A robot excitation trajectory planning method and system based on the weighted condition number of the observation matrix

Abstract

This invention belongs to the field of robot dynamics parameter identification and discloses a method and system for robot excitation trajectory planning based on the weighted condition number of the observation matrix. The method includes: establishing a robot dynamics parameter model under a linear friction model, performing linear parameterization, and transforming the model into a minimal parameter set to obtain the basic parameters and their observation matrix; randomly generating a sufficient number of joint position, velocity, and acceleration values, substituting them into the observation matrix, and stacking them column-wise to obtain the observation matrix corresponding to the entire motion range; performing singular value decomposition on the observation matrix corresponding to the entire motion range to obtain a left singular vector matrix, a singular value matrix, and a right singular vector matrix; calculating the weight matrix of the excitation trajectory observation matrix; and using the condition number of the product of the trajectory observation matrix and the weight matrix as the objective function for excitation trajectory planning. This invention can effectively handle various robot configurations and joint constraints, improving the accuracy of torque prediction after parameter identification.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of robot dynamics parameter identification technology, and particularly relates to a robot excitation trajectory planning method and system based on the weighted condition number of the observation matrix. Background Technology

[0002] In the field of robot dynamics parameter identification, the planning of excitation trajectories is crucial for the identification of dynamic model parameters and the establishment of the dynamic model. Existing methods mostly employ trajectories in the form of finite Fourier series, with the minimization of the condition number of the observation matrix as the objective function. However, traditional methods have the following limitations:

[0003] Anomalies in the observation matrix condition number: Due to differences in robot joint characteristics, such as varying joint reduction ratios and inconsistent dimensions of joint angles between linear and rotational degrees of freedom, the singular values ​​of the observation matrix may exhibit an unbalanced distribution, resulting in a persistently high condition number and difficulty in optimization convergence. This is especially problematic for robots with special configurations (such as robots with mixed joint types or strict joint constraints).

[0004] The correlation between trajectory planning and torque prediction accuracy is insufficient: condition number optimization only reflects the numerical stability of parameter identification and does not directly relate to actual torque prediction errors. High parameter identification accuracy does not equate to excellent model torque prediction performance, the latter being a core requirement of practical control. Traditional methods lack a unified framework from parameter identification to model validation, failing to ensure the generalization ability of identified parameters.

[0005] The aforementioned problems limit the application of traditional excitation trajectory planning methods in complex robotic scenarios.

[0006] Based on the above analysis, the urgent technical problems that need to be solved in the existing technology are:

[0007] There is an urgent need for a trajectory optimization strategy that can both suppress condition number anomalies and directly correlate with the accuracy of torque prediction. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides a robot excitation trajectory planning method and system based on the weighted condition number of the observation matrix.

[0009] This invention is implemented as follows: a robot excitation trajectory planning method based on the weighted condition number of the observation matrix, characterized in that the robot excitation trajectory planning method based on the weighted condition number of the observation matrix specifically includes:

[0010] S1: Based on the Newton-Euler method, Lagrange method, etc., establish the robot dynamic parameter model under the linear friction model, perform linear parameterization on the parameters in the model, and transform the model into the form of a minimum parameter set to obtain the basic parameters and their observation matrix;

[0011] S2: Based on the range of joint position, velocity, and acceleration, randomly generate a sufficient number of joint position, velocity, and acceleration values, substitute them into the observation matrix, and stack them column by column to obtain the observation matrix corresponding to the full range of motion;

[0012] S3: Perform singular value decomposition on the observation matrix corresponding to the entire motion range to obtain the left singular vector matrix, the singular value matrix and the right singular vector matrix.

[0013] S4: Calculate the weight matrix of the excitation trajectory observation matrix based on the singular value matrix and the right singular vector matrix;

[0014] S5: Use the condition number of the product of the trajectory observation matrix and the weight matrix as the objective function for excitation trajectory planning.

[0015] Furthermore, for a serial robotic arm with n joints, the dynamic parameter model of S1 can be generalized as follows:

[0016]

[0017] in: Indicates joint torque. These represent the angle, angular velocity, and angular acceleration of the robot's joints, respectively. For the robot's inertia matrix, Represents the Coriolis force matrix of centrifugal force. For gravitational torque, For frictional torque, when the frictional torque is linear, the frictional force at joint k is usually expressed as:

[0018]

[0019] Among them, F r,k F represents the frictional force at joint k. v,k F represents the viscous friction parameter of joint k. c,k The Coulomb friction parameters of joint k can be represented as follows after the model is transformed into a minimal parameter set form:

[0020]

[0021] in: Let m represent the kinetic basis parameters, and m represent the number of basis parameters. This represents the observation matrix corresponding to the basis parameters.

