Path following control method and device, aircraft, intelligent terminal and storage medium

Abstract

The application discloses a path following control method and device, an aircraft, an intelligent terminal and a storage medium. The path following control method comprises the following steps: acquiring a predicted step number and a current coordinate of a followed object; acquiring a following target benefit function of a following object and a followed target benefit function of the followed object; performing iterative calculation based on the current coordinate of the followed object, the following target benefit function and the followed function, and acquiring a target predicted coordinate vector of the followed object; and calculating the target predicted coordinate vector to obtain a target following coordinate corresponding to a next step of the following object through the following target benefit function, and controlling the following object to move to the target following coordinate. Compared with the prior art, the application can effectively reduce the requirement for computing resources, does not need to perform complex model training and use process, is favorable for reducing the time consumption of the calculation process, and is favorable for improving the efficiency of path following.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of path following, and particularly relates to a path following control method and device, an aircraft, an intelligent terminal and a storage medium. BACKGROUND

[0002] With the development of science and technology, path planning technology and path following (path tracking) technology have also been rapidly developed and widely applied. In the path following process, the following object needs to track the followed object, and it is necessary to ensure that the two objects are in a relatively static state as much as possible.

[0003] In the prior art, a complex model predictive control (MPC) is usually used for prediction tracking, for example, a model for prediction tracking is trained for the followed object, and then the motion of the following object is controlled according to the model, but the model training and use process are relatively complex, require high computing resources and have a long time-consuming calculation process, which is not conducive to improving the efficiency of path following.

[0004] Therefore, the prior art still needs to be improved and developed. SUMMARY

[0005] The main purpose of the present application is to provide a path following control method and device, an aircraft, an intelligent terminal and a storage medium, which aims to solve the problem that in the prior art, when a complex model predictive control (MPC) is used for prediction tracking, the model training and use process are relatively complex, require high computing resources and have a long time-consuming calculation process, which is not conducive to improving the efficiency of path following.

[0006] In order to achieve the above purpose, the first aspect of the present application provides a path following control method, wherein the method comprises:

[0007] obtaining a prediction step number and a current coordinate of the followed object;

[0008] The following object is obtained by following the target benefit function of the object and the above-mentioned target benefit function of the object being followed, based on the current coordinates of the object being followed, the above-mentioned target benefit function of the object being followed and the above-mentioned target benefit function of the object being followed, iterative calculation is performed to obtain a target predicted coordinate vector of the object being followed, wherein, in the iterative calculation process, the target benefit function of the object being followed is used to calculate a predicted following coordinate vector of the object being followed based on an input object being followed coordinate vector to obtain the maximum function value, the target benefit function of the object being followed is used to calculate a predicted following coordinate vector of the object being followed based on an input object being followed coordinate vector to obtain the maximum function value, the target predicted coordinate vector satisfies a first preset condition or a second preset condition, the first preset condition is that the number of iterations is greater than a preset iteration threshold, the second preset condition is that the difference between the target predicted coordinate vector and the predicted following coordinate vector of the object being followed obtained in the previous iteration is less than a preset coordinate difference threshold, the object being followed coordinate vector and the object being followed coordinate vector each include a predicted number of coordinates, the predicted following coordinate vector includes a predicted number of predicted following coordinates, and the predicted following coordinate vector includes a predicted number of predicted following coordinates, in the first iteration calculation process, the object being followed coordinate vector corresponding to the target benefit function of the object being followed is a vector generated based on the current coordinates of the object being followed.

[0009] According to the above-mentioned target predicted coordinate vector, the target following coordinate corresponding to the next step of the object being followed is calculated by the above-mentioned target benefit function of the object being followed, and the object being followed is controlled to move to the target following coordinate.

[0010] Optionally, the object being followed and the object being followed are each an aircraft.

[0011] Optionally, the current coordinates of the object being followed include:

[0012] The current coordinates of the object being followed are obtained by a sensor of the object being followed.

[0013] Optionally, in one iteration process, the function value of the target benefit function of the object being followed is equal to the difference between a first distance and a second distance, wherein the first distance is the sum of the distances between each predicted following coordinate and a preset coordinate origin, and the second distance is the sum of the distances between each coordinate of the object being tracked input into the target benefit function and the preset coordinate origin.

[0014] Optionally, the function value of the followed target benefit function in one iteration process is equal to the difference between a third distance and a fourth distance, wherein the third distance is the sum of distances between each of the predicted followed coordinates and the preset coordinate origin, and the fourth distance is the sum of distances between each of the coordinates of the followed object input into the followed target benefit function and the preset coordinate origin.

[0015] Optionally, the preset coordinate origin is the starting point of the movement of the followed object.

[0016] Optionally, the followed target benefit function satisfies a preset following constraint condition, and the following constraint condition comprises a continuity constraint sub-condition, a distance constraint sub-condition and a maximum speed constraint sub-condition.

[0017] The continuity constraint sub-condition is used to limit the relationship between the current predicted followed coordinate, the predicted followed coordinate of the previous step and the speed of the followed object.

[0018] The distance constraint sub-condition is used to limit the distance between the current predicted followed coordinate and the corresponding input coordinate, wherein the input coordinate is the coordinate of the followed object input into the followed target benefit function.

[0019] The maximum speed constraint sub-condition is used to limit the speed of the followed object.

[0020] Optionally, the target followed coordinate corresponding to the next step of the followed object is obtained by inputting the target predicted coordinate vector into the followed target benefit function and calculating the target followed vector of the followed object according to the target benefit function, and the followed object is controlled to move to the target followed coordinate.

[0021] The target predicted coordinate vector is input into the followed target benefit function, and the target followed vector of the followed object is calculated according to the target benefit function.

[0022] The first coordinate in the target followed vector is taken as the target followed coordinate corresponding to the next step of the followed object.

[0023] The followed object is controlled to move to the target followed coordinate.

[0024] Optionally, the prediction step number is equal to 1.

[0025] The second aspect of the present application provides a path following control device, wherein the device comprises:

[0026] A data acquisition module is configured to acquire a prediction step number and a current coordinate of a followed object.

