Robot force and position hybrid control method and device based on Gaussian process regression

Abstract

The invention belongs to the technical field of robot motion control, and discloses a robot force-position hybrid control method and device based on Gaussian process regression, and the method comprises the steps: constructing a Gaussian process regression model of a stiffness coefficient; inputting the speed obtained in real time, the position error of the robot tail end and the contact force error between the robot tail end and the environment into the trained Gaussian process regression model; taking a rigidity coefficient output by the Gaussian process regression model as an optimization reference value, constructing a convex optimization problem, and solving the convex optimization problem to obtain an optimized rigidity coefficient; and in combination with an impedance control model of the robot, according to the optimized rigidity coefficient, the expected position of the tail end of the robot and the expected contact force between the tail end of the robot and the environment are obtained, and constant contact force control over the tail end of the robot in the operation process is achieved. Impedance parameters are dynamically adjusted according to environment feedback, and the precision of robot tail end contact force control is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot motion control, and in particular relates to a robot force-position hybrid control method and device based on Gaussian Process Regression (GPR). Background Art

[0002] With the development of robotics technology, force-position hybrid control has shown great potential and advantages in multi-scenario applications. In the fields of industrial manufacturing, precision assembly, massage therapy, etc., robots need to have both high-precision position control and flexible force control capabilities to adapt to changing operating environments and task requirements. Force-position hybrid control adjusts the force and position applied by the robot during operation in real time to ensure that it can maintain a stable motion trajectory when in contact with the external environment and flexibly adjust the contact force based on feedback. This technology provides key guarantees for robots to perform tasks in complex and uncertain environments, and achieves an organic combination of high precision and high adaptability.

[0003] In the application of massage and physiotherapy robots, force-position hybrid control requires the robot to accurately adjust the force applied when contacting the human body to avoid discomfort caused by excessive or insufficient pressure or affecting the treatment effect. At the same time, the robot must also have high-precision position control capabilities to ensure that the massage techniques and motion trajectories meet the needs of specific parts of the human body. For example, when massaging the back of the human body, the robot needs to perform force control operations accurately along the curved trajectory of the human skin based on flexible contact, so as to achieve safe and effective pressing.

[0004] Among the force-position hybrid control methods, impedance control, as a classic technology, is widely used in various interactive tasks. Impedance control is mainly divided into two categories: fixed impedance control and variable impedance control. Fixed impedance control is suitable for scenarios with small environmental changes and relatively simple tasks. Because of its simple implementation and good stability, it is often used in simple force control tasks such as precision assembly. However, fixed impedance control has limitations when dealing with dynamic environments and complex tasks. It cannot adjust impedance parameters in real time, so it is difficult to adapt to complex external environmental changes. In contrast, variable impedance control is suitable for complex, dynamic, and uncertain task environments, and can dynamically adjust impedance parameters according to real-time feedback, thereby achieving better adaptability and flexibility. The advantages of variable impedance control enable it to perform well in applications such as rehabilitation, massage, and contact with flexible objects. For example, the intelligent variable impedance method based on neural networks can automatically adjust the damping coefficient, but the force tracking accuracy on inclined surfaces and complex curved surfaces is low, and the dynamic performance is poor. Especially in massage scenarios, it is difficult to balance the dynamic performance of force tracking with steady-state errors, and the overall control performance still has room for improvement. Summary of the invention

[0005] The purpose of the present invention is to provide a robot force-position hybrid control method and device based on Gaussian process regression. During the robot trajectory operation, Gaussian process regression and convex optimization are used to realize adaptive variable impedance control of the robot end. This method can help the robot to apply constant force in a complex dynamic environment, and dynamically adjust the impedance parameters according to the feedback of the environment, thereby improving the accuracy of the contact force control of the robot end.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] A robot force-position hybrid control method based on Gaussian process regression, comprising:

