A Segmented DMP Robot Polishing Skill Learning Method Based on Trajectory Segmentation

Abstract

The present invention belongs to the technical field related to grinding and polishing, and discloses a segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation. It includes the following steps: S1 collects the posture and normal force corresponding to each sampling point of the robot end during the grinding process, and calculates the combined speed of each sampling point during the grinding process; S2 calculates the normal force segmentation threshold and the speed segmentation threshold, constructs the trajectory segmentation condition, traverses all sampling points, and divides the motion trajectory of the robot end into three stages: approach-grinding-withdrawal; S3 learns the motion trajectories of the three stages respectively, and uses different regular systems for modeling; for the grinding stage, uses the arc length-probabilistic motion primitive to establish the grinding and polishing force model of the grinding stage, thereby realizing the robot grinding and polishing skill learning process. Through the present invention, the different stages of the teaching trajectory are segmented according to the trajectory data and force data, ensuring the accuracy of the trajectory segmentation and improving the efficiency of trajectory and grinding and polishing force learning.

Description

Technical Field

[0001] The present invention belongs to the technical field related to grinding and polishing processing, and more specifically, relates to a segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation. Background Art

[0002] Currently, robots can significantly improve productivity in industrial manufacturing. However, in unstructured environments, obtaining an accurate workpiece geometry model is difficult, posing a significant challenge to precise robot programming. Demonstration-based learning, through task learning through instruction, can improve robot programming efficiency, reduce the technical requirements for professionals, and alleviate the difficulty of manual programming. During the robot instruction process, the operator drags the robot's end-point and records the task trajectory. To reduce the amount of trajectory data and ensure generalization, dynamic motion primitives are used to learn demonstration-based learning trajectories, which are computationally efficient. Given the system's initial state, target state, and instructional trajectory, the robot's trajectory can be solved using differential equations, enabling the reproduction and generalization of the robot's trajectory. Using arc-length-probability motion primitives to model contact forces during the grinding phase, the temporal component of the contact force can be projected onto the trajectory in the spatial domain, enabling force planning to perform velocity scaling tasks in different scenarios.

[0003] Currently, CN113043251A discloses a robot teaching and reproducing trajectory learning method. This method draws on the virtual fixture method and Gaussian kernel function to establish a virtual point attraction potential field function for the positions of a few individual value points in the teaching trajectory, and couples it to the standard position dynamic motion primitive conversion system function through feedback. However, this method is not effective for trajectories with sudden changes or large shape changes. The trajectory needs to be segmented according to the characteristics of the trajectory in order to better reproduce the trajectory. Moreover, this method only considers the learning of the trajectory and does not consider the learning of the contact force in the contact task. Summary of the Invention

[0004] To address the above-mentioned deficiencies or improvements in the prior art, the present invention provides a segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation, addressing the problem of simultaneously learning both grinding and polishing trajectories and force skills during grinding and polishing teaching tasks. To achieve the above-mentioned objectives, the present invention provides a segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation, comprising the following steps:

[0005] S1 drags the robot end along a preset trajectory to perform grinding teaching, collects the posture and normal force corresponding to each sampling point of the robot end during the grinding process, forms a posture data set and a normal force data set, and uses the posture data set to calculate the resultant velocity corresponding to each sampling point during the grinding process to form a resultant velocity data set;

[0006] S2 constructs the relationship between the normal force segmentation threshold and the velocity segmentation threshold based on the normal force data and the combined velocity data set, thereby calculating the normal force segmentation threshold and the velocity segmentation threshold, constructing the trajectory segmentation condition, and traversing all sampling points to divide the motion trajectory of the robot end into three stages: approach-grinding-withdrawal;

[0007] S3 learns the motion trajectories of the three stages respectively and uses different regular systems to model them; for the grinding stage, the arc length-probability motion primitive is used to establish the grinding and polishing force model of the grinding stage, thereby realizing the robot grinding and polishing skill learning process.