[0022] Furthermore, in step S2, based on the joint position range, velocity and acceleration limits, k sets of joint position velocities and accelerations are randomly generated (k must satisfy n·k >> m):

[0023]

[0024] Where q i , and Let q represent the generated position, velocity, and acceleration of the i-th joint group, respectively. max and q min Indicates the vertical and horizontal limitations of the joint position. and This represents the joint velocity and acceleration limits, and rand(x,y) represents a random number generation function that generates random numbers in the interval [x,y] with average probability.

[0025] Then substitute the k sets of joint position velocity and acceleration data generated above into... Obtain k observation matrices Stack them to get:

[0026]

[0027] in This is the observation matrix corresponding to the entire range of motion, which reflects the general situation of the observation matrix of the robot for all trajectories within the feasible range.

[0028] Furthermore, the formula for S3 is as follows:

[0029]

[0030] in, Describes a left singular vector matrix. Represents a singular value matrix. This represents a right singular vector matrix.

[0031] Furthermore, in step S4, the singular value matrix is ​​first extracted. The first m rows form a matrix

[0032] Σ a =[E m×m 0]·Σ

[0033] in It is the identity matrix;

[0034] The weights are then calculated using the following formula:

[0035]

[0036] in This is the required weight matrix.

[0037] Furthermore, in step S5, a finite Fourier series is used as the excitation trajectory, which takes the form:

[0038]

[0039] Where q i (t) represents the position of joint i at time t, ω f Let L be the fundamental frequency of the Fourier series, and L be the order of the finite Fourier series. and These are called the l-th order sine and cosine Fourier coefficients of joint i, respectively, q i,0 This is called the positional bias term;

[0040] Then, the sine and cosine Fourier coefficients of the above excitation trajectory and the position offset term are used as parameters. The condition number of the product of the observation matrix and the weight matrix λ corresponding to the excitation trajectory is used as the objective function for excitation trajectory planning; the method for calculating the observation matrix corresponding to the excitation trajectory is as follows:

[0041] First, let the period T... Divide according to time interval dt:

[0042] t = 0, dt, 2dt, ..., j·dt

[0043] in [·] denotes the floor function, and then the position, velocity, and acceleration values ​​q(t) of all joints at each discrete time point are calculated. Substitution Stacking the columns yields the observation matrix corresponding to the excitation trajectory.

[0044]

[0045] Subsequently, the observation matrix Y tarj The product of the observation matrix and the weight matrix λ (the product of the observation matrix) Right multiplication of the weight matrix The condition number is used as the objective function for excitation trajectory planning.

[0046]

[0047] in The parameter to be optimized is represented by `cond(·)`, which is a function to calculate the condition number of a matrix. i (t), and Let q represent the position, velocity, and acceleration of joint i at time t, respectively. i,min q i,min and q i,max Indicates the lower and upper limits of the position of joint i. and These represent the velocity and acceleration limits of joint i, respectively.

[0048] Another objective of this invention is to provide a robot excitation trajectory planning system based on the weighted condition number of the observation matrix, the system specifically comprising:

[0049] The robot dynamics parameter model building module is used to establish the robot dynamics parameter model under the linear friction model.

[0050] The observation matrix acquisition module is used to obtain the observation matrix corresponding to the entire motion range;

[0051] The singular value decomposition module is used to perform singular value decomposition on the observation matrix corresponding to the entire motion range, and obtain the left singular vector matrix, the singular value matrix and the right singular vector matrix.

[0052] The weight matrix calculation module is used to calculate the weight matrix of the excitation trajectory observation matrix based on the singular value matrix and the right singular vector matrix.

[0053] The excitation trajectory planning module is used to plan excitation trajectories using the condition number of the product of the trajectory observation matrix and the weight matrix as the objective function.

[0054] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0055] This invention improves the objective function calculation method for excitation trajectory planning, which can effectively cope with various robot configurations and joint constraints.

[0056] This invention provides a planning method for torque prediction accuracy directly oriented towards parametric models, which can effectively improve the accuracy of torque prediction after parameter identification.

[0057] The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0058] Given the increasing applications of robots in more and more fields, this invention has enormous expected benefits and commercial value.

