Moxibustion robot temperature self-adaptive regulation method and system and storage medium

Abstract

This invention relates to the field of control, and in particular to a method, system, and storage medium for adaptive temperature control of a moxibustion robot. The method involves acquiring the measured temperature of the skin surface, using a composite thermal model combining partial differential equations of heat conduction and Gaussian process regression to predict the skin temperature over a finite time domain, and compensating for model errors using Gaussian process regression. The optimal control sequence is calculated by solving a finite-time domain optimization problem. In the objective function programming, the penalty for overheating is adjusted based on the measured rate of change of temperature, ensuring that the penalty for overheating is always greater than the penalty for underheating. Simultaneously, a penalty weight for changes in control input is set based on the confidence interval of the Gaussian process prediction. After optimization, the first element of the control sequence is applied to the end effector of the moxibustion robot. When the sliding mean of the model prediction residual exceeds a threshold, the boundary conditions of the heat conduction model are updated based on recent temperature data, thus achieving adaptive adjustment of the moxibustion temperature.

Description

Technical Field

[0001] This application belongs to the field of control, and in particular relates to a method, system and storage medium for temperature adaptive regulation of a moxibustion robot. Background Technology

[0002] The core technological challenge of moxibustion robots lies in how to accurately and safely regulate the skin surface temperature of the moxibustion area, maintaining it stably within the treatment temperature range. This requires ensuring the cumulative effect of thermal stimulation to achieve therapeutic efficacy while avoiding burns caused by excessive heat. Currently, temperature control in moxibustion robots mostly employs traditional PID control methods. However, due to the complexity, time-varying nature, and individual variability of human skin's thermal properties, the control effect often falls short of ideal. The thermal parameters of human skin tissue are complex, exhibit significant individual differences, and change during moxibustion due to physiological responses such as blood flow variations. The models relied upon by control methods are often oversimplified, resulting in low control accuracy and a tendency for temperature overshoot or slow response. Furthermore, existing control strategies typically impose equal penalty weights on insufficient heating and temperature overshoot, failing to fully reflect the priority of preventing burns, thus posing safety risks when faced with external disturbances or model mismatch. When the model's confidence in predicting future temperatures is low, if the controller still performs significant adjustments, it may exacerbate system instability. Therefore, there is an urgent need for a temperature control method that can balance safety and handle uncertainty in order to improve the clinical application effect of moxibustion robots. Summary of the Invention

[0003] This invention proposes a temperature adaptive control method for moxibustion robots to address the shortcomings of existing methods that fail to adequately reflect the core safety requirement of preventing burns and neglect the inherent uncertainty of model predictions. The method includes the following steps: Obtain the measured surface temperature of the skin in the moxibustion area, as determined by the temperature sensor at the end of the moxibustion robot; Based on a composite thermal model consisting of a partial differential equation module for heat conduction and a Gaussian process regression module, the skin surface temperature in the future within a finite time domain is predicted, wherein the Gaussian process regression module is used to compensate for the prediction error of the partial differential equation module for heat conduction. A finite-time optimization problem is constructed and solved to obtain the control input sequence for controlling the end effector of the moxibustion robot. When constructing the objective function of the optimization problem: the penalty weight for predicted skin surface temperature exceeding the upper bound of the target temperature range is adjusted based on the rate of change of the current measured skin surface temperature, ensuring that the penalty weight is always greater than the penalty weight for predicted skin surface temperature falling below the lower bound of the target temperature range; and the penalty weight for changes in the control input is set based on the width of the predicted confidence interval output by the Gaussian process regression module. The first element of the control input sequence is used as the control quantity in the current control cycle and applied to the end effector. When the residual moving average of the predicted value output by the heat conduction partial differential equation module and the measured temperature of the skin surface exceeds a preset threshold, the boundary conditions of the heat conduction partial differential equation module are updated using the recently collected measured temperature data of the skin surface.

[0004] Optionally, the prediction of skin surface temperature within a finite time domain based on the composite thermal model composed of a partial differential equation module for heat conduction and a Gaussian process regression module, wherein the Gaussian process regression module is used to compensate for the prediction error of the partial differential equation module for heat conduction, including: The control input of the end effector of the moxibustion robot is used as the input of the heat conduction partial differential equation module to obtain the predicted value of the skin surface temperature in the future finite time domain. The difference between the measured skin surface temperature at a historical moment and the predicted value output by the heat conduction partial differential equation module is used as the training data for the Gaussian process regression module to obtain the compensation value for the prediction error in the future finite time domain. The predicted value is added to the compensation value for the prediction error to obtain the predicted value of the skin surface temperature within a finite time domain in the future.

