A multi-aerial-vehicle cooperative formation control method and system

Abstract

The present application belongs to the field of aerospace technology, and discloses a kind of multi-glider aircraft cooperative formation control method and system, solve the problem of underactuated of multi-glider aircraft in high-speed reentry environment, the problem that three-dimensional configuration and collision avoidance and obstacle avoidance are not considered in existing method and longitudinal error does not converge.Firstly, the task scenario is defined, a three-degree-of-freedom mass center dynamics model is established, and three-dimensional configuration, collision avoidance and obstacle avoidance and control constraints are defined;Then, a preset time consistency control based on preset performance is designed to realize lateral and height formation;For longitudinal error, task condition correction and leader-follower cooperative control strategy are set for same / different height scenarios respectively;Improved artificial potential field method is used to set collision avoidance and obstacle avoidance strategy;Finally, a control framework is constructed to calculate the instruction.The present application realizes preset time error convergence, longitudinal configuration maintenance and collision avoidance safety, and improves the cluster capability of aircraft.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to a method and system for cooperative formation control of multiple gliders. Background Technology

[0002] Multi-glide vehicle cooperative formation can overcome the shortcomings of single-glide vehicles, such as limited mission types and susceptibility to interference, thus significantly improving their multi-mission capabilities and anti-interference capabilities. It is an essential means to achieve cooperative detection and positioning. However, during high-speed reentry, the complex and variable near-space environment and underactuated flight characteristics make it difficult for multi-glide vehicles to achieve strict cooperative formation flight. Furthermore, the introduction of complex constraints such as three-dimensional formation configuration and collision / obstacle avoidance significantly increases the difficulty of rapidly solving the cooperative formation control problem for underactuated gliders. Therefore, it is necessary to conduct research on multi-glide vehicle cooperative formation control technology that considers three-dimensional configuration maintenance and collision / obstacle avoidance to improve the anti-interference capability, penetration capability, and mission expansion capability of vehicle swarms.

[0003] Existing methods for cooperative formation control of multiple gliders mainly include those based on multi-constraint optimization, control theory, and two-stage control. Multi-constraint optimization methods typically consider process and control constraints comprehensively, using pseudospectral methods, convex optimization, and distributed model predictive control to solve for optimal formation control commands to maintain a preset formation configuration over long distances. These methods offer strong constraint satisfaction and command optimality, but their solution efficiency is low and they struggle to converge efficiently and reliably. Control theory-based methods, on the other hand, use consensus theory, sliding mode control, and event-triggered control to solve for formation control commands for each aircraft in real time. These methods offer high command calculation efficiency and can fully utilize formation member state information, exhibiting good robustness and multi-tasking adaptability. However, they often struggle to satisfy relative position constraints considering the formation's firing direction, only satisfying formation configuration constraints in the altitude and lateral directions. The two-stage control method replaces the altitude-direction position constraint with a balanced gliding constraint and divides the formation trajectory into two stages: formation formation and formation maintenance. In the formation formation stage, corresponding control commands are obtained by analyzing the relative positions and velocities of each aircraft. In the formation maintenance stage, the relative positions of the firing directions are effectively adjusted by controlling the angle of attack. This method can meet the relative position constraints of the firing directions through adaptive adjustment of the command solution mode, exhibiting high command solution efficiency. However, its cooperative strategy is complex, and the method design is challenging. Furthermore, while the above method solves the problem of cooperative formation control of multiple gliders to some extent, it still has shortcomings such as not considering the requirements for three-dimensional configuration maintenance and collision / obstacle avoidance. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method and system for cooperative formation control of multiple gliders. This invention achieves convergence of preset time errors, maintenance of longitudinal configuration, and collision avoidance safety, thereby enhancing the swarm capability of the aircraft.

[0005] A method for cooperative formation control of multiple gliders includes the following steps:

[0006] S1. Description of the cooperative formation problem:

[0007] The mission scenario, motion model and constraint model of multi-gliding aircraft cooperative formation are clearly defined. The mission scenario is set as having a small degree of initial configuration mismatch (the position error of each aircraft from the preset configuration is no more than 3km). Each gliding aircraft actively controls its flight state using aerodynamics to achieve time and position state consistency convergence and rapid formation of the preset formation configuration and long-range maintenance.

