A data-driven based hot updrafts positioning method

Abstract

The application discloses a data-driven hot updraft positioning method. For a long time, unmanned aerial vehicles have been indispensable in industries such as surveillance tasks, geographic mapping and target reconnaissance. Flight endurance is a key limitation for the widespread use of unmanned aerial vehicles. However, despite researchers' efforts to modify and optimize aerodynamic shapes to reduce glider drag or replace battery reactants, there are limitations to using these methods to improve flight endurance. The present application aims to harness the energy of nature by collecting wind energy. The present application considers estimating the updraft, then estimating the position of the wind field through a sparse identification algorithm of nonlinear dynamics. The proposed SINDy-based method and its characteristics of accurately identifying the mathematical physics specification model achieve hot positioning, improve the ability to identify hot updrafts, and increase the energy of the aircraft.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of data-driven thermal updraft localization, in particular to a data-driven thermal updraft localization method. BACKGROUND

[0002] There are two main sources of updrafts, one of which is terrain. They form mainly around fixed ridges or tall structures and change position depending on the direction of the incoming air flow. Flight tests in the air flow in front of the mountains and buildings provide evidence for the potential use of terrain updrafts. The other source of updrafts is the uneven ground temperature caused by the cloud cover blocking the sun. The lighter air mass above the heated surface rises, causing the surrounding air to converge towards the center and create an updraft. Birds, including hawks and frigatebirds, have been observed actively tracking this updraft for aerial surveillance and hunting.

[0003] A key technical challenge that must be addressed before simulating bird unpowered flight is the localization of thermal cells. To estimate the center and parameters of the thermal updraft, an algorithm based on the centroid method is designed, which can use the measured air flow velocity to determine the position of the thermal updraft, in addition, the convergence of the updraft amplitude and radius is achieved by iterative least squares error minimization.

[0004] The shape of the thermal updraft is generalized from a Gaussian distribution to an elliptical cross-section. This generalization can estimate the center position and other parameters. However, these methods require the storage of batch data for solving and iteration, which consumes the storage space of the aircraft computer. To overcome this problem, two extended Kalman filters can be used, which are commonly used in flight controllers to estimate the localization of thermal updrafts, as well as the orientation and distance relative to the glider. In this algorithm, only the state vector and covariance matrix of the filter need to be stored for long-term use. A more complete thermal model is constructed using a spline curve, which can also be estimated using Kalman filtering to estimate the model coefficients. Another innovative method involves using an onboard camera to remotely measure and estimate the thermal updraft under cumulus clouds. This method develops a Kalman filter to estimate the lifetime and strength of the thermal.

[0005] Multi-thermal updraft localization algorithms can provide more opportunities for global planning algorithms. However, identifying the parameters of a single thermal updraft is very beneficial for locating them in a small range, especially when the monitoring range of the glider is limited. In previous work, thermal updrafts were usually treated as a nonlinear model. Although it may be difficult to derive the thermal updraft model parameters from first principles, data-driven methods have helped researchers uncover the laws of physics. This prompted us to use sparse identification of nonlinear dynamics (SINDy) to address the challenge of estimating unknown parameters.

[0006] The core idea of the SINDy algorithm is to use sparse regression techniques to identify the nonlinear differential equations of a dynamic system from measurement data. It assumes that the dynamics of the system can be described by a linear combination of a few functions from a function library. Through an optimization algorithm, SINDy can select the few functions that have the most impact on the system dynamics and determine their coefficients, thus constructing a concise and accurate mathematical model. This usually requires collecting observation data of the system, which typically includes time series of the system state. Through an optimization algorithm, SINDy can select the few functions that have the most impact on the system dynamics and determine their coefficients, thus constructing a concise and accurate mathematical model. Finally, according to the results of sparse regression, a mathematical model of the system is constructed. This model is usually a nonlinear differential equation that describes the dynamic behavior of the system.

[0007] The SINDy method has the following advantages. First, it does not rely on prior knowledge, but learns the dynamics of the system from observation data. This makes it a powerful tool for dealing with complex systems, especially in the absence of detailed physical models. It also has interpretability. Through the derived dynamic equations, researchers can gain a deeper understanding of the behavior and interactions of the system. This provides strong support for the interpretability of the system. Therefore, the SINDy method has been successfully applied in many fields, including dynamic systems, fluid mechanics, chemical reaction networks, etc. Its application in practical problems demonstrates its applicability to nonlinear dynamic modeling.