[0005] Optionally, adjusting the penalty weight for the predicted skin surface temperature exceeding the upper bound of the target temperature range based on the rate of change of the currently measured skin surface temperature includes: The penalty weight during control period k is calculated using the following formula. :

[0006] in, To preset the base penalty weight, This is the adjustment coefficient, in units of... , and These are the measured skin surface temperatures for the current control cycle and the previous control cycle, respectively. To control the cycle duration.

[0007] Optionally, ensuring that the penalty weight is always greater than the penalty weight for the predicted skin surface temperature being below the lower bound of the target temperature range includes: The penalty weight will be applied to the predicted skin surface temperature being below the lower bound of the target temperature range. Set to a fixed positive number; In each adjustment Then, update according to the following formula:

[0008] in, It is a preset positive integer.

[0009] Optionally, setting the penalty weight for changes in the control input based on the width of the predicted confidence interval output by the Gaussian process regression module includes: Obtain the Gaussian process regression module's performance in predicting the future finite time domain. Variance of predicted values ​​at each sampling time j ; The penalty weight for changes in control input during control period k is calculated using the following formula. :

[0010] in, To preset the base penalty weight, This is the adjustment coefficient, in units of... .

[0011] Optionally, constructing the objective function of the optimization problem includes: The objective function J of the optimization problem is expressed as:

[0012] in, To predict the time domain, To control the time domain; and These are the deviation relaxation variables for the predicted skin surface temperature exceeding the upper bound and falling below the lower bound of the target temperature range in the j-th prediction step, respectively. The change in control input at the j-th control step; , R(k) and R(k) are the corresponding penalty weights, respectively.

[0013] Optionally, when the residual moving average between the predicted value output by the heat conduction partial differential equation module and the measured skin surface temperature exceeds a preset threshold, updating the boundary conditions of the heat conduction partial differential equation module using recently collected measured skin surface temperature data includes: In each control cycle, the absolute value of the difference between the measured temperature of the skin surface and the predicted value output by the heat conduction partial differential equation module is calculated as the residual for the current cycle. Calculate the moving average of the residuals for a first preset number of recent control cycles; When the residual moving average value is greater than the preset temperature threshold, the boundary conditions of the heat conduction partial differential equation module are updated by solving the inverse heat conduction problem using the measured skin surface temperature data of the second preset number of recent control cycles and the corresponding control input data.

[0014] Furthermore, the present invention also relates to a temperature adaptive control system for a moxibustion robot, comprising the following modules: The acquisition module is used to acquire the measured temperature of the skin surface in the moxibustion area as measured by the temperature sensor at the end of the moxibustion robot. The prediction module is used to predict the skin surface temperature in the future within a finite time domain based on a composite thermal model consisting of a heat conduction partial differential equation module and a Gaussian process regression module, wherein the Gaussian process regression module is used to compensate for the prediction error of the heat conduction partial differential equation module. A construction module is used to construct and solve a finite-time optimization problem to obtain a control input sequence for controlling the end effector of the moxibustion robot. Specifically, when constructing the objective function of the optimization problem: the penalty weight for predicted skin surface temperatures exceeding the upper bound of the target temperature range is adjusted based on the rate of change of the current measured skin surface temperature, ensuring that the penalty weight is always greater than the penalty weight for predicted skin surface temperatures falling below the lower bound of the target temperature range; and the penalty weight for changes in the control input is set based on the predicted confidence interval width output by the Gaussian process regression module. An update module is used to take the first element of the control input sequence as the control quantity in the current control cycle and apply it to the end effector; when the residual moving average of the predicted value output by the heat conduction partial differential equation module and the measured temperature of the skin surface exceeds a preset threshold, the boundary conditions of the heat conduction partial differential equation module are updated using recently collected measured temperature data of the skin surface.

[0015] Preferably, the method for predicting the skin surface temperature over a finite time domain based on a composite thermal model consisting of a partial differential equation module for heat conduction and a Gaussian process regression module includes: The control input of the end effector of the moxibustion robot is used as the input of the heat conduction partial differential equation module to obtain the predicted value of the skin surface temperature in the future finite time domain. The difference between the measured skin surface temperature at a historical moment and the predicted value output by the heat conduction partial differential equation module is used as the training data for the Gaussian process regression module to obtain the compensation value for the prediction error in the future finite time domain. The predicted value is added to the compensation value for the prediction error to obtain the predicted value of the skin surface temperature within a finite time domain in the future.

[0016] Preferably, adjusting the penalty weight for the predicted skin surface temperature exceeding the upper bound of the target temperature range based on the rate of change of the current measured skin surface temperature includes: The penalty weight during control period k is calculated using the following formula. :

[0017] in, To preset the base penalty weight, This is the adjustment coefficient, in units of... , and These are the measured skin surface temperatures for the current control cycle and the previous control cycle, respectively. To control the cycle duration.

