MPC-based unmanned aerial vehicle formation control algorithm

Abstract

The invention discloses an MPC-based unmanned aerial vehicle formation control algorithm, and relates to the technical field of unmanned formation control algorithms, and the algorithm comprises the steps: building a dynamical model of an unmanned aerial vehicle formation system, obtaining the state information of each unmanned aerial vehicle at the current moment, and predicting the system state evolution of a plurality of control periods in the future based on the dynamical model, therefore, accurate path tracking and formation maintenance of the unmanned aerial vehicle formation are realized. Constructing a prediction model of formation control according to the dynamic model, and executing a model prediction control process in each control period; according to the MPC-based unmanned aerial vehicle formation control algorithm, in a simulation comparison experiment, the MPC-based algorithm provided by the invention is tested in three path scenes (a small circular path, a large circular path and a waveform path), and the path tracking error of the MPC-based unmanned aerial vehicle formation control algorithm is obviously smaller than that of a comparison algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned formation control algorithm, in particular to a kind of unmanned aerial vehicle formation control algorithm based on MPC. BACKGROUND

[0002] As an important part of modern technology, unmanned aerial vehicle technology has made remarkable development achievements in recent years worldwide, with its application fields expanding and influence increasing. The application of unmanned aerial vehicles is increasingly valued in various fields, with unique advantages in multiple areas. However, a single unmanned aerial vehicle has very limited capabilities and can only complete a single task with low efficiency. Multi-unmanned aerial vehicle formation coordination can fully utilize the advantages of unmanned aerial vehicle formation to achieve wider task coverage and more efficient task execution. Unmanned aerial vehicle formation refers to the control of multiple unmanned aerial vehicles under the action of a certain controller to complete their attitude or position control, enabling the unmanned aerial vehicles to reach the desired attitude or position, and to complete formation keeping, formation transformation, formation obstacle avoidance, and other motion coordination requirements while adapting to the surrounding environment constraints.

[0003] Foreign research on unmanned aerial vehicle formation control started early and has achieved fruitful results in theory and algorithms. Various classic algorithms have been deeply researched and applied in control algorithms. In recent years, consensus theory has received increasing attention in unmanned aerial vehicle formation control. This theory enables unmanned aerial vehicles to adjust their flight states through information exchange between neighbors in a distributed manner to form precise formations, with good adaptability, high robustness, and strong reliability.

[0004] Domestic unmanned aerial vehicle formation has also achieved remarkable results in practical applications. Future research priorities will include further optimization of consensus control algorithms, improvement of formation coordination and stability, exploration of more formation control methods based on emerging technologies such as artificial intelligence and reinforcement learning to adapt to complex and changing task environments, and strengthening of practical application research of multi-unmanned aerial vehicle formation in different scenarios to enhance its reliability and practicality.

[0005] Based on the above, the following problems exist:

[0006] (1) Physical constraints are not fully considered. Traditional unmanned aerial vehicle formation control algorithms (such as pure pursuit control PP, LQR, leader-follower, etc.) often do not fully consider physical constraints such as speed limits and steering angle saturation in actual flight, which can lead to insufficient system stability when performing path tracking tasks, and even cause control failure.

[0007] (2) Strong dependence on high-frequency communication. Many existing algorithms require high-frequency communication and state synchronization between unmanned aerial vehicles, which not only requires high communication bandwidth in reality, but also makes it difficult to adapt to network environment problems such as communication delay, data packet loss, and bandwidth bottleneck, severely affecting system coordination efficiency and stability.

[0008] (3) The flexibility and adaptive ability of the control algorithm is weak, and the formation control method based on preset path or fixed protocol (such as leader-follower method, virtual structure method, etc.) has poor flexibility, and it is difficult to cope with the challenges brought by dynamic environment and complex task changes in actual tasks. SUMMARY

[0009] The purpose of the present application is to provide a UAV formation control algorithm based on MPC to solve the above-mentioned deficiencies in the prior art.

[0010] In order to achieve the above-mentioned purpose, the present application provides the following technical scheme: a UAV formation control algorithm based on MPC, comprising establishing a dynamic model of a UAV formation system, for obtaining state information of each UAV at the current time and predicting system state evolution in the future multiple control periods based on the dynamic model, to realize accurate path tracking and formation maintenance of the UAV formation;

[0011] A prediction model for formation control is constructed according to the dynamic model, and in each control period, a model predictive control process is executed, comprising the following steps: S1, establishing a kinematic model of the UAV formation system for describing the dynamic changes of the position, speed and heading of each UAV; S2, executing the model predictive control process in each control period: a) predicting the system state evolution in the future multiple control periods based on the current state; b) constructing a multi-objective optimization function containing path tracking error, formation keeping error and control amount change; c) setting system constraint conditions containing flight performance, safety distance and communication limit; d) calculating the optimal control sequence by using an optimization algorithm and implementing the first control instruction; S3, using a rolling horizon strategy to repeat the above control process in the next period.

[0012] Preferably, the kinematic model comprises: a position update equation calculated by a trigonometric function of linear velocity and heading angle; a heading angle update equation calculated by an integral of angular velocity; and each UAV state including planar position coordinates, motion velocity and heading angle. Preferably, the multi-objective optimization function comprises: path following accuracy for minimizing position deviation and heading angle deviation between actual flight trajectory of the UAV and preset reference path, the position deviation evaluation being measured by the shortest distance from the current position of the UAV to the reference path, the heading angle deviation evaluation being measured by the included angle between the current heading and the tangent direction of the path, and the path following accuracy having an adjustable weight coefficient to balance the control priority of position and heading; formation shape keeping for maintaining the relative position relationship among the UAVs, the formation shape keeping comprising relative distance deviation evaluation, relative angle deviation evaluation and overall shape deformation evaluation of the formation based on the shape keeping degree of the geometric center of the formation; control smoothness for ensuring the continuity and stability of control commands, the control smoothness comprising control quantity change rate limitation, control energy consumption evaluation and actuator wear evaluation, the control quantity change rate limitation being used to restrict the change amplitude of adjacent period control commands, the control energy consumption evaluation being used to consider the energy consumption of motor speed change and rudder deflection, and the actuator wear evaluation being used to reduce mechanical wear caused by frequent large action control; and a dynamic weight adjustment mechanism for automatically adjusting each weight according to the flight stage (e.g., focusing on path following in the take-off stage and focusing on formation keeping in the cruising stage), adaptively adjusting the optimization focus according to the degree of environmental disturbance, supporting manual adjustment of weight parameters by an operator, and providing a learning optimization function of weight parameters.

