Redundancy allocation and rigidity enhancement method and system based on task space stochastic optimization

Abstract

The invention discloses a redundancy allocation and rigidity enhancement method and system based on task space stochastic optimization, and is applied to the technical field of robot intelligent manufacturing and trajectory planning. The method comprises the following steps: performing task space redundancy parameterization on a given discrete path point sequence, and constructing a tail end attitude family meeting tail end position constraint; the multiple candidate redundant sequences are disturbed through zero-mean-value Gaussian, the weight of each candidate sequence is calculated, the weighted expectation of disturbance is solved, and iterative updating optimization is carried out; calculating a multi-target composite cost based on the joint configuration corresponding to each path point; s curve time parameterization is carried out, smooth interpolation of the tail end position and the posture is carried out at each interpolation time point, and finally a joint track sequence is obtained through inverse kinematics solving. According to the method, on the premise of strict path tracking, redundant parameters are globally and continuously optimized, rigidity maximization and singularity avoidance are both considered, seamless coupling with S curve time parameterization is achieved, and a high-implementability track capable of being directly issued is output.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and trajectory planning technology for robots, and more specifically to a method and system for redundancy allocation and stiffness enhancement based on task space stochastic optimization. Background Technology

[0002] Six-axis industrial robots are widely used for milling and surface machining of large and complex surfaces due to their large workspace and flexible arrangement. However, compared with computer numerical control (CNC), industrial robots have inherent shortcomings such as low body structural stiffness and strong attitude dependence, which makes end-effector displacement, vibration and texture defects induced by cutting forces more likely to occur, thus affecting dimensional accuracy and surface quality. At the same time, although the existence of redundant degrees of freedom can bring better attitude selection, existing joint space trajectory optimization methods (such as CHOMP, STOMP, etc.) are prone to getting trapped in local optima in high-dimensional, multi-objective, and non-convex cost landscapes, and it is difficult to simultaneously ensure strict path tracking and global continuity of redundancy; methods based on discrete point angle search often produce joint trajectory discontinuity problems, which are not conducive to actual execution and drive safety.

[0003] Therefore, existing six-axis industrial robots still have the following shortcomings: 1. Stiffness deterioration: The lack of redundancy distribution for machining stiffness throughout the process results in significant fluctuations in end-effector stiffness at different configurations along the path, which can easily lead to vibration and surface defects. 2. Singular / Near-singular risk: Failure to systematically move away from singular regions while maintaining pose constraints can lead to Jacobian matrix degradation, velocity amplification, and control instability. 3. Insufficient trajectory continuity: Independent optimization of discrete points causes sudden pulses in joint angles, making it difficult to meet the execution requirements of smooth acceleration and deceleration.

[0004] Therefore, how to provide a method and system for redundancy allocation and stiffness enhancement based on task space stochastic optimization 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 redundancy allocation and stiffness enhancement method and system based on task space stochastic optimization. Under the premise of strict path tracking, the redundancy parameters are globally and continuously optimized to balance stiffness maximization and singularity avoidance. It is also seamlessly coupled with S-curve time parameterization to output a highly feasible trajectory that can be directly deployed.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for redundancy allocation and stiffness enhancement based on task space stochastic optimization includes the following steps: S1 receives discrete path point sequences, machine tool parameters, robot parameters, speed limit data, acceleration limit data, and joint limit data; S2. Perform task space redundancy parameterization on the given discrete path point sequence, introduce a redundant rotation angle for each path point, construct an end pose family that satisfies the end position constraint, and transform the joint space constrained optimization into the task space unconstrained optimization. S3. Use zero-mean Gaussian perturbation to perturb multiple candidate redundant sequences, calculate the weight of each candidate sequence, calculate the weighted expectation of the perturbation to estimate the descent direction, and iteratively update and optimize the candidate redundant sequences until the convergence condition is met. S4. Calculate the multi-objective composite cost based on the joint configuration corresponding to each path point, including stiffness cost and singular cost; S5. Perform S-curve time parameterization on the optimized geometric path, apply velocity, acceleration and jerk constraints, perform smooth interpolation of end position and attitude at each interpolation time point, and finally obtain a continuous and executable joint trajectory sequence by solving inverse kinematics. S6. Convert the joint trajectory sequence into an executable instruction stream from the robot controller ROS interface and send it down for execution.