[0059] The technical solution of this invention fills a technological gap in the industry both domestically and internationally:

[0060] This invention fills the gap in current excitation trajectory planning, which fails to directly address the torque prediction accuracy of parametric models. The excitation trajectory planned using the weighted method of this invention has superior torque prediction performance.

[0061] The technical solution of this invention solves a technical problem that people have long desired to solve but have been unable to achieve:

[0062] This invention solves the problem of abnormal observation matrices in robots with special configurations (such as robots that use both rotary and linear joints, or robots that use both direct-drive motors and high-reduction-ratio reducers) and robots with special joint limitations (such as a small peak velocity of a certain joint). By weighting and balancing the inherent singularity anomalies of the observation matrix, the invention enables the excitation trajectory to be carried out normally. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the overall process of robot excitation trajectory planning based on observation matrix weighted condition number provided by the present invention;

[0064] Figure 2 This is a block diagram of the robot excitation trajectory planning system based on the observation matrix weighted condition number provided by the present invention;

[0065] Figure 3 This is the planning situation of two objective functions under the first joint constraint condition provided by the present invention;

[0066] Figure 4 This is the planning situation of two objective functions under the second joint constraint condition provided by the present invention;

[0067] Figure 5 This is the distribution of the observation matrix condition number and the weighted condition number of the observation matrix for the ten excitation trajectories provided in this invention example;

[0068] Figure 6 This is the comprehensive error result of the cross-identification verification of the ten excitation trajectories provided in the example of this invention;

[0069] Figure 7 This is a box plot of the joint error distribution for cross-identification verification of ten excitation trajectories provided in this invention example. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0071] like Figure 1 As shown, this embodiment of the invention provides a robot excitation trajectory planning method based on the weighted condition number of the observation matrix. The method specifically includes:

[0072] S1: Based on the Newton-Euler method, Lagrange method, etc., establish the robot dynamic parameter model under the linear friction model, perform linear parameterization on the parameters in the model, and transform the model into the form of a minimum parameter set to obtain the basic parameters and their observation matrix;

[0073] S2: Based on the range of joint position, velocity, and acceleration, randomly generate a sufficient number of joint position, velocity, and acceleration values, and substitute them into the observation matrix. The observation matrix Y corresponding to the entire motion range is obtained by stacking the columns. full ;

[0074] S3: The observation matrix Y corresponding to the entire range of motion full Perform singular value decomposition to obtain the left singular vector matrix, the singular value matrix, and the right singular vector matrix;

[0075] S4: Calculate the weight matrix λ of the excitation trajectory observation matrix based on the singular value matrix Σ and the right singular vector matrix V;

[0076] S5: Use the condition number of the product of the trajectory observation matrix and the weight matrix λ as the objective function for excitation trajectory planning.

[0077] For the serial robotic arm with n joints, the dynamic parameter model of S1 can be generalized as follows:

[0078]

[0079] in: Indicates joint torque. These represent the angle, angular velocity, and angular acceleration of the robot's joints, respectively. For the robot's inertia matrix, Represents the Coriolis force matrix of centrifugal force. For gravitational torque, This is the frictional torque.

[0080] When the frictional torque is linear, the frictional force at joint k is usually expressed as:

[0081]

[0082] Among them, F r,k F represents the frictional force at joint k. v,k F represents the viscous friction parameter of joint k. c,k This represents the Coulomb friction parameter of joint k.

[0083] The model, after being transformed into a minimal parameter set form, can be expressed as:

[0084]

[0085] in: These represent the dynamic basis parameters, and there are a total of m basis parameters. This represents the observation matrix corresponding to the basis parameters.

[0086] S2, based on the joint position range, velocity and acceleration limits, randomly generates k sets of joint position velocities and accelerations (k must satisfy n·k >> m):

[0087]

[0088] Where q i , and Let q represent the generated position, velocity, and acceleration of the i-th joint group, respectively. max and q min Indicates the vertical and horizontal limitations of the joint position. and The limits of joint velocity and acceleration are represented by , and rand(x,y) represents a random number generation function that generates random numbers in the interval [x,y] with average probability.

[0089] Then substitute the k sets of joint position velocity and acceleration data generated above into... Obtain k observation matrices Stack them to get:

[0090]

[0091] in This is the observation matrix corresponding to the entire range of motion, which reflects the general situation of the observation matrix of the robot for all trajectories within the feasible range.