[0008] Step 1: Collect the position x and speed of the robot end during actual operation Acceleration and the desired end position x d , and the contact force F between the end of the collection robot and the environment e and the expected contact force F between the robot end and the environment d , calculate the position error Δx of the robot end and the contact force error ΔF between the robot end and the environment;

[0009] Step 2: The position error Δx of the robot end and the contact force error ΔF between the robot end and the environment are subjected to noise reduction processing, and the stiffness coefficient is initialized to construct a training set D;

[0010] Step 3: construct a Gaussian process regression model of the stiffness coefficient and use the training set D for training;

[0011] Step 4: Get the real-time speed The position error Δx of the robot end and the contact force error ΔF between the robot end and the environment are input into the trained Gaussian process regression model to obtain the stiffness coefficient output by the Gaussian process regression model;

[0012] Step 5: Use the stiffness coefficient output by the Gaussian process regression model as an optimization reference value, combine the position error Δx of the robot end and the contact force error ΔF between the robot end and the environment, construct a convex optimization problem, and solve the convex optimization problem to obtain the optimized stiffness coefficient;

[0013] Step 6: Combined with the impedance control model of the robot, according to the optimized stiffness coefficient, the desired end position x of the robot is obtained. d and the desired contact force F between the robot end and the environment d , to achieve constant contact force control of the robot end during operation.

[0014] Several optional methods are also provided below, but they are not intended to be additional limitations on the above-mentioned overall solution, but are merely further supplements or preferences. Under the premise that there are no technical or logical contradictions, each optional method can be combined with the above-mentioned overall solution separately, and multiple optional methods can also be combined.

[0015] Preferably, the position error Δx of the robot end is calculated as follows: Δx=|xx d |, the contact force error ΔF between the robot end and the environment is calculated as follows: ΔF = |F e -F d |.

[0016] Preferably, the Gaussian process regression model for constructing the stiffness coefficient comprises:

[0017] The stiffness coefficient K is set as the output of the Gaussian process regression model, and K obeys the following Gaussian distribution:

[0018] K~GP(m(X),k(X,X'))

[0019] m(X)=0

[0020] k(X,X')=E[(Xm(X))(X'-m(X'))]

[0021] Where GP(·) represents Gaussian distribution, E(·) represents expected function, m(·) represents mean function, X and X' are two different data sets taken from training set D, m(X) represents mean of data set X, m(X') represents mean of data set X', k(·) represents kernel function, k(X,X') represents kernel function value with input as data set X and X';

[0022] Therefore, for the prior w, the posterior distribution is:

[0023] p(K|X,w)=N(X T w,σ 2 I)

[0024] Where I is the identity matrix, σ 2 is the variance of the noise, p(K|X,w) represents the posterior distribution of the stiffness coefficient K given the input data set X and the prior w, N(X T w,σ 2 I) means that the mean is X T w and variance is σ 2 Gaussian distribution of I;

[0025] Assume that the prior w satisfies the following multivariate normal distribution:

[0026] w~N(0,∑ p )

[0027] Among them, ∑ p It is represented as the covariance matrix of the prior w, and the subscript p represents the prior probability distribution, that is, the prior probability distribution p(w) with the prior w:

[0028]

[0029] According to the Bayesian formula, we can get:

[0030]

[0031] From the above formula, we can see that the Bayesian formula also conforms to the Gaussian distribution and satisfies:

[0032]

[0033] in:

[0034]

[0035] Among them, p(w|X,K) represents the posterior distribution of the prior w given the input data set X and the stiffness coefficient K. is the maximum a posteriori estimate of the prior w, A is the precision matrix of the posterior distribution of the prior w, It means that the mean is and variance is A -1 Gaussian distribution of

[0036] When the new input data of the Gaussian process regression model is x * When the predicted output stiffness coefficient K * The probability distribution that satisfies is:

[0037]

[0038] The predicted mean and predicted variance are as follows:

[0039]

[0040] Among them, K train represents the stiffness coefficient matrix obtained by training the training set D, p(K * |x * ,X,K train ) means that given new input data x * , data set X and stiffness coefficient matrix K train The new stiffness coefficient K obtained under the condition of * The posterior distribution of It means that the mean is and the variance is Gaussian distribution, Expressed as the predicted mean, Var(K * ) represents the prediction variance, k(x * ,x * ) indicates that the input is x * and x * The kernel function, k * Represents the new input data x * and the covariance between the training set D.