[0007] Optionally, the objective function for unconstrained optimization of the transformed task space in S2 is: ; In the formula, It is a redundant rotation angle sequence. C Indicates the compound cost. This indicates the solution using inverse kinematics. For end pose family, For about i Redundant rotation angle of the shaft, This is a second-order difference regularization term used to enhance the smoothness of the entire path.

[0008] Optionally, in S3, the weight of each candidate sequence is calculated, and the weighted expectation of the perturbation is calculated to estimate the descent direction. Specifically: ; In the formula, For the first k The weights of the candidate sequences, K The total number of candidate sequences. To control the adjustment parameters of the weights, Let cost function be For the first k Candidate parameter sequence, For the first j Candidate parameter sequence, Expressing expectations, This represents the weighted expectation.

[0009] Optionally, in S4, the multi-objective composite cost is calculated based on the joint configuration corresponding to each path point as follows: ; In the formula, For joint configuration Multi-objective composite cost, , , These are the weighting coefficients. As a cost for stiffness, For the cost of singularity, This is the collision cost term.

[0010] Optionally, the cost of singular terms is as follows: ; ; In the formula, The scaling factor for the singular cost. For operability, Offset It is a Jacobian matrix.

[0011] Optionally, the stiffness cost is as follows: ; ; In the formula, This is a scaling factor for the stiffness cost. is the smallest eigenvalue of the matrix. This is the offset. For exponential coefficients, Here is the task space stiffness matrix. It is the inverse of the joint space flexibility matrix.

[0012] Optionally, in S4, the smooth interpolation of the end position and attitude at each interpolation time point is performed as follows: The quaternion representing the end-effector attitude is interpolated using spherical linear interpolation: ; ; ; ; In the formula, Instantaneous velocity For the maximum permissible speed, For the maximum permissible acceleration, For the maximum permissible jerk, The joint angle changes over time. For spherical linear interpolation, , It is the quaternion of the end-point attitude at adjacent path points. These are interpolation parameters. The joint angles are calculated using inverse kinematics. The end position, This is the end-point attitude matrix.

[0013] A redundancy allocation and stiffness enhancement system based on task space stochastic optimization, applying the aforementioned redundancy allocation and stiffness enhancement method based on task space stochastic optimization, includes: The data input module is used to receive discrete path point sequences, machine tool parameters, robot parameters, speed limit data, acceleration limit data, and joint limit data; The redundancy parameterization and sampling optimization module, connected to the data input module, is used to sample, weight, and update the redundant angles in the task space to minimize the compound cost and ensure smoothness. The time parameterization and attitude interpolation module, connected to the redundant parameterization and sampling optimization module, is used to perform S-curve time calibration and interpolation on the path and output a satisfactory sampling sequence. The trajectory delivery module, connected to the time parameterization and attitude interpolation modules, converts the joint trajectory sequence into an executable command stream from the robot controller's ROS interface and delivers it for execution.

[0014] As can be seen from the above technical solutions, compared with the prior art, the present invention provides a method and system for redundancy allocation and stiffness enhancement based on task space stochastic optimization, which has the following beneficial effects: under the premise of strict path tracking, the redundancy angle is optimized throughout the process to improve the stiffness of the weakest direction at the end, corresponding to continuous and executable joint trajectories; through the cost term driven by operability, the trajectory stays away from singular / near-singular regions throughout the process, reducing the risk of speed amplification and numerical instability; the global optimization of task space redundancy is organically coupled with the time parameterization of the S-curve, which not only ensures zero / near-zero Cartesian error, but also takes into account the driving friendliness and the improvement of processing surface quality. Attached Figure Description

[0015] 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.

