SMA driving parallel attitude adjustment platform control method based on Gaussian process regression optimization

Abstract

The invention relates to the technical field of redundant drive systems, in particular to an SMA drive parallel attitude adjustment platform control method based on Gaussian process regression optimization, a temperature-force / length response model based on shape memory alloy and Gaussian regression optimization are adopted, the model accuracy is improved, and an existing complex model is simplified. Through the redundant driving device, position parameters are converted into torque, and a combination force optimization model and a negative feedback control algorithm are combined, so that real-time accurate control of the system is realized, the response speed and the system performance are effectively improved, and the problems of hysteresis effect and untimely response are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of redundant drive systems, and specifically to a control method for an SMA-driven parallel attitude adjustment platform based on Gaussian process regression optimization. Background Art

[0002] Shape memory alloy (SMA) is a material with unique deformation memory properties, which can achieve reversible deformation under different temperature conditions. This makes SMA widely used in high-precision control and micro-drive fields. The deformation ability of SMA comes from its sensitivity to temperature: at different temperatures, SMA undergoes martensite and austenite phase transformations, resulting in significant changes in mechanical properties (such as length, stress, etc.). In order to give full play to the potential of SMA in complex control systems, redundant drive technology came into being.

[0003] In the application of shape memory alloy (SMA) drive and redundant drive systems, although the technology is relatively mature, there are still some key issues and challenges that limit its widespread application in high-precision control systems. The phase change of SMA involves complex thermodynamic and mechanical processes. The stress-strain response of the material varies with temperature and external force. Due to the nonlinearity and hysteresis of the martensite-austenite phase transformation, the behavior is difficult to accurately describe by linear models. Common phase change models and stress-strain models usually rely on a large amount of experimental data, which increases the complexity of modeling.

[0004] The nonlinear characteristics, hysteresis and temperature response time of SMA make it difficult for traditional control algorithms to cope with it. Especially in redundant drive systems, multiple drives work simultaneously to improve fault tolerance and reliability, but it is more complicated to coordinate their force or position output. Coupling between drives may cause interference and reduce control accuracy. If a drive fails, the system needs to quickly judge and reallocate tasks to ensure that other drives compensate for the failure, which requires higher control strategies and algorithm designs. In addition, coordinating the work of multiple drives requires complex redundant control algorithms to ensure the stability and fault tolerance of the system, which places higher requirements on the computing power and response speed of the control system. Summary of the invention

[0005] In view of the shortcomings of the prior art, the object of the present invention is to provide a SMA driven parallel attitude adjustment platform control method based on Gaussian process regression optimization.

[0006] To achieve the above object, the present invention provides the following technical solution: a SMA driven parallel attitude adjustment platform control method based on Gaussian process regression optimization, the steps of which are:

[0007] (1) Establish a preliminary model based on the relationship between temperature and force of SMA materials, generate temperature and force matching data with input as temperature T and output as force F, and fit the model through Gaussian regression optimization;

[0008] (2) Redundant drive uses multiple SMA units to work together and achieve multi-dimensional motion through temperature-controlled deformation. The force optimization model is used to ensure that the SMA always has a positive tightening force. Combined with closed-loop feedback and PID control, position deviations are corrected in real time to ensure accurate and rapid response.

[0009] (3) The control output torque is used as the Gaussian regression input to further refine the model and output actual control variables such as temperature, thus realizing the nesting of two control closed loops.

[0010] In some embodiments, according to steps (1)-(3), the specific method is:

[0011] The time series data of temperature, force and deformation of SMA are obtained through multiple experiments, and then fitted using local Gaussian process regression.

[0012] The data is randomly classified into 5 regions, each corresponding to a local area;

[0013] By establishing a grid in the feature space, the data is divided into different grid cells;

[0014] The input vector is x = [T], and the output vector is y = [F],

[0015] Where T represents the temperature of SMA, and F is the contraction force generated by SMA when its length remains unchanged after being heated;

[0016] Since the relationship between the contraction force F and the deformation L is relatively simple, the least squares method is used to directly fit it.