[0018] Preferably, ensuring that the penalty weight is always greater than the penalty weight for the predicted skin surface temperature being below the lower bound of the target temperature range includes: The penalty weight will be applied to the predicted skin surface temperature being below the lower bound of the target temperature range. Set to a fixed positive number; In each adjustment Then, update according to the following formula:

[0019] in, It is a preset positive integer.

[0020] Preferably, the step of setting the penalty weight for changes in the control input based on the width of the predicted confidence interval output by the Gaussian process regression module includes: Obtain the Gaussian process regression module's performance in predicting the future finite time domain. Variance of predicted values ​​at each sampling time j ; The penalty weight R(k) for changes in control input during control period k is calculated using the following formula:

[0021] in, To preset the base penalty weight, This is the adjustment coefficient, in units of... .

[0022] Preferably, constructing the objective function of the optimization problem includes: The objective function J of the optimization problem is expressed as:

[0023] in, To predict the time domain, To control the time domain; and These are the deviation relaxation variables for the predicted skin surface temperature exceeding the upper bound and falling below the lower bound of the target temperature range in the j-th prediction step, respectively. The change in control input at the j-th control step; , and These are the corresponding penalty weights.

[0024] Preferably, when the residual moving average between the predicted value output by the heat conduction partial differential equation module and the measured skin surface temperature exceeds a preset threshold, updating the boundary conditions of the heat conduction partial differential equation module using recently collected measured skin surface temperature data includes: In each control cycle, the absolute value of the difference between the measured temperature of the skin surface and the predicted value output by the heat conduction partial differential equation module is calculated as the residual for the current cycle. Calculate the moving average of the residuals for a first preset number of recent control cycles; When the residual moving average value is greater than the preset temperature threshold, the boundary conditions of the heat conduction partial differential equation module are updated by solving the inverse heat conduction problem using the measured skin surface temperature data of the second preset number of recent control cycles and the corresponding control input data.

[0025] This invention improves the accuracy of skin surface temperature prediction by constructing a composite thermal model combining heat conduction mechanisms and Gaussian process regression, utilizing a compensation mechanism. In optimized control, preventing burns is the core safety objective. A penalty weight significantly higher than the lower limit is applied to cases where the predicted temperature exceeds the upper limit, and this weight is correlated with the rate of temperature change, thereby enhancing the safety of the moxibustion process. Furthermore, the uncertainty of the model prediction is represented and input into the controller. When the prediction confidence is low, drastic changes in the control output are suppressed, resulting in a smoother temperature regulation process. By monitoring long-term prediction deviations and correcting the model's boundary conditions, the reliability of the control system is ensured throughout the treatment process, achieving safe and stable temperature control for moxibustion. Attached Figure Description

[0026] Figure 1 This is a flowchart of the first embodiment. Detailed Implementation

[0027] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0028] In the first embodiment, the present invention proposes a method for adaptive temperature control of a moxibustion robot, such as... Figure 1 This includes the following steps: S1, Obtain the measured temperature of the skin surface in the moxibustion area as measured by the temperature sensor at the end of the moxibustion robot; An infrared temperature sensor is installed on the end effector of the moxibustion robot, such as the moxibustion head. The sensor is continuously aligned with the center of the skin in the target acupoint area, collects real-time temperature data of the skin surface, and transmits the data to the main controller for processing.

[0029] S2, Based on a composite thermal model consisting of a partial differential equation module for heat conduction and a Gaussian process regression module, the skin surface temperature within a finite time domain is predicted in the future, wherein the Gaussian process regression module is used to compensate for the prediction error of the partial differential equation module for heat conduction. A partial differential equation module based on the Pennes biological heat conduction equation was established. This module uses the moxibustion heat source as the heat flux boundary condition and performs discretization solving based on standard human tissue thermal parameters to obtain the predicted value of the skin surface temperature over the next N control cycles. Simultaneously, historical mechanistic prediction values ​​are compared with corresponding measured skin surface temperatures to calculate the prediction error sequence. A Gaussian process regression module is used to learn this error sequence, establishing a mapping relationship from the current system state (e.g., current temperature), past control inputs, to future prediction errors. The predicted values ​​from the partial differential equation module are added to the error compensation values ​​output by the Gaussian process regression module to obtain the predicted sequence of skin surface temperature over the next N control cycles.