[0008] The motion model is based on the assumptions that the Earth is a sphere and does not consider the Earth's curvature and rotation, and that all aircraft models are the same. The three-degree-of-freedom center-of-mass dynamic equations of each aircraft are established.

[0009] The constraint model includes three-dimensional formation configuration constraints, collision avoidance and obstacle avoidance constraints, and control constraints. The three-dimensional formation configuration constraints transform the multi-glider formation control problem into a consistent control problem of the coordinated variables of each aircraft. The collision avoidance constraints limit the spatial distance between each aircraft to no less than the preset collision avoidance safety distance. The obstacle avoidance constraints limit the distance between the aircraft and the center of the no-fly zone (set as an infinitely high cylinder) to no less than the radius of the no-fly zone. The control constraints limit the amplitude of the angle of attack and the roll angle.

[0010] S2. Design of a pre-set time consistency cooperative formation control method based on preset performance:

[0011] First, a second-order preset time convergence controller based on preset performance is designed. Then, the backstepping method is introduced and applied to a second-order leader-follower multi-agent system. The time gain function H and the preset time performance function are selected, the error transformation function is defined, and the tracking control law is designed so that each follower can reach consensus and track the leader within a preset time while the tracking error meets the preset performance conditions.

[0012] Next, the coordinated formation command is solved. The lead missile generates formation control commands by tracking the preset altitude and velocity profiles and heading angle and velocity profiles, and adopts a fixed-time consistency control method. The follow missiles are based on the lead missile's state and the preset time consistency control method based on preset performance. Combined with the introduction of virtual control quantities into the dynamic model, a control model is constructed. The tracking control law is applied and the actual control input is obtained by using the angle of attack calculation and display expression of the previous cycle to generate formation control commands, thereby realizing coordinated formation control in altitude and lateral directions.

[0013] S3, Cooperative Formation Vertical Configuration Preservation Strategy Design:

[0014] For collaborative formation missions within the same altitude plane, a longitudinal configuration maintenance strategy based on mission condition modification is designed. The dynamic equations are analyzed to obtain the relationship between the longitudinal position and velocity of each aircraft at any time and the initial longitudinal position and velocity. A set of two nonlinear equations about the initial longitudinal position and velocity is constructed and solved using the Newton-Raphson iteration method. The initial longitudinal position and velocity of each aircraft are adjusted so that each aircraft has the same longitudinal state at any time to maintain the longitudinal configuration.

[0015] For cooperative formation missions in planes with different altitudes, a longitudinal configuration maintenance strategy based on the coordinated control of leader and follower aircraft is designed. The speed control rules of leader and follower aircraft and the activation conditions of the longitudinal configuration maintenance strategy are set (the longitudinal position error between the leader missile and a follower missile is greater than a preset threshold). Deceleration maneuver methods are designed for the leader missile (reducing the longitudinal velocity component by adding small-range lateral maneuvers) and the follower missile (establishing the relationship between longitudinal velocity error and added lateral force). The lateral maneuver modes of the leader / follower missiles are adjusted to keep the longitudinal position error between each aircraft within the allowable range.

[0016] S4. Cooperative Formation Collision and Obstacle Avoidance Strategy Design:

[0017] Based on the improved artificial potential field method, collision avoidance repulsion field, obstacle avoidance repulsion field, and virtual handover point gravitational field are designed respectively. In the collision avoidance repulsion field, the first... The aircraft to the first The repulsive force between two aircraft increases as the distance between them decreases. In the obstacle avoidance repulsive field, the repulsive force of the no-fly zone on an aircraft increases as the distance from the aircraft to the center of the no-fly zone decreases. The virtual handover point gravitational field is used to guide aircraft that have completed obstacle avoidance maneuvers to fly along the designated formation direction.

[0018] Calculate the resultant force on each aircraft to obtain the additional lateral force required to complete the collision avoidance, obstacle avoidance, and virtual handover point guidance tasks;

[0019] S5. Cooperative formation control method execution process:

[0020] Input the mission conditions for multi-aircraft cooperative formation and iteratively correct the mission conditions;

[0021] Generate virtual formation commands based on the current aircraft status to maintain altitude and lateral configuration;

[0022] Determine the type of cooperative formation mission. If it is a mission in a different altitude plane, generate additional lateral forces for maintaining longitudinal configuration. If it is a mission in a plane at the same altitude, proceed directly to the next step. Generate additional lateral forces for collision avoidance, obstacle avoidance, and directional guidance.

[0023] Calculate the lift component required by each aircraft and solve the actual formation commands;

[0024] Determine whether the handover conditions have been met. If they have, end the algorithm. If not, obtain the status of each aircraft at the next moment through trajectory integration and return to the virtual formation generation instruction step for repeated execution.

[0025] Furthermore, the expression for the three-degree-of-freedom center-of-mass dynamic equation in S1 is:

[0026]

[0027] In the formula, the subscript The aircraft is numbered, among which For the bullet number, Assign a serial number to the ammunition; For the first The position of each aircraft in the formation coordinate system For speed, and These are the track angle and the heading angle, respectively. The tilt angle, It is the acceleration due to gravity. and These are acceleration due to lift and acceleration due to drag, respectively.

[0028] Furthermore, the three-dimensional formation configuration constraints in S1 are specifically the... One aircraft satisfies:

[0029]

[0030] In the formula, , , For the first Coordination variables for each aircraft , , For the first The aircraft along , , The direction is relative to the reference point, and this distance is determined by the preset formation configuration;

[0031] The formation control objective is described as follows: .

[0032] Furthermore, the specific form of the collision avoidance constraint in S1 is as follows:

[0033]

[0034] In the formula, For the first The spatial position vector of an aircraft; Representing the With the The spatial distance between the aircraft; The safe distance for collision avoidance of each aircraft can be determined according to the formation requirements;

[0035] The specific form of obstacle avoidance constraints is as follows:

[0036] In the formula, The coordinates of the center of the no-fly zone This is the radius of the no-fly zone; this distance can be determined based on the formation mission requirements.

[0037] The specific form of control constraints is as follows:

[0038] In the formula, , , , These are the upper and lower limits of the amplitude of the angle of attack and the tilt angle, respectively.

[0039] Furthermore, the time gain function H in S2 is:

[0040]

[0041] In the formula, , , This is the gain coefficient. For time, for Reference value; To preset the stabilization time, For the shortest time of signal transmission and processing in a real physical system, the matrix ,in Laplace matrix ,at the same time

[0042]

[0043] but The first derivative with respect to time can be expressed as:

[0044]

[0045] The preset time performance function is selected as follows:

[0046]

[0047] Solving for the first derivative of the preset time performance function with respect to time yields:

[0048]

[0049] In the formula, For positive integers, , These are the initial value and convergence value of the performance function, respectively.

[0050] Further, we can obtain The first derivative with respect to time is:

[0051]

[0052] If the performance function of a multi-agent system satisfies:

[0053]

[0054] In the formula, It is a constant. , If the function is monotonically decreasing, then the multi-agent system is said to satisfy the preset performance conditions.

[0055] Define the following error transformation function to transform the error Limited to a preset range:

[0056]

[0057] Further consideration about The first derivative of is then:

[0058]

[0059] In the formula,

[0060]

[0061] .

[0062] Furthermore, the altitude, velocity profiles, heading angle, and velocity profiles tracked by the S2 missile are as follows: ,

[0063] From the process of solving the missile coordinated formation command, the control equations can be obtained by applying a second-order preset time-converged tracking control law based on preset performance.

[0064]

[0065] Thus, under the action of the control law, each aircraft achieves synchronized timing, forming... , To the formation,

[0066] To avoid due to Implicit and and The inability to display the solution in the numerical iterative method results in a long computation time, which is utilized up to the period angle of attack. calculate and through calculate The display expression, the specific process is as follows:

[0067]

[0068] Based on the inherent properties of reentry gliding, the actual control input of the aircraft can be obtained as follows:

[0069] .

[0070] Furthermore, in the longitudinal configuration preservation strategy based on task condition modification in S3, the prediction formula is:

[0071]

[0072] In the formula, and All are the initial longitudinal positions of each aircraft. ,speed The function; based on this, further consideration At any given moment, the position and velocity of each aircraft should be consistent with that of the lead missile, where the lead missile's information can be obtained by integrating the dynamic equations; thus constructing a... and A system of two nonlinear equations:

[0073]

[0074] The above equation can be solved quickly using Newton's iteration method. The iteration stops when the error between the position and velocity of the follower and the leader is less than the allowable error.

[0075] Furthermore, in the longitudinal configuration maintenance strategy based on the coordinated control of leader and follower aircraft in S3, the activation condition of the longitudinal configuration maintenance strategy is as follows: In the formula, The longitudinal position error threshold;

[0076] The additional lateral force design of the missile leader is as follows: In the formula, The direction of the lateral force applied to the missile leader can be determined by the boundary of the missile leader's lateral maneuver distance. The magnitude of the lateral force added to the missile leader is calculated using the following formula:

[0077]

[0078] In the formula, This refers to the average lateral position of the projectile;

[0079] The additional lateral force from the projectile is designed as follows:

[0080]

[0081] In the formula, Let be the longitudinal acceleration of each projectile.

[0082] Furthermore, in S4, the first The aircraft to the first The repulsive potential energy function of the aircraft is:

[0083]

[0084] In the formula, To avoid collision repulsion coefficient, For the first The aircraft and the first The distance between the aircraft To establish a preset safe distance;

[0085] The collision avoidance repulsion force is expressed as:

[0086]

[0087] No. The obstacle avoidance repulsion force of each aircraft is:

[0088]

[0089]

[0090] In the formula, From the center of the no-fly zone towards the first The direction of the aircraft From the The aircraft is pointing towards the virtual handover point;

[0091] No. The gravitational pull of the spacecraft is:

[0092]

[0093] In the formula, Here are the coordinates of the virtual handover point; therefore, the resultant force received by each aircraft is:

[0094]

[0095] The additional lateral forces required by each aircraft to complete collision avoidance, obstacle avoidance, and virtual handover point guidance tasks are as follows:

[0096]

[0097] In the formula, This represents a function that takes the z-component of the independent variable.

[0098] The present invention also provides a multi-glider cooperative formation control system, comprising:

[0099] Problem description module: used to clarify the mission scenario, motion model and constraint model of multi-gliding aircraft cooperative formation, providing basic information for subsequent control method design;

[0100] Preset time consistency control module: used to realize coordinated formation control in altitude and lateral directions, including a second-order preset time convergence controller design unit and a coordinated formation command solving unit. The controller design unit designs the tracking control law through backstepping method, time gain function, preset time performance function and error transformation function. The command solving unit generates formation control commands for lead missile and follow missile respectively.

[0101] The longitudinal configuration maintenance module includes a mission condition correction unit for cooperative formation missions in the same altitude plane and a leader-follower coordination control unit for cooperative formation missions in different altitude planes. The longitudinal configuration is maintained by adjusting the initial longitudinal state and the lateral maneuver mode, respectively.

[0102] Collision and obstacle avoidance module: Based on the improved artificial potential field method, a collision avoidance repulsion field, an obstacle avoidance repulsion field, and a virtual handover point gravitational field are designed, and additional lateral forces are calculated to realize the collision and obstacle avoidance function;

[0103] Control Flow Execution Module: Used to execute the overall process of collaborative formation control, including task condition input and correction, virtual formation command generation, additional lateral force generation, required lift component calculation, actual formation command solution and trajectory integral update of aircraft status until the handover conditions are met.

[0104] The beneficial effects of this invention are as follows:

[0105] (1) Compared with existing formation control methods, the proposed preset time consistency formation control method based on preset performance can complete the convergence of the formation position error of each aircraft in the lateral and altitude directions within a preset time, and ensure that the error convergence curve is included in the preset performance envelope.

[0106] (2) Compared with existing formation control methods, the proposed cooperative formation control framework can effectively solve the problem of non-convergence of longitudinal error in cooperative formation of gliders without significantly disrupting the formation configuration, and achieve long-range maintenance of longitudinal configuration.

[0107] (3) Compared with existing formation control methods, the proposed cooperative formation control framework can effectively consider collision avoidance and obstacle avoidance constraints, so as to control the distance between each aircraft and the distance between the aircraft and the no-fly zone within a safe range during the formation and maintenance of the formation configuration, which greatly improves the safety and multi-mission execution capability of the proposed method. Attached Figure Description

[0108] Figure 1 A flowchart for generating collaborative formation instructions according to the present invention;

[0109] Figure 2 This is a simulation result of the three-dimensional trajectory curve of the present invention;

[0110] Figure 3 This is a simulation result diagram of the longitudinal configuration error curve of the present invention;

[0111] Figure 4 This is a simulation result diagram of the height orientation configuration error curve of the present invention;

[0112] Figure 5 This is a simulation result of the lateral configuration error curve of the present invention. Detailed Implementation

[0113] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0114] This invention studies a cooperative formation control method for multiple gliders considering three-dimensional configuration maintenance and collision / obstacle avoidance. First, the cooperative formation problem is described, introducing the mission scenario, motion model, and control objective, and analyzing the flight characteristics of glider cooperative formation. Second, a pre-set time consistency cooperative formation control method based on preset performance is proposed to achieve formation and maintenance of formation configuration in the lateral and altitude directions. Then, addressing the longitudinal error non-convergence problem caused by the underactuated characteristics of gliders, a longitudinal configuration maintenance strategy for cooperative formation is proposed to achieve long-range maintenance of the longitudinal formation configuration without significantly disrupting the formation configuration. Furthermore, for cooperative formation considering collision / obstacle avoidance constraints, a cooperative formation collision / obstacle avoidance strategy based on an improved artificial potential field method is proposed to control the distances between aircraft and between aircraft and no-fly zones within safe ranges during formation and maintenance. Based on this, a cooperative formation control framework considering three-dimensional configuration maintenance and collision / obstacle avoidance is designed to solve cooperative formation control commands. The specific technical solution is as follows:

[0115] Reference Figure 1 A method for cooperative formation control of multiple gliders includes the following steps:

[0116] Step 1: Collaborative Formation Problem Description

[0117] 1.1 Task Scenario

[0118] This invention describes a multi-glider cooperative formation mission scenario to provide background support for subsequent method design. The cooperative formation mission scenario is described as follows: Under conditions of minimal initial configuration mismatch (each glider's positional error from the preset configuration is no greater than 3 km), each glider actively controls its flight state using aerodynamics, thereby achieving consistent convergence of the time and positional states of multiple gliders. Then, under the constraints of three-dimensional configuration and collision / obstacle avoidance, the preset formation configuration is rapidly formed and maintained for a long range until the handover conditions are met.

[0119] 1.2 Motion Model

[0120] Assuming the Earth is a sphere, neglecting the effects of Earth's curvature and rotation, and assuming all spacecraft are of the same model, the three-degree-of-freedom center-of-mass dynamic equations for each spacecraft are described as follows:

[0121] (1)

[0122] In the formula, the subscript The aircraft is numbered, among which For the bullet number, Assign a serial number to the ammunition; For the first The position of each aircraft in the formation coordinate system For speed, and These are the track angle and the heading angle, respectively. The tilt angle, It is the acceleration due to gravity. and These are acceleration due to lift and acceleration due to drag, respectively.

[0123] 1.3 Constraint Model

[0124] (1) Three-dimensional formation configuration constraints

[0125] During multi-aircraft coordinated formation, it should be ensured that each aircraft conforms to the preset three-dimensional formation configuration constraints. (Setting the...) Each aircraft should meet the following constraints:

[0126] (2)

[0127] In the formula, , , For the first Coordination variables for each aircraft , , For the first The aircraft along , , The direction is relative to the position of the reference point, and this distance is determined by the preset formation configuration.

[0128] Based on this, the multi-glide vehicle formation control problem can be transformed into a consistent control problem of the coordination variables of each vehicle, and the formation control objective can then be described as:

[0129] (3)

[0130] (2) Collision and obstacle avoidance constraints

[0131] To ensure the safety and reliability of coordinated formation flight, in addition to three-dimensional formation configuration constraints, collision avoidance and obstacle avoidance constraints for each aircraft should also be considered. The specific form of collision avoidance constraints is as follows:

[0132] (4)

[0133] In the formula, For the first The spatial position vector of an aircraft; Representing the With the The spatial distance between the aircraft; The safe distance for collision avoidance for each aircraft can be determined according to the formation requirements.

[0134] If the no-fly zone model is set as an infinitely tall cylinder, then the specific form of the obstacle avoidance constraint is as follows:

[0135] (5)

[0136] In the formula, The coordinates of the center of the no-fly zone; This is the radius of the no-fly zone, and this distance can be given according to the formation mission requirements.

[0137] (3) Control constraints

[0138] Control constraints only limit the angle of attack based on the aircraft's actuators. with tilt angle Amplitude, i.e.:

[0139] (6)

[0140] In the formula, , , , These are the upper and lower limits of the amplitude of the angle of attack and the tilt angle, respectