the homogeneous transformation matrices between the links of the ER80-2600 robot, the following transformation matrix can be obtained: (1)
[0064] in:
[0065] This formula represents the transformation matrix of the ER80-2600 robot, which describes the transformation relationship between the robot's end coordinate system and the base coordinate system. Equation (1) is the result of the forward kinematics solution.
[0066] Trajectory generation is the core component, primarily implementing spatial path construction based on fifth-order Bézier curves. This layer employs an adaptive control point optimization algorithm, dynamically adjusting control point positions according to actual working conditions to ensure that the generated trajectory meets both geometric and dynamic requirements. The trajectory generation layer uses fifth-order Bézier curves as the core planning tool, and its control point distribution strategy utilizes the boundary conditions of a fifth-order polynomial trajectory to ensure the continuity of velocity and acceleration between the starting and ending points.
[0067] Specifically, the control point distribution strategy for the boundary condition design of a quintic polynomial trajectory includes: When creating an environmental model for a sheet metal bending robot, the entire processing environment can be considered as a three-dimensional space, and a specific model needs to be created for each component in the working environment. Since some models have complex structures, key components can be simplified into geometric shapes, and their positions and orientations can be described using a coordinate system. This not only reduces the modeling difficulty but also ensures the accuracy of the robot's working environment modeling. A simple 3D model of the environment is created by measuring the dimensions of relevant components within the bending robot's working environment.
[0068] Establishing a corresponding coordinate system is fundamental to path planning and motion control for robots. This mainly involves establishing two coordinate systems: the user coordinate system and the tool coordinate system.
[0069] The user coordinate system describes the robot's global position in the workspace and is a coordinate system relative to the robot's base. Establishing the user coordinate system requires consideration of the machining environment layout; it is typically based on a fixed point as the origin, with the X, Y, and Z axes corresponding to the length, width, and height of the workspace, respectively.
[0070] The tool coordinate system is a coordinate system relative to the robot's end effector, used to describe the tool's position and orientation. Establishing the tool coordinate system requires considering the tool's geometry and motion characteristics. Typically, the origin is the tool's center point, and the X, Y, and Z axes correspond to the tool's front, left, and top directions, respectively.
[0071] Using these two coordinate systems, the robot's motion can be decomposed into global motion and local motion. Global motion is described by the user coordinate system, and local motion is described by the tool coordinate system. This decomposition method simplifies path planning, making the robot's motion more flexible and precise. The robot's end-effector pose in the world coordinate system can be determined using an intermediate matrix. It is derived from transformation.
[0072]
[0073] in , , It is the angle of rotation of the world coordinate axes about the X, Y, and Z axes.
[0074] (1) Suction Cup Tool Coordinate System
[0075] During operation, the sheet metal part is held by a suction cup and undergoes a series of bending processes. The midpoint of its suction surface is set as the origin Os. The transformation matrix between its coordinate system and the robot's end effector coordinate system is:
[0076] User coordinate system for picking and unloading platforms
[0077] The user coordinate system for the material handling platform is Od, and the user coordinate system for the material unloading platform is Og. The conversion to the world coordinate system is as follows:
[0078] For the middle platform user coordinate system
[0079] The user coordinate system for the central platform is Oh, with the lowest point of the platform surface as the origin. The X and Y axes coincide with the platform surface, and the Z axis is in the direction perpendicular to the platform surface upwards. Its transformation to world coordinates is as follows:
[0080] Bending machine user coordinate system
[0081] The user coordinate system for the bending machine is Ok, where the center point of the lower die is the origin, and the matrix of the robot's end effector suction cup in the world coordinate system is:
[0082] The generation of path points includes: In the feeding process, the robot needs to move the sheet metal from its initial position to the bending position. To achieve this, a series of path points need to be generated, which describe the key positions of the robot during its movement.
[0083] During the bending process, the robot needs to pass through the following path points in sequence. First, after completing the previous bending process, the robot is at the gripping preparation point. Then, it falls to the gripping point, and after the suction cup picks up the sheet metal, the robot moves to the centering platform to prepare for centering. Above the centering platform, the robot releases the suction cup from the sheet metal, allowing it to fall freely onto the centering platform. The sheet metal will be centered due to the shape of the centering platform. Then, the robot descends to pick up the centered sheet metal and moves to the bending preparation point of the bending machine for bending. Next, it moves to the bending completion point, and finally, the robot moves to the unloading point of the unloading table to complete the bending process. During the bending process, a sheet metal can be bent multiple times. After completing the first bend, the robot can rotate and translate to perform a second bend, a third bend, and so on after moving to the bending completion point. However, the manufacturability of the bent part must be considered.
[0084] The critical path points in the bending process are: 1. Grip preparation point; 2. Grip point; 3. Centering preparation point; 4. Centering completion point; 5. Bending preparation point; 6. Bending completion point; 7. Unloading point. Schematic diagrams of the bending process points are shown in Figures 3(a)-3(c).
[0085] The transformation matrices can be obtained from the coordinate system information of the end effector on the robot teach pendant.
[0086] The transformation matrix T between the robot's end effector suction cup and the flange coordinate system. s for:
[0087] The transformation matrix of the loading and unloading platform is:
[0088] The RPY rotation angles between the central platform coordinate system and the world coordinate system are -89.576°, -29.967°, and 41.113°, respectively. The transformation matrix for the central platform is:
[0089] The transformation matrix of the bending machine is:
[0090] Sheet metal bending robots need to plan collision-free, efficient motion trajectories that meet process requirements within complex workpiece geometries and limited workspaces. This also requires considering robot kinematic constraints, tool posture adjustments, and bending sequence optimization. In sheet metal bending scenarios, path planning not only needs to avoid collisions between the robot and workpieces, fixtures, or environmental obstacles, but also needs to optimize the bending sequence to reduce idle travel time and improve production efficiency.
[0091] In the field of sheet metal robot trajectory planning, fifth-order polynomial trajectory planning has significant advantages in motion smoothness and constraint adaptability, making it a key technology for improving bending accuracy and efficiency. Sheet metal bending processes require robotic arms to achieve precise positioning under complex geometric constraints, while also ensuring the continuity of speed and acceleration during movement to minimize workpiece deformation and wear on related equipment caused by vibration or impact. Fifth-order polynomials can generate continuous and smooth joint space trajectories by freely setting boundary conditions such as speed and acceleration at the start and end points, avoiding mechanical vibration problems caused by sudden acceleration changes compared to traditional cubic polynomials. By adjusting the coefficients, the motion characteristics of the robotic arm during bending can be precisely controlled, achieving smooth acceleration and deceleration at the beginning and end of the bending process, while maintaining efficient and uniform speed in the middle stages, thereby reducing idle travel time and improving cycle time.
[0092] When machining sheet metal parts, the sheet metal material will spring back. Fifth-order polynomial programming can further optimize the bending path and dynamically compensate for machining errors. Moreover, with the increasing sophistication of real-time trajectory correction algorithms and digital twin technology, fifth-order polynomial programming can also provide core support for sheet metal bending robots to achieve high-precision, high-flexibility, and intelligent machining, becoming an important technical path for industrial automation upgrades.
[0093] Specifically, control point optimization is a crucial step in the application of fifth-order Bézier curves. Intermediate control points are distributed proportionally within Cartesian space. During the initial control point generation stage, the system uses linear interpolation to evenly distribute intermediate control points between the start and end points. In practice, the displacement vector from the start to the end point is first calculated, and then the offset of each control point is determined according to a preset proportional coefficient. Intermediate points are offset along the normal direction of the sheet metal plane to avoid interference with the bending die. This generation method ensures a smooth curve transition while reserving sufficient adjustment space for subsequent optimization.
[0094] See Figure 2 On the other hand, Embodiment 1 of the present invention also discloses a sheet metal bending robot path optimization system based on a fifth-order Bézier curve, comprising: The environment modeling module is used to establish the multi-coordinate system environment model and determine the key path points; The inverse kinematics solution module is used to calculate the joint angles of each joint of the robot based on the pose of the key path points. The trajectory planning module is used to generate smooth motion trajectories of each joint of the robot based on the joint angle using a fifth-order Bézier curve. The trajectory planning module has a built-in control point generation unit, which is used to execute the asymmetric layout rules to generate intermediate control points. A motion control module is used to drive the robot to move according to the smooth motion trajectory.
[0095] In another aspect, Embodiment 1 of the present invention also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a path optimization method for sheet metal bending robots based on a fifth-order Bézier curve.
[0096] Example 2: To verify the effectiveness of the sheet metal bending robot path optimization method based on fifth-order Bézier curves provided by this invention, this embodiment 2 uses MATLAB for simulation analysis.
[0097] Simulation settings:
[0098] Robot Model: The ER80-2600 bending robot was used, and the kinematic model was established based on the DH parameters as shown below.
[0099] Simulation environment: Set initial and target points, generate intermediate path points. The path generation method for fifth-degree polynomials differs from that for Bézier curves, as shown below: Path point generation for quintic polynomials:
[0100] Path point generation for Bézier curves:
[0101] The above procedures show that the bending robot takes 5 seconds to run this section. The fifth-order polynomial generates 50 interpolation points between the starting and ending points, and the Bezier curve generates four control points in the middle to control the trajectory.
[0102] Because calculating the trajectory of a fifth-order Bézier curve is quite complex, it requires specialized code, as shown below:
[0103] First, a fifth-order polynomial is simulated and the corresponding simulation results are obtained. Then, a segment of the trajectory is simulated using a fifth-order Bézier curve to compare the simulation results and observe the advantages and disadvantages of the two path optimization methods.
[0104] The complete code for the quintic polynomial is as follows:
[0105] The simulation results of the fifth-order polynomial are a real-time image of a robot's trajectory and its position, velocity, and acceleration at corresponding times, such as... Figure 4 As shown.
[0106] Then, the simulation results of the fifth-order Bézier curve are compared with those of the fifth-order polynomial. First, the trajector trajector of the end effector planned by the fifth-order Bézier curve and the fifth-order polynomial trajectory are compared. Figure 5 As shown
[0107] Finally, the path planning for the sheet metal bending robot using Bézier curves and quintic polynomial programming was implemented via MATLAB code. A comparison of the velocities and accelerations of each joint is shown in the figure below. Figure 6 As shown.
[0108] Through observation Figure 4-6 The information shown clearly demonstrates that the fifth-order Bézier curve outperforms the fifth-order polynomial in several aspects of path planning for sheet metal bending robots.
[0109] Firstly, the trajectory of the robot's end effector shows that the fifth-order Bézier curve is smoother, resulting in smaller operating angles for each joint, thus reducing energy consumption and improving energy efficiency. Secondly, comparing the joint velocities of the fifth-order polynomial and the fifth-order Bézier curve, it is clear that the velocities of each joint in the trajectory planned by the fifth-order Bézier curve are smoother, and the peak velocities are significantly lower than those in the fifth-order polynomial. Finally, the joint accelerations of the trajectory planned by the fifth-order Bézier curve are also significantly smoother than those of the fifth-order polynomial, and the peak accelerations are also lower. This makes the robot run more smoothly and reduces mechanical vibration. Furthermore, for more complex bending tasks, the fifth-order polynomial may not be sufficient. It might be necessary to divide the path into multiple segments and use the fifth-order polynomial for path planning for each segment. The intermediate control points of the fifth-order Bézier curve can be adjusted in real time according to different work routes, making it a more flexible planning method for complex and varied path planning to meet work needs. By combining Bézier curves with other path planning methods, functions such as real-time obstacle avoidance can also be achieved. Specific comparison results are shown below. Figure 7 As shown.