[0013] Preferably, the constraint conditions of flight performance comprise maximum speed, minimum turning radius and maximum acceleration limit; the constraint conditions of safety distance comprise minimum separation distance among UAVs and anti-collision safety threshold; and the constraint conditions of communication guarantee comprise maximum communication distance and minimum communication quality requirement.

[0014] Preferably, the optimal control sequence calculation in the step S2 is solved by a sequential quadratic programming algorithm and a maximum number of iterations is set to ensure real-time performance.

[0015] Preferably, the event-triggered communication mechanism further comprises a trigger condition including triggering communication when the state change amount exceeds an adaptive state threshold; the state threshold adopts an exponential decay variation law; a minimum state threshold lower limit is set to guarantee basic communication demand; and a communication priority dynamic adjustment is supported.

[0016] Preferably, the event-triggered communication mechanism further comprises a communication guarantee and optimization function, which comprises an integrated neighbor state prediction and compensation module, contains a time-varying communication delay compensation algorithm, is provided with an abnormal state forced communication guarantee mechanism, and adopts an adaptive data compression transmission technology.

[0017] Preferably, a formation adaptive reconstruction function is further included, which comprises automatically adjusting formation parameters, dynamically re-planning a reference trajectory, optimizing a communication network topology structure, and adaptively setting control parameters when the number of UAVs changes.

[0018] Preferably, the steps of the MPC-based UAV formation control algorithm according to any one of claims 1-8 are implemented when a computer program in the system is executed.

[0019] The MPC-based UAV formation control algorithm has the following beneficial effects:

[0020] 1. Path tracking accuracy is significantly improved. In the simulation comparison experiment, the path tracking error of the MPC-based algorithm proposed in the application is significantly smaller than that of the comparative algorithm in three path scenarios (small circular path, large circular path, and wave path). The average path tracking error of the MPC algorithm is 0.28 m; the error of the comparative Pure Pursuit (PP) algorithm is 0.76 m, and the error of the LQR algorithm is 0.51 m.

[0021] 2. Communication frequency is significantly reduced, and efficiency is improved. After adopting the event-triggered communication (ETC) mechanism, the system communication frequency is significantly reduced compared with the traditional continuous communication mechanism. In 200 seconds of simulation time, the average communication frequency of each UAV is about 60 times; if the continuous communication mechanism is adopted, the communication frequency can reach more than 1000 times. Description: The communication burden is reduced by more than 90%, and the system is more adaptable in bandwidth-limited or delay environment.

[0022] 3. Control input meets actual physical constraints. The control inputs u1 (differential thrust) and u2 (total thrust) in the entire flight process: are kept in the agreed physical range (such as u2≤m·g≈9.81N), without sharp oscillation, and the maximum control change rate is stable within the acceptable range. Description: The algorithm is not only effective in theory, but also has good feasibility and safety in engineering implementation. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments described in the present application, and other drawings can also be obtained by those skilled in the art based on these drawings.

[0024] Figure 1An ETC algorithm sequential flowchart provided for an embodiment of the present application;

[0025] Figure 2 An MPC combined ETC algorithm interaction sequential flowchart provided for an embodiment of the present application;

[0026] Figure 3 A communication topology graph provided for an embodiment of the present application;

[0027] Figure 4 A communication topology graph provided for an embodiment of the present application;

[0028] Figure 5 A UAV flight trajectory graph provided for an embodiment of the present application;

[0029] Figure 6 A UAV control input u1 and UAV control input u2 graph provided for an embodiment of the present application;

[0030] Figure 7 A triangular formation trajectory graph provided for an embodiment of the present application;

[0031] Figure 8 A circular formation trajectory graph provided for an embodiment of the present application;

[0032] Figure 9 A triangular formation path tracking error convergence graph provided for an embodiment of the present application;

[0033] Figure 10 A circular formation path tracking error convergence graph provided for an embodiment of the present application;

[0034] Figure 11 A structural schematic provided for an embodiment of the present application;

[0035] Figure 12 A triangular formation communication triggering frequency graph provided for an embodiment of the present application;

[0036] Figure 13 A circular formation communication triggering frequency graph provided for an embodiment of the present application;

[0037] Figure 14 A triangular formation coordination error and triggering threshold function schematic under communication delay provided for an embodiment of the present application;

[0038] Figure 15 A circular formation coordination error and triggering threshold function schematic under communication delay provided for an embodiment of the present application;

[0039] Figure 16 A longitudinal error comparison graph provided for an embodiment of the present application. DETAILED DESCRIPTION

[0040] In order for those skilled in the art to better understand the technical solutions of the present application, the present application will be further described in detail below with reference to the drawings.

[0041] Please refer to Figures 1-16 The embodiment of the present application provides a UAV formation control algorithm based on MPC. Model predictive control (MPC) is an advanced control algorithm that predicts the output of a system over a future period of time using a dynamic model of the system and optimizes the current control input to achieve optimal control of the system. The core idea of the MPC algorithm is to predict the system output over a future period of time based on the current state and system model at each sampling time, and then determine the optimal control input at the current time by solving an optimization problem. This optimization problem usually includes an objective function for measuring the deviation between the system output and the desired output, and the variation of the control input. The MPC algorithm also considers the constraints of the system, such as the amplitude and rate limits of the control input, to ensure the safe and stable operation of the system. The principle of MPC is as follows:

[0042] The discrete-time dynamic model of the system is:

[0043] x k +1 =f( x k , u k )

[0044] where x k ∈R n is the state of the system at time k, u k ∈R m is the control input, and f: R n ×R m →R n is the dynamic model of the system.

[0045] At each sampling time k, the MPC algorithm determines the optimal control input sequence by solving the following optimization problem:

[0046] min

[0047]

[0048] subject to x k+i+1 =f( x k +i, u k +i ),i=0,1,...,N-1

[0049] u min ≤ u k +i ≤ u max ,i=0,1,...,N-1

[0050] x min ≤ x k +i ≤ x max i = 0, 1,..., N

[0051] where N is the length of prediction horizon, x ref，k+i and u ref，k+i are the reference state and reference control input, Q and R are weight matrices for adjusting the relative importance of state and control input, u min and u max are the lower and upper bounds of control input, x min and x max are the lower and upper bounds of state. After solving the above optimization problem, the optimal control input sequence is obtained as In practical applications, only the first control input is used as the control input at the current time, and then the above process is repeated at the next sampling time k+1 to form a rolling optimization control strategy.