[0017] Therefore, local Gaussian process regression is only used to fit the relationship between temperature T and force F, given the input data x and output data y

[0018] x={x1,x2,…,x n},y={y1,y2,…,y n} (1)

[0019] Among them, x i is the input variable, y i is the output variable (such as torque or length), and there are n sets of data in total.

[0020] In some embodiments, the input space x is divided into a plurality of local regions, and the local model centers are uniformly distributed between the minimum and maximum values ​​of x.

[0021] c={c1,c2,…,c k} (2)

[0022] Among them, c kis the center of each local model, the number of models is k,

[0023] In Gaussian process regression, the Gaussian kernel function k(x p ,x q ) to calculate the input point x p and x q Similarity between

[0024]

[0025] in, represents the variance of the vector, W represents the width of the Gaussian kernel, in the present invention, the initial kernel width is 1, the noise variance is 0.1,

[0026] In Gaussian process regression, for the input data point X and the query point X*, the joint distribution is Gaussian, usually expressed as

[0027]

[0028] Among them, K(X,X) is the covariance matrix between training points, K(X,X * ) is the covariance matrix between the training points and the query points, K(X * ,X * ) is the covariance matrix between query points,

[0029] For each local model, select the k The training data of the training set is x local and local , the data is obtained by calculating the distance of each point from the center and taking the nearest data point:

[0030] x local ={x local,1 ,x local,2 ,…,x local,m},y local ={y local,1 ,y local,2 ,…,y local,m} (5)

[0031] After fitting the model, the optimized Gaussian regression model is compared with the experimental data to verify its accuracy.

[0032] In some of the embodiments, the fitting effect is evaluated by comparing the fitting output with the actual measurement data. According to the verification results, the Gaussian regression model is fine-tuned to ensure that the fitting error is within an acceptable range, and the generalization ability of the model is further optimized to make it stable under different conditions.

[0033] In some of the embodiments, in order to verify the robustness and predictive ability of the model, data prediction values ​​are randomly generated within the input data range.

[0034] x new ={x new,1 ,x new,2 ,…,x new,m} (6)

[0035] The input data will be predicted on each local model.

[0036] For each new input x new,i , calculate its relationship with each local model center c k The distance between them is calculated using the Gaussian kernel function to calculate the weight of the input in different local models:

[0037]

[0038] Where W is the kernel width, which controls the decay rate of the weight with distance.

[0039] For each local model k based on the new input x new,i , using the previously trained Gaussian process regression model LGPR k Make predictions and get local prediction values and standard deviation

[0040]

[0041] Among them, k # is the new input x new,i and the training data, and K is the kernel matrix of the training data.

[0042] The standard deviation is predicted to be

[0043]

[0044] According to the prediction values ​​and weights of each local model, for each new input x new,i The prediction results are weighted averaged to obtain the total prediction value

[0045]

[0046] At the same time, the square of the standard deviation σ 2 (x new,i ) is also weighted by the square of the weight

[0047]

[0048] The final standard deviation is

[0049]

[0050] To test the final results, the MATLAB graphics tool plots the predicted results together with the 95% confidence interval to show the predicted values And its uncertainty range:

[0051]

[0052] In some of the embodiments, through the above process, the local Gaussian process regression model can make predictions based on new input data, and perform weighted averaging of the prediction results of multiple local models through distance weights, and finally output a global prediction value and its uncertainty.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] 1. This patent realizes accurate offline identification of system behavior by constructing a Gaussian regression model, and efficiently integrates multi-source information to improve control accuracy. At the same time, the system makes full use of sensor data to form a data-driven intelligent control framework. Combined with the visual PID closed-loop control system, it can obtain the position and state information of the moving platform in real time, and optimize the control instructions based on feedback. This efficient feedback mechanism significantly improves the control accuracy and response speed of the moving platform, enabling the system to respond flexibly in a rapidly changing environment.