[0008] Existing literature has shown that it is possible to sample some data from sensors under flow conditions to identify a series of mathematical and physical canonical models, such as the Korteweg-de Vries (KdV) or Navier-Stokes equations. Several strongly nonlinear systems, such as the dynamics of the F8 fighter jet, can also be accurately identified. The SINDy algorithm is a data-driven algorithm with the ability to identify models concisely and in real time.

[0009] The proposed method based on SINDy significantly improves the identification of hot updrafts under observation conditions. This is achieved through the characteristics of the proposed SINDy-based method and its accurate identification of mathematical models. The error of the parameter estimation process can be ignored, which is superior to existing methods. Compared with traditional algorithms, this method does not require the adjustment of algorithm parameters. In addition, it is found that certain parameters of the heat source can be accurately estimated under unobservable conditions. We verified the proposed method through hardware-in-the-loop simulation on a compact embedded hardware platform of a UAV. The method is feasible in real-time online applications. These results may provide promising progress for the accurate positioning of autonomous flying heat sources. SUMMARY

[0010] The present application aims at the deficiencies of the prior art, and provides a hot updraft positioning method based on data driving.

[0011] The present application aims at the deficiencies of the prior art, and provides a hot updraft positioning method based on data driving.

[0012] The hot updraft is characterized by using a mathematical model, so as to reduce false parameter estimation and balance between environmental fidelity and calculation cost.

[0013] According to the energy conservation law of the glider, the working principle of the net variometer is fused to estimate the hot updraft, so as to solve the airflow perception problem.

[0014] The state information matrix is constructed by the collected hot updraft information, the data with large estimation deviation in the hot updraft information is eliminated, and the eliminated data is arranged in a matrix to form a column vector.

[0015] The dynamic process is extracted from the heat source data by sparse identification of nonlinear dynamics (SINDy algorithm), and a low-dimensional dynamic model is reconstructed by using prior knowledge of high-dimensional measurement data; the parameter identification problem is formulated as a sparse regression problem and solved.

[0016] The solution of the sparse regression is taken as an identified parameter, and the solved parameter is further backstepped to solve the hot updraft position.

[0017] Further, the mathematical model adopts a two-dimensional Gaussian model as an application object of parameter identification, and can also be characterized by the algorithm.

[0018] Further, the hot updraft is characterized by using a mathematical model, specifically: integrating the mathematical model in a simulation platform, defining a fixed-wing glider required by itself by modifying aerodynamic coefficients in SIMULINK, adding a hot updraft physical model to the environment to make the environment generate hot updraft, and the hot updraft physical model is as follows:

[0019]

[0020] wherein, w z represents the hot updraft, w represents the wind intensity of the hot center, p n and p e represent the position of the heat source on the two-dimensional coordinate axis; x n and x e represent the real-time position recorded in the flight process of the glider, and R represents the range of the hot core; the model follows a circular bell-shaped curve.

[0021] Further, the hot updraft is estimated by a physical formula and a model to estimate its speed and intensity, as shown in the following formula:

[0022]

[0023] where x, y, z represent the position coordinates of the UAV, Va represents the airspeed, T BW is a rotation matrix;

[0024] The absolute motion velocity obtained by the global positioning system GPS is composed of the relative airspeed and the wind speed; since the wind speed is necessary in the inertial coordinate system, the airspeed vector is transformed; T BW is a rotation matrix, which converts the vector from the wind coordinate system to the body coordinate system, T IB represents the rotation matrix of the vector from the body coordinate system to the inertial coordinate system; Va represents the velocity in the heading direction, which is directly measured by the airspeed indicator; in combination with the rotation matrix T BW estimated by the extended pitot tube, the relative motion in the body coordinate system is obtained by the above formula.