[0030] In an optional embodiment, the prediction of skin surface temperature over a finite time domain based on a composite thermal model consisting of a partial differential equation module for heat conduction and a Gaussian process regression module, wherein the Gaussian process regression module is used to compensate for the prediction error of the partial differential equation module for heat conduction, including: The control input of the end effector of the moxibustion robot is used as the input of the heat conduction partial differential equation module to obtain the predicted value of the skin surface temperature in the future finite time domain. The difference between the measured skin surface temperature at a historical moment and the predicted value output by the heat conduction partial differential equation module is used as the training data for the Gaussian process regression module to obtain the compensation value for the prediction error in the future finite time domain. The predicted value is added to the compensation value for the prediction error to obtain the predicted value of the skin surface temperature within a finite time domain in the future.

[0031] The first step is to use the partial differential equation module for heat conduction to make predictions. This module is based on the Pennes biological heat transfer equation, and its governing equation is in the form of: Where ρ, c, and k are the density, specific heat capacity, and thermal conductivity of the tissue, respectively; Blood perfusion rate; , The density and specific heat capacity of blood; Arterial blood temperature; Metabolic heat production rate. The general tissue thermophysical properties ρ, c, k, and baseline blood perfusion rate in the model. and blood parameters , The initial values, derived from publicly available biomedical thermal property databases or typical literature values, and the control inputs of the moxibustion robot, such as the heating power P(k) of the moxibustion head or the height h(k) above the skin, are transformed into heat flux density boundary conditions applied to the skin surface. Where r represents the location on the skin surface, and the function f is determined through pre-heat calibration experiments of the robotic system. In each control cycle k, the control input sequence is based on the currently estimated tissue internal temperature field distribution T(x,k) obtained recursively from the prediction results of the previous cycle or from the state estimator, and the future assumptions provided by the optimizer. The above partial differential equations are numerically solved using efficient numerical methods such as order-reduction models or pre-calculated parameterized responses. This yields a skin surface temperature sequence over, for example, 10 sampling times within the future prediction time domain; this is the predicted value. .

[0032] The second step is to use the Gaussian process regression module to compensate for the model's prediction error by collecting historical data, such as measured skin surface temperatures over a past period, including the most recent L=60 sampling periods. Compared with the predicted value calculated by the heat conduction module using historical control inputs at the same time. The difference As training data. Crucially, each error sample... Corresponding input features It is a state vector reflecting the dynamics of the system at a given moment, and its components include: the control inputs at the current moment and several past moments. Measured temperature Predicted values And their combinations and derived characteristics. Gaussian process regression models learn from datasets... Establish a system dynamic state To prediction error The model uses probability mapping. The core of the model is the kernel function, such as the radial basis function kernel, which defines the correlation of errors between different system states. The training process involves optimizing the hyperparameters of the kernel function based on data. After training, to predict future time-domain errors, it is necessary to first construct state feature vectors corresponding to each future time step based on the current system state and the future assumptions provided by the optimizer. These feature vectors are then input into the trained Gaussian process regression model. The model will output the mean and variance of the prediction error at the corresponding time step, where the mean is the compensation value for the prediction error. For example, if the historical error fluctuates around 0.5℃, the model will predict a future compensation value sequence close to 0.5℃.

[0033] The third step is to combine the two sets of results to obtain the predicted value. The predicted value sequence output by the heat conduction partial differential equation module is added point-by-point according to time step to the predicted error compensation value sequence output by the Gaussian process regression module. For example, if the predicted temperature at the next moment is 42.5℃, and the error compensation value is 0.6℃, then the predicted skin surface temperature is 43.1℃. The former provides the basic trend of temperature change, while the latter compensates for model mismatch caused by complex factors such as individual differences and environmental changes, thereby improving the accuracy of temperature prediction.

[0034] S3, Construct and solve a finite-time optimization problem to obtain the control input sequence for controlling the end effector of the moxibustion robot, wherein, when constructing the objective function of the optimization problem: Specifically, in each control cycle, a model predictive control optimization problem is constructed. The objective function of this problem is a comprehensive cost function, and the decision variables are the control input sequence over the next N control cycles, such as the distance sequence between the moxibustion head and the skin or the heating power sequence of the moxibustion head. The optimization problem is solved using a numerical optimization algorithm, such as sequential quadratic programming, to obtain an optimal control input sequence.

[0035] Based on the rate of change of the current measured skin surface temperature, adjust the penalty weight for the predicted skin surface temperature exceeding the upper limit of the target temperature range, and ensure that the penalty weight is always greater than the penalty weight for the predicted skin surface temperature falling below the lower limit of the target temperature range. Specifically, the objective function sets a penalty for predicted temperatures falling below the lower bound of the target temperature range, with a weight set to a relatively small normal number; and a penalty for predicted temperatures exceeding the upper bound of the target temperature range, with a base weight set to a value much larger than the former, such as ten times the former. This upper bound penalty weight is adjusted in real time based on the measured rate of temperature change at the current moment. For example, when a rapid temperature rise is detected, this penalty weight is further increased through a gain function, thereby causing the controller to take a more conservative action to actively avoid the risk of burns.