[0016] Figure 1This is a flowchart of the Redundancy Allocation and Stiffness Enhancement (CROSO) method based on task space stochastic optimization of the present invention; Figure 2 This is a schematic diagram of the angle search algorithm generating joint angles on a U-shaped path in an embodiment of the present invention; Figure 3 This is a schematic diagram of joint angle generation on the spiral path of the angle search algorithm in an embodiment of the present invention; Figure 4 This is a schematic diagram of the STOMP algorithm generating joint angles on a U-shaped path in an embodiment of the present invention; Figure 5 This is a schematic diagram of the STOMP algorithm generating joint angles on a spiral path in an embodiment of the present invention; Figure 6 This is a schematic diagram of the CROSO algorithm disclosed in this embodiment of the invention generating joint angles on a U-shaped path; Figure 7 This is a schematic diagram of the CROSO algorithm disclosed in this embodiment of the invention generating joint angles on a spiral path; Figure 8 This is a schematic diagram illustrating the stiffness cost and singularity cost of the angle search algorithm on a U-shaped path in an embodiment of the present invention; Figure 9 This is a schematic diagram illustrating the stiffness cost and singularity cost of the angle search algorithm on the spiral path in an embodiment of the present invention; Figure 10 This is a schematic diagram illustrating the stiffness cost and singularity cost of the CROSO and STOMP algorithms on a U-shaped path in an embodiment of the present invention. Figure 11 This is a schematic diagram illustrating the stiffness cost and singularity cost of the CROSO and STOMP algorithms on a spiral path in an embodiment of the present invention. Figure 12 This is a schematic diagram of the surface finish of the helical path milled on a real machine before optimization using the CROSO algorithm in this embodiment of the invention. Figure 13 This is a schematic diagram of the surface milling result of the spiral path optimized by the CROSO algorithm in an embodiment of the present invention. Figure 14 This is a schematic diagram of the surface milling result of the U-shaped path before optimization by the CROSO algorithm in this embodiment of the invention; Figure 15 This is a schematic diagram of the surface milling result of the U-shaped path after optimization by the CROSO algorithm in an embodiment of the present invention; Figure 16 This is a schematic diagram of the overall robot processing system of the present invention. Detailed Implementation

[0017] 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.

[0018] This invention discloses a method for redundancy allocation and stiffness enhancement based on task space stochastic optimization, such as... Figure 1 As shown, it includes the following steps: S1 receives discrete path point sequences, machine tool parameters, robot parameters, speed limit data, acceleration limit data, and joint limit data; S2. Perform task space redundancy parameterization on the given discrete path point sequence, introduce a redundant rotation angle for each path point, construct an end pose family that satisfies the end position constraint, and transform the joint space constrained optimization into the task space unconstrained optimization. S3. Use zero-mean Gaussian perturbation to perturb multiple candidate redundant sequences, calculate the weight of each candidate sequence, calculate the weighted expectation of the perturbation to estimate the descent direction, and iteratively update and optimize the candidate redundant sequences until the convergence condition is met. S4. Calculate the multi-objective composite cost based on the joint configuration corresponding to each path point, including stiffness cost and singular cost; S5. Perform S-curve time parameterization on the optimized geometric path, apply velocity, acceleration and jerk constraints, perform smooth interpolation of end position and attitude at each interpolation time point, and finally obtain a continuous and executable joint trajectory sequence by solving inverse kinematics. S6. Convert the joint trajectory sequence into an executable instruction stream from the robot controller ROS interface and send it down for execution.

[0019] In this embodiment of the invention, task space redundancy parameterization specifically refers to: for a given discrete path position... ,direction Introducing information about i Redundant rotation angle of the shaft Construct an end-effector pose family that satisfies the main task constraints: .

[0020] Furthermore, the objective function for unconstrained optimization of the transformed task space in S2 is: ; In the formula, It is a redundant rotation angle sequence. C Indicates the compound cost. This indicates the solution using inverse kinematics. For end pose family, For about i Redundant rotation angle of the shaft, This is a second-order difference regularization term used to enhance the smoothness of the entire path.

[0021] Furthermore, in S3, the weight of each candidate sequence is calculated, and the weighted expectation of the perturbation is calculated to estimate the descent direction. Specifically: ; In the formula, For the first k The weights of the candidate sequences, K The total number of candidate sequences. To control the adjustment parameters of the weights, Let cost function be For the first k Candidate parameter sequence, For the first j Candidate parameter sequence, Expressing expectations, This represents the weighted expectation. In this embodiment, the sampling process forces the inverse solution to be feasible and the constraints to be satisfied, ensuring that the generated sequence is executable.