[0041] Preferably, the convex optimization problem is expressed as follows:

[0042]

[0043] subject_to:|K opt -K * |≤ε 2

[0044] Among them, K opt is the stiffness coefficient to be optimized, that is, the optimized stiffness coefficient obtained by solving the convex optimization problem, represents the objective function of the convex optimization problem, θ is the weighted coefficient of position and contact force, and w gpr is the weight coefficient of the Gaussian process regression model, K * is the stiffness coefficient output by the Gaussian process regression model, subject_to represents the constraint condition, and ε represents the allowable deviation range.

[0045] Preferably, the impedance control model is expressed as:

[0046]

[0047] Among them, M is the inertia coefficient, B is the damping coefficient, K opt Optimized stiffness coefficient.

[0048] A robot force-position hybrid control device based on Gaussian process regression comprises a processor and a memory storing a plurality of computer instructions. When the computer instructions are executed by the processor, the steps of the robot force-position hybrid control method based on Gaussian process regression are implemented.

[0049] In order to further improve the performance of force-position hybrid control, the present invention provides a robot force-position hybrid control method and device based on Gaussian process regression, which can not only provide a prediction of the system state, but also provide an uncertainty assessment of the prediction, and adjust the relationship between the force and position applied by the robot in real time, so that the control strategy is more stable and accurate in a dynamically changing environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1The present invention is a flowchart of a robot force-position hybrid control method based on Gaussian process regression. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0053] The present invention uses Gaussian process regression to predict the impedance parameters in variable impedance control, and introduces a convex optimization link to further correct the impedance parameters to improve the accuracy of the robot's force-position hybrid control. The robot's force-position hybrid control based on Gaussian process regression can adjust the impedance parameters in real time to achieve better force control effects.

[0054] like Figure 1 As shown, a robot force-position hybrid control method based on Gaussian process regression includes the following steps:

[0055] Step 1: Collect the position x and speed of the robot end during actual operation Acceleration and the desired end position x d , and the contact force F between the robot end and the environment e and the expected contact force F between the robot end and the environment d , calculate the position error Δx of the robot end and the contact force error ΔF between the robot end and the environment.

[0056] The calculation formula of the position error Δx at the end of the robot is: Δx=|xx d |, the contact force error ΔF between the robot end and the environment is calculated as; ΔF=|F e -F d |. The collected data is the continuous operation data of the robot over a period of time.

[0057] Step 2: Speed The position error Δx of the robot end and the contact force error ΔF between the robot end and the environment are denoised, and the stiffness coefficient is initialized to construct the training set D.

[0058] This embodiment uses a weighted smoothing filter method for noise reduction processing. For data with a window length of N, the smoothed output y at the tth moment is t 'for:

[0059]

[0060] Among them, y i is the i-th original data, α i is the weight coefficient corresponding to the i-th original data, and N is the filtering window size.

[0061] The training set expression obtained after denoising is:

[0062]

[0063] Among them, j represents the index value of the sample, n represents the total number of samples in the training set, and Δx j represents the position error of the robot end of the jth sample, represents the velocity of the jth sample, ΔF j represents the contact force error between the robot end and the environment of the jth sample, K j The stiffness coefficient of the jth sample is the initial value of the stiffness coefficient of the sample in the training set D. The subscript j in the training set is only for reference. The actual data does not contain the subscript, that is, the input is the current state vector The output is the stiffness coefficient K.

[0064] Step 3: Construct a Gaussian process regression model of the stiffness coefficient and use the training set D for training.