[0008] Further preferably, in step S1, the combined speed is calculated according to the following relationship:

[0009]

[0010] Among them, v i represents the total velocity of the grinding wheel at point i in the world coordinate system, v x,i , v y,i , v z,i They represent the speed of the i-th point on the x-axis, y-axis, and z-axis directions of the grinding wheel end in the world coordinate system.

[0011] Further preferably, in step S1, after the combined velocity is calculated, mean filtering is performed on the data to make the obtained combined velocity data set smoother.

[0012] Further preferably, in step S2, the normal force segmentation threshold is calculated according to the following relationship:

[0013]

[0014] Among them, F * represents the contact force segmentation threshold, i represents the i-th point of the trajectory data, N is the total number of trajectory data points, F i represents the normal force obtained after filtering at the i-th point.

[0015] Further preferably, before calculating the normal force segmentation threshold, it is necessary to perform a first-order low-pass filtering process on the normal force dataset.

[0016] Further preferably, in step S2, the speed segmentation threshold is calculated according to the following relationship:

[0017]

[0018] Where N is the total number of sampling points, σ(v) represents the standard deviation of the terminal velocity, and V * represents the speed segmentation threshold, V iis the velocity of the i-th sampling point.

[0019] Further preferably, in step S2, the trajectory segmentation condition is performed as follows: the data points collected from the entire trajectory are traversed from front to back, and the first data point that satisfies the contact force greater than the force threshold and the speed less than the speed threshold is the contact point; the data points collected from the entire trajectory are traversed from back to front, and the first data point that satisfies the contact force greater than the threshold and the speed less than the threshold is the separation point.

[0020] Further preferably, in step S2, the result of the trajectory segmentation is performed as follows:

[0021] p c ,p s ∈{p|(F p >F * )∩(v p <V * )}

[0022] Among them, p c Indicates the data point where the robot end and the workpiece first come into contact, p s represents the data point where the robot end separates from the workpiece, p represents each trajectory data point, and F * represents the force segmentation threshold, V * represents the speed segmentation threshold, F p represents the contact force at the end of the robot, v p Indicates the velocity of the robot end.

[0023] Further preferably, in step S3, the DMP regularization system of each stage is performed as follows:

[0024] The regular system of the approach phase is:

[0025]

[0026] The canonical system of the grinding stage is:

[0027]

[0028] The regular system for the withdrawal phase is:

[0029]

[0030] Among them, α c is the constant of the power function canonical system, α s is a constant of the linear canonical system, α r is the constant of the exponential canonical system, s is the system state variable, and τ is the time domain scaling factor, which is used to specify the nonlinear change of the demonstration speed curve to adapt to the grinding and polishing strategy.

[0031] Further preferably, in step S3, the distribution relationship of the polishing force in space is:

[0032] By introducing the trajectory arc length into the canonical system of probabilistic motion primitives of the force, the temporal component of the contact force during the grinding stage is projected onto the motion trajectory in the spatial domain.

[0033]

[0034]

[0035]

[0036] Among them, s f is a canonical system related to the temporal evolution of the preset trajectory, the trajectory p is the result of the above DMP trajectory modeling, x(t) is the arc length of the position trajectory under time evolution, and L is the spatial length of the entire trajectory in the time [0, T].

[0037] Further preferably, in step S3, the polishing force model is performed as follows:

[0038] F Gz =λ(Φ T ω+ε f )

[0039] p(F Gz |ω)=Π t N(F Gz |λ·Φ T ω,λ·Σ f )

[0040] ε f ~N(0,Σ f )

[0041]

[0042] Among them, F Gz Represents the force after the GMM model is constructed, The basis matrix consists of K basis functions, ω is the weight coefficient, Σ f is the variance of the contact force, λ is the force scaling factor, and the AL-ProMP method combined with GMM is used to extract the contact force distribution characteristics of the grinding and polishing task, and the contact force change characteristics in the time domain are projected onto the position trajectory.