[0027] The target prediction coordinate vector calculation module is configured to obtain a following target benefit function of a following object and a followed target benefit function of a followed object, and perform iterative calculation based on a current coordinate of the followed object, the following target benefit function, and the followed target benefit function to obtain a target prediction coordinate vector of the followed object, wherein, in the iterative calculation, the following target benefit function is configured to calculate a prediction following coordinate vector of the following object corresponding to an input followed object coordinate vector to obtain a maximum function value of the following target benefit function, the followed target benefit function is configured to calculate a prediction followed coordinate vector of the followed object corresponding to an input following object coordinate vector to obtain a maximum function value of the followed target benefit function, the target prediction coordinate vector satisfies a first preset condition or a second preset condition, the first preset condition is that an iteration number is greater than a preset iteration number threshold, the second preset condition is that a difference between the target prediction coordinate vector and a prediction followed coordinate vector of the followed object obtained in a previous iteration is less than a preset coordinate difference threshold, the followed object coordinate vector and the following object coordinate vector each include a prediction step number of coordinates, the prediction following coordinate vector includes a prediction step number of prediction following coordinates, the prediction followed coordinate vector includes a prediction step number of prediction followed coordinates, and in a first iteration calculation, the followed object coordinate vector corresponding to the following target benefit function is a vector generated according to the current coordinate of the followed object.

[0028] The following control module is configured to calculate a target following coordinate corresponding to a next step of the following object by using the following target benefit function according to the target prediction coordinate vector, and control the following object to move to the target following coordinate.

[0029] The third aspect of the present application provides an aircraft, wherein the aircraft serves as a following object, and the aircraft performs path following on a followed object according to any of the path following control methods.

[0030] The fourth aspect of the present application provides an intelligent terminal, wherein the intelligent terminal includes a memory, a processor, and a path following control program stored in the memory and executable on the processor, and the path following control program implements the steps of any of the path following control methods when executed by the processor.

[0031] The fifth aspect of the present application provides a computer readable storage medium, wherein the computer readable storage medium stores a path following control program, and the path following control program implements the steps of any of the path following control methods when executed by a processor.

[0032] From the above, the path following control method in the scheme of the present application comprises: obtaining a predicted step number and a current coordinate of a followed object; obtaining a following target benefit function of a following object and a followed target benefit function of the followed object, performing iterative calculation based on the current coordinate of the followed object, the following target benefit function and the followed function, and obtaining a target predicted coordinate vector of the followed object, wherein, in the iterative calculation process, the following target benefit function is used to calculate and obtain a predicted following coordinate vector corresponding to the following object based on an input followed object coordinate vector to obtain a maximum function value as a target, the followed target benefit function is used to calculate and obtain a predicted followed coordinate vector corresponding to the followed object based on an input following object coordinate vector to obtain a maximum function value as a target, the target predicted coordinate vector satisfies a first preset condition or a second preset condition, the first preset condition is that the number of iterations is greater than a preset iteration threshold, the second preset condition is that the difference between the target predicted coordinate vector and the predicted followed coordinate vector corresponding to the followed object obtained at the previous iteration is less than a preset coordinate difference threshold, the followed object coordinate vector and the following object coordinate vector each include a predicted step number of coordinates, the predicted following coordinate vector includes a predicted step number of predicted following coordinates, and the predicted followed coordinate vector includes a predicted step number of predicted followed coordinates, in the first iteration calculation process, the followed object coordinate vector corresponding to the following target benefit function is a vector generated according to the current coordinate of the followed object; a target following coordinate corresponding to the next step of the following object is calculated through the following target benefit function according to the target predicted coordinate vector, and the following object is controlled to move to the target following coordinate.

[0033] Compared with the prior art, in the present application, a corresponding model does not need to be trained for the followed object, and only iterative calculation according to the following target benefit function and the followed target benefit function can realize target tracking, so that the requirement for computing resources can be effectively reduced, and complex model training and use process are not required, which is beneficial to reduce the time consumption of the calculation process and improve the efficiency of path following. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0035] Figure 1 is a flowchart of a path following control method provided by an embodiment of the present application;

[0036] Figure 2 This is an embodiment of the present invention. Figure 1 A detailed flowchart of step S300 is shown below;

[0037] Figure 3 This is a schematic diagram of a specific process for path following control provided in an embodiment of the present invention;

[0038] Figure 4 This is a schematic diagram illustrating the effect of path following control based on a path following control method provided in an embodiment of the present invention;

[0039] Figure 5 This is a schematic diagram of the structure of a path following control device provided in an embodiment of the present invention;

[0040] Figure 6 This is a block diagram illustrating the internal structure of a smart terminal provided in an embodiment of the present invention. Detailed Implementation

[0041] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0042] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0043] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0044] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0045] As used in the present specification and the accompanying claims, the term “if’ can be interpreted as meaning “when” or “upon” or “in response to a determination” or “in response to a detection” depending on the context. Similarly, the phrase “if it is determined” or “if [the described condition or event] is detected” can be interpreted as meaning “upon a determination” or “in response to a determination” or “upon a detection of [the described condition or event]” or “in response to a detection of [the described condition or event]” depending on the context.

[0046] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings of the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative effort belong to the scope of protection of the present application.

[0047] In the following description, a large number of specific details are set forth in order to facilitate a thorough understanding of the present application, but the present application can also be implemented in other manners different from those described herein, and those skilled in the art can make similar generalizations without departing from the spirit and scope of the present application, therefore the present application is not limited to the specific embodiments disclosed below.

[0048] With the development of science and technology, path planning technology and path following (path tracking) technology have also been rapidly developed and widely applied. In the path following process, it is necessary to control the follower to track the followed object, and to try to ensure that the two are in a relatively static state. For example, a microsatellite can be controlled to follow a space station to achieve monitoring and reconnaissance of the space station.

[0049] Specifically, with the research and development of space stations, long-term stable operation in orbit cannot be achieved without monitoring and reconnaissance of spacecraft. Microsatellites have small size, light weight and low cost, and play an increasingly important role in completing many complex space tasks, such as detection and reconnaissance of space stations, repair of other malfunctioning spacecraft, etc. Since these spacecraft in space are not in a static state, when a satellite needs to complete these tasks, it usually needs to track the trajectory of the target, so that the satellite is in a relatively static state compared to the spacecraft.