[0065] The position error Δx of the robot end, the contact force error ΔF between the robot end and the environment, and the actual collected speed As the input of the Gaussian process regression model; the stiffness coefficient K is used as the output of the Gaussian process regression model, and the Gaussian process regression model is constructed as follows:

[0066] Set the stiffness coefficient K as the output of the Gaussian process regression model and assume that K obeys the following Gaussian distribution

[0067] K~GP(m(X),k(X,X'))(3)

[0068] m(X)=0 (4)

[0069] k(X,X')=E[(Xm(X))(X'-m(X'))] (5)

[0070] Where GP(·) represents Gaussian distribution, E(·) represents the expected function, m(·) represents the mean function, X and X' are two different data sets taken from the training set D, m(X) represents the mean of data set X, m(X') represents the mean of data set X', k(·) represents the kernel function, k(X,X') represents the kernel function value with input as data sets X and X', and E[(Xm(X))(X'-m(X'))] represents the expectation of (Xm(X))(X'-m(X')).

[0071] Therefore, for the prior (i.e., the weight parameter of the model) w, based on the above analysis, the posterior distribution can be obtained as:

[0072] p(K|X,w)=N(X T w,σ 2 I) (6)

[0073] Where I is the identity matrix, σ 2 is the variance of the noise, p(K|X,w) represents the posterior distribution of the stiffness coefficient K given the input data set X and the prior w, N(X T w,σ 2 I) means that the mean is X T w and variance is σ 2 Gaussian distribution of I.

[0074] Assume that the prior w satisfies the following multivariate normal distribution:

[0075] w~N(0,Σ p )(7)

[0076] Among them, Σ p It is represented as the covariance matrix of w; the subscript p represents the prior probability distribution.

[0077] That is, there is a prior probability distribution p(w) of w:

[0078]

[0079] According to the Bayesian formula, we can get:

[0080]

[0081] From the above formula, we can see that this formula also conforms to the Gaussian distribution and satisfies:

[0082]

[0083] in:

[0084]

[0085] Among them, p(w|X,K) represents the posterior distribution of the prior w given the input data set X and the stiffness coefficient K. is the maximum a posteriori estimate of the prior w, A is the precision matrix of the posterior distribution of the prior w, It means that the mean is and variance is A -1 Gaussian distribution.

[0086] When the new input data of the Gaussian process regression model is x * (data at one time point), the predicted output stiffness coefficient K * The probability distribution that satisfies is:

[0087]

[0088] Based on the joint Gaussian distribution conditional distribution, the predicted mean and predicted variance of the Gaussian process can be obtained:

[0089]

[0090] Among them, K train represents the stiffness coefficient matrix obtained by training the training set D, p(K * |x * ,X,K train ) means that given new input data x * , data set X and stiffness coefficient matrix K train The new stiffness coefficient K obtained under the condition of * The posterior distribution of It means that the mean is and the variance is Gaussian distribution, Expressed as the predicted mean, Var(K * ) represents the prediction variance, k(x * ,x * ) indicates that the input is x * and x * The kernel function, k * Represents the new input data x * and the covariance between the training set D.

[0091] Step 4: Get the real-time speed The position error Δx of the robot end and the contact force error ΔF between the robot end and the environment are input into the trained Gaussian process regression model to obtain the stiffness coefficient K output by the Gaussian process regression model. * , which is the impedance parameter required for the predicted current task.

[0092] Step 5: The stiffness coefficient K output by the Gaussian process regression model *As the optimization reference value, the position error Δx of the robot end and the contact force error ΔF between the robot end and the environment are combined to construct a convex optimization problem, and the optimized stiffness coefficient is obtained by solving the convex optimization problem.