[0043] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0044] 1. The present invention uses DMP to learn the trajectory of each stage of grinding teaching, and uses a small number of parameters to model the teaching trajectory. These parameters can quickly reproduce the teaching trajectory. When reproducing the teaching trajectory, some task parameters can be added to generalize and change the original trajectory.

[0045] 2. The present invention uses trajectory data and force data to teach different stages of the trajectory for segmentation, shortening the calculation time and improving the efficiency of trajectory segmentation;

[0046] 3. The present invention uses AL-ProMP to extract the distribution characteristics of grinding and polishing forces. Its time scaling factor and force scaling factor enable force planning to have better robustness in speed scaling tasks and grinding and polishing tasks in different scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flowchart of a segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation constructed according to a preferred embodiment of the present invention;

[0048] Figure 2 It is the original trajectory of the robot drag teaching;

[0049] FIG3( a ) is a threshold diagram of robot force segmentation calculated according to a preferred embodiment of the present invention;

[0050] FIG3( b ) is a threshold diagram of robot velocity segmentation calculated according to a preferred embodiment of the present invention;

[0051] Figure 4 is a schematic diagram of a grinding process segment according to a preferred embodiment of the present invention;

[0052] Figure 5 is the result of segmentation of the original trajectory obtained according to the preferred embodiment of the present invention;

[0053] Figure 6 is a representation of different regular systems of the DMP constructed according to the preferred embodiment of the present invention, wherein: (a) a linear regular system, (b) a power function regular system, and (c) an exponential regular system;

[0054] Figure 7 is the generalized trajectory learning result constructed according to the preferred embodiment of the present invention;

[0055] Figure 8 It is the construction result of the polishing force model constructed according to the preferred embodiment of the present invention. DETAILED DESCRIPTION

[0056] To make the objectives, technical solutions, and advantages of the present invention more apparent, embodiments of the present invention will be further described below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0057] like Figure 1 As shown in FIG, a segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation specifically includes the following steps:

[0058] (a) If Figure 2 As shown, the trajectory data of the robot grinding and polishing teaching is obtained, and the required force data and posture data are extracted to form a set respectively.

[0059] (b) The velocity of the robot end is calculated by the central difference method, and then the velocity is smoothed using a sliding mean filter.

[0060] (c) As shown in Figure 3(a) and Figure 3(b), after low-pass filtering the contact force of the robot end, the segmentation threshold of the contact force and the segmentation threshold of the velocity are calculated respectively.

[0061] (d) If Figure 4 As shown, the teaching trajectory is divided into three parts. According to the force segmentation threshold and the speed segmentation threshold, the teaching trajectory is divided into three parts of approach-grinding-withdrawal to meet the corresponding conditions. The results are shown in Figure 5 shown.

[0062] (e) If Figure 6 As shown in the figure, the DMP of different regular systems is used to learn the three teaching trajectories respectively. The results of trajectory learning are shown in Figure 7 shown.

[0063] (f) The arc length-probability motion primitive is used to establish the grinding and polishing force model in the grinding stage. The results are shown in the figure below. Figure 8 shown.

[0064] Preferably, in step (a), it is necessary to obtain the standard DH model of the UR robot and establish the robot's coordinate system based on the relationship between the connecting rods. Then, the end of the robot is dragged to perform grinding teaching. The operator holds the end of the robot with the grinding and polishing tool and moves along the surface of the workpiece of the unknown geometric model. The Cartesian space pose data during the grinding process is collected at a frequency of 50Hz. and normal force data N represents the number of points collected during the grinding process, px i ,py i ,pz iRepresents the position data of the i-th point in the x-axis, y-axis, and z-axis directions, qx i ,qy i ,qz i ,qw i Represents the direction data represented by quaternion. Construct a collection based on the collected data. For subsequent data processing.