[0055] 2. The dual closed-loop control structure is adopted, combining the predictive feedback of the Gaussian regression model with the real-time adjustment of the visual PID control, and adding the force optimization model, so that the system can maintain stability through real-time monitoring and adaptive adjustment when facing external disturbances and environmental changes. This design not only improves the stability of the system, but also enhances its ability to adapt to complex environments and tasks, making the system more robust under uncertain and dynamic conditions.

[0056] 3. Due to the use of Gaussian regression model for offline identification, the system modeling process is simplified, allowing engineers to more conveniently update and optimize the model during design and maintenance. At the same time, the dual closed-loop control structure reduces the complexity of the control system, making function implementation and fault diagnosis more intuitive, and facilitating subsequent maintenance and upgrades. In addition, the optimized control strategy reduces the energy consumption of the dynamic platform when performing tasks and improves energy utilization efficiency. This feature makes the technology have broad application potential in many fields such as robots, automated production lines, and medical equipment, further expanding the actual application scope and market prospects of the technology.

[0057] Details of one or more embodiments of the present application are presented in the following drawings and descriptions to make other features, purposes and advantages of the present application more concise and easy to understand. The present application is fully described and understood through the embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The basic structure of the redundant parallel robot of the embodiment;

[0059] Figure 2 A top view of a redundant robot of an embodiment;

[0060] Figure 3 It is the basic framework of the present invention and the connection between the frameworks.

[0061] In the figure: 1. plane frame; 2. memory alloy wire; 3. moving platform; 4. camera mounting frame; 5. camera. DETAILED DESCRIPTION

[0062] 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.

[0063] See also Figure 3 The present invention provides a technical solution: a control method for an SMA-driven parallel attitude adjustment platform based on Gaussian process regression optimization, which first identifies the temperature, torque and length of the SMA, uses a Gaussian regression fitting model, and introduces a closed-loop feedback control system. The platform position deviation is monitored in real time through a negative feedback mechanism, and the temperature input of the SMA is adjusted to achieve deformation correction. At the same time, a force optimization model is introduced to keep the SMA in a tensioned state at all times. Combined with the PID control strategy, the device can quickly respond to dynamic environments and achieve full-process automated control from input to output. The steps are as follows:

[0064] (1) Establish a preliminary model based on the relationship between temperature and force of SMA materials, generate temperature and force matching data (input is temperature (T), output is force (F)), and fit the model through Gaussian regression optimization;

[0065] (2) Redundant drive uses multiple SMA units to work together and achieve multi-dimensional motion through temperature-controlled deformation. The force optimization model is used to ensure that the SMA always has a positive tightening force. Combined with closed-loop feedback and PID control, position deviations are corrected in real time to ensure accurate and rapid response.

[0066] (3) The control output torque is used as the Gaussian regression input to further refine the model and output actual control variables such as temperature, thus realizing the nesting of two control closed loops.

[0067] According to steps (1)-(3), the specific implementation method is:

[0068] Through multiple experiments, the time series data of temperature, force and deformation of SMA are obtained, and then fitted using local Gaussian process regression (LGPR). LGPR reduces the computational complexity of the standard Gaussian process through local modeling, and improves the efficiency and scalability of processing large-scale data. At the same time, it can flexibly adapt to the local characteristics of the data, enhance prediction accuracy, reduce storage requirements and training time, and is very suitable for processing large-scale and heterogeneous data.

[0069] In this scheme, the data are randomly classified into five regions, each corresponding to a local area;

[0070] By establishing a grid in the feature space, the data is divided into different grid cells;

[0071] The input vector is x = [T], and the output vector is y = [F],

[0072] Where T represents the temperature of SMA, and F is the contraction force generated by SMA when its length remains unchanged after being heated;

[0073] Since the relationship between the contraction force F and the deformation L is relatively simple, the least squares method is used to directly fit it.