[0050] In the prior art, a complex model predictive control (MPC) is usually used for predictive tracking, for example, a model for predictive tracking is trained for the followed object, and then the motion of the follower is controlled according to the model, but the model training and use process are relatively complex, require high computing resources and take a long time in the calculation process, which is not conducive to improving the efficiency of path following. Specifically, the predictive tracking method used by the current satellite formation is mostly MPC, which requires high computing resources, and therefore requires high hardware requirements for the satellite.

[0051] Meanwhile, when using model predictive control for predictive tracking, model training is usually required for each followed object respectively, i.e., one model in the model predictive control scheme cannot be applied to different followed objects, and the scheme has low applicability. Moreover, the model relies on a large amount of data collected from the followed object, the following environment, etc., and is difficult to obtain.

[0052] To solve one or more problems in the prior art, the present application provides a path following control method, which realizes path following based on game theory. For a followed object, a decision is made according to the position of the other party (the followed object), the decision of the followed object is predicted according to the decision of the other party by using the same algorithm, and the iteration is repeated until the Nash equilibrium is reached, i.e., the optimal decision of the followed object is obtained, so that target following is realized, and the required computing resources are reduced.

[0053] Specifically, the path following control method includes: obtaining a prediction step number and a current coordinate of a followed object; obtaining a following target reward function of a following object and a followed target reward function of the followed object, performing iterative calculation based on the current coordinate of the followed object, the following target reward function and the followed function, and obtaining a target prediction coordinate vector of the followed object, wherein, in the iterative calculation process, the following target reward function is used to calculate a prediction following coordinate vector corresponding to the following object based on an input followed object coordinate vector to obtain a maximum function value, the followed target reward function is used to calculate a prediction followed coordinate vector corresponding to the followed object based on an input following object coordinate vector to obtain a maximum function value, the target prediction coordinate vector satisfies a first preset condition or a second preset condition, the first preset condition is that the number of iterations is greater than a preset iteration threshold, the second preset condition is that a difference between the target prediction coordinate vector and a prediction followed coordinate vector corresponding to the followed object obtained in the previous iteration is less than a preset coordinate difference threshold, the followed object coordinate vector and the following object coordinate vector each include a prediction step number of coordinates, the prediction following coordinate vector includes a prediction step number of prediction following coordinates, and the prediction followed coordinate vector includes a prediction step number of prediction followed coordinates, in the first iteration calculation process, the followed object coordinate vector corresponding to the following target reward function is a vector generated according to the current coordinate of the followed object; a target following coordinate corresponding to the next step of the following object is calculated by the following target reward function according to the target prediction coordinate vector, and the following object is controlled to move to the target following coordinate.

[0054] Compared with the prior art, in the application, a corresponding model does not need to be trained for the followed object, and target tracking can be realized only by iterative calculation according to the following target reward function and the followed target reward function, so that the requirement for computing resources can be effectively reduced, and complex model training and use process are not needed, which is beneficial to reduce the time consumption of the calculation process and improve the efficiency of path following.

[0055] Exemplary method

[0056] As Figure 1 shown, the embodiment of the application provides a path following control method, and specifically, the above method comprises the following steps:

[0057] Step S100, obtaining a predicted step number and a current coordinate of the followed object.

[0058] The predicted step number is a step number set for limiting the planning of future movement of the followed object in each path following control process, for example, when the value of the predicted step number is 3, the corresponding planning step number is 3, that is, the future 3 steps of the followed object are planned to move to which coordinate. The more the planning step number is, the longer the calculation time required for planning in the path following process is, and the more complex the calculation process is, but the target predicted coordinate vector obtained finally can also make the following effect better, so the predicted step number can be set according to actual requirements.

[0059] It should be noted that the predicted step number can be set in advance or input and adjusted in real time by the user according to actual requirements, which is not limited here. In this embodiment, even if multi-step prediction is performed, that is, the predicted step number is greater than 1, only the first step after planning is used as the actual movement target. For example, the coordinates of the future 3 steps of the followed object are planned, the first step is selected as the actual movement target, and then the coordinates of the future 3 steps are re-planned after moving 1 step, and so on.

[0060] Further, in this embodiment, N represents the predicted step number, and the predicted step number is an integer greater than 0.

[0061] It should be noted that in this embodiment, the followed object and the following object are both aircrafts, and specifically, the followed object can be a space station or a tracked satellite, and the following object can be a microsatellite, so that the space station can be monitored and surveyed by the microsatellite. The following object is an object that can be controlled according to the path following control method, and the followed object is not controlled and cannot obtain the strategy of the followed object at the next moment, so it is assumed in this embodiment that the strategy of the followed object and the following object reaches Nash equilibrium. The strategy can be regarded as the position (i.e. coordinate) to be reached at the next moment.

[0062] Specifically, in the embodiment, the current coordinates of the followed object are obtained by the sensors of the following object. The following object is provided with multiple sensors, which can obtain the current coordinates of the target to be followed according to the following object, and plan the path following according to the current coordinates.

[0063] In step S200, the following target benefit function of the following object and the followed target benefit function of the followed object are obtained, and the target predicted coordinate vector of the followed object is obtained by iterative calculation based on the current coordinates of the followed object, the following target benefit function and the followed function.

[0064] In the iterative calculation process, the following target benefit function is used to calculate the predicted following coordinate vector of the following object corresponding to the input followed object coordinate vector to obtain the maximum function value, the followed target benefit function is used to calculate the predicted followed coordinate vector of the followed object corresponding to the input following object coordinate vector to obtain the maximum function value, the target predicted coordinate vector satisfies the first preset condition or the second preset condition, the first preset condition is that the iteration number is greater than the preset iteration number threshold, the second preset condition is that the difference between the target predicted coordinate vector and the predicted followed coordinate vector of the followed object corresponding to the previous iteration is less than the preset coordinate difference threshold, the followed object coordinate vector and the following object coordinate vector each include a predicted number of coordinates, the predicted following coordinate vector includes a predicted number of predicted following coordinates, the predicted followed coordinate vector includes a predicted number of predicted followed coordinates, and in the first iteration calculation process, the followed object coordinate vector corresponding to the following target benefit function is a vector generated according to the current coordinates of the followed object.