[0065] Preferably, in step (b), the velocity of the entire trajectory is calculated by the central difference method based on the obtained position data to obtain the combined velocity at the end. v i represents the total velocity of the grinding wheel at point i in the world coordinate system, v x,i , v y,i , v z,i Respectively represent the speed of the i-th point in the x-axis, y-axis, and z-axis directions of the grinding wheel end in the world coordinate system. The mean filter is used to calculate the terminal sum speed. Smoothing to obtain smoother data.

[0066] Preferably, in step (c), a first-order low-pass filter is used to smooth the force data, and the calculation formula is as follows:

[0067]

[0068] Among them F i-1 represents the normal force obtained after filtering at point i-1, Indicates the actual measured force at point i, F i Represents the force obtained after filtering at point i, α is the filter coefficient, α∈(0,1). After filtering the measured contact force, the average value of the normal contact force is used as the force segmentation threshold, which is calculated as follows F * Represents the contact force segmentation threshold. Then the velocity segmentation threshold is calculated based on the mean and standard deviation of the velocity. The calculation results of the velocity segmentation threshold are as follows: N represents the data volume of the entire grinding track, σ(v) represents the standard deviation of the terminal speed, V * Indicates the speed segmentation threshold.

[0069] Preferably, in step (d), the data points of the trajectory are first segmented according to the obtained speed threshold and force threshold, and the data of the entire trajectory is traversed from front to back to find the contact point, and the data points of the entire trajectory are traversed from back to front to find the time separation point. The two required data points simultaneously meet the contact force greater than the force threshold and the speed less than the speed threshold. The first point obtained from the two traversals that meets the requirements is the two required segmentation points. The segmentation result is expressed as follows:

[0070]

[0071] Among them, p c Indicates the data point where the robot end and the workpiece first come into contact, p s Indicates the data point where the robot end separates from the workpiece, and p represents the data of each trajectory point F * is the force segmentation threshold, V * represents the speed segmentation threshold, F p represents the contact force at the end of the robot, v p Indicates the velocity of the robot end.

[0072] According to the contact point moment and separation point The entire trajectory is divided into three sections: approach-grinding-retraction. represents the set of approaching stage points, represents the set of points in the grinding and polishing stages, represents the set of withdrawal phase points, where t start represents the start time of the movement, t pc Indicates the moment when the grinding disc contacts the workpiece, t ps Indicates the moment when the grinding disc and the workpiece are separated, t end Indicates the moment when the movement ends.

[0073] Preferably, in step (e), after the drag grinding teaching, the motion data of each joint space and the contact force data of the robot end are collected, and the data set is obtained after the difference method is processed. p k ∈R 3 Indicates position data (p x ,p y ,p z ), q k ∈S 3 The quaternion (q x ,q y ,q z ,q w ), p k ∈R 3 represents Euclidean space, S 3 R 4 unit sphere, Indicates speed, represents acceleration, t k The steps for trajectory learning using DMP are as follows:

[0074] 1) Learning polishing skills using parametric equations of a nonlinear dynamic system, where the trajectory is encoded by a system of nonlinear differential equations of position p and direction q. The equation encoding the three-dimensional coordinate position p is:

[0075]

[0076]

[0077] The quaternion q encoding equation is:

[0078]

[0079]

[0080]

[0081] Where s is the system state variable and τ(s) is the time domain scaling factor, which is used to specify the nonlinear change of the demonstration speed curve to adapt to the grinding and polishing strategy. p , β p represents the positive gain of the linear part of the DMP system, g p Indicates the end point of the teaching trajectory, q0, q g denote the initial posture and the target posture respectively, Represents its conjugate quaternion, e q Represents the quaternion error between the current direction value and the target direction value, f p (s) and f q (s) represents the nonlinear term, and s∈[0,1] is the phase variable.