[0036] Based on the width of the predicted confidence interval output by the Gaussian process regression module, a penalty weight is set for changes in the control input. Specifically, the Gaussian process regression module outputs a prediction variance along with the error compensation value. This variance represents the degree of uncertainty in the model's prediction. The objective function includes a term that penalizes changes in the control input, and its weight is positively correlated with this prediction variance. When the prediction variance provided by the Gaussian process regression module is large, i.e., the confidence interval is wide, indicating that the model is uncertain about the prediction of the current state, this weight will be increased accordingly. This suppresses drastic control actions by the controller, ensuring the smoothness of the control process.

[0037] To achieve temperature control safety adjustment, in one optional embodiment, adjusting the penalty weight for the predicted skin surface temperature exceeding the upper bound of the target temperature range based on the rate of change of the currently measured skin surface temperature includes: The penalty weight during control period k is calculated using the following formula. :

[0038] in, To preset the base penalty weight, This is the adjustment coefficient, in units of... , and These are the measured skin surface temperatures for the current control cycle and the previous control cycle, respectively. To control the cycle duration.

[0039] When skin temperature rises rapidly, it indicates a higher risk of overheating. Therefore, the penalty for exceeding the target temperature limit needs to be increased, causing the controller to take more conservative control actions. The measured skin surface temperature values ​​for the current control cycle k and the previous control cycle k-1 are obtained. and For example, let the control cycle duration be... For 1 second, It was 43.5℃. The temperature was 43.2℃.

[0040] Calculate the rate of change of skin surface temperature, i.e. In this example, it is ℃ / s. A positive value indicates that the temperature is trending upward. Calculate the new penalty weight according to the given formula. Assume a pre-defined base penalty weight. The adjustment coefficient is 100. If the value is 50s / ℃, then the new penalty weight is: Conversely, if the temperature is decreasing, for example... If the temperature is 43.0℃, then the rate of temperature change is -0.2℃ / s, and the new penalty weight will be adjusted to 90. In this way, the penalty weight... It adjusts according to the rate of temperature change, making the model predictive control system more cautious when the temperature rises rapidly, prioritizing safety.

[0041] In an optional embodiment, ensuring that the penalty weight is always greater than the penalty weight for the predicted skin surface temperature being below the lower bound of the target temperature range includes: The penalty weight will be applied to the predicted skin surface temperature being below the lower bound of the target temperature range. Set to a fixed positive number; In each adjustment Then, update according to the following formula:

[0042] in, It is a preset positive integer.

[0043] A mandatory constraint is added to the safety control strategy: preventing skin burns always takes precedence over maintaining the temperature within the therapeutic warming range. A weight is set to penalize temperatures falling below the lower bound of the target range. For example, the weight can be set to a constant of 50. A preset positive constant can be set. As a safety margin, for example The value is 10. This indicates the penalty weight for overheating. Must always be at least .

[0044] In each control cycle, a temporary [condition] is calculated based on the rate of temperature change using the method described above. Value. Perform comparison and update operations. Calculated values ​​change as temperature rises. The value is 115. This value is compared to the threshold 60, i.e. The updated It remains at 115. Considering the temperature drop, the calculated value is... 90, execute The updated value is 90. However, if the temperature drops very quickly, it will cause the calculated value to be... If the value is less than 60, for example, 45, then execute... , The setting is forced to 60. This ensures that even with a decreasing temperature trend, the controller remains minimally vigilant against potential overheating risks, thus guaranteeing control safety.

[0045] To adjust the aggressiveness of the controller's behavior based on the uncertainty of the model predictions, in one optional embodiment, setting the penalty weight for changes in the control input based on the width of the predicted confidence interval output by the Gaussian process regression module includes: Obtain the Gaussian process regression module's performance in predicting the future finite time domain. Variance of predicted values ​​at each sampling time j ; The penalty weight for changes in control input during control period k is calculated using the following formula. :

[0046] in, To preset the base penalty weight, This is the adjustment coefficient, in units of... .

[0047] A key characteristic of Gaussian process regression models is that they provide not only the predicted mean but also the predicted variance. The variance represents the confidence level of the model's prediction for future time j. A larger variance indicates higher uncertainty. The first step is to obtain the future prediction time domain from the Gaussian process regression module at each control cycle. The prediction variance values ​​at all sampling times are used to form a variance sequence. For example, suppose the prediction time domain is... With a step size of 10, the obtained variance sequence may be: .