[0025] Further, the state information matrix constructed by the collected hot updraft airflow information is specifically: collecting the estimated updraft airflow at a consistent sampling rate to determine the parameters of the hot pattern; wherein each data is represented by x(t m ), assuming that the number of collected data is t m , the X matrix information is defined and created as follows:

[0026]

[0027] Further, the construction of the state information matrix includes: the key is to calculate at discrete time, apply the SINDy algorithm to the discrete dynamic system, and regard the spatiotemporal variation caused by the relative motion between the hot updraft airflow and the glider as a nonlinear dynamic system, which is represented in the following discrete form:

[0028] x k+1 =F(x k );

[0029] where x represents the state vector of the dynamic system to be solved.

[0030] Further, the conversion of the parameter identification problem into a sparse regression problem for solving is specifically: minimizing the least square error between the measured value and the estimated value Θ(X), as shown in the following formula:

[0031]

[0032] Wherein, X represents state matrix information, ξ represents the coefficient to be solved, and Θ represents a function library; a regularization term is added in the formula to improve the sparsity of the activation term coefficient, although the convergence of the equation cannot be guaranteed, but in order to avoid calculation errors in the optimization process, the sequential threshold least square method or sparse regularization relaxation regression can be used to solve the equation.

[0033] Further, the solution of the sparse regression is taken as an identification parameter, and the solved parameter is further processed, and the formula is as follows:

[0034]

[0035] Wherein, ξ1, ξ2 and ξ i Used to represent the 1st, 2nd and i-th elements of a column vector, p e And p n That is, the position of the airflow.

[0036] The beneficial effects of the present application are:

[0037] 1. The present application proposes a new heat source online identification and positioning method. The SINDy algorithm is introduced and slightly modified, which can more accurately estimate the parameters.

[0038] 2. Compared with the previous method of estimating a single heat field, the identification ability is significantly enhanced, and the rising air flow can be accurately searched. The performance and reliability of the SINDy algorithm integrated with the flight control system are verified. It not only can better avoid overfitting, but also can achieve a good balance between data memory and calculation accuracy.

[0039] 3. The algorithm is tested by hardware-in-the-loop, and the HITL shows the feasibility of deploying the proposed algorithm in actual scenarios. The present application provides an innovative idea for promoting future autonomous flight technology. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 It is a flow chart of SINDy, wherein (a) is step A: a schematic diagram of thermal prior knowledge of unknown parameters, (b) is step B: a schematic diagram of data collection, (c) is step C: a schematic diagram of selecting a candidate term library, (d) is step D: a schematic diagram of solving a sparse regression problem, and (e) is step E: a schematic diagram of a thermal rising air flow identified by SINDy.

[0041] Figure 2 It is a three-dimensional flight trajectory diagram under observable conditions.

[0042] Figure 3 It is a schematic diagram of the mean absolute error (MAE) and the standard deviation (Std) of the estimated SINDy, wherein (a)-(f) are respectively six case result diagrams.

[0043] Figure 4 Fig. 13 is a schematic diagram of a thermal position estimation result obtained by SINDy;

[0044] Figure 5 Fig. 14 is a flowchart of the present application. DETAILED DESCRIPTION

[0045] The present application will be described in detail below with reference to the accompanying drawings in conjunction with specific embodiments.

[0046] As shown in the figure, the data-driven thermal updraft positioning method provided by the embodiment of the present application comprises the following steps: Figure 5

[0047] Step S1. Add a heat source model in the simulation platform.

[0048] The experiment is carried out on the advanced platform RflySim developed by the reliable flight control group. The core of RflySim is that it supports a customized high-fidelity simulation framework, which is realized through special components such as the carefully designed simulator CopterSim. By using RflySim, researchers can efficiently design models, develop and verify control algorithms, and verify hardware systems, thereby reducing the time required for algorithm conception and deployment.

[0049] The construction of the environment is realized by integrating mathematical models in the Rflysim platform. First, the fixed-wing glider required by itself is defined by modifying the aerodynamic coefficients in SIMULINK. Then, a thermal updraft physical model is added to the environment to enable the environment to generate thermal updrafts. The position of the heat source is determined according to the take-off location of the glider. In this experiment, the take-off location of the glider is defined at the origin of the three-dimensional coordinate system. The added heat source model is as follows:

[0050]

[0051] where w z represents the thermal updraft, w represents the wind intensity of the thermal center, p n and p e represent the position of the heat source on the two-dimensional coordinate axis; x n and x e represent the real-time position recorded during the flight of the glider, and R represents the range of the thermal core; the thermal model follows a circular bell-shaped curve.