[0082] 2) Define the nonlinear forcing term f p (s) and f q (s), which is formed by the normalized linear superposition of M radial basis functions,

[0083]

[0084]

[0085] where Ψ i (s)=exp(-h i (sc i ) 2 ), represents the Gaussian radial basis function, where Represents the center and width of the radial basis function distribution, w i Represents the weight corresponding to each basis function, and N represents the number of basis functions.

[0086] 3) For the three segments of the trajectory S after segmentation approach , S grinding , S withdraw The phase variable s is controlled by the regular system, and the regular system in the approaching stage is

[0087]

[0088] The canonical system of the grinding stage is:

[0089]

[0090] The regular system for the withdrawal phase is:

[0091]

[0092] The grinding stage adopts the linear regular system α s , making the data representation error of the entire grinding process more uniform. The power function regular system α is used in the approach and departure stages respectively. c and the exponential regular system α r , which makes the modeling accuracy of contact points and separation points higher.

[0093] Preferably, in step (f),

[0094] 1) By introducing the trajectory arc length into the canonical system of probabilistic motion primitives (ProMP) of forces, the temporal component of the contact force during the grinding stage is projected onto the motion trajectory in the spatial domain.

[0095]

[0096]

[0097]

[0098] Among them, s f is a canonical system related to the temporal evolution of the task trajectory, the trajectory p is the result of the above DMP trajectory modeling, x(t) is the arc length of the position trajectory under time evolution, and L is the spatial length of the entire trajectory in the time [0, T].

[0099] 2) Due to the vibration characteristics of the contact force during the grinding stage, the distribution characteristics of the end normal contact force data are analyzed using the Gaussian mixture model (GMM). The probability model of the data is established using GMM:

[0100]

[0101] Among them, Π k ∈[0,1] is the prior probability and and are the mean and variance of the Gaussian model in GMM. The expectation maximization method (EM) is used to obtain the parameters of the GMM model and extract the features of the force data.

[0102] 3) Gaussian mixture regression (GMR) was used to reconstruct the force data. The GMM model was regressed based on the linear superposition of conditional probability and Gaussian distribution to obtain the reconstructed force data under variance constraints, namely, the fitted data curve and two sets of force data curves with upper and lower bias variances.

[0103] 4) Construct an arc length-probabilistic motion primitive algorithm to model the contact force data reconstructed by GMM-GMR.

[0104] F Gz =λ(Φ T ω+ε f )

[0105] p(F Gz |ω)=Π t N(F Gz |λ·Φ T ω,λ·Σ f )

[0106] ε f ~N(0,Σ f )

[0107]

[0108] Among them, F Gz Represents the force after the GMM model is constructed, The basis matrix consists of K basis functions, ω is the weight coefficient, Σ f is the variance of the contact force, and λ is the force scaling factor. The AL-ProMP method combined with GMM extracts the contact force distribution characteristics of the grinding and polishing task, and projects the contact force variation characteristics in the time domain to the position trajectory.

[0109] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation, characterized in that: The method comprises the following steps: S1 drags the robot end along a preset trajectory to perform grinding teaching, collects the posture and normal force corresponding to each sampling point of the robot end during the grinding process, forms a posture data set and a normal force data set, and uses the posture data set to calculate the resultant velocity corresponding to each sampling point during the grinding process to form a resultant velocity data set; S2 constructs the relationship between the normal force segmentation threshold and the velocity segmentation threshold based on the normal force data set and the combined velocity data set, thereby calculating the normal force segmentation threshold and the velocity segmentation threshold, and constructs the trajectory segmentation condition to traverse all sampling points, thereby dividing the motion trajectory of the robot end into three stages: approach-grinding-withdrawal; S3 learns the motion trajectories of the three stages respectively and uses different regular systems to model them; for the grinding stage, the arc length-probability motion primitive is used to establish the grinding and polishing force model of the grinding stage for the distribution of the grinding and polishing force in space, thereby realizing the robot grinding and polishing skill learning process.