[0065] In the embodiment, the following target benefit function and the followed target benefit function are set in advance according to the needs of path following control, and in actual use, they can also be input in real time by the user or adjusted according to actual needs, which is not limited here.

[0066] In each iteration calculation process, the input of the following target benefit function (or the followed target benefit function) is a vector (or an array) containing N coordinates, and the input vector is used to predict and calculate the maximum function value, and all coordinates corresponding to the future N steps are predicted and combined into an output vector (or an array) containing N coordinates. Repeat the iteration until the obtained result converges, i.e., reaches Nash equilibrium. When N = 1, each vector only includes one coordinate.

[0067] It should be noted that in the process of iterative calculation, the predicted following coordinate vector calculated and output according to the following target benefit function is taken as the input of the followed target benefit function, and then a predicted followed coordinate vector is calculated and output according to the followed target benefit function, and then the obtained predicted followed coordinate vector is taken as the input of the following target benefit function again, so as to realize repeated iteration.

[0068] Further, in the first iteration (i.e. initial iteration), the initial input (i.e. the followed object coordinate vector) corresponding to the following target benefit function is generated according to the current coordinate of the followed object. When N is equal to 1, the initial input of the following target benefit function is the above-mentioned current coordinate. When N is greater than 1, the first coordinate in the initial input of the following target benefit function is the above-mentioned current coordinate, and the second to Nth coordinates can be initial values set in advance, can be random values, or can all be the above-mentioned current coordinate, which is not specifically limited here.

[0069] The iteration threshold is a maximum iteration number set in advance, which is used to prevent repeated iteration from stopping when convergence cannot be reached, causing program exceptions. The iteration threshold can also be set and adjusted according to actual needs, which is not specifically limited here. The difference between the vectors needs to be calculated in the second preset condition, and each vector includes N coordinates. The difference between the vectors can be the sum of the distances between the corresponding N coordinates. The target predicted coordinate vector is a followed object coordinate vector that finally satisfies the preset condition. The difference between the target predicted coordinate vector and the followed object coordinate vector obtained in the previous iteration is less than the preset coordinate difference threshold. The coordinate difference threshold can be set in advance or adjusted according to actual needs, which is not specifically limited here.

[0070] Specifically, in the process of one iteration, the function value of the above-mentioned following target benefit function is equal to the difference between the first distance and the second distance, wherein the first distance is the sum of the corresponding distances between each of the above-mentioned predicted following coordinates and the preset coordinate origin, and the second distance is the sum of the corresponding distances between each of the coordinates of the above-mentioned tracked object input into the above-mentioned target benefit function and the above-mentioned preset coordinate origin.

[0071] In the process of one iteration, the function value of the above-mentioned followed target benefit function is equal to the difference between the third distance and the fourth distance, wherein the third distance is the sum of the corresponding distances between each of the above-mentioned predicted followed coordinates and the above-mentioned preset coordinate origin, and the fourth distance is the sum of the corresponding distances between each of the coordinates of the above-mentioned following object input into the above-mentioned followed target benefit function and the above-mentioned preset coordinate origin.

[0072] In the embodiment, the distance between the preset coordinate origin and the corresponding income is taken as the function value of the followed target income function or the function value of the followed target income function.

[0073] In the embodiment, the coordinates are determined by a pre-constructed coordinate system, and the origin of the coordinate system can be preset according to actual needs. In the embodiment, the coordinate origin is set as the starting point of the movement of the followed object, so as to simplify the calculation process, speed up the calculation, and thus improve the efficiency of path following control.

[0074] Specifically, in the embodiment, the followed target income function satisfies a preset following constraint condition, and the following constraint condition includes a continuity constraint sub-condition, a distance constraint sub-condition, and a maximum speed constraint sub-condition.

[0075] The continuity constraint sub-condition is used to limit the relationship among the current predicted following coordinate, the predicted following coordinate of the previous step, and the speed of the followed object.

[0076] The distance constraint sub-condition is used to limit the distance between the current predicted following coordinate and the corresponding input coordinate of the followed object input into the followed target income function.

[0077] The maximum speed constraint sub-condition is used to limit the speed of the followed object.

[0078] It should be noted that in actual use, the following constraint condition can further include other components, i.e., other sub-conditions, which are not limited here.

[0079] In step S300, the target following coordinate corresponding to the next step of the followed object is calculated by the followed target income function according to the target predicted coordinate vector, and the followed object is controlled to move to the target following coordinate.

[0080] The target predicted coordinate vector is calculated according to the followed target income function and the followed target income function, and is the position to which the followed object will move in the next N steps in the case of game and Nash equilibrium between the followed object and the followed object. According to the predicted coordinate vector, the path of the followed object can be planned. Specifically, in the embodiment, in the process of one-time path planning, the followed object is controlled for one step, as shown in Figure 2 The step S300 specifically includes the following steps:

[0081] In step S301, the target predicted coordinate vector is input into the followed target income function, and a target following vector corresponding to the followed object is calculated according to the target income function.

[0082] Step S302, taking the first coordinate in the target following vector as the target following coordinate corresponding to the next step of the following object.

[0083] Step S303, controlling the following object to move to the target following coordinate.

[0084] In an application scenario, in order to reduce the calculation difficulty and the time required for calculation, the prediction step number N is set to 1 in advance.

[0085] In this embodiment, the path following control method is also specifically described based on a specific application scenario, Figure 3 is a specific flowchart of path following control provided by an embodiment of the present application, Figure 3 In this embodiment, the working satellite is the following object, and the working satellite tracks the tracked satellite (i.e., the following object).

[0086] Specifically, in this embodiment, the payoff function of the working satellite in a game process is s i (p i )-s j (p j ), where p i represents the coordinate (or coordinate vector) corresponding to the working satellite, p j represents the coordinate (or coordinate vector) corresponding to the tracked satellite, and correspondingly, p i and p j may also be understood as strategies, and the strategy of a satellite is the position to be reached at the next time (i.e., the next step). s i (p i ) represents the payoff of the working satellite, i.e., the distance length of the working satellite from a preset coordinate origin at p i , s j (p j ) represents the payoff of the tracked satellite, i.e., the distance length of the tracked satellite from a preset coordinate origin at p j , and the distance is the distance corresponding to the movement of the satellite. In this embodiment, the preset coordinate origin is the starting point of the movement of the working satellite, and if the tracked satellite does not pass through the point, the straight line between the tracked satellite and the coordinate origin at the time when the path following starts can be taken as the distance of this segment. It should be noted that s i (p i ), s j (p j ), p i , and p jEach step involves an optimization calculation at a specific moment, resulting in a solution (strategy). Path following control is then performed based on this solution. This embodiment uses the calculation and control at a single moment as an example. In actual use, after performing path following control based on the current coordinates of the object being followed at the current moment, the calculation and control are performed in the same way at the next moment. This will not be elaborated further here.

[0087] Furthermore, max[s i (p i )-s j (p j The denoted ] represents the maximum possible difference between the revenue of the working satellite and the revenue of the tracked satellite at each moment, i.e., maximizing the final actual revenue. It also represents the working satellite's ability to get as close to the tracked satellite as possible at each moment. It should be noted that the ultimate goal in this embodiment is satellite tracking. The working satellite's speed is actually less than that of the tracked satellite, and maximizing the revenue means maximizing the distance the working satellite travels in each decision. Because the working satellite always moves towards the tracked satellite and cannot overtake it, maximizing the distance traveled in each decision means getting as close to the tracked satellite as possible. Furthermore, subtracting the tracked satellite's revenue from the working satellite's revenue at each moment enables interaction between the working and tracked satellites.

[0088] The optimization objective in this embodiment is to achieve a Nash equilibrium in the payoffs of the operational satellite and the tracked satellite. However, the path-following control method described above can only control the operational satellite, not the tracked satellite. Therefore, it is impossible to know the next-moment strategy of the tracked satellite, i.e., it is impossible to accurately calculate s. j (p j Therefore, in this embodiment, to ensure the operational satellite obtains the optimal practical benefits, it is assumed that the tracked satellite adopts an optimal strategy, and that the tracked satellite's benefit is based on the operational satellite's coordinates p. i Calculate the payoff under the obtained Nash equilibrium This means that the coordinates p of the working satellite are used. i The predicted gains from the tracked satellites are used. Here, α is a hyperparameter (preset parameter), which is adjustable and can be greater than or equal to 0 based on practical experience and experiments. In this embodiment, α remains unchanged once given. Specifically, This can represent the corresponding optimal strategy (i.e., the strategy p of the working satellite). i The next point in time for the tracked satellite.

[0089] Therefore, in this embodiment, the payoff function of the working satellite following the target in a single game process can be obtained. In this embodiment, for Further expansion and transformation are performed to facilitate the calculation of the maximum value of the following target profit function. First, take p i as the independent variable, and take as the dependent variable, and perform a first-order Taylor expansion on the neighborhood of the solution of the last iteration to obtain the following formula (1):

[0090]

[0091] wherein, the value of is the coordinate obtained after the last iteration calculation, and the corresponding profit is also determined, i.e. is a constant, and the purpose of the present embodiment is to obtain the maximum value of , and the constant has no effect on this, so

[0092] Specifically, in the present embodiment, both the above-mentioned target profit function and the followed target profit function satisfy the distance constraint sub-condition, which is used to avoid collision between the working satellite and the tracked satellite. Specifically, the distance constraint is wherein y is a preset distance threshold value, which can be set and adjusted according to actual requirements. The corresponding distance constraint is expressed as Correspondingly, after the first-order Taylor expansion, the following formula (2) can be obtained:

[0093]

[0094] wherein l represents the iteration number, and l is not greater than L, and L represents a preset iteration number threshold value. In formula (2), is also a constant, which can be ignored, so can be converted to and because wherein represents the direction parameter of the working satellite, and the direction is the direction of the working satellite pointing to the tracked satellite, then represents the addition of the direction to the corresponding coordinate, so as to represent that the working satellite moves in the direction towards the tracked satellite. p i is the coordinate of the working satellite, and p j is the coordinate of the tracked satellite, and the superscript l represents the corresponding value obtained by the lth iteration calculation, for example, is the coordinate of the tracked satellite obtained by the lth iteration calculation, and the like, which will not be described herein again. Therefore, after ignoring the corresponding constant, we can obtain wherein k represents the kth step of the decision, and k takes an integer value between 1 and N, ​is an iterative hyperparameter, that is, a parameter that dynamically changes in the iteration process of the algorithm, and in each iteration process, The specific values of k and l are different and can be adjusted according to actual needs. The superscript k and l represent the value corresponding to the kth step of the decision in the lth iteration. When N = 1, k can also be ignored, that is, the decision of which step does not need to be considered, but only the iteration times need to be considered. It should be noted that in the formula of the present embodiment, the parameters without the superscript k represent the case where k is ignored when N = 1, and the corresponding superscript k can also be added according to actual needs. The superscript T of represents the transpose of the matrix, represents the direction parameter of the working satellite corresponding to the kth step in the lth iteration process (that is, the direction of the working satellite in the kth step towards the tracked satellite), since p i is a column vector, so the corresponding β is also a column vector, where β is a column vector composed of all In order to obtain a numerical value and facilitate optimization, the transpose of β is performed in the present embodiment.