[0074] Therefore, local Gaussian process regression is only used to fit the relationship between temperature T and force F, given the input data x and output data y

[0075] x={x1,x2,…,x n},y={y1,y2,…,y n} (1)

[0076] Among them, x i is the input variable, y i is the output variable (such as torque or length), and there are n sets of data in total.

[0077] The input space x is divided into multiple local regions, and the local model centers are evenly distributed between the minimum and maximum values ​​of x.

[0078] c={c1,c2,…,c k} (2)

[0079] Among them, c k is the center of each local model, the number of models is k,

[0080] In Gaussian process regression, the Gaussian kernel function k(x p ,x q ) to calculate the input point x p and x q Similarity between

[0081]

[0082] in, represents the variance of the vector, W represents the width of the Gaussian kernel, in the present invention, the initial kernel width is 1, the noise variance is 0.1,

[0083] In Gaussian process regression, for the input data point X and the query point X*, the joint distribution is Gaussian, usually expressed as

[0084]

[0085] Among them, K(X,X) is the covariance matrix between training points, K(X,X * ) is the covariance matrix between the training points and the query points, K(X * ,X * ) is the covariance matrix between query points,

[0086] For each local model, select the k The training data of the training set is x local and local , the data is obtained by calculating the distance of each point from the center and taking the nearest data point:

[0087] x local ={x local,1 ,x local,2 ,…,x local,m},y local ={y local,1 ,y local,2 ,…,y local,m} (5)

[0088] After fitting the model, the optimized Gaussian regression model is compared with the experimental data to verify its accuracy.

[0089] The fitting effect is evaluated by comparing the fitting output with the actual measured data. Based on the verification results, the Gaussian regression model is fine-tuned to ensure that the fitting error is within an acceptable range, and the generalization ability of the model is further optimized to make it stable under different conditions.

[0090] In order to verify the robustness and predictive ability of the model, we randomly generated data prediction values ​​within the input data range.

[0091] x new ={x new,1 ,x new,2 ,…,x new,m} (6)

[0092] The input data will be predicted on each local model.

[0093] For each new input x new,i , calculate its relationship with each local model center c k The distance between them is calculated using the Gaussian kernel function to calculate the weight of the input in different local models:

[0094]

[0095] Where W is the kernel width, which controls the decay rate of the weight with distance.

[0096] For each local model k based on the new input x new,i , using the previously trained Gaussian process regression model LGPR k Make predictions and get local prediction values and standard deviation

[0097]

[0098] Among them, k # is the new input x new,i and the training data, and K is the kernel matrix of the training data.

[0099] The standard deviation is predicted to be

[0100]

[0101] According to the prediction values ​​and weights of each local model, for each new input x new,i The prediction results are weighted averaged to obtain the total prediction value

[0102]

[0103] At the same time, the square of the standard deviation σ 2 (x newi ) is also weighted by the square of the weight

[0104]

[0105] The final standard deviation is

[0106]

[0107] To test the final results, the MATLAB graphics tool plots the predicted results together with the 95% confidence interval to show the predicted values And its uncertainty range:

[0108]

[0109] Through the above process, the local Gaussian process regression model can make predictions based on new input data, and perform weighted averaging of the prediction results of multiple local models through distance weights, and finally output the global prediction value and its uncertainty.

[0110] Through this technical solution, the structure of this article is as follows Figure 1-2 As shown in the figure, it includes a flat square frame and a moving platform at its center. Four shape memory alloy (SMA) wires are led out from the four corners of the square frame, and the other ends are fixed on the four corners of the moving platform. The moving platform can move freely in the XY plane, and the SMA changes its length through its own thermal phase change effect, thereby controlling the movement of the moving platform. In this design, a camera is installed in the center just above to monitor the position of the moving platform in real time. The camera identifies the position of the moving platform through a visual algorithm and tracks the XY coordinates of the moving platform by establishing a coordinate system. The data collected by the camera is used as a feedback signal for the closed-loop control system, providing real-time position information to ensure that the control system accurately controls the position of the moving platform.