2. The segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation according to claim 1 is characterized in that: In step S1, the resultant velocity is calculated according to the following relationship: Among them, v i represents the total velocity of the grinding wheel at point i in the world coordinate system, v x,i , v y,i , v z,i Respectively represent the speed of the i-th point on the x-axis, y-axis, and z-axis of the end of the grinding wheel in the world coordinate system; After the combined velocity is calculated, the data needs to be processed by mean filtering to make the obtained combined velocity data set smoother.

3. The segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation according to claim 1 is characterized in that: In step S2, the normal force segmentation threshold is calculated according to the following relationship: Among them, F * represents the contact force segmentation threshold, i represents the i-th point of the trajectory data, N represents the total number of trajectory data points, F i represents the normal force obtained after filtering at the i-th point.

4. A segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation as claimed in claim 3, characterized in that: Before calculating the normal force segmentation threshold, it is necessary to perform a first-order low-pass filtering process on the normal force data set.

5. The segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation according to claim 3 is characterized in that: In step S2, the speed segmentation threshold is calculated according to the following relationship: Where N is the total number of sampling points, σ(v) is the standard deviation of the terminal velocity, and V * represents the speed segmentation threshold, V i Represents the velocity of the i-th sampling point.

6. A segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation as claimed in claim 5, characterized in that: In step S2, the trajectory segmentation condition is constructed by traversing all sampling points as follows: The data points collected from the entire trajectory from front to back are the first data point that satisfies the contact force greater than the force threshold and the speed less than the speed threshold as the contact point. The data points collected from the entire trajectory from back to front are the first data point that satisfies the contact force greater than the threshold and the speed less than the threshold as the separation point.

7. A segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation as claimed in claim 6, characterized in that: In step S2, the result of the trajectory segmentation is performed as follows: p c ,p s ∈{p|(F p >F * )∩(v p <V * )} Among them, p c Indicates the data point where the robot end and the workpiece first come into contact, p s represents the data point where the robot end separates from the workpiece, p represents each trajectory data point, and F * represents the force segmentation threshold, V * represents the speed segmentation threshold, F p represents the contact force at the end of the robot, v p Indicates the velocity of the robot end.

8. The segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation according to claim 1 is characterized in that: In step S3, the DMP regularization system of each stage is performed as follows: The regular system of the approach phase is: The canonical system of the grinding stage is: The regular system for the withdrawal phase is: Among them, α c is the constant of the power function canonical system, α s is a constant of the linear canonical system, α r is the constant of the exponential canonical system, s is the system state variable, and τ is the time domain scaling factor, which is used to specify the nonlinear change of the demonstration speed curve to adapt to the grinding and polishing strategy.

9. A segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation as claimed in claim 1 or 2, characterized in that: In step S3, the distribution of the polishing force in space is performed as follows: The arc length of the trajectory is introduced into the canonical system of the probabilistic motion primitive of the force, and the time component of the contact force in the grinding stage is projected onto the motion trajectory in the spatial domain. Among them, s f is a canonical system related to the temporal evolution of the preset trajectory, the trajectory p is the result of the above DMP trajectory modeling, x(t) is the arc length of the position trajectory under time evolution, and L is the spatial length of the entire trajectory in the time [0, T].

10. A segmented DMP robot grinding and polishing skill learning method based on trajectory segmentation according to claim 1 or 2, characterized in that: In step S3, the polishing force model is performed as follows: F Gz =λ(Φ T oh+e f ) p(F Gz |ω)=P t N(F Gz |l·F T oh,l·S f ) e f ~N(0,Σ f ) Among them, F Gz Represents the force after the GMM model is constructed, The basis matrix consists of K basis functions, ω represents the weight coefficient, Σ f represents the variance of the contact force, λ represents the force scaling factor, and the AL-ProMP method combined with GMM is used to extract the contact force distribution characteristics of the grinding and polishing task, and the contact force change characteristics in the time domain are projected onto the position trajectory.

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