[0048] The second step is to calculate the penalty weight for changes in the control input based on the variance value. Calculate the average of all variances within the prediction time domain. This represents the average uncertainty of the model's overall future predictions. In the example above, the average variance is assumed to be 0.06. The formula is used to calculate... Set a preset base penalty weight. The adjustment coefficient is 0.5. for .but . The value will be used in the objective function to penalize changes in the control input. When model uncertainty is high, the mean variance increases. This increase in uncertainty leads the controller to tend to produce smoother, smaller changes in control action, avoiding risky operations based on uncertain predictions. Conversely, when the model prediction is very certain, Reducing the size allows the controller to make a more sensitive response.

[0049] In an optional embodiment, constructing the objective function of the optimization problem includes: The objective function J of the optimization problem is expressed as:

[0050] in, To predict the time domain, To control the time domain; and These are the deviation relaxation variables for the predicted skin surface temperature exceeding the upper bound and falling below the lower bound of the target temperature range in the j-th prediction step, respectively. The change in control input at the j-th control step; , R(k) and R(k) are the corresponding penalty weights, respectively.

[0051] The objective function is the mathematical expression of the model predictive control core optimization, aiming to find an optimal control input sequence in each control cycle, balancing efficacy and safety. The first term of the function... The focus is on the entire prediction time domain in the future. Temperature control performance within the range. For example, assuming the target temperature range is 42 to 44°C, if the predicted temperature is 44.5°C in the j-th prediction step, then the upper bias slack variable... The lower deviation is 0.5. The value is 0; if the predicted temperature is 41.8℃, then... =0, The value is 0.2. This term multiplies the square of the deviation by the corresponding penalty weight. and The summation is then performed to minimize the deviation of the predicted temperature from the target range, particularly the deviation from the over-temperature range.

[0052] The second term of the objective function The focus is on the smoothness of the control input. For example, if the control input u is the heating power, the current power is 50 watts, and the planned power for the next control step is 52 watts, then... The value is 2 watts. This function aims to suppress drastic changes in control input, making the moxibustion robot's movements smoother and more stable. In summary, the optimization solver searches for a set of future control input changes in each control cycle. , , This minimizes the value of the overall objective function J. It represents the optimal trade-off between meeting temperature control requirements and ensuring control stability.

[0053] S4, take the first element of the control input sequence as the control quantity in the current control cycle and apply it to the end effector; when the residual sliding average of the predicted value output by the heat conduction partial differential equation module and the measured temperature of the skin surface exceeds a preset threshold, update the boundary conditions of the heat conduction partial differential equation module using the recently collected measured temperature data of the skin surface.

[0054] After solving the optimization problem and obtaining the optimal control input sequence containing N elements, only the first control input value of the sequence is extracted. This value is sent to the underlying driver of the moxibustion robot's end effector. For example, if the control variable is the height of the moxibustion head, the servo motor is instructed to move to that height; if the control variable is the heating power, the heater power is set to that value. In the next control cycle, the measurement, prediction, and optimization are repeated, and the entire process is repeated.

[0055] The system continuously calculates the difference between the predicted values ​​from the partial differential equation of heat conduction and the measured temperature of the skin surface—the residual—in the background. It also calculates a moving average of the residual values ​​over a recent period, such as the past minute. A preset residual threshold, for example, 0.5℃, is used. If the absolute value of this moving average exceeds this threshold, it indicates a systematic bias in the mechanistic model. At this point, a parameter identification program is automatically invoked. Using recently collected measured temperature data and corresponding control input data, it re-estimates the heat flux boundary condition parameters in the partial differential equation of heat conduction using methods such as least squares, thus completing the online correction of the mechanistic model.

[0056] In an optional embodiment, when the residual moving average between the predicted value output by the heat conduction partial differential equation module and the measured skin surface temperature exceeds a preset threshold, updating the boundary conditions of the heat conduction partial differential equation module using recently collected measured skin surface temperature data includes: In each control cycle, the absolute value of the difference between the measured temperature of the skin surface and the predicted value output by the heat conduction partial differential equation module is calculated as the residual for the current cycle. Calculate the moving average of the residuals for a first preset number of recent control cycles; When the residual moving average value is greater than the preset temperature threshold, the boundary conditions of the heat conduction partial differential equation module are updated by solving the inverse heat conduction problem using the measured skin surface temperature data of the second preset number of recent control cycles and the corresponding control input data.

[0057] To address the issue of model parameter drift over time, online calibration of the model itself is implemented. The first step is to continuously monitor the model's accuracy. In each control cycle k, the actual skin temperature measured by the sensor is recorded. Predicted values ​​output by the partial differential equation module for heat conduction under the same conditions The two are compared, and the absolute difference is calculated as the residual for the current period. For example, if... It was 43.1℃. If the temperature is 42.5℃, then the current residual is 0.6℃.