[0052] According to the above MPC principle, in the unmanned aerial vehicle formation control, the MPC algorithm is used to design the controller to realize the accurate path tracking and formation maintenance of the unmanned aerial vehicle. Specifically, an unmanned aerial vehicle formation control algorithm based on MPC includes establishing a dynamic model of the unmanned aerial vehicle formation system, obtaining the state information of each unmanned aerial vehicle at the current time, and predicting the evolution of the system state in the future multiple control periods based on the dynamic model, to realize the accurate path tracking and formation maintenance of the unmanned aerial vehicle formation;

[0053] According to the dynamic model, a prediction model for formation control is constructed, and in each control period, a model predictive control process is performed, including the following steps:

[0054] S1, a kinematic model of the unmanned aerial vehicle formation system is established to describe the dynamic changes of the positions, velocities and headings of each unmanned aerial vehicle; S2, in each control period, a model predictive control process is performed: a) predicting the evolution of the system state in the future multiple control periods based on the current state; b) constructing a multi-objective optimization function including path tracking error, formation maintenance error and control amount change; c) setting system constraint conditions including flight performance, safety distance and communication limit; d) using an optimization algorithm to calculate the optimal control sequence and implement the first control instruction; S3, using a rolling horizon strategy to repeat the above control process in the next period.

[0055] The dynamic model includes a position update equation that calculates using a linear velocity and a trigonometric function of a heading angle, a heading angle update equation that calculates using an angular velocity integral, and each UAV state including a planar position coordinate, a movement velocity, and a heading angle. Specifically, after a prediction model is established, a prediction model of a UAV position and orientation in a future period of time is established according to a dynamic model of the UAV. The model will consider the current state of the UAV, control input, and dynamic characteristics of the system.

[0056] Based on this, for the UAV movement in a two-dimensional plane, the dynamic model can be expressed as:

[0057] x[i] = u[i] cos(Ψ[i])

[0058] y[i] = u[i] sin(Ψ[i])

[0059] Ψ[i] = r[i]

[0060] where x[i] and y[i] are the position coordinates of the UAV i in the inertial coordinate system, u[i] is the linear velocity of the UAV i, Ψ[i] is the orientation angle of the UAV i, and r[i] is the angular velocity of the UAV i.

[0061] Further, the multi-objective optimization function includes: path tracking accuracy, which is used to minimize the position deviation and heading angle deviation between the actual flight trajectory of the UAV and the preset reference path, the position deviation is evaluated by measuring the shortest distance from the current position of the UAV to the reference path, the heading angle deviation is evaluated by measuring the included angle between the current heading and the tangent direction of the path, and the path tracking accuracy can be adjusted by a weight coefficient to balance the control priority of position and heading; formation shape maintenance, which is used to maintain the relative position relationship between the UAVs, the formation shape maintenance includes relative distance deviation evaluation, relative angle deviation evaluation and overall shape change evaluation of the formation, the distance deviation evaluation is the difference between the actual distance and the expected distance, the relative angle deviation evaluation is the difference between the actual azimuth angle and the expected azimuth angle, and the overall shape change evaluation of the formation is based on the shape maintenance degree of the geometric center of the formation; control smoothness, which is used to ensure the continuity and stability of the control instruction, the control smoothness includes control quantity change rate limitation, control energy consumption evaluation and actuator wear evaluation, the control quantity change rate limitation is used to restrict the change amplitude of adjacent period control instructions, the control energy consumption evaluation is used to consider the energy consumption of motor speed change and rudder deflection, and the actuator wear evaluation is used to reduce the mechanical loss caused by frequent large action control; dynamic weight adjustment mechanism, which automatically adjusts the weights according to the flight stage (such as focusing on path tracking in the take-off stage and focusing on formation maintenance in the cruise stage), adaptively adjusts the optimization focus according to the degree of environmental disturbance, supports manual adjustment of weight parameters by the operator, and provides learning optimization function of weight parameters. Specifically, a target function is defined for measuring the deviation between the actual position and orientation of the UAV and the expected position and orientation, as well as the change amount of the control input. The target function usually includes path tracking error, formation shape error and control input energy consumption, and the target function can be expressed as:

[0062]

[0063] where e pf，i is the path following error, u i is the current control input, u ref，i is the reference control input, and Q and R are weight matrices.

[0064] where the constraint conditions of flight performance include maximum speed, minimum turning radius, maximum acceleration limit; the constraint conditions of safety distance include the minimum interval distance between UAVs and the anti-collision safety threshold; the constraint conditions of communication guarantee include the maximum communication distance and the minimum communication quality requirement. Specifically, in the optimization process, the physical constraints of the UAV, such as maximum speed and minimum turning radius, are considered to ensure the feasibility of the control input and the safety of the system. For example, the speed constraint can be expressed as:

[0065] u min ≤u[]≤ u max

[0066] The angular velocity constraint can be expressed as:

[0067] r min ≤r[i]r max

[0068] Where the optimal control sequence calculation in step S2 is numerically solved using a sequential quadratic programming algorithm and a maximum number of iterations is set to ensure real-time performance. Specifically, at each sampling time, based on the current state and the prediction model, the optimization problem is solved to obtain the current optimal control input. This usually requires the use of numerical optimization algorithms such as sequential quadratic programming (SQP) or interior point method, etc.

[0069] Finally, update and implement. The optimal control input obtained is applied to the UAV, and then the above process is repeated at the next sampling time to realize real-time control.

[0070] Through the above steps, the MPC controller can adjust the control input in real time to adapt to the dynamic changes of the UAV and external disturbances, thereby achieving accurate path tracking and formation control. The application of MPC algorithm in UAV formation can effectively handle the nonlinearity, multivariable coupling and constraint conditions of the system, providing a flexible and efficient control solution.

[0071] Wherein, it also includes an event-triggered communication mechanism, the triggering conditions of which include: triggering communication when the state change exceeds the adaptive state threshold; the state threshold adopts an exponential decay variation law; a minimum state threshold lower limit is set to ensure basic communication needs; and dynamic adjustment of communication priority is supported. It should be noted that the event-triggered communication mechanism also includes communication guarantee and optimization functions, which include an integrated neighbor state prediction and compensation module, a time-varying communication delay compensation algorithm, an abnormal state forced communication guarantee mechanism, and an adaptive data compression transmission technology. Specifically, the event-triggered communication mechanism is a strategy that decides whether to communicate according to predefined triggering conditions, aiming to reduce the number of communications and reduce communication overhead while ensuring system performance. In the ETC mechanism, each UAV decides whether to send information to neighbors according to its own state change or other predefined events.

[0072] Further, the core idea of the ETC mechanism is to define a triggering condition, and only when this condition is met, the UAV communicates. Common triggering conditions include the change of state variables exceeding a certain threshold, the time interval reaching a certain length, etc. For example, the state-based triggering condition can be expressed as:

[0073] IIx[i](t)-x[i]( t last )II≥δ

[0074] where x[i](t) is the current state of UAV i at time t, x[i](t last ) is the state of UAV i at the last communication, and δ is a predefined triggering threshold.

[0075] According to the basic principle of ETC mechanism, in UAV formation control, ETC mechanism is used to optimize the communication process, reduce unnecessary communication, and improve the efficiency and robustness of the system.

[0076] In this paper, the triggering condition of event-triggered communication (ETC) algorithm is based on the comparison of estimation error and preset threshold. Specifically, the triggering condition is as follows:

[0077] For each UAV, calculate the estimation error Y tilde tilde of its path parameter Y and compare it with the preset threshold η. If the absolute value of the estimation error exceeds the threshold, communication is triggered.

[0078] First, calculate the estimation error:

[0079]

[0080] where Y is the estimated value of the vehicle path parameter, and Y is the actual value of the vehicle path parameter.

[0081] Then calculate the threshold:

[0082]

[0083] where c1 is a constant used to adjust the size of the threshold, α is a decay coefficient used to control the decay rate of the threshold over time, i is the current time step, Ts is the sampling interval of ε0, and ε0 is a very small positive number used to ensure that the threshold is always greater than zero.

[0084] Finally, calculate the triggering condition. If the absolute value of the estimation error exceeds the threshold, communication is triggered:

[0085] if |Y tilde tilde| ≥ η

[0086] The triggering condition of event-triggered communication (ETC) is based on the comparison of the estimation error Ytilde of the path parameter Y and the preset threshold η. If the absolute value of the estimation error exceeds the threshold, communication is triggered, the estimated value is updated and data is sent. This mechanism can effectively reduce unnecessary communication and improve the communication efficiency of the system.

[0087] According to the triggering condition, the communication protocol can be implemented. When the triggering condition is met, the UAV sends the current state information to its neighbors; otherwise, it remains silent. This can be achieved by embedding the triggering condition judgment logic in the control algorithm of the UAV.

[0088] After receiving the neighbor information, the UAV processes the information and updates the state according to the predefined rules. For example, the received information can be used to update the estimate of the neighbor state, or adjust the control input of itself to maintain the formation shape for information processing and updating.

[0089] Through the ETC mechanism, the UAV only communicates when necessary, thereby significantly reducing the number of communications and data transmission, reducing the load of the communication network, reducing communication overhead, and improving the overall efficiency of the system. The ETC mechanism can enable the UAV formation to maintain good performance in an environment with limited communication or interference, because the communication dependence is reduced, the tolerance of the system to communication failure or delay is enhanced, and the robustness is improved.

[0090] Through the above steps, the ETC mechanism balances the communication efficiency and system performance in the UAV formation control, and provides support for stable operation and efficient cooperation of the formation.

[0091] Further, as a preferred embodiment of the present application, a single-path tracking algorithm for a constrained UAV based on MPC is designed, which is a single-UAV path following problem, that is, while ensuring the speed curve required by the speed tracking of the corresponding path parameters, the UAV approaches a path.

[0092] Among them, the relevant data of the kinematic model of the UAV is clear, and the dynamic model of the UAV is a mathematical expression for describing its motion in space. For motion in a two-dimensional plane, the model can be simplified as position update and orientation update.

[0093] Specifically, first, the position update, the position (x[i], y[i]) of the UAV in the inertial coordinate system changes with time, which is determined by its speed u[i] and orientation Ψ[i], and the specific equation is:

[0094] x[i]=u[i]cos(ψ[i])

[0095] y[i]=u[i]sin(ψ[i])

[0096] Where u[i] is the linear speed of UAV i, and Ψ[i] is the orientation angle of UAV i.

[0097] Second, the orientation update, the change rate of the orientation angle Ψ[i] of the UAV is determined by its angular velocity r[i], and the equation is:

[0098] ψ[i]=r[i]

[0099] Where r[i] is the angular velocity of UAV i.

[0100] The model assumes that the motion of the UAV is in a two-dimensional plane, and does not consider the vertical motion component. Through the above dynamic equation, the position and orientation changes of the UAV under the action of the control input (velocity and angular velocity) can be described, providing a basis for the design of subsequent formation control algorithms.

[0101] Further, in order to realize path tracking, path-related parameters are introduced. The path is parameterized by variable (y [i] ) and the position vector of the point on the path p d [i] (y [i] ) = [x d [i] (y [i] ), y d [i] (y [i] )] T , and the angle between the tangent and the x1 axis Ψ d [i] (y [i] ). Through these parameters, the path tracking error vector is constructed, the position error vector in the inertial frame is e I = p - p d (y), and the direction error is e Ψ = Ψ - Ψ d (y). For ease of processing, the rotation matrix is used to convert the position error to the parallel transmission frame, and is obtained, and the comprehensive path tracking error vector is defined.

[0102] In addition, a virtual reference speed new input v is introduced for the design of the controller, which is used to control the evolution of the path parameter y, and v is located in the constraint set u v : = {v: |v| ≤ v max}, and v max needs to be determined according to the actual situation as a design parameter. By adjusting v, the UAV can travel along the path and keep the speed vector aligned with the path tangent.

[0103] Based on the above data processing results, a system model of single UAV constrained path tracking is constructed. According to the kinematics of the UAV and the relationship between the path parameters, the dynamic changes of the path tracking error in the parallel transmission frame are described by the following equation:

[0104]

[0105] where g(y), K(y), v = y., u are the input vectors of the path tracking error system. This model takes into account the motion state of the UAV (velocity, heading angle, etc.), the geometric characteristics of the path (curvature K(y)), and the influence of the new input v on the path parameters. In the model, g(y) reflects the relationship between the path parameterization and the actual path length change, and K(y) reflects the influence of the path curvature on the UAV motion control. Through this system model, the error change of the UAV in the process of tracking the path can be described, which provides a core framework for the subsequent design of feedback control law to achieve the path tracking goal. At the same time, the parameters and variables in the model are related to each other, which determines the dynamic characteristics of the system and provides a basis for in-depth analysis of system performance and design of effective control strategy.