[0110] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.
[0111] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A path optimization method for sheet metal bending robots based on fifth-order Bézier curves, characterized in that, include: S1: Based on the working environment of sheet metal bending tasks, establish a multi-coordinate system environment model including tool coordinate system and multiple user coordinate systems, and determine multiple key path points that the robot needs to pass through when performing bending tasks. S2: Based on the pose of the key path points, the joint angles corresponding to each key path point are obtained by using the inverse kinematics equations of the robot. S3: For a path segment formed by two adjacent critical path points, a fifth-order Bézier curve is used for trajectory planning in the joint space based on the joint angle; wherein, the start and end control points of the fifth-order Bézier curve are determined by the joint angle of the two adjacent critical path points. S4: According to the preset asymmetric layout rules, generate the intermediate control points of the fifth-order Bézier curve, so that the robot has a speed and acceleration that tend to be zero at the beginning and end of the path segment, and reduce the peak acceleration during the motion process. S5: Calculate the motion trajectory of each joint of the robot based on the generated fifth-order Bézier curve, and drive the robot to move along the motion trajectory.
2. The method for optimizing the path of a sheet metal bending robot based on a fifth-order Bézier curve according to claim 1, characterized in that, In S3, the first and last control points are: In the formula, j represents the trajectory of the j-th joint, and the first and last control points are respectively... and .
3. The method for optimizing the path of a sheet metal bending robot based on a fifth-order Bézier curve according to claim 1, characterized in that, In S4, intermediate control points are generated according to the following rules: Velocity and acceleration approach zero at the boundaries of motion: In the formula, Indicates intermediate control points, where, and Closer to the start and finish lines, This represents the coordinate increment from the start point to the end point of the j-th joint. , and These are the coordinates of the starting point and the ending point, respectively.
4. The method for optimizing the path of a sheet metal bending robot based on a fifth-order Bézier curve according to claim 1, characterized in that, The parameterized equation of the fifth-order Bézier curve is: in, Let t be the number of combinations, and t be the normalized time parameter; Each control point P i The degree of influence on the curve is determined by the Bernstein basis functions. Decide.
5. The method for optimizing the path of a sheet metal bending robot based on a fifth-order Bézier curve according to claim 3, characterized in that, Using the first, second, and third derivatives of the fifth-order Bézier curve, the motion velocity, acceleration, and jerk of the robot joints are calculated respectively, with the following expressions: In the formula, t is the normalized time parameter. These are the coordinates of the three-dimensional control points.
6. The method for optimizing the path of a sheet metal bending robot based on a fifth-order Bézier curve according to claim 1, characterized in that, In step S3, the fifth-order Bézier curve is extended to a three-dimensional Cartesian space to plan the motion path of the robot end effector in three-dimensional space.
7. The method for optimizing the path of a sheet metal bending robot based on a fifth-order Bézier curve according to claim 6, characterized in that, The expression for extending the fifth-order Bézier curve to three-dimensional Cartesian space is: Where P i = (x i ,y i ,z i () represents the coordinates of the three-dimensional control point.
8. A sheet metal bending robot path optimization system for implementing the method as described in any one of claims 1 to 7, characterized in that, include: The environment modeling module is used to establish the multi-coordinate system environment model and determine the key path points; The inverse kinematics solution module is used to calculate the joint angles of each joint of the robot based on the pose of the key path points. The trajectory planning module is used to generate smooth motion trajectories of each joint of the robot based on the joint angle using a fifth-order Bézier curve. The trajectory planning module has a built-in control point generation unit, which is used to execute the asymmetric layout rules to generate intermediate control points. A motion control module is used to drive the robot to move according to the smooth motion trajectory.
9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a sheet metal bending robot path optimization method based on a fifth-order Bézier curve as described in any one of claims 1 to 7.