[0058] The second step is to determine if model mismatch has occurred. This involves maintaining a queue containing, for example, the residuals from the most recent 20 control cycles and calculating the moving average of these residuals. This filters out the influence of noise from single measurements, focusing on the model's persistent, systematic biases. For example, if the moving average of the residuals from the most recent 20 cycles is 0.8℃, and the preset temperature threshold for triggering an update is 0.7℃, the update procedure will be initiated because the moving average is greater than the threshold.

[0059] The third step is to perform a model update. Once the update is triggered, historical data is retrieved, such as the measured skin surface temperature sequence over the past 60 control cycles and the corresponding control input sequence of the moxibustion robot. Using this data, an inverse heat conduction problem is solved. Unlike the direct problem, which solves for the temperature field based on boundary conditions and physical properties, the inverse problem infers unknown boundary condition parameters, such as the convective heat transfer coefficient or the applied heat flux density, from the known temperature field response. Through numerical optimization algorithms, a new set of boundary condition parameters is found, under which the heat conduction model's predictions for the aforementioned 60 cycles of historical data best match the actual measurements. The updated boundary conditions replace the old parameters for subsequent predictive control, thereby improving the model's accuracy.

[0060] In a second embodiment, the present invention also provides a temperature adaptive control system for a moxibustion robot, comprising the following modules: The acquisition module is used to acquire the measured temperature of the skin surface in the moxibustion area as measured by the temperature sensor at the end of the moxibustion robot. The prediction module is used to predict the skin surface temperature in the future within a finite time domain based on a composite thermal model consisting of a heat conduction partial differential equation module and a Gaussian process regression module, wherein the Gaussian process regression module is used to compensate for the prediction error of the heat conduction partial differential equation module. The module is used to construct and solve a finite-time optimization problem to obtain the control input sequence for controlling the end effector of the moxibustion robot. Specifically, when constructing the objective function of the optimization problem: Based on the rate of change of the current measured skin surface temperature, adjust the penalty weight for the predicted skin surface temperature exceeding the upper limit of the target temperature range, and ensure that the penalty weight is always greater than the penalty weight for the predicted skin surface temperature falling below the lower limit of the target temperature range. Based on the width of the predicted confidence interval output by the Gaussian process regression module, a penalty weight is set for changes in the control input. An update module is used to take the first element of the control input sequence as the control quantity in the current control cycle and apply it to the end effector; when the residual moving average of the predicted value output by the heat conduction partial differential equation module and the measured temperature of the skin surface exceeds a preset threshold, the boundary conditions of the heat conduction partial differential equation module are updated using recently collected measured temperature data of the skin surface.

[0061] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can be referred to each other.

[0062] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for adaptive temperature control of a moxibustion robot, characterized in that, Includes the following steps: Obtain the measured surface temperature of the skin in the moxibustion area, as determined by the temperature sensor at the end of the moxibustion robot; Based on a composite thermal model consisting of a partial differential equation module for heat conduction and a Gaussian process regression module, the skin surface temperature in the future within a finite time domain is predicted, wherein the Gaussian process regression module is used to compensate for the prediction error of the partial differential equation module for heat conduction. A finite-time optimization problem is constructed and solved to obtain the control input sequence for controlling the end effector of the moxibustion robot. When constructing the objective function of the optimization problem: the penalty weight for predicted skin surface temperature exceeding the upper bound of the target temperature range is adjusted based on the rate of change of the current measured skin surface temperature, ensuring that the penalty weight is always greater than the penalty weight for predicted skin surface temperature falling below the lower bound of the target temperature range; and the penalty weight for changes in the control input is set based on the width of the predicted confidence interval output by the Gaussian process regression module. The first element of the control input sequence is used as the control quantity in the current control cycle and applied to the end effector. When the residual moving average of the predicted value output by the heat conduction partial differential equation module and the measured temperature of the skin surface exceeds a preset threshold, the boundary conditions of the heat conduction partial differential equation module are updated using the recently collected measured temperature data of the skin surface.

2. The method according to claim 1, characterized in that, The composite thermal model, based on a partial differential equation module for heat conduction and a Gaussian process regression module, predicts the skin surface temperature over a finite time domain. The Gaussian process regression module is used to compensate for the prediction error of the partial differential equation module for heat conduction, and includes: The control input of the end effector of the moxibustion robot is used as the input of the heat conduction partial differential equation module to obtain the predicted value of the skin surface temperature in the future finite time domain. The difference between the measured skin surface temperature at a historical moment and the predicted value output by the heat conduction partial differential equation module is used as the training data for the Gaussian process regression module to obtain the compensation value for the prediction error in the future finite time domain. The predicted value is added to the compensation value for the prediction error to obtain the predicted value of the skin surface temperature within a finite time domain in the future.