[0095] Since the tracking effect needs to be obtained in the present embodiment, and s i (p i ) is added to introduce this concept, and can also be ignored in the solving process, so the final objective function can be obtained as follows:

[0096]

[0097] It should be noted that in one application scenario, the part that does not affect the solution of the maximum value can also be ignored, and the above formula (3) can be directly used as the following object tracking target benefit function. The tracking constraint condition corresponding to the above target tracking benefit function is shown in the following formula (4):

[0098]

[0099] The first term of formula (4) is a continuity constraint sub-condition, represents the coordinates of the working satellite in the kth step, represents the coordinates of the working satellite in the k-1th step, represents the speed of the working satellite in the kth step, and t represents the unit time (that is, the time spent by the working satellite in each step), and the continuity constraint sub-condition is used to ensure that the distance between the planned step and the previous step of the working satellite is the same as the time length of the working satellite in the unit time. The second term of formula (4) is a distance constraint sub-condition, which is used to limit the coordinates of the working satellite in the kth step and the coordinates of the tracked satellite distance between the kth step of the tracked satellite and the kth step of the working satellite is not less than a preset distance threshold y to prevent collision. The third term of formula (4) is a maximum speed constraint sub-condition for limiting the speed of the working satellite at the kth step to be not more than a maximum speed threshold of the working satellite

[0100] Further, in the embodiment, assuming that a Nash equilibrium is reached, the tracked satellite (i.e., the followed object) has the same optimization strategy as the working satellite (i.e., the following object), and thus the profit function of the followed satellite can be obtained as max[s j (p j )-s i (p i )], or further, the followed target profit function of the followed object is shown in formula (5) as follows:

[0101]

[0102] wherein, represents an iteration parameter of the followed object, represents a direction parameter of the followed object (i.e., the tracked satellite) corresponding to the kth step in the lth iteration process, represents a coordinate of the followed object corresponding to the kth step.

[0103] Further, the followed target profit function satisfies the following constraint of the followed object, and the following constraint includes a continuity constraint sub-condition, a distance constraint sub-condition, and a maximum speed constraint sub-condition. The constraint satisfied by the followed target profit function is shown in formula (6) as follows:

[0104]

[0105] wherein, the first term of formula (6) is the continuity constraint sub-condition, represents a coordinate of the tracked satellite at the kth step, represents a coordinate of the tracked satellite at the (k-1)th step, represents a speed of the tracked satellite at the kth step, and t represents a unit time (i.e., a time spent by the tracked satellite for walking one step). The continuity constraint sub-condition is used to ensure that the distance between the coordinate of the tracked satellite at the kth step and the coordinate of the tracked satellite at the (k-1)th step is the same as the time length of the tracked satellite walking in the unit time. The second term of formula (6) is the distance constraint sub-condition for limiting the distance between the kth step of the tracked satellite and the kth step of the working satellite to be not less than a preset distance threshold y to prevent collision. The third term of formula (6) is the maximum speed constraint sub-condition for limiting the speed of the tracked satellite at the kth step to be not more than a maximum speed threshold of the tracked satellite It should be noted that the same optimization strategy is assumed for the tracked satellite and the working satellite in the embodiment, and therefore the speed and maximum speed threshold of the tracked satellite at the kth step can be considered the same as those of the working satellite.

[0106] Specifically, after obtaining the following target benefit function and the followed target benefit function, the corresponding constraint conditions are combined, and the flow shown in the following formula is iteratively calculated. Figure 3 Figure 3 In the formula, the current coordinates of the target to be followed are obtained by the working satellite through various sensors, and then the working satellite can be initialized according to the coordinates of the tracked satellite obtained by the depth camera, or the initial coordinates p j of the working satellite can be initialized. Then, the corresponding followed object coordinate vector is generated according to the current coordinates of the tracked object, and the followed target benefit function is solved by a preset mathematical optimization algorithm (at this time, p j is considered unknown), to obtain a predicted followed coordinate vector (i.e., a decision coordinate vector of the working satellite), which is used as the input of the followed target benefit function, and the followed target benefit function is solved by a preset mathematical optimization algorithm (at this time, p i is considered unknown), to obtain a predicted followed coordinate vector of the tracked satellite (i.e., a decision coordinate vector of the tracked satellite). At this time, it is determined whether the iteration number l is greater than the iteration number threshold L (i.e., the first preset condition) or the value obtained by solving is convergent (i.e., the second preset condition). If neither condition is met, the iteration number is increased by one, and the next iteration process is entered. Otherwise, the iteration is ended, and the predicted followed coordinate vector obtained in the current iteration is used as the target predicted coordinate vector. It should be noted that the prediction of the followed object is also performed in the following object, but the corresponding target function is optimized from the perspective of the followed object, i.e., the decision made by the tracked satellite is predicted by the working satellite. The above-mentioned preset mathematical optimization algorithm can be the Lagrange multiplier method, the Newton iteration method, etc. After repeated iterations, the predicted followed coordinate vector of the followed object is obtained when convergence is achieved (i.e., Nash equilibrium is reached, i.e., the preset accuracy is reached), and is used as the target predicted coordinate vector. Then, the target predicted coordinate vector is used as the input of the followed target benefit function, and the followed target benefit function is solved to make the next decision for the followed object (i.e., the working satellite). Specifically, the first coordinate in the target followed vector obtained by solving the followed target benefit function is used as the corresponding target followed coordinate of the working satellite in the next step, and the working satellite is controlled to move to the coordinate, and the current time following control is ended.

[0107] Figure 4 is an effect diagram of path following control based on the path following control method provided by the embodiment of the present application,​Figure 4 In the figure, the thin gray line represents the preset flight trajectory range of the followed object, i.e., the followed object flies inside the trajectory during the experiment. The thick light gray (lower gray level) line is the actual flight trajectory of the followed object, and the thick black (higher gray level) line is the actual flight trajectory of the follower. It should be noted that the starting point of the thick black line is the point in the upper right corner, and the flight directions of the two are counterclockwise. The overlapping part of the actual flight trajectory of the followed object and the actual flight trajectory of the follower does not represent a collision, but the followed object first passes through the corresponding trajectory, and the follower reaches the corresponding position at the next moment or several moments. According to the Figure 4 It can be known that, based on the path following control method in the embodiment, a better path following effect can be obtained. Figure 4

[0108] It can be known that, based on the path following control method in the embodiment, a better path following effect can be obtained.

[0109] ​Compared with the prior art, in the application, a corresponding model does not need to be trained for the followed object, and only iterative calculation according to the following target reward function and the followed target reward function can realize target tracking, so that the requirement for computing resources can be effectively reduced, and complex model training and use process are not needed, which is beneficial to reduce the time consumption of the computing process, and is beneficial to improve the efficiency of path following.