[0052] Step S2. Set three heat source positions.

[0053] ​Three heat source locations are set in the global environment, which are (800, 100), (1000, 500), (600, 800) respectively. The coordinates are given in the form of (east, north). The glider flies in the form of a "lawnmower" to ensure the observability of the heat source and avoid encountering non-objective situations during flight.

[0054] Step S3. Start the estimation algorithm of the thermal updraft.

[0055] After the glider takes off, the estimation algorithm of the thermal updraft is started. The pitch angle, roll angle and yaw angle of the glider are extracted from the IMU module, and the position of the glider in the inertial coordinate system is extracted from the GPS. Based on this information, a state transformation matrix is constructed to provide data for estimating the thermal airflow.

[0056] The airspeed of the flight is extracted from the airspeed tube module, and the thermal updraft is calculated based on the above data. Physical formulas and models are used to estimate the speed and strength of the updraft. The estimated airspeed of the aircraft by PX4 and the estimated pitch angle and yaw angle by the IMU element are used to estimate the thermal updraft. The calculation formula is as follows:

[0057]

[0058] where x, y, z represent the position coordinates of the UAV, Va represents the airspeed, T BW is a rotation matrix.

[0059] The absolute motion speed obtained by the global positioning system (GPS) is composed of the relative airspeed and the wind speed. Since the wind speed is necessary in the inertial coordinate system, the vector is transformed. T BW is a rotation matrix that converts the vector from the wind coordinate system to the body coordinate system. Similarly, T IB converts the vector from the body coordinate system to the inertial coordinate system. Va represents the speed in the heading direction, which is directly measured by the airspeed indicator. Combined with the rotation matrix T BW estimated by the extended pitot tube, the relative motion in the body coordinate system is obtained.

[0060] Step S4. Construct the state information matrix about the thermal updraft.

[0061] In the case of thermal identification, the key is the vertical airflow, so the column dimension of the matrix is equal to 1. Where each data is represented by x(t m ), assuming that the number of collected data is t m , define and create the X matrix information as follows:

[0062]

[0063] Parameters of the thermal model are determined to collect the estimated updrafts at a consistent sampling rate.

[0064] Step S5. Remove elements with large estimated bias.

[0065] If the collected airflow information is abnormal, further processing of the data is required, for example, the numerical value of the updraft is greater than 5m / s, or a lower airflow is generated, then this case should be terminated in this area of flight, the condition for judgment is that the estimated value is less than -3m / s. These data should also be removed.

[0066] For the estimation algorithm, in order to ensure the neatness of the matrix, the following formula is used to remove:

[0067] w z >5m / sorw z <-3m / s

[0068] Step S6. Solve the sparse regression problem.

[0069] The sparse regression method is used to determine which functions in the function library have a significant impact on the system dynamics. This step usually involves an optimization problem, the goal of which is to minimize the error while making the number of selected functions as small as possible (i.e. sparsity). The goal of the present invention is to approximate the measured values, so the regression problem becomes:

[0070]

[0071] For most application scenarios, the solution of sparse regression is used as the identified parameter. However, in the embodiment of the present invention, the identified parameter needs to be further processed. For the convenience of expression, ξ i is used to represent the i-th element of the column vector. The formula is expressed as follows:

[0072]

[0073] In the identification case of the present invention, preliminary knowledge about the system is possessed, which eliminates the need to consider scanning the candidate function library. This further reduces the training execution time. It is worth noting that before further expanding the sparse regression to identify the thermal updraft parameters, the identified model is considered to be decoupled from x e and x n , which eliminates the x e ·x n term.

[0074] Step S7. Optimize the results of the thermal updraft.

[0075] Solving sparse regression problems involves the inversion of matrices, so when the matrix is singular, the hot position needs to be further optimized, and for the area of the hot updraft, if the estimated position is more than 300m away from the area where the aircraft is flying, these estimated results cannot be taken into account. These anomalies should also be excluded, whether the position is in the east direction or the estimated position in the north direction. The present invention optimizes the hot air flow positioning by the following formula:

[0076] | x e - p e | < 300 and | x n - p n | < 300

[0077] Before performing the above steps, a sequence of consecutive updrafts is collected, and once a sufficient number of updrafts has been accumulated, the SINDy algorithm begins to run. The data is organized into a matrix, and the logarithmic form of this matrix is calculated. Then a library of candidate functions is constructed according to the position of the aircraft. The present invention solves the coefficients of these candidate functions to minimize the cost function. Finally, the coefficients are converted into heat source parameters.

[0078] Before actual flight testing, a hardware-in-the-loop simulation was performed to evaluate the performance of SINDy. Unlike SITL, the fixed-wing model in HITL is running in real time, synchronized with the actual clock, ensuring accurate results. Win10 WSL is used as a cross-compilation environment to flash firmware onto the Pixhawk4 autopilot hardware.

[0079] The SINDy algorithm is uploaded into the flight control hardware environment. Pixhawk4 integrates a powerful processor, sensor technology, and the NuttX real-time operating system, enabling flexible and reliable control of the glider. At this stage, communication is established using cable signal lines, not virtual network transmission. CopterSim transmits sensor data, including barometer and magnetometer readings, to Pixhawk4 through serial communication. The PX4 firmware running on the flight controller estimates state information using filtering algorithms such as EKF.

[0080] The state information is broadcast to the information bus. The controller subscribes to messages from the information bus, calculates control commands, and sends them back to CopterSim. In addition, a wireless data transmission module is equipped to transmit the status and flight parameters of the glider to QGC for monitoring. When the glider deviates from the expected flight path or loses control, the operator can intervene. HITL facilitates the deployment and execution of control algorithms on real embedded systems, providing an indoor simulation environment for outdoor flight testing.

[0081] As Figure 1The steps for final localization based on the algorithm results are summarized in FIGS. (a)-(e). First, a series of data is calculated based on the estimated thermal updraft method described above, and then the estimated data is created in a matrix form. The thermal updraft problem is further converted into a parameter identification problem, and the formula for solving the problem is solved by sparse regression to solve the coefficients of the matrix. Finally, based on the formula in FIG. (e), the coefficients of the thermal updraft are converted into the location of the heat source. Figure 1

[0082] To fully demonstrate the performance of SINDy, the present application verifies the results of our algorithm through an example

[0083] The identification is evaluated in the observable flight mode. The flight trajectory of the glider is simulated in the lawnmower mode, which is mainly composed of irregular curves. This mode is chosen to minimize the occurrence of straight and circular flights, thereby ensuring that the parameters to be estimated have relatively high observability. Figure 2 The flight trajectory is composed of two parts in light blue and orange. The thick solid orange line represents the trajectory during the detection of the updraft, whose amplitude exceeds a certain threshold within the defined duration.

[0084] The estimation performance of the SINDy algorithm is summarized in FIGS. (a)-(f) in Figure 3 The mean absolute error is in the range of 20 meters. For Case 1 to Case 6, the estimation accuracy of the SINDy algorithm is very high. Moreover, its standard deviation is also acceptable. Throughout the flight, SINDy performed six times as shown in Figure 4 The true value is represented by the green and blue dashed lines, while the estimated value obtained by the traditional method is represented by the solid line. In Case 1, the traditional method gradually converges, and the 3σ error band tends to be stable in the later flight. Compared with the results of SINDy, there is still a deviation in the estimated heat source location.

[0085] In Case 2, although the 3σ error band remains stable, there is a slight estimation error in the eastward position. In both cases, the heat localization of the SINDy algorithm has almost no error. This phenomenon is also observed in the last run when the algorithm is activated. The triangle and circle represent the east and north directions, respectively. To enhance clarity and simplicity, the points in the plot are drawn at fixed intervals, which are lower than the frequency of SINDy execution.

[0086] Figure 4 ​It is shown that SINDy outperforms the traditional method in terms of position estimation from Case 3 to Case 6. No matter the east or north position of the heat source is estimated, the identification error of the traditional algorithm is several to tens of times larger than that of the SINDy algorithm. In Case 3 and Case 4, SINDy shows a slight bias in estimating the east position. However, in most cases, its estimated value is consistent with the set value. It is worth noting that since SINDy needs to accumulate a certain number of physical quantities to calculate the information matrix, once the collected updraft reaches the predetermined threshold, SINDy can accurately locate the heat unit.