3. The method according to claim 1, characterized in that, The step of adjusting the penalty weight for predicted skin surface temperatures exceeding the upper bound of the target temperature range based on the rate of change of the currently measured skin surface temperature includes: The penalty weight during control period k is calculated using the following formula. : in, To preset the base penalty weight, This is the adjustment coefficient, in units of... , and These are the measured skin surface temperatures for the current control cycle and the previous control cycle, respectively. To control the cycle duration.

4. The method according to claim 3, characterized in that, Ensuring that the penalty weight is always greater than the penalty weight for the predicted skin surface temperature being below the lower bound of the target temperature range includes: The penalty weight will be applied to the predicted skin surface temperature being below the lower bound of the target temperature range. Set to a fixed positive number; In each adjustment Then, update according to the following formula: in, It is a preset positive integer.

5. The method according to claim 1 or 4, characterized in that, The step of setting penalty weights for changes in control input based on the predicted confidence interval width output by the Gaussian process regression module includes: Obtain the Gaussian process regression module's performance in predicting the future finite time domain. Variance of predicted values ​​at each sampling time j ; The penalty weight for changes in control input during control period k is calculated using the following formula. : in, To preset the base penalty weight, This is the adjustment coefficient, in units of... .

6. The method according to claim 1, characterized in that, The objective function for constructing the optimization problem includes: The objective function J of the optimization problem is expressed as: in, To predict the time domain, To control the time domain; and These are the deviation relaxation variables for the predicted skin surface temperature exceeding the upper bound and falling below the lower bound of the target temperature range in the j-th prediction step, respectively. The change in control input at the j-th control step; , and These are the corresponding penalty weights.

7. The method according to claim 1, characterized in that, When the residual moving average between the predicted value output by the heat conduction partial differential equation module and the measured skin surface temperature exceeds a preset threshold, the boundary conditions of the heat conduction partial differential equation module are updated using recently collected measured skin surface temperature data, including: In each control cycle, the absolute value of the difference between the measured temperature of the skin surface and the predicted value output by the heat conduction partial differential equation module is calculated as the residual for the current cycle. Calculate the moving average of the residuals for a first preset number of recent control cycles; When the residual moving average value is greater than the preset temperature threshold, the boundary conditions of the heat conduction partial differential equation module are updated by solving the inverse heat conduction problem using the measured skin surface temperature data of the second preset number of recent control cycles and the corresponding control input data.

8. A temperature adaptive control system for a moxibustion robot, characterized in that, Includes the following modules: The acquisition module is used to acquire the measured temperature of the skin surface in the moxibustion area as measured by the temperature sensor at the end of the moxibustion robot. The prediction module is used to predict the skin surface temperature in the future within a finite time domain based on a composite thermal model consisting of a heat conduction partial differential equation module and a Gaussian process regression module, wherein the Gaussian process regression module is used to compensate for the prediction error of the heat conduction partial differential equation module. A construction module is used to construct and solve a finite-time optimization problem to obtain a control input sequence for controlling the end effector of the moxibustion robot. Specifically, when constructing the objective function of the optimization problem: the penalty weight for predicted skin surface temperatures exceeding the upper bound of the target temperature range is adjusted based on the rate of change of the current measured skin surface temperature, ensuring that the penalty weight is always greater than the penalty weight for predicted skin surface temperatures falling below the lower bound of the target temperature range; and the penalty weight for changes in the control input is set based on the predicted confidence interval width output by the Gaussian process regression module. An update module is used to take the first element of the control input sequence as the control quantity in the current control cycle and apply it to the end effector; when the residual moving average of the predicted value output by the heat conduction partial differential equation module and the measured temperature of the skin surface exceeds a preset threshold, the boundary conditions of the heat conduction partial differential equation module are updated using recently collected measured temperature data of the skin surface.

9. The system according to claim 8, characterized in that, The composite thermal model, based on a partial differential equation module for heat conduction and a Gaussian process regression module, predicts the skin surface temperature over a finite time domain. The Gaussian process regression module is used to compensate for the prediction error of the partial differential equation module for heat conduction, and includes: The control input of the end effector of the moxibustion robot is used as the input of the heat conduction partial differential equation module to obtain the predicted value of the skin surface temperature in the future finite time domain. The difference between the measured skin surface temperature at a historical moment and the predicted value output by the heat conduction partial differential equation module is used as the training data for the Gaussian process regression module to obtain the compensation value for the prediction error in the future finite time domain. The predicted value is added to the compensation value for the prediction error to obtain the predicted value of the skin surface temperature within a finite time domain in the future.

10. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when executed by a processor, implements the method as described in any one of claims 1-7.

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