[0110] Exemplary device

[0111] As Figure 5 shown, corresponding to the path following control method, the embodiment of the application further provides a path following control device, and the path following control device comprises:

[0112] The data acquisition module 410 is configured to acquire the predicted step number and the current coordinates of the followed object.

[0113] The predicted step number is a step number set for limiting the planning of the future movement of the followed object in each path following control process, for example, when the value of the predicted step number is 3, the corresponding planning step number is 3, that is, the future 3 steps of the followed object are planned to move to which coordinates. The more the planning step number is, the longer the calculation time required for planning in the path following process is, and the more complex the calculation process is, but the finally obtained target prediction coordinate vector can also make the following effect better, so the predicted step number can be set according to actual requirements.

[0114] The target prediction coordinate vector calculation module 420 is configured to obtain a following target benefit function of a following object and a followed target benefit function of a followed object, and perform iterative calculation based on a current coordinate of the followed object, the following target benefit function and the followed target benefit function, to obtain a target prediction coordinate vector of the followed object, wherein in the iterative calculation, the following target benefit function is used to calculate a prediction following coordinate vector of the following object corresponding to an input followed object coordinate vector, the followed target benefit function is used to calculate a prediction followed coordinate vector of the followed object corresponding to an input following object coordinate vector, and the target prediction coordinate vector satisfies a first preset condition or a second preset condition, the first preset condition is that an iteration number is greater than a preset iteration number threshold, the second preset condition is that a difference between the target prediction coordinate vector and a prediction followed coordinate vector of the followed object obtained in a previous iteration is less than a preset coordinate difference threshold, the followed object coordinate vector and the following object coordinate vector each include a prediction step number of coordinates, the prediction following coordinate vector includes a prediction step number of prediction following coordinates, and the prediction followed coordinate vector includes a prediction step number of prediction followed coordinates, and in a first iteration calculation, the followed object coordinate vector corresponding to the following target benefit function is a vector generated according to the current coordinate of the followed object.

[0115] The following control module 430 is configured to calculate a target following coordinate corresponding to a next step of the following object by using the following target benefit function according to the target prediction coordinate vector, and control the following object to move to the target following coordinate.

[0116] The target prediction coordinate vector is a position to which the followed object will move in the next N steps in a case where the following object and the followed object game and reach a Nash equilibrium according to the following target benefit function and the followed target benefit function. According to the prediction coordinate vector, path planning can be performed on the following object. Specifically, in the embodiment, the following object is controlled for one step in one path planning.

[0117] Based on the above embodiment, the application further provides a flying object, which serves as a following object, and the flying object performs path following on a followed object based on any one of the path following control methods.

[0118] Based on the above embodiment, the application further provides an intelligent terminal, a principle block diagram of which can be as shown in Figure 6The intelligent terminal shown in the figure includes a processor, a memory, a network interface and a display screen connected through a system bus. The processor of the intelligent terminal is used to provide computing and control capabilities. The memory of the intelligent terminal includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a path following control program. The internal memory provides an environment for the operating system and the path following control program in the non-volatile storage medium to run. The network interface of the intelligent terminal is used to communicate with external terminals through network connection. The path following control program, when executed by the processor, implements the steps of any one of the path following control methods described above. The display screen of the intelligent terminal can be a liquid crystal display screen or an electronic ink display screen.

[0119] Those skilled in the art can understand that Figure 6 The block diagram shown in the figure is only a block diagram of part of the structure related to the present application scheme, and does not constitute a limitation on the intelligent terminal to which the present application scheme is applied. A specific intelligent terminal can include more or fewer components than those shown in the figure, or combine certain components, or have a different component arrangement.

[0120] The embodiment of the present application also provides a computer readable storage medium, and the path following control program is stored on the computer readable storage medium. The path following control program, when executed by the processor, implements the steps of any one of the path following control methods provided by the embodiment of the present application.

[0121] It should be understood that the sequence numbers of the steps in the above embodiments do not mean the order of execution. The execution order of each process should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiment of the present application.

[0122] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above functional units and modules is taken as an example. In actual application, the above functions can be completed by different functional units and modules according to needs, that is, the internal structure of the above device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or software. In addition, the specific names of each functional unit and module are only for easy distinction, and do not limit the protection scope of the present application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, which will not be described here.

[0123] In the above embodiments, the description of each embodiment focuses on different aspects, and the parts not described in detail or recorded in a certain embodiment can be referred to the relevant description of other embodiments.

[0124] Those skilled in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0125] In the embodiments provided by the present application, it should be understood that the disclosed apparatus / terminal device and method can be implemented in other ways. For example, the above-described apparatus / terminal device embodiments are merely schematic, for example, the division of the above modules or units is merely a logical function division, and an actual implementation can be a division in another way, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0126] The above integrated modules / units, if realized in the form of software function units and sold or used as independent products, can be stored in a computer readable storage medium. Based on this understanding, all or part of the processes in the above-mentioned embodiment methods can also be completed by computer programs instructing related hardware, and the above-mentioned computer programs can be stored in a computer readable storage medium, and the computer programs can realize the steps of the above-mentioned various method embodiments when executed by a processor. The above-mentioned computer programs include computer program codes, which can be in the form of source code, object code, executable files or some intermediate forms, etc. The above-mentioned computer readable medium can include any entity or device, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier wave signal, telecommunication signal and software distribution medium, etc. capable of carrying the above-mentioned computer program codes. It should be noted that the above-mentioned computer readable storage medium contains contents which can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction.