[0092] The formula for S3 is as follows:

[0093]

[0094] in, Describes a left singular vector matrix. Represents a singular value matrix. This represents a right singular vector matrix.

[0095] S4 first involves extracting the singular value matrix. The first m rows form a matrix

[0096] Σ a =[E m×m 0]·Σ

[0097] in It is an identity matrix.

[0098] The weights are then calculated using the following formula:

[0099]

[0100] in This is the required weight matrix.

[0101] S5 uses a finite Fourier series as the excitation trajectory, and its form is as follows:

[0102]

[0103] Where q i (t) represents the position of joint i at time t, ω f Let L be the fundamental frequency of the Fourier series, L be the order of the finite Fourier series, and a be the frequency of the Fourier series. l i and b l i These are called the l-th order sine and cosine Fourier coefficients of joint i, respectively, q i,0 This is called the positional bias term.

[0104] Then, the sine and cosine Fourier coefficients of the above excitation trajectory and the position offset term are used as parameters. The condition number of the product of the observation matrix and the weight matrix λ corresponding to the excitation trajectory is used as the objective function for excitation trajectory planning.

[0105] The method for calculating the observation matrix corresponding to the excitation trajectory is as follows:

[0106] First, let the period T... Divide according to time interval dt:

[0107] t = 0, dt, 2dt, ..., j·dt

[0108] in [·] denotes the floor function, and then the position, velocity, and acceleration values ​​q(t) of all joints at each discrete time point are calculated. Substitution Stacking the columns yields the observation matrix corresponding to the excitation trajectory.

[0109]

[0110] Subsequently, the observation matrix Y tarj The product of the observation matrix and the weight matrix λ (the product of the observation matrix) Right multiplication of the weight matrix The condition number is used as the objective function for excitation trajectory planning.

[0111]

[0112] in The parameter to be optimized is represented by `cond(·)`, which is a function to calculate the condition number of a matrix. i (t), and Let q represent the position, velocity, and acceleration of joint i at time t, respectively. i,min q i,min and q i,max Indicates the lower and upper limits of the position of joint i. and These represent the velocity and acceleration limits of joint i, respectively.

[0113] like Figure 2 As shown in the figure, an embodiment of the present invention provides a robot excitation trajectory planning system based on the weighted condition number of the observation matrix, which specifically includes:

[0114] The robot dynamics parameter model building module is used to establish the robot dynamics parameter model under the linear friction model.

[0115] The observation matrix acquisition module is used to obtain the observation matrix corresponding to the entire motion range;

[0116] The singular value decomposition module is used to perform singular value decomposition on the observation matrix corresponding to the entire motion range, and obtain the left singular vector matrix, the singular value matrix and the right singular vector matrix.

[0117] The weight matrix calculation module is used to calculate the weight matrix of the excitation trajectory observation matrix based on the singular value matrix and the right singular vector matrix.

[0118] The excitation trajectory planning module is used to plan excitation trajectories using the condition number of the product of the trajectory observation matrix and the weight matrix as the objective function.

[0119] This invention provides an example of excitation trajectory planning and parameter identification for a collaborative robot (model HSRCo610-1400) to illustrate the application and effects of the proposed method. The following description is in conjunction with the accompanying drawings.

[0120] S1. Based on the Newton-Euler method, Lagrange method, etc., establish the dynamic parameter model of HSRCo610-1400 robot under the linear friction model, perform linear parameterization on the parameters in the model, and transform the model into the form of a minimal parameter set to obtain the basic parameters and their observation matrix.

[0121] S2. Based on the range of joint position, velocity, and acceleration, randomly generate 1000 sets of joint position, velocity, and acceleration values, and substitute them into the observation matrix. The observation matrix Y corresponding to the entire motion range is obtained by stacking the columns. full .

[0122] Two ranges of joint position, velocity, and acceleration are used respectively. The first type is shown in the table below:

[0123]

[0124] The second method, based on the first, only modifies the sixth axis as follows: the upper limit of velocity is reduced to 0.1 rad / s, and the upper limit of acceleration is reduced to 0.2 rad. 2 / s, with other parameters remaining constant. Compared to the first case, the condition number of the observation matrix in the second case has an inherent singularity anomaly due to its inherent velocity limitation.

[0125] The condition number cond(Y) of the observation matrix corresponding to the full range of motion in the first case can be calculated. full1 ) = 80.94, the second case's cond(Y) full2 = 971.6414.