[0022] Furthermore, in S4, the multi-objective composite cost is calculated based on the joint configuration corresponding to each path point as follows: ; In the formula, For joint configuration Multi-objective composite cost, , , These are the weighting coefficients. As a cost for stiffness, For the cost of singularity, This represents the collision cost term. Joint constraints and inverse kinematics feasibility are directly guaranteed through sampling constraints.

[0023] Furthermore, the cost of singular terms is specifically as follows: ; ; In the formula, The scaling factor for the singular cost. For operability, Offset It is a Jacobian matrix.

[0024] Furthermore, the stiffness cost is specifically as follows: ; ; In the formula, This is a scaling factor for the stiffness cost. is the smallest eigenvalue of the matrix. This is the offset. For exponential coefficients, Here is the task space stiffness matrix. It is the inverse of the joint space flexibility matrix.

[0025] Furthermore, in S4, the smooth interpolation of the end position and attitude at each interpolation time point is specifically performed as follows: The quaternion representing the end-effector attitude is interpolated using spherical linear interpolation: ; ; ; ; In the formula, Instantaneous velocity For the maximum permissible speed, For the maximum permissible acceleration, For the maximum permissible jerk, The joint angle changes over time. For spherical linear interpolation, , It is the quaternion of the end-point attitude at adjacent path points. These are interpolation parameters. The joint angles are calculated using inverse kinematics. The end position, This is the end-point attitude matrix.

[0026] In one embodiment of the present invention, the CROSO algorithm disclosed in this embodiment is compared with the angle search algorithm and the STOMP algorithm. The robot machining system, as shown... Figure 16 As shown, the angle search algorithm generates joint angles on the U-shaped path and the spiral path respectively. Figure 2 and Figure 3 As shown, the stiffness cost and singularity cost of the angle search algorithm on the U-shaped path and the spiral path are respectively as follows: Figure 8 and Figure 9 As shown, the STOMP algorithm generates joint angles on U-shaped and spiral paths respectively. Figure 4 and Figure 5 As shown, the CROSO algorithm generates joint angles on U-shaped and spiral paths respectively. Figure 6 and Figure 7 As shown, the stiffness cost and singularity cost of the CROSO and STOMP algorithms on a U-shaped path are as follows: Figure 10As shown, the stiffness cost and singularity cost of the CROSO and STOMP algorithms on the spiral path are as follows: Figure 11 As shown, the actual milling surface results of the helical path before and after CROSO algorithm optimization are as follows: Figure 12 and Figure 13 As shown; the actual milling surface results of the U-shaped path before and after CROSO algorithm optimization are respectively as follows. Figure 14 and Figure 15 As shown, under strict path tracking, optimizing the redundant angle throughout the entire process to improve the stiffness in the weakest direction at the end point reduces stiffness cost and singularity cost by approximately 27%–30% and 29%–36% respectively on representative U-shaped / spiral paths, significantly outperforming the slight improvement of STOMP by 0.2%–6%; the corresponding joint trajectories are continuous and executable.

[0027] and Figure 1 Corresponding to the method described above, this embodiment of the invention also discloses a redundancy allocation and stiffness enhancement system based on task space stochastic optimization. Applying the above-described redundancy allocation and stiffness enhancement method based on task space stochastic optimization includes: The data input module is used to receive discrete path point sequences, machine tool parameters, robot parameters, speed limit data, acceleration limit data, and joint limit data; The redundancy parameterization and sampling optimization module, connected to the data input module, is used to sample, weight, and update the redundant angles in the task space to minimize the compound cost and ensure smoothness. The time parameterization and attitude interpolation module, connected to the redundant parameterization and sampling optimization module, is used to perform S-curve time calibration and interpolation on the path and output a satisfactory sampling sequence. The trajectory delivery module, connected to the time parameterization and attitude interpolation modules, converts the joint trajectory sequence into an executable command stream from the robot controller's ROS interface and delivers it for execution.