[0111] First, the dynamic model of the mechanism is established

[0112]

[0113] Among them, X, represents the generalized coordinate vector representing the position and posture of the end effector as well as the velocity and acceleration, M(X) represents the inertia matrix, represents the Coriolis and centrifugal force matrices, G(X) is the gravity term, d represents the external disturbance acting on the moving platform, J(X) represents the Jacobian matrix, and f is the tension vector of the SMA.

[0114] The PID controller is used as a closed-loop control method to control the SMA-driven moving platform. The goal is to make the actual position of the moving platform track the reference trajectory through the PID control algorithm. In order to eliminate static error, dynamic feedforward is added to the model control. Combined with PID, the control law of the present invention is:

[0115]

[0116] Since the present invention is redundantly driven, the Jacobian matrix of the mechanism is a non-square matrix. T J is reversible, and the general solution is:

[0117]

[0118] in, is the minimum solution, and

[0119]

[0120] In order to improve the stability of the system, improve the precise control of the platform and the energy efficiency of the system, and ensure that all SMAs maintain tension during control work, the present invention also introduces a force optimization model. The Jacobian matrix J represents the relationship between the movement of the end effector and the cable tension. According to the static equilibrium equation of the system, it can be expressed as:

[0121] J T f=F (18)

[0122] The null space of the Jacobian matrix N(J T ) represents all force vectors that will not affect the position and posture of the end effector.

[0123]

[0124] Any force represented by a vector v in the null space will not change the force state of the end effector. In order to keep the SMA in proper tension during motion, a positive vector v∈N(J T ) is added to the current SMA tension, as shown in Equation 16.

[0125] Since v∈N(J T ), so the added force v will not change the force on the end effector, that is, it will not affect the posture of the system. The goal of this optimization method is to use internal forces to maintain the appropriate range of cable tension, thereby ensuring the motion control stability of the entire system. target =2N.

[0126] That is, the following equations are constrained during force optimization:

[0127]

[0128] By combining the local Gaussian process regression (LGPR) model with the control system, a dual closed-loop control structure is formed, which improves the efficiency and accuracy of the system. In this design, the output torque F of the control system is used as a feedback signal to return to the identified Gaussian regression model. This feedback mechanism enhances the regulation ability and robustness of the system, and can quickly respond to dynamic changes in the system and external disturbances. By using the feedback torque F as input, the output of the Gaussian regression model is adjusted in real time to ensure the accuracy of control. For example, when the output torque deviates, the system can automatically adjust the model parameters according to the deviation and optimize the control instructions. This closed-loop feedback mechanism ensures that the system can maintain high-precision control and fast response in a dynamic environment through real-time updates, while reducing the impact of external disturbances on system performance.

[0129] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

[0130] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A SMA-driven parallel attitude adjustment platform control method based on Gaussian process regression optimization, characterized in that: The steps are: (1) Establish a preliminary model based on the relationship between temperature and force of SMA materials, generate temperature and force matching data with input as temperature T and output as force F, and fit the model through Gaussian regression optimization; (2) Redundant drive uses multiple SMA units to work together and achieve multi-dimensional motion through temperature-controlled deformation. The force optimization model is used to ensure that the SMA always has a positive tightening force. Combined with closed-loop feedback and PID control, position deviations are corrected in real time to ensure accurate and rapid response. (3) The control output torque is used as the Gaussian regression input to further refine the model and output actual control variables such as temperature, thus realizing the nesting of two control closed loops.