[0126] S3, for matrix Y full (Y full1 and Y full2 Perform singular value decomposition to obtain the left singular vector matrix, the singular value matrix, and the right singular vector matrix.

[0127] S4. Calculate the weight matrix λ of the excitation trajectory observation matrix based on the singular value matrix Σ and the right singular vector matrix V. Let the weight matrices corresponding to the ranges of the two joint positions, velocities, and accelerations be λ1 and λ2, respectively.

[0128] S5. The condition number of the product of the trajectory observation matrix and the weight matrix λ is used as the objective function for excitation trajectory planning. The Particle Swarm Optimization (PSO) algorithm is selected as the optimization method, and a penalty function method is employed to handle constraints.

[0129] For the first case, the traditional method uses the observation matrix condition number cond(Y). tarj The objective function is cond(Y) and the condition number of the weighted observation matrix proposed in this paper is used as the condition number. tarj The optimization effect of λ1) as the objective function is compared to, for example... Figure 3 As shown.

[0130] For the second case, the traditional method uses the observation matrix condition number cond(Y). tarj The objective function is cond(Y) and the condition number of the weighted observation matrix proposed in this paper is used as the condition number. tarj The optimization effect of ·λ2) as the objective function is compared to, for example... Figure 4 As shown.

[0131] By comparing the excitation trajectory planning performance under these two scenarios, it is found that using the weighted observation matrix condition number as the objective function leads to effective excitation trajectory planning without resulting in an excessively large objective function. This is particularly true for the second scenario, where the traditional method significantly reduces the required observation matrix condition number (cond(Y)).tarj If the value remains greater than 1000, it indicates that the optimization of the excitation trajectory is ineffective. The method proposed in this paper, which uses the weighted observation matrix condition number as the objective function, can effectively balance the inherent imbalance in the magnitude of the singular values ​​of the observation matrix, ensuring the effective implementation of optimization.

[0132] Furthermore, to verify the planning effect of the torque prediction accuracy of the present invention directly targeting the parametric model, an identification experiment was conducted in the first case (within the range of the first joint position, velocity, and acceleration), using the observation matrix condition number cond(Y) respectively. tarj ) and the condition number of the weighted observation matrix cond(Y) tarj Using λ1) as the objective function, multiple sets of excitation trajectories are used to perform cross-parameter identification and verification to see if the torque prediction accuracy is improved.

[0133] The condition number of the observation matrix, cond(Y) tarj Five trajectories are planned using Y as the objective function, named N-1, N-2, N-3, N-4, and N-5, and the condition number of the weighted observation matrix, cond(Y), is used. tarj Five trajectories, named W-1, W-2, W-3, W-4, and W-5, were planned using λ1 as the objective function. Their condition numbers (the condition number of the observation matrix corresponding to the trajectory, hereinafter the same) and weighted observation condition numbers (the condition number of the matrix obtained by right-multiplying the observation matrix corresponding to the trajectory by the weight matrix, hereinafter the same) are calculated and listed in the table below:

[0134]

[0135]

[0136] The condition number and weighted condition number distribution of these ten trajectories can be found in... Figure 5 Among them, the N-1 to 5 trajectories have lower condition numbers, while the W-1 to 5 trajectories have lower weighted condition numbers. By verifying the torque prediction performance of the parameters identified by these two types of trajectories, the torque prediction performance using weighted condition numbers and traditional condition numbers as objective functions can be compared.

[0137] These ten trajectories were used for parameter identification, and the comprehensive error was calculated for each of the ten trajectories. The weighted least squares method was used for identification, and the error was calculated according to the following formula:

[0138]

[0139] Where, τ i,actu τ represents the actual torque of joint i. i,pred Let ξ represent the predictive force of joint i, ||·|| represent the L2 norm calculation function, and ξ represent the predictive force of joint i. i Let ξ represent the error of joint i, and let ξ represent the combined error of the six joints.

[0140] The combined error of the cross-validation of these ten trajectories is listed below. Figure 6 In the study, the trajectory using the weighted condition number as the objective function achieved an average error of 12.87%, while the trajectory using the condition number as the objective function had an average error of 14.98%.

[0141] Meanwhile, the error ξ for different joints i To make a comparison, the training trajectories are divided into W-1~5 and N-1~5, and ξ is calculated. i Box plots of different joint error distributions can be found in Figure 7 In the middle, the trajectories (W-1 to W-5) using the weighted condition number as the objective function for each joint have lower errors.