[0028] 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 systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0029] 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 method for redundancy allocation and stiffness enhancement based on task space stochastic optimization, characterized in that, Includes the following steps: S1 receives discrete path point sequences, machine tool parameters, robot parameters, speed limit data, acceleration limit data, and joint limit data; S2. Perform task space redundancy parameterization on the given discrete path point sequence, introduce a redundant rotation angle for each path point, construct an end pose family that satisfies the end position constraint, and transform the joint space constrained optimization into the task space unconstrained optimization. S3. Use zero-mean Gaussian perturbation to perturb multiple candidate redundant sequences, calculate the weight of each candidate sequence, calculate the weighted expectation of the perturbation to estimate the descent direction, and iteratively update and optimize the candidate redundant sequences until the convergence condition is met. S4. Calculate the multi-objective composite cost based on the joint configuration corresponding to each path point, including stiffness cost and singular cost; S5. Perform S-curve time parameterization on the optimized geometric path, apply velocity, acceleration and jerk constraints, perform smooth interpolation of end position and attitude at each interpolation time point, and finally obtain a continuous and executable joint trajectory sequence by solving inverse kinematics. S6. Convert the joint trajectory sequence into an executable instruction stream from the robot controller ROS interface and send it down for execution.

2. The method for redundancy allocation and stiffness enhancement based on task space stochastic optimization according to claim 1, characterized in that, The objective function for unconstrained optimization of the task space after transformation in S2 is: ； In the formula, This is a redundant rotation angle sequence. C Indicates the compound cost. This indicates the solution using inverse kinematics. For end pose family, For about i Redundant rotation angle of the shaft, This is a second-order difference regularization term used to enhance the smoothness of the entire path.

3. The method for redundancy allocation and stiffness enhancement based on task space stochastic optimization according to claim 1, characterized in that, In S3, the weight of each candidate sequence is calculated, and the weighted expectation of the perturbation is used to estimate the descent direction. Specifically: ； In the formula, For the first k The weights of the candidate sequences, K The total number of candidate sequences. To control the adjustment parameters of the weights, Let cost function be For the first k Candidate parameter sequence, For the first j Candidate parameter sequence, Expressing expectations, This represents the weighted expectation.

4. The method for redundancy allocation and stiffness enhancement based on task space stochastic optimization according to claim 1, characterized in that, In S4, the multi-objective composite cost is calculated based on the joint configuration corresponding to each path point as follows: ； In the formula, For joint configuration Multi-objective composite cost, , , These are the weighting coefficients. As a cost for stiffness, For the cost of singularity, This is the collision cost term.

5. The method for redundancy allocation and stiffness enhancement based on task space stochastic optimization according to claim 4, characterized in that, The cost of singular terms is as follows: ； ； In the formula, The scaling factor for the singular cost. For operability, Offset It is a Jacobian matrix.

6. The method for redundancy allocation and stiffness enhancement based on task space stochastic optimization according to claim 4, characterized in that, The specific cost of the stiffness term is as follows: ； ； In the formula, This is a scaling factor for the stiffness cost. is the smallest eigenvalue of the matrix. This is the offset. For exponential coefficients, Here is the task space stiffness matrix. It is the inverse of the joint space flexibility matrix.

7. The method for redundancy allocation and stiffness enhancement based on task space stochastic optimization according to claim 1, characterized in that, In S4, the smooth interpolation of the end position and attitude at each interpolation time point is specifically performed as follows: The quaternion representing the end-effector attitude is interpolated using spherical linear interpolation: ； ； ； ； In the formula, Instantaneous velocity For the maximum permissible speed, For the maximum permissible acceleration, For the maximum permissible jerk, The joint angle changes over time. For spherical linear interpolation, , It is the quaternion of the end-point attitude at adjacent path points. These are interpolation parameters. The joint angles are calculated using inverse kinematics. The end position, This is the end-point attitude matrix.

8. A redundancy allocation and stiffness enhancement system based on task space stochastic optimization, characterized in that, The redundancy allocation and stiffness enhancement method based on task space stochastic optimization according to any one of claims 1-7 includes: The data input module is used to receive discrete path point sequences, machine tool parameters, robot parameters, speed limit data, acceleration limit data, and joint limit data; The redundancy parameterization and sampling optimization module, connected to the data input module, is used to sample, weight, and update the redundant angles in the task space to minimize the compound cost and ensure smoothness. The time parameterization and attitude interpolation module, connected to the redundant parameterization and sampling optimization module, is used to perform S-curve time calibration and interpolation on the path and output a satisfactory sampling sequence. The trajectory delivery module, connected to the time parameterization and attitude interpolation modules, converts the joint trajectory sequence into an executable command stream from the robot controller's ROS interface and delivers it for execution.

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