[0093] In this embodiment, the convex optimization link is combined to define the optimization objective function including the error between the expected contact force and the actual contact force and the error between the actual position and the expected position. The stiffness coefficient K output by GPR is * As the optimization reference value, the weighted sum of the contact force error and the position error is minimized, and the impedance control parameters are further optimized. The convex optimization problem is expressed as:

[0094]

[0095] subject_to:|K opt -K gpr |≤ε 2 (17)

[0096] Among them, K opt is the stiffness coefficient to be optimized, that is, the optimized stiffness coefficient obtained by solving the convex optimization problem, represents the objective function of the convex optimization problem, e f 、e p They represent the contact force error and position error, which are equivalent to ΔF and Δx, respectively. θ is the weighting coefficient of position and contact force, and w gpr is the weighting coefficient of the GPR prediction value, subject_to is the constraint condition, and ε is the allowable deviation range.

[0097] Step 6: Combine the impedance control model of the robot and according to the optimized stiffness coefficient K opt , get the desired end position x of the robot d and the desired contact force F between the robot end and the environment d , to achieve constant contact force control of the robot end during operation, that is, adaptive variable impedance control.

[0098] This embodiment combines the adaptive variable impedance control strategy and the impedance parameters obtained in the above steps to achieve constant contact force control of the robot end during trajectory operation. The impedance control model is:

[0099]

[0100] Among them, M, B, K * They are the inertia coefficient matrix, damping coefficient matrix and stiffness coefficient respectively.

[0101] The present invention realizes high-precision force-position hybrid control of the robot by designing a Gaussian process regression model and a convex optimization link to online predict and update the robot's variable impedance controller parameters.

[0102] In another embodiment, the present invention also provides a robot force-position hybrid control device based on Gaussian process regression, comprising a processor and a memory storing a plurality of computer instructions, wherein the computer instructions, when executed by the processor, implement the steps of the robot force-position hybrid control method based on Gaussian process regression.

[0103] For the specific limitations of the robot force-position hybrid control device based on Gaussian process regression, please refer to the limitations of the robot force-position hybrid control method based on Gaussian process regression in the above text, which will not be repeated here.

[0104] The memory and the processor are electrically connected directly or indirectly to achieve data transmission or interaction. For example, these elements can be electrically connected to each other through one or more communication buses or signal lines. The memory stores a computer program that can be run on the processor, and the processor implements the method of the present invention by running the computer program stored in the memory.

[0105] The memory may be, but is not limited to, a random access memory (RAM), a read only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), etc. The memory is used to store a program, and the processor executes the program after receiving an execution instruction.

[0106] The processor may be an integrated circuit chip with data processing capabilities. The above-mentioned processor may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc. The methods, steps and logic block diagrams disclosed in the embodiments of the present invention may be implemented or executed. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0107] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0108] The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A robot force-position hybrid control method based on Gaussian process regression, characterized in that: The robot force-position hybrid control method based on Gaussian process regression includes: Step 1: Collect the position x and speed of the robot end during actual operation Acceleration and the desired end position x d , and the contact force F between the end of the collection robot and the environment e and the expected contact force F between the robot end and the environment d , calculate the position error Δx of the robot end and the contact force error ΔF between the robot end and the environment; Step 2: The position error Δx of the robot end and the contact force error ΔF between the robot end and the environment are subjected to noise reduction processing, and the stiffness coefficient is initialized to construct a training set D; Step 3: construct a Gaussian process regression model of the stiffness coefficient and use the training set D for training; Step 4: Get the real-time speed The position error Δx of the robot end and the contact force error ΔF between the robot end and the environment are input into the trained Gaussian process regression model to obtain the stiffness coefficient output by the Gaussian process regression model; Step 5: Use the stiffness coefficient output by the Gaussian process regression model as an optimization reference value, combine the position error Δx of the robot end and the contact force error ΔF between the robot end and the environment, construct a convex optimization problem, and solve the convex optimization problem to obtain the optimized stiffness coefficient; Step 6: Combined with the impedance control model of the robot, according to the optimized stiffness coefficient, the desired end position x of the robot is obtained. d and the desired contact force F between the robot end and the environment d , to achieve constant contact force control of the robot end during operation.