[0142] This indicates that although the condition numbers of W-1 to 5 are large (low weighted condition number), their predictive performance is better than that of trajectories with low condition numbers (high weighted condition number) (N-1 to 5). Therefore, it can be inferred that the weighted condition number index is more strongly correlated with predictive performance, and trajectories planned using the weighted condition number as the objective function have better torque prediction performance.

[0143] This invention addresses the problem that traditional methods for excitation trajectory planning can suffer from excessively large structural anomalies in the observation matrix condition number, which cannot effectively reduce optimization costs. Specific details are as follows:

[0144] When the reduction ratios of the reducers are not uniform, or the speed range of a certain joint is too small, the condition number of the calculated trajectory observation matrix will become abnormal due to the large difference in the magnitude of the singular values, resulting in an excessively large condition number.

[0145] This method uses k sets (n·k>>m) of randomly generated joint angle positions, velocities, and accelerations within the feasible range of the joint to calculate Y. full , which represents the observation matrix for all possible trajectories, and the weight λ satisfies: cond(Y full ·λ)=1:

[0146]

[0147] Therefore, the weight λ normalizes the singular values ​​of the observation matrix in the feasible space of all joints. Thus, using this weighting method can effectively avoid the inherent singular value anomalies of the robot and achieve effective planning of the excitation trajectory.

[0148] This invention implements a planning method for improving the torque prediction accuracy of parametric models, effectively enhancing the torque prediction accuracy of dynamic models. Specifically:

[0149] When solving the linear system of equations Ax = b, when the observed value b changes by δb, the parameter x to be identified will change by δx accordingly, satisfying the following relationship:

[0150]

[0151] Therefore, the condition number reflects the upper limit of the change δx of the observed value x when the observed value b changes by δb. However, when considering the accuracy of the parametric prediction model rather than the accuracy of the parameters, a unified framework for parameter identification and model prediction needs to be established:

[0152]

[0153] in This represents the parameter identification process, where τ tarj The torque representing the excitation trajectory used for identification. χ represents the observation matrix used to identify the excitation trajectory, and χ represents the basic parameters of the identification. This represents the model accuracy verification process, where τ full Represents the joint torque for any feasible verification trajectory. The set of observation matrices corresponding to any feasible trajectory is the observation matrix corresponding to the entire motion range mentioned above.

[0154] Therefore, the torque prediction accuracy error The upper limit can be expressed as:

[0155]

[0156] When directly considering the accuracy of torque prediction, cond(Y) should be used. full )·cond(Y tarj Using cond(Y) as the objective function, traditional methods only use cond(Y) tarj Since it is used as an optimization objective, it cannot directly ensure the accuracy of the model's torque prediction.

[0157] When using the weighting method proposed in this invention, the unified framework for parameter identification and model prediction is established as follows:

[0158]

[0159] Where λ is the weighting matrix obtained according to the method in this paper. Therefore, the torque prediction accuracy error... The upper limit can be expressed as:

[0160]

[0161] Because cond(Y full λ) = 1, therefore only cond(Y) is needed. tarj When λ) decreases, cond(Y) can be fully guaranteed.full λ)·cond(Y tarj The decrease of λ) is directly due to the condition number cond(Y) of the product of the observation matrix and weights of the excitation trajectory. tarj Using λ as the objective function to plan the excitation trajectory can achieve a planning method that directly addresses the torque prediction accuracy of parametric models.

[0162] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0163] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A robot excitation trajectory planning method based on the weighted condition number of the observation matrix, characterized in that, The method specifically includes: S1: Based on the Newton-Euler method, Lagrange method, etc., establish the robot dynamic parameter model under the linear friction model, perform linear parameterization on the parameters in the model, and transform the model into the form of a minimum parameter set to obtain the basic parameters and their observation matrix; S2: Based on the range of joint position, velocity, and acceleration, randomly generate a sufficient number of joint position, velocity, and acceleration values, substitute them into the observation matrix, and stack them column by column to obtain the observation matrix corresponding to the full range of motion; S3: Perform singular value decomposition on the observation matrix corresponding to the entire motion range to obtain the left singular vector matrix, the singular value matrix and the right singular vector matrix. S4: Calculate the weight matrix of the excitation trajectory observation matrix based on the singular value matrix and the right singular vector matrix; S5: Use the condition number of the product of the trajectory observation matrix and the weight matrix as the objective function for excitation trajectory planning; S2, based on the joint position range, velocity and acceleration limits, randomly generates k sets of joint position velocities and accelerations, where k must satisfy n·k >> m: Where q i , and Let q represent the position, velocity, and acceleration of the i-th joint, respectively. max and q min Indicates the vertical and horizontal limitations of the joint position. and This represents the joint velocity and acceleration limits, and rand(x,y) represents a random number generation function that generates random numbers in the interval [x,y] with average probability. Then substitute the k sets of joint position velocity and acceleration data generated above into... Obtain k observation matrices Stack them to get: in This is the observation matrix corresponding to the entire range of motion, which reflects the general situation of the observation matrix of the robot for all trajectories within the feasible range; The formula for S3 is as follows: in, Describes a left singular vector matrix. Represents a singular value matrix. This represents a right singular vector matrix.

2. The robot excitation trajectory planning method based on the weighted condition number of the observation matrix as described in claim 1, characterized in that, For a serial robotic arm with n joints, the dynamic parameter model of S1 can be generalized as follows: in: Indicates joint torque. These represent the angle, angular velocity, and angular acceleration of the robot's joints, respectively. For the robot's inertia matrix, Represents the Coriolis force matrix of centrifugal force. For gravitational torque, For frictional torque, when the frictional torque is linear, the frictional force at joint k is usually expressed as: Among them, F r,k F represents the frictional force at joint k. v,k F represents the viscous friction parameter of joint k. c,k The Coulomb friction parameters of joint k can be represented as follows after the model is transformed into a minimal parameter set form: in: These represent the dynamic basis parameters, and there are a total of m basis parameters. This represents the observation matrix corresponding to the basis parameters.

3. The robot excitation trajectory planning method based on the weighted condition number of the observation matrix as described in claim 1, characterized in that, S4 first involves extracting the singular value matrix. The first m rows form a matrix S a =[E m×m 0]·S in It is the identity matrix; The weights are then calculated using the following formula: in This is the required weight matrix.

4. The robot excitation trajectory planning method based on the weighted condition number of the observation matrix as described in claim 1, characterized in that, S5 uses a finite Fourier series as the excitation trajectory, and its form is as follows: Where q i (t) represents the position of joint i at time t, ω f Let L be the fundamental frequency of the Fourier series, and L be the order of the finite Fourier series. and These are called the l-th order sine and cosine Fourier coefficients of joint i, respectively, q i,0 This is called the positional bias term; Then, the sine and cosine Fourier coefficients of the above excitation trajectory and the position offset term are used as parameters. The condition number of the product of the observation matrix and the weight matrix λ corresponding to the excitation trajectory is used as the objective function for excitation trajectory planning; the method for calculating the observation matrix corresponding to the excitation trajectory is as follows: First, let the period T be... Divide according to time interval dt: t = 0, dt, 2dt, ..., j·dt in [·] denotes the floor function, and then calculates the position, velocity, and acceleration values ​​of all joints at each discrete time point. Substitution Stacking the columns yields the observation matrix corresponding to the excitation trajectory. Subsequently, the observation matrix Y tarj The condition number of the product of the product with the weight matrix λ is used as the objective function for excitation trajectory planning, and the observation matrix... Right multiplication of the weight matrix in The parameter to be optimized is represented by `cond(·)`, which is a function to calculate the condition number of a matrix. i (t), and Let q represent the position, velocity, and acceleration of joint i at time t, respectively. i,min q i,min and q i,max Indicates the lower and upper limits of the position of joint i. and These represent the velocity and acceleration limits of joint i, respectively.

5. A system based on the robot excitation trajectory planning method based on the observation matrix weighted condition number as described in any one of claims 1-4, characterized in that, The system specifically includes: The robot dynamics parameter model building module is used to establish the robot dynamics parameter model under the linear friction model. The observation matrix acquisition module is used to obtain the observation matrix corresponding to the entire motion range; The singular value decomposition module is used to perform singular value decomposition on the observation matrix corresponding to the entire motion range, and obtain the left singular vector matrix, the singular value matrix and the right singular vector matrix. The weight matrix calculation module is used to calculate the weight matrix of the excitation trajectory observation matrix based on the singular value matrix and the right singular vector matrix. The excitation trajectory planning module is used to plan excitation trajectories using the condition number of the product of the trajectory observation matrix and the weight matrix as the objective function.

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