Claims

1. A data-driven based hot-rising plume positioning method, characterized in that, It comprises the following steps: a hot air flow is characterized using a mathematical model to reduce false parameter estimation and balance between environmental fidelity and computational cost; a hot updraft is estimated according to the energy conservation law of a glider and the working principle of a net variometer to solve the air flow perception problem; a state information matrix is constructed from collected hot updraft information, data with large estimated deviation in the hot updraft information is eliminated, and the eliminated data is arranged in a matrix to form a column vector; a dynamic process is extracted from hot source data through a sparse identification of nonlinear dynamics (SINDy) algorithm, a low-dimensional dynamic model is reconstructed using prior knowledge of high-dimensional measurement data, a parameter identification problem is formulated as a sparse regression problem and solved, and the solution of the sparse regression is taken as an identified parameter. The solution of the parameter is further backstepped to solve the position of the hot updraft.

2. The data-driven thermal updrafts localization method of claim 1, wherein, The mathematical model adopts a two-dimensional Gaussian model as an application object of parameter identification and can also be characterized by the SINDy algorithm.

3. The data-driven thermal updrafts localization method of claim 2, wherein, The hot air flow is characterized using a mathematical model by integrating the mathematical model in a simulation platform, defining a fixed-wing glider required by itself by modifying aerodynamic coefficients in SIMULINK, adding a hot updraft physical model to the environment to enable the environment to generate a hot updraft, and the hot updraft physical model is as follows: where w z represents the thermal updraft, w represents the wind intensity at the thermal center, p n and p e represent the position of the thermal source on the two-dimensional coordinate axis; x n and x e represent the real-time position recorded during the glider flight, R represents the range of the thermal core; the model follows a circular bell curve.

4. The data-driven thermal updrafts localization method of claim 1, wherein, The hot updraft is estimated by a physical formula and a model to estimate its speed and intensity, as shown in the following formula: wherein x, y, z represent the position coordinates of the UAV, Va represents the airspeed, T BW represents a rotation matrix; The absolute motion velocity obtained by the global positioning system (GPS) consists of the relative airspeed and the wind speed; since the wind speed is necessary in the inertial coordinate system, the airspeed vector is transformed; T BW is a rotation matrix that converts the vector from the wind coordinate system to the body coordinate system, T IB represents the rotation matrix that converts the vector from the body coordinate system to the inertial coordinate system; Va represents the velocity in the heading direction, which is directly measured by the airspeed indicator; in combination with the rotation matrix T BW estimated by the extended pitot tube, the airspeed in the body coordinate system is obtained by the above formula.

5. The data-driven thermal updrafts localization method of claim 1, wherein, The state information matrix constructed from the collected hot updraft airflow information is specifically: collecting the estimated updraft airflow at a consistent sampling rate to determine the parameters of the hot mode; wherein each data is represented by x(t m ), assuming that the number of collected data is t m , and the X matrix information is defined and created as follows:

6. The data-driven thermal updrafts localization method of claim 5, wherein, The state information matrix is constructed by applying the SINDy algorithm to a discrete dynamic system, regarding the spatiotemporal change caused by the relative motion between the hot updraft and the glider as a nonlinear dynamic system, and the nonlinear dynamic system is represented in the following discrete form: x k+1 = F(x k ); Wherein, x represents a state vector of the solved dynamic system, and k represents the number of data.

7. The data-driven thermal updrafts localization method of claim 1, wherein, The parameter identification problem is converted into a sparse regression problem for solving, and the solution of the sparse regression is taken as an identified parameter. Wherein, X represents state matrix information, ξ represents a coefficient to be solved, and Θ represents a function library.

8. The data-driven thermal updrafts localization method of claim 1, wherein, The solution of the parameter is further processed, and the formula is as follows: where ξ1, ξ2, and ξ i to denote the 1st, 2nd, and i-th elements of a column vector, p e and p n i.e. the position of the air flow.

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