2. The robot force-position hybrid control method based on Gaussian process regression according to claim 1 is characterized in that: The calculation formula of the position error Δx of the robot end is: Δx=|xx d |, the contact force error ΔF between the robot end and the environment is calculated as follows: ΔF = |F e -F d |.

3. The robot force-position hybrid control method based on Gaussian process regression according to claim 1 is characterized in that: The Gaussian process regression model for constructing the stiffness coefficient includes: The stiffness coefficient K is set as the output of the Gaussian process regression model, and K obeys the following Gaussian distribution: K~GP(m(X),k(X,X')) m(X)=0 k(X,X')=E[(Xm(X))(X'-m(X'))] Where GP(·) represents Gaussian distribution, E(·) represents expected function, m(·) represents mean function, X and X' are two different data sets taken from training set D, m(X) represents mean of data set X, m(X') represents mean of data set X', k(·) represents kernel function, k(X,X') represents kernel function value with input as data set X and X'; Therefore, for the prior w, the posterior distribution is: p(K|X,w)=N(X T w,σ 2 I) Where I is the identity matrix, σ 2 is the variance of the noise, p(K|X,w) represents the posterior distribution of the stiffness coefficient K given the input data set X and the prior w, N(X T w,σ 2 I) means that the mean is X T w and variance is σ 2 Gaussian distribution of I; Assume that the prior w satisfies the following multivariate normal distribution: w~N(0,Σ p ) Among them, ∑ p It is represented as the covariance matrix of the prior w, and the subscript p represents the prior probability distribution, that is, the prior probability distribution p(w) with the prior w: According to the Bayesian formula, we can get: From the above formula, we can see that the Bayesian formula also conforms to the Gaussian distribution and satisfies: in: Among them, p(w|X,K) represents the posterior distribution of the prior w given the input data set X and the stiffness coefficient K. is the maximum a posteriori estimate of the prior w, A is the precision matrix of the posterior distribution of the prior w, It means that the mean is and variance is A -1 Gaussian distribution of When the new input data of the Gaussian process regression model is x * When the predicted output stiffness coefficient K * The probability distribution that satisfies is: The predicted mean and predicted variance are as follows: Among them, K train represents the stiffness coefficient matrix obtained by training the training set D, p(K * |x * ,X,K train ) means that given new input data x * , data set X and stiffness coefficient matrix K train The new stiffness coefficient K obtained under the condition of * The posterior distribution of It means that the mean is and the variance is Gaussian distribution, Expressed as the predicted mean, Var(K * ) represents the prediction variance, k(x * ,x * ) indicates that the input is x * and x * The kernel function, k * Represents the new input data x * and the covariance between the training set D.

4. The robot force-position hybrid control method based on Gaussian process regression according to claim 1 is characterized in that: The convex optimization problem is expressed as follows: subject_to:|K opt -K * |≤ε 2 Among them, K opt is the stiffness coefficient to be optimized, that is, the optimized stiffness coefficient obtained by solving the convex optimization problem, represents the objective function of the convex optimization problem, θ is the weighted coefficient of position and contact force, and w gpr is the weight coefficient of the Gaussian process regression model, K * is the stiffness coefficient output by the Gaussian process regression model, subject_to represents the constraint condition, and ε represents the allowable deviation range.

5. The robot force-position hybrid control method based on Gaussian process regression according to claim 1 is characterized in that: The impedance control model is expressed as: Among them, M is the inertia coefficient, B is the damping coefficient, K opt Optimized stiffness coefficient.

6. A robot force-position hybrid control device based on Gaussian process regression, comprising a processor and a memory storing a plurality of computer instructions, characterized in that: When the computer instructions are executed by the processor, the steps of the robot force-position hybrid control method based on Gaussian process regression described in any one of claims 1 to 5 are implemented.

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