A robot force-position hybrid control method and device based on Gaussian process regression

Abstract

The present invention belongs to the field of robot motion control technology and discloses a robot force-position hybrid control method and device based on Gaussian process regression. The method constructs a Gaussian process regression model for the stiffness coefficient. The method inputs the trained Gaussian process regression model with the real-time acquired velocity, position error of the robot end, and contact force error between the robot end and the environment. The stiffness coefficient output by the Gaussian process regression model is used as an optimization reference value to construct a convex optimization problem. The convex optimization problem is solved to obtain the optimized stiffness coefficient. The method combines the robot's impedance control model and, based on the optimized stiffness coefficient, obtains the desired position of the robot end and the desired contact force between the robot end and the environment, thereby achieving constant contact force control of the robot end during operation. The method also dynamically adjusts the impedance parameters based on environmental feedback to improve the accuracy of contact force control of the robot end.

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, hybrid force-position control has shown great potential and advantages in a variety of application scenarios. In fields such as industrial manufacturing, precision assembly, and massage therapy, robots need to possess both high-precision position control and flexible force control capabilities to adapt to changing operating environments and task requirements. Hybrid force-position control ensures that the robot maintains a stable motion trajectory when in contact with the external environment by adjusting the force and position applied by the robot in real time during operation, while also flexibly adjusting the contact force based on feedback. This technology provides a key guarantee for robots to perform tasks in complex and uncertain environments, achieving an organic combination of high precision and high adaptability.

[0003] In massage and physical therapy robot applications, hybrid force-position control requires the robot to precisely adjust the force applied when contacting the human body to avoid discomfort caused by excessive or insufficient pressure or compromised therapeutic outcomes. Furthermore, the robot must possess high-precision position control capabilities to ensure that massage techniques and motion trajectories meet the needs of specific body parts. For example, when massaging the back, the robot must maintain flexible contact while precisely controlling force along the curved path of the skin to achieve safe and effective compression.

[0004] Among force-position hybrid control methods, impedance control, a classic technique, is widely used in various interactive tasks. Impedance control can be broadly categorized into two types: constant impedance control and variable impedance control. Constant impedance control is suitable for scenarios with minimal environmental variability and relatively simple tasks. Due to its simple implementation and good stability, it is often used for simple force control tasks such as precision assembly. However, constant impedance control has limitations when dealing with dynamic environments and complex tasks. Its inability to adjust impedance parameters in real time makes it difficult to adapt to complex external environmental changes. In contrast, variable impedance control is suitable for complex, dynamic, and uncertain task environments. It can dynamically adjust impedance parameters based on real-time feedback, achieving greater adaptability and flexibility. The advantages of variable impedance control make it particularly effective in applications such as rehabilitation, massage, and contact with flexible objects. For example, intelligent variable impedance methods based on neural networks can automatically adjust the damping coefficient, but they suffer from low force tracking accuracy on inclined and complex curved surfaces and poor dynamic performance. Especially in massage scenarios, it is difficult to balance the dynamic performance of force tracking with steady-state error, and overall control performance still needs 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 acquisition robot and the environment e and the desired 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 the training set D;

[0010] Step 3: Construct a Gaussian process regression model of the stiffness coefficient and train it using the training set D;

[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 the optimization reference value. Combined with the position error Δx of the robot end and the contact force error ΔF between the robot end and the environment, a convex optimization problem is constructed. The convex optimization problem is solved to obtain the optimized stiffness coefficient.

[0013] Step 6: Combine the impedance control model of the robot and obtain the desired end position x of the robot according to the optimized stiffness coefficient. 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. They are merely further supplements or optimizations. Under the premise that there are no technical or logical contradictions, each optional method can be combined separately for the above-mentioned overall solution, or multiple optional methods can 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 includes:

[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 the expected function, m(·) represents the mean function, X and X' are two different datasets taken from the training set D, m(X) represents the mean of dataset X, m(X') represents the mean of dataset X', k(·) represents the kernel function, and k(X,X') represents the kernel function value with the input datasets X and X'.

[0022] Therefore, for the prior w, the posterior distribution can be obtained as:

[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 under the given input data set X and 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 expressed 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 under the given input data set X and 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, Indicates that the mean is and variance is A -1 Gaussian distribution;

[0036] When the new input data of the Gaussian process regression model is x * When the predicted output stiffness coefficient K * The probability distribution of satisfaction 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 Indicates 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 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, w gpr is the weighted 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 includes 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 applied by the robot and the position 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 1This is a flowchart of a robot force-position hybrid control method based on Gaussian process regression according to the present invention. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall 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] This paper uses Gaussian process regression to predict the impedance parameters in variable impedance control and introduces a convex optimization process to further modify the impedance parameters to improve the accuracy of the robot's force-position hybrid control. This Gaussian process regression-based robot force-position hybrid control can adjust the impedance parameters in real time to achieve better force control.

[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 terminal and the environment e and the desired 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 for 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 follows; 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 adopts weighted smoothing filtering method when performing 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, 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 differentiation. 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, assuming 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 expectation function, m(·) represents the mean function, X and X' are two different datasets taken from the training set D, m(X) represents the mean of dataset X, m(X') represents the mean of dataset X', k(·) represents the kernel function, k(X, X') represents the kernel function value with the input datasets X and X', and E[(Xm(X))(X'-m(X'))] represents the expectation of (Xm(X))(X'-m(X')).

[0071] Therefore, for the prior (that is, 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 under the given input data set X and 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 under the given input data set X and 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, Indicates 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 of satisfaction 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 Indicates 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 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 optimization reference values, 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] This embodiment combines the convex optimization link and defines the optimization objective function, which includes 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 weighted 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 * 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 parameters of the robot's variable impedance controller.

[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 above, which will not be repeated here.

[0104] The memory and processor are electrically connected, directly or indirectly, to enable data transmission or interaction. For example, these components may be electrically connected via one or more communication buses or signal lines. The memory stores a computer program executable on the processor, and the processor implements the method of the present invention by executing 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 programmable 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 processor may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor may be a microprocessor or any conventional processor.

[0107] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned 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-described embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that a person skilled in the art would be able to make numerous modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended 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 acquisition robot and the environment e and the desired 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 the training set D; Step 3: Construct a Gaussian process regression model of the stiffness coefficient and train it using the training set D; 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 the optimization reference value. Combined with the position error Δx of the robot end and the contact force error ΔF between the robot end and the environment, a convex optimization problem is constructed. The convex optimization problem is solved to obtain the optimized stiffness coefficient. Step 6: Combine the impedance control model of the robot and obtain the desired end position x of the robot according to the optimized stiffness coefficient. 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 the expected function, m(·) represents the mean function, X and X' are two different datasets taken from the training set D, m(X) represents the mean of dataset X, m(X') represents the mean of dataset X', k(·) represents the kernel function, and k(X,X') represents the kernel function value with the input datasets X and X'. Therefore, for the prior w, the posterior distribution can be obtained as: 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 under the given input data set X and 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 expressed 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 under the given input data set X and 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, Indicates that the mean is and variance is A -1 Gaussian distribution; 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 Indicates 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 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, w gpr is the weighted 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.

Images