[0106] where the Figure 1 is the MPC algorithm flowchart, including initialization state, optimization problem construction and solution, and state update.

[0107] In the scenario of multi-UAV cooperative path tracking, data processing provides the basis for effective coordination between UAVs. First, a series of key assumptions and parameters are clarified before cooperative path tracking. It is assumed that each UAV is equipped with a path tracking controller that can solve the single UAV constrained path tracking problem, and the expected speed curve of all UAVs along the path is the same, while the network topology between UAVs is time-invariant.

[0108] In order to realize the coordination between UAVs, the path is parameterized in a special way. For example, when multiple UAVs need to travel along concentric circles and align radially, the path is parameterized as γ [i] = s [i] / 2π, where s [i] is the curvilinear coordinate along path i. Through this parameterization, when the path parameter γ [i] (t) = γ [j] (t) and , the UAV can perform cooperative maneuvers at the expected normalized path speed to achieve the desired formation effect.

[0109] During the coordination process, new variables are introduced to assist in analysis and control. Define:

[0110]

[0111] Intuitively, it measures the time spent by agent i from state 0 to γ [i] . Since v d (γ) > 0, the synchronization of path parameters v d (γ) > 0 (i.e., ) is equivalent to the synchronization of variable z [i] (i.e., ). To describe the coordination error between UAVs, a coordination error vector is defined. where W = I N -11 T / N, Thus, the problem of path parameter synchronization between UAVs is converted into the problem of driving coordination error vector ξ to the origin, which is convenient for subsequent design of control law for coordination control.

[0112] Based on the parameters and variables determined in the data processing stage, the coordination system model of multi-UAV cooperative path tracking is constructed. Assuming that the UAVs run independently and the path tracking controller makes the UAVs asymptotically approach the path x[ i ] = 0 and ensures that the path parameters evolve according to the expected speed curve v [i] = v d (γ [i] ), the standard speed of the UAV u [i] = g [i] (γ [i] ) v d (γ [i] ) is obtained.

[0113] To achieve the desired formation, the speed of the UAV needs to be adjusted, and a correction term is introduced. At this time, the actual speed of the UAV is The dynamic change of the path parameter is extended to

[0114] In this system, the coordination problem is reduced to finding the appropriate so that the total speed of each UAV satisfies the constraint condition while ensuring the synchronization of path parameters and evolving according to the common speed curve v d (·).

[0115] To handle the coordination problem under different communication scenarios, for the continuous communication scenario, a distributed control law Under the event-triggered communication (ETC) mechanism, considering the cases of no communication delay and communication delay, the corresponding control law and state estimator are designed. For example, under the ETC mechanism without communication delay, and by designing appropriate estimators and event-triggered functions, the effective exchange and coordination of data between UAVs are realized; in the case of communication delay, the estimator is modified.

[0116] Based on Figure 2 the flowchart of the ETC algorithm, including error calculation, trigger judgment and communication control.

[0117] Furthermore, the ETC mechanism reduces communication between drones, ensuring that drones only communicate with their neighbors when necessary. Specifically, based on certain criteria, once the corrected speed is calculated, the MPC controller guides the drone to approach and follow a designated path. In other words, the MPC controller stabilizes the path-following error between the drone and its designated path.

[0118] Furthermore, to address the coordination problem, we define new variables:

[0119]

[0120] It measures agent i from state 0 to state γ [i] Time spent. Due to v d (γ)>0, path parameter γ [i] Synchronization is equivalent to z [i Synchronization. Then, a coordination error vector is defined. W = I N -11 T / N will drive z[ i The problem of reaching a consensus is transformed into the problem of making ξ approach the origin, which provides a basis for designing distributed control laws.

[0121] Furthermore, in the study of coordination problems in collaborative path tracing, under certain conditions, a specific distributed control law can enable all agents to asymptotically reach a consensus on their states (path parameters). When the graph is undirected and connected, the distributed control law... in To meet Positive gain, This allows all agents to asymptotically reach a consensus on their states (path parameters), meaning the origin of the coordination error vector ξ becomes globally asymptotically stable. For the special case where the velocity curve is constant, v... d (γ [i] If c > 0, the distributed control law can also make the path parameters reach a consensus asymptotically, and the calculation is simpler.

[0122] The ETC mechanism with communication delay, under this mechanism, shows in Theorem 1 that it can ensure... and Meanwhile, Theorem 2 states that the closed-loop coordinated error system with respect to the state ξ input η:=[η [1] ,...,η [N] ] T The input η is the state that is stable (ISS). This means that if the input η is bounded, then the state ξ is bounded, and if η(t) → 0, then ξ(t) → 0. This mechanism extends the related event triggering mechanism by customizing the trigger threshold function η. [i] (t) offers greater flexibility in reducing the frequency of communication between drones.

[0123] The ETC mechanism with communication delay considers more realistic time-varying and non-homogeneous communication delay scenarios, and modifies the ETC mechanism. A time delay signal is defined and the estimator is modified to compensate the delay effect. By analysis, the result of estimation error is obtained:

[0124]

[0125] Further, define The closed-loop coordinated error system is ISS in ξ and σ when the relevant conditions hold. When the communication delay is zero, it degenerates to the case of Theorem 2; when and , it recovers to the result of Theorem 1.

[0126] After modifying the velocity of the UAV, the total velocity of the UAV is Substitute it into the kinematic equation of the path following of the single UAV, the path following error system of the UAV i is obtained:

[0127]

[0128] where u [i] = (v [i] , r [i] ), and u [i] is restricted to the set

[0129]

[0130] Further, define the finite horizon open-loop optimal control problem whose objective is to minimize the cost function: subject to a series of constraints, such as dynamic equation constraints, initial condition constraints, etc. In these constraints, the variables with a tilde represent predicted variables. In addition, it contains a stability constraint based on a Lyapunov function V: 3 → ≥0 and a related stabilizing control law to guarantee the stability of the system. In the state feedback sampled-data MPC, the optimal control problem is solved repeatedly at every discrete sampling time t i = iδ, i ∈ + , δ is the sampling interval. The MPC control law is defined as where is the optimal solution of the optimal control problem OCP(·).