[0127] The above-described embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand; it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements are not the essence of the corresponding technical solutions, which deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A path following control method characterized by, The method comprises: obtaining a predicted step number and a current coordinate of a followed object; obtaining a following target benefit function of a following object and a followed target benefit function of the followed object, and performing iterative calculation based on the current coordinate of the followed object, the following target benefit function and the followed target benefit function to obtain a target predicted coordinate vector of the followed object, wherein, in the iterative calculation process, the following target benefit function is used to calculate a predicted following coordinate vector corresponding to the following object based on an input followed object coordinate vector to obtain a maximum function value, the followed target benefit function is used to calculate a predicted followed coordinate vector corresponding to the followed object based on an input following object coordinate vector to obtain a maximum function value, the target predicted coordinate vector satisfies a first preset condition or a second preset condition, the first preset condition is that an iteration number is greater than a preset iteration number threshold, the second preset condition is that a difference between the target predicted coordinate vector and a predicted followed coordinate vector corresponding to the followed object obtained in a previous iteration is less than a preset coordinate difference threshold, the followed object coordinate vector and the following object coordinate vector each include a predicted step number of coordinates, the predicted following coordinate vector includes a predicted step number of predicted following coordinates, the predicted followed coordinate vector includes a predicted step number of predicted followed coordinates, in a first iteration calculation process, the followed object coordinate vector corresponding to the following target benefit function is a vector generated according to the current coordinate of the followed object; in one iteration process, a function value of the following target benefit function is equal to a difference between a first distance and a second distance, wherein the first distance is a sum of distances corresponding to the predicted following coordinates and a preset coordinate origin, and the second distance is a sum of distances corresponding to the coordinates of the followed object input into the following target benefit function and the preset coordinate origin; in one iteration process, a function value of the followed target benefit function is equal to a difference between a third distance and a fourth distance, wherein the third distance is a sum of distances corresponding to the predicted followed coordinates and the preset coordinate origin, and the fourth distance is a sum of distances corresponding to the coordinates of the following object input into the followed target benefit function and the preset coordinate origin; according to the target predicted coordinate vector, calculating a target following coordinate corresponding to a next step of the following object through the following target benefit function, and controlling the following object to move to the target following coordinate.

2. The path following control method according to claim 1, characterized by, The followed object and the following object are each an aircraft.

3. The path following control method according to claim 1, characterized by, The method further comprises: obtaining the current coordinate of the followed object through a sensor of the following object.

4. The path following control method according to claim 1, characterized by, The preset coordinate origin is a starting point of movement of the following object.

5. The path following control method according to claim 1, characterized by, The following target pursuit function meets preset pursuit constraint conditions, and the pursuit constraint conditions include continuity constraint sub-conditions, distance constraint sub-conditions and maximum speed constraint sub-conditions; The continuity constraint sub-conditions are used to limit the relationship among the current predicted pursuit coordinates, the predicted pursuit coordinates of the last step and the speed of the pursuit object; The distance constraint sub-conditions are used to limit the distance between the current predicted pursuit coordinates and the corresponding input coordinates of the predicted pursuit coordinates, wherein the input coordinates are the coordinates of the followed object input into the target pursuit function; The maximum speed constraint sub-conditions are used to limit the speed of the pursuit object.

6. The path following control method of claim 1, wherein, The target pursuit function is used to calculate the target pursuit coordinates corresponding to the next step of the pursuit object according to the target predicted coordinate vector, and the pursuit object is controlled to move to the target pursuit coordinates, including: The target predicted coordinate vector is input into the target pursuit function, and a target pursuit vector corresponding to the pursuit object is calculated according to the target pursuit function; The first coordinate in the target pursuit vector is taken as the target pursuit coordinates corresponding to the next step of the pursuit object; The pursuit object is controlled to move to the target pursuit coordinates.

7. The path following control method according to any one of claims 1-6, characterized by, The prediction step number is equal to 1.

8. A path following control device characterized by comprising: The device includes: a data acquisition module configured to acquire a prediction step number and current coordinates of a followed object; The target prediction coordinate vector calculation module is configured to obtain a following target benefit function of a following object and a followed target benefit function of a followed object, and perform iterative calculation based on a current coordinate of the followed object, the following target benefit function and the followed target benefit function to obtain a target prediction coordinate vector of the followed object, wherein, in the iterative calculation process, the following target benefit function is configured to calculate a prediction following coordinate vector corresponding to the following object based on an input followed object coordinate vector to obtain a maximum function value, the followed target benefit function is configured to calculate a prediction followed coordinate vector corresponding to the followed object based on an input following object coordinate vector to obtain a maximum function value, the target prediction coordinate vector satisfies a first preset condition or a second preset condition, the first preset condition is that an iteration number is greater than a preset iteration number threshold, the second preset condition is that a difference between the target prediction coordinate vector and the prediction followed coordinate vector corresponding to the followed object obtained in a previous iteration is less than a preset coordinate difference threshold, the followed object coordinate vector and the following object coordinate vector each include a prediction step number of coordinates, the prediction following coordinate vector includes a prediction step number of prediction following coordinates, the prediction followed coordinate vector includes a prediction step number of prediction followed coordinates, in a first iteration calculation process, the followed object coordinate vector corresponding to the following target benefit function is a vector generated according to the current coordinate of the followed object; in one iteration process, a function value of the following target benefit function is equal to a difference between a first distance and a second distance, wherein the first distance is a sum of distances corresponding to the prediction following coordinates and a preset coordinate origin, and the second distance is a sum of distances corresponding to the coordinates of the followed object input into the following target benefit function and the preset coordinate origin; in one iteration process, a function value of the followed target benefit function is equal to a difference between a third distance and a fourth distance, wherein the third distance is a sum of distances corresponding to the prediction followed coordinates and the preset coordinate origin, and the fourth distance is a sum of distances corresponding to the coordinates of the following object input into the followed target benefit function and the preset coordinate origin. The following control module is configured to calculate a target following coordinate corresponding to a next step of the following object through the following target benefit function based on the target prediction coordinate vector, and control the following object to move to the target following coordinate.

9. An aircraft, characterized in that The aircraft serves as a following object, and the aircraft performs path following on a followed object based on the path following control method according to any one of claims 1-7.

10. A smart terminal, characterized by The intelligent terminal comprises a memory, a processor, and a path following control program stored in the memory and executable on the processor, and the path following control program, when executed by the processor, implements the steps of the path following control method according to any one of claims 1-7.

11. A computer readable storage medium, characterized in that, The computer readable storage medium stores a path following control program, and the path following control program, when executed by the processor, implements the steps of the path following control method according to any one of claims 1-7.

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