2. The SMA-driven parallel attitude adjustment platform control method based on Gaussian process regression optimization according to claim 1 is characterized in that: According to steps (1)-(3), the specific method is as follows: The time series data of temperature, force and deformation of SMA are obtained through multiple experiments, and then fitted using local Gaussian process regression. The data is randomly classified into 5 regions, each corresponding to a local area; By establishing a grid in the feature space, the data is divided into different grid cells; The input vector is x = [T], and the output vector is y = [F], Where T represents the temperature of SMA, and F is the contraction force generated by SMA when its length remains unchanged after being heated; Since the relationship between the contraction force F and the deformation L is relatively simple, the least squares method is used to directly fit it. Therefore, local Gaussian process regression is only used to fit the relationship between temperature T and force F, given the input data x and output data y x={x1,x2,…,x n },y={y1,y2,…,y n } (1) Among them, x i is the input variable, y i is the output variable (such as torque or length), and there are n sets of data in total.

3. The SMA-driven parallel attitude adjustment platform control method based on Gaussian process regression optimization according to claim 2 is characterized in that: The input space x is divided into multiple local regions, and the local model centers are evenly distributed between the minimum and maximum values ​​of x. c={c1,c2,…,c k } (2) Among them, c k is the center of each local model, the number of models is k, In Gaussian process regression, the Gaussian kernel function k(x p ,x q ) to calculate the input point x p and x q Similarity between in, represents the variance of the vector, W represents the width of the Gaussian kernel, in the present invention, the initial kernel width is 1, the noise variance is 0.1, In Gaussian process regression, for the input data point X and the query point X*, the joint distribution is Gaussian, usually expressed as Among them, K(X,X) is the covariance matrix between training points, K(X,X * ) is the covariance matrix between the training points and the query points, K(X * ,X * ) is the covariance matrix between query points, For each local model, select the k The training data of the training set is x local and local , the data is obtained by calculating the distance of each point from the center and taking the nearest data point: x local ={x local,1 ,x local,2 ,…,x local,m },and local ={and local,1 ,and local,2 ,…,and local,m } (5) After fitting the model, the optimized Gaussian regression model is compared with the experimental data to verify its accuracy.

4. The SMA-driven parallel attitude adjustment platform control method based on Gaussian process regression optimization according to claim 3 is characterized in that: The fitting effect is evaluated by comparing the fitting output with the actual measured data. Based on the verification results, the Gaussian regression model is fine-tuned to ensure that the fitting error is within an acceptable range, and the generalization ability of the model is further optimized to make it stable under different conditions.

5. The SMA-driven parallel attitude adjustment platform control method based on Gaussian process regression optimization according to claim 4 is characterized in that: In order to verify the robustness and predictive ability of the model, we randomly generated data prediction values ​​within the input data range. x new ={x new,1 ,x new,2 ,…,x new,m } (6) The input data will be predicted on each local model. For each new input x new,i , calculate its relationship with each local model center c k The distance between them is calculated using the Gaussian kernel function to calculate the weight of the input in different local models: Where W is the kernel width, which controls the decay rate of the weight with distance. For each local model k based on the new input x new,i , using the previously trained Gaussian process regression model LGPR k Make predictions and get local prediction values and standard deviation Among them, k # is the new input x new,i and the training data, and K is the kernel matrix of the training data. The standard deviation is predicted to be According to the prediction values ​​and weights of each local model, for each new input x new,i The prediction results are weighted averaged to get the total prediction value At the same time, the square of the standard deviation σ 2 (x new,i ) is also weighted by the square of the weight The final standard deviation is To test the final results, the MATLAB graphics tool plots the predicted results together with the 95% confidence interval to show the predicted values And its uncertainty range:

6. The SMA-driven parallel attitude adjustment platform control method based on Gaussian process regression optimization according to claim 5 is characterized in that: Through the above process, the local Gaussian process regression model can make predictions based on new input data, and perform weighted averaging of the prediction results of multiple local models through distance weights, and finally output the global prediction value and its uncertainty.

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