[0131] Before solving the path following problem using this MPC scheme, two assumptions are proposed. Assumption A2.1 is the stage cost l [i](·) is continuous and positive definite, and when and , l [i] (·) = 0; Assume A2.2 exists Lyapunov function V satisfies positive definite and V(x [i] ) = 0 only when V(x [i] ) = 0, and the relevant nonlinear feedback control law u n satisfies and can globally stabilize the path tracking error system. Based on these assumptions, Theorem 4 (Path following with MPC) is obtained: under the condition that the path tracking error system is controlled by the input constraint set U pf and assumption 2 is established, the origin of the path tracking error is globally asymptotically stable. At the same time, Lemma 3 (Global Constrained Nonlinear PF Controller) is given to prove that there exists a control law u n (x) and Lyapunov function V(x) that can make the origin of the path tracking error system globally asymptotically stable (GAS) and satisfy assumption 2. This MPC scheme avoids constructing the terminal set, has a global attractive domain, and has certain advantages compared with other methods. Figure 3 The interactive flowchart of the MPC algorithm combined with the ETC algorithm.

[0132] In the experimental scenario set based on the above:

[0133] The simulation scenario of the MPC algorithm under flight constraints uses the model predictive control (MPC) method to control the quadrotor unmanned aerial vehicle to fly from the initial position to the specified final position while satisfying flight constraint conditions such as avoiding obstacles and limiting the pitch angle range, optimizing the flight trajectory. An obstacle is set at a certain position. The initial position of the unmanned aerial vehicle is set at the origin, and the initial speed and pitch angle are both 0. The simulation is performed for 50 time steps, and in each time step, the MPC controller calculates the optimal control command according to the current state, updates the unmanned aerial vehicle state, and real-time visualizes the predicted trajectory, actual trajectory, and body attitude.

[0134] The simulation scenario of the MPC-based event-triggered mechanism algorithm aims to simulate a multi-UAV cooperative path following task, focusing on the formation control performance of UAVs in complex communication environments. The simulation environment uses a two-dimensional plane, and the UAVs need to fly on a given path while maintaining a preset geometric formation. The path planning includes two task scenarios: triangular formation and circular formation, which are used to verify the performance of the algorithm under different geometric shapes and path-dependent speeds. The simulation time is 200 seconds, and the sampling interval is 0.2 seconds. The initial positions and velocities of all UAVs are randomly generated, but they meet the initial conditions of path tracking. Communication delays and event-triggered communication mechanisms are also introduced in the simulation to simulate communication limitations in actual applications.

[0135] This paper also studies the comparison of different algorithms, focusing on UAV path tracking in the same simulation environment. Three different road scenarios are set for selection. They are small circular path, large circular path and wave test path. Each path has a specific trajectory length and radius, and the simulation end condition is related to the y-coordinate of the UAV and the travel time. The UAV will complete the path tracking task in these scenarios according to different path tracking algorithms.

[0136] Table 1 UAV parameters for MPC algorithm with flight constraints

[0137] UAV mass Moment of inertia Force arm length Controller gravity acceleration Model gravity acceleration 1 kg 0.01 kg-m 2 ]] 0.1m 10.9 m / s 2 ]]> 9.81 m / s 2 ]]

[0138] Table 2 UAV parameters for MPC-based event-triggered mechanism algorithm

[0139] Number of UAVs Velocity constraint Turn rate constraint Vehicle index Communication link 5 u i ∈[0.2,2]m / s]]> r i ∈ [-0.2, 0.2] rad / s N＝{1,2,3,4,5} Bidirectional connection

[0140] Table 3 UAV parameters for comparison of different algorithms

[0141] Maximum turn angle Maximum angular velocity UAV velocity Maximum acceleration Maximum deceleration 0.925 rad 0.925 rad / s 10 m / s 11 m / s 2 ]] 12 m / s 2 ]]

[0142] Table 1 Table 2 These parameters reflect the physical limitations of UAVs in actual applications, such as the performance boundaries of the power system and the steering system. In addition, the simulation assumes that the speed of the UAV is strictly positive, which is consistent with the actual characteristics of fixed-wing UAVs and some autonomous ocean robots.

[0143] At the same time in the simulation, the communication network between UAVs adopts a fixed and undirected topology structure, as shown in Figure 4 Each UAV exchanges information with adjacent UAVs through a bidirectional communication link. The fixed nature of the communication topology ensures the stability of the communication network during the simulation, while simplifying the algorithm design.

[0144] The prediction horizon of the MPC algorithm is set to 12 time steps, each with a duration of 0.2 s. The optimization algorithm parameters are optimized using the fmincon function, with the interior-point optimization algorithm selected. The maximum number of iterations is set to 30,000, and the maximum number of function evaluations is set to 30,000. The objective of the cost function is to make the final position, attitude, velocity, and control input of the UAV as close as possible to the desired values. Specifically, the UAV is expected to reach a position of x = 60, z = 60, a pitch angle of 0, a pitch angle velocity of 0, and a common-mode control input equal to the product of the UAV's mass and the gravitational acceleration used by the controller. Ensuring that the updates to the UAV's state conform to its dynamics model is achieved by discretizing the continuous dynamics model using the Euler method. The pitch angle of the UAV is limited to prevent it from exceeding the specified range, and the UAV is required to avoid obstacles during flight.

[0145] In the MPC-based event-triggered mechanism algorithm, model predictive control (MPC) and event-triggered communication (ETC) mechanisms are used to achieve coordinated path tracking. The MPC controller is designed based on the kinematic model of the UAV and input constraints, and the control input is optimized to minimize the path tracking error. The ETC mechanism is used to reduce communication frequency and improve communication efficiency.

[0146] The parameters of the MPC controller are configured as follows:

[0147] The sampling interval δ = 0.2 s, and the prediction time range = 2 s. The step cost function of MPC is defined as:

[0148] l i (x i ,u i )=x i T Qx i +u i T Ru i

[0149] where Q = diag(1, 1, 2) and R = diag(2, 20).

[0150] The parameters of the ETC mechanism are configured as follows:

[0151] The trigger threshold function is designed as a time-dependent function to ensure that the communication frequency is higher in the initial stage and gradually decreases as the system tends to be stable. The event-triggered threshold function is: i (t)=c1e -αt +ò

[0152] where c1=0.1, a=0.2, e=5x10-3. The configuration of these parameters aims to ensure high-efficiency cooperative path following while satisfying the input constraints. By reasonably designing the communication delay and triggering threshold, we are able to significantly reduce the communication cost while guaranteeing the performance of cooperative control.

[0153] In the comparison of different algorithms, the Pure Pursuit (PP) algorithm is configured with a preview distance speed coefficient and minimum and maximum preview distances to determine the preview distance of the UAV for path tracking. The LQR_model3 algorithm sets the time discretization interval, reference index, prediction horizon size, and weight matrices of the state and control to achieve path tracking based on the linear quadratic regulator. The MPC algorithm sets the dynamic parameters of the UAV, such as front and rear wheel cornering stiffness, UAV mass, front and rear axle to center of mass distance, and z-axis rotational inertia, as well as numerous parameters such as matrix dimensions and weight matrices, to achieve path tracking based on model predictive control. The LQR_apollo algorithm has similar parameters to the MPC algorithm, including its own time discretization interval, prediction horizon size, weight matrices of the state and control, and is used to achieve another path tracking based on the linear quadratic regulator.

[0154] Based on the experimental results and analysis of the above scenarios, the experimental part first verifies the MPC algorithm designed based on the mathematical model of a single four-rotor UAV under flight constraints. Through MATLAB simulation, the control input, state variable, and UAV flight trajectory are obtained, confirming the reliability of the controller. Then, the focus is on verifying the effectiveness of the proposed MPC-based event-triggered mechanism algorithm in the cooperative path following (CPF) task of the limited autonomous UAV through simulation. Two typical formation tasks are discussed.

[0155] Figure 5 The flight trajectory of a single UAV in a two-dimensional plane is shown, where the red dots represent the predicted flight trajectory and the blue squares represent the actual flight trajectory. The degree of overlap between the red predicted trajectory and the blue actual trajectory reflects the prediction accuracy of the MPC. The UAV body color is orange, which is drawn according to the current attitude (angle) and position of the UAV to visually demonstrate the orientation and position of the UAV in the two-dimensional plane.

[0156] Figure 6 The control input of the UAV as a function of time is shown, including the differential thrust u1 and the total thrust u2. In the model predictive control framework, the control inputs u1 and u2 are defined as differential thrust and total thrust, respectively, where u1 adjusts the UAV attitude angle by driving the yaw moment, and u2 achieves position tracking by adjusting the total lift. Both work together on the nonlinear dynamics model to minimize the trajectory tracking error. From the figure, we can see that the control input of the UAV changes smoothly over time, and the differential thrust u1 and the total thrust u2 are well coordinated to achieve the desired trajectory tracking. Figure 6It can be seen that the control inputs are constantly adjusted during the flight to meet the flight requirements of the UAV. u1 (differential thrust) is used to control the yaw angle, and its variation should match the adjustment requirements of the θ angle. u2 (total thrust) needs to meet physical constraints (such as u2 ≤ mass * gravity), and the curve should be smooth to avoid sudden thrust changes. In the initial stage of flight, the control inputs change greatly to quickly adjust the state of the UAV; as the UAV approaches the target position, the control inputs gradually stabilize. Through the analysis of the simulation results, the following conclusions can be drawn: the MPC-based flight controller of the UAV can effectively handle flight constraint conditions, enabling the UAV to achieve trajectory optimization while meeting various constraint conditions. The flight trajectory of the UAV can follow the predicted trajectory and gradually approach the final target position. The state variables and control inputs of the UAV remain relatively stable during the flight, indicating that the MPC controller has good control effect

[0157] In the triangular formation task, the UAVs need to fly along parallel paths while maintaining a triangular formation. The simulation results show that the UAVs successfully fly along the predetermined paths and maintain the desired formation during the task. Figure 7 The trajectories of the UAVs in the triangular formation task are shown. As can be seen from the figure, the trajectories of the UAVs are highly consistent with the expected paths, verifying the effectiveness of the path tracking control algorithm. In Figure 7 , the solid line represents the expected path, and the dashed line represents the actual trajectory of the UAV. It can be seen that the UAVs quickly adjust to the expected path in the initial stage and maintain a stable triangular formation in the subsequent process.

[0158] In the circular formation task, the UAVs need to fly along nested circular paths while maintaining a circular formation. The simulation results show that the UAVs successfully fly along the nested circular paths and maintain the desired formation during the task.

[0159] Figure 8 The trajectories of the UAVs in the circular formation task are shown. As can be seen from the figure, the trajectories of the UAVs are highly consistent with the expected paths, verifying the effectiveness of the path tracking control algorithm. In Figure 8 , the solid line represents the expected path, and the dashed line represents the actual trajectory of the UAV. It can be seen that the UAVs quickly adjust to the expected path in the initial stage and maintain a stable circular formation in the subsequent process. The convergence of the path tracking error is an important indicator of the performance of the algorithm.

[0160] Figures 9-10 The evolution process of the path tracking error is shown. As can be seen from the figure, the path tracking error gradually converges to zero during the simulation, verifying the global asymptotic stability of the algorithm. In Figure 10In the middle, the horizontal axis represents time (seconds), and the vertical axis represents path tracking error. It can be seen that the error decreases rapidly in the initial stage and gradually tends to zero in the subsequent process, indicating that the control algorithm can effectively guide the UAV to the desired path.

[0161] Figures 11-12 The frequency of communication triggering in triangular formation and circular formation tasks is demonstrated. From Figures 11-12 It can be seen that at the beginning of the simulation, the communication triggering frequency is high, because the UAVs need to adjust frequently to reach the desired formation. As the simulation time progresses, the UAVs gradually approach the desired formation, and the communication triggering frequency significantly decreases. This indicates that the proposed event-triggered communication mechanism can effectively reduce unnecessary communication, thereby improving communication efficiency.

[0162] Communication delay is an inevitable factor in practical applications and has a significant impact on formation coordination performance. Figures 13-14 The impact of communication delay on coordination state is demonstrated. From Figures 13-14 It can be seen that although there is communication delay, the coordination state of the UAVs can still gradually converge. This indicates that the proposed cooperative control algorithm has certain robustness to communication delay. In addition, the orange line represents the threshold, and the figure also demonstrates the changes in the estimation error and the triggering threshold function. It can be seen that the estimation error is always within the triggering threshold range, further verifying the effectiveness of the event-triggered mechanism.

[0163] In the simulation environment, the tracking accuracy of each algorithm can be intuitively compared under the condition of complete and initial state. Literature 12 points out that the LQR algorithm, by selecting appropriate weight matrices Q and R, weights the state variables and control inputs to optimize system performance. Literature 16 points out that the PP algorithm focuses on planning the optimal or feasible path for the agent from the starting point to the end point in a specific environment. Literature 5 points out that the MPC algorithm, i.e., model predictive control algorithm, takes the current state of the system as the starting point to predict the future state, constructs a target function containing state and control input, and solves it within a finite time domain to obtain the control sequence acting on the system, while being able to handle constraint conditions, and is widely used in multiple fields to achieve efficient and stable control of the system. Figures 15-16 The lateral and longitudinal errors of PP, LQR, and MPC algorithms are plotted against time to help analyze the tracking accuracy of different algorithms in the lateral and longitudinal directions. The closer the error is to 0, the higher the tracking accuracy of the algorithm. For example, when the time is 66 seconds, the MPC algorithm has a lateral error of 0.08 meters, the PP algorithm has an error of -0.6 meters, and the LQR algorithm has an error of 0.2 meters. From the image smoothness, it can be seen that the MPC algorithm has the smallest error and the highest trajectory tracking accuracy. In this paper, the MPC algorithm is chosen as the main algorithm

[0164] The foregoing merely illustrates some exemplary embodiments of the application, and no doubt numerous modifications and alterations thereto will be apparent to those skilled in the art. Accordingly, the above description is intended for purposes of illustration only and should not be construed as limiting the scope of the application.

Claims

1. An MPC-based UAV formation control algorithm, characterized in that, The application relates to a dynamic model of a UAV formation system, which is used to obtain state information of each UAV at a current time and predict system state evolution in a plurality of control periods in the future based on the dynamic model, so as to realize accurate path tracking and formation maintenance of the UAV formation. A prediction model of formation control is constructed according to the dynamic model, and a model prediction control process is executed in each control period, including the following steps: S1, a kinematic model of the UAV formation system is established, which is used to describe dynamic changes of positions, speeds and headings of the UAVs; S2, the model prediction control process is executed in each control period: a) predicting system state evolution in a plurality of control periods in the future based on the current state; b) constructing a multi-objective optimization function containing path tracking errors, formation maintenance errors and control quantity changes; c) setting system constraint conditions containing flight performance, safe distance and communication limitation; d) calculating an optimal control sequence by using an optimization algorithm and implementing a first control instruction; S3, a rolling horizon strategy is adopted to repeat the above control process in the next period.

2. The MPC-based UAV formation control algorithm of claim 1, wherein, The dynamic model includes a position updating equation which is calculated by using a trigonometric function relationship of linear speed and heading angle, a heading angle updating equation which is calculated by using angular speed integration, and states of each UAV containing plane position coordinates, motion speed and heading angle.

3. The MPC-based UAV formation control algorithm of claim 2, wherein, The multi-objective optimization function contains: path tracking accuracy which is used to minimize position deviation and heading angle deviation between an actual flight trajectory of the UAV and a preset reference path, the position deviation is evaluated by using the shortest distance measurement from the current position of the UAV to the reference path, the heading angle deviation is evaluated by using the included angle measurement of the current heading and the tangent direction of the path, and the path tracking accuracy can be adjusted by a weight coefficient to balance the control priority of the position and the heading; formation shape maintenance which is used to maintain the relative position relationship among the UAVs, the formation shape maintenance includes relative distance deviation evaluation, relative angle deviation evaluation and overall shape deformation evaluation of the formation, the relative distance deviation evaluation is the difference between the actual distance and the expected distance, the relative angle deviation evaluation is the difference between the actual azimuth angle and the expected azimuth angle, and the overall shape deformation evaluation of the formation is based on the shape maintenance degree of the geometric center of the formation; control smoothness which is used to ensure continuity and stability of the control instruction, the control smoothness includes control quantity change rate limitation, control energy consumption evaluation and actuator wear evaluation, the control quantity change rate limitation is used to restrict the change amplitude of the control instruction in adjacent periods, the control energy consumption evaluation is used to consider energy consumption of motor speed change and rudder deflection, and the actuator wear evaluation is used to reduce mechanical loss caused by frequent large action control; a dynamic weight adjustment mechanism which automatically adjusts each weight according to a flight stage, adaptively adjusts optimization emphasis according to the degree of environmental disturbance, supports manual adjustment of the weight parameter by an operator, and provides a learning optimization function of the weight parameter.

4. The MPC-based UAV formation control algorithm of claim 1, wherein, The constraint conditions of the flight performance include maximum speed, minimum turning radius and maximum acceleration limitation; the constraint conditions of the safe distance include minimum interval distance among the UAVs and anti-collision safety threshold; and the constraint conditions of the communication guarantee include maximum communication distance and minimum communication quality requirement.

5. The MPC-based UAV formation control algorithm of claim 1, wherein, The optimal control sequence calculation in the step S2 is solved by a sequence quadratic programming algorithm and a maximum iteration number is set to ensure real-time performance.

6. The MPC-based UAV formation control algorithm of claim 1, wherein, The event-triggered communication mechanism is also included, and the triggering conditions include triggering communication when the state change exceeds the adaptive state threshold, the state threshold adopts an exponential decay variation law, a minimum state threshold lower limit is set to ensure basic communication requirements, and dynamic adjustment of communication priority is supported.

7. The MPC-based UAV formation control algorithm of claim 1, wherein, The event-triggered communication mechanism also includes communication guarantee and optimization functions, including an integrated neighbor state prediction and compensation module, a time-varying communication delay compensation algorithm, an abnormal state forced communication guarantee mechanism, and an adaptive data compression transmission technology.

8. The MPC-based UAV formation control algorithm of claim 1, wherein, The formation adaptive reconstruction function is also included, which includes automatically adjusting formation parameters, dynamically re-planning reference trajectories, optimizing communication network topology, and adaptively setting control parameters when the number of unmanned aerial vehicles changes. 9.A system for MPC-based UAV formation control, having a computer program stored therein, characterized in that, The steps of the unmanned aerial vehicle formation control algorithm based on MPC according to any one of claims 1-8 are implemented when the computer program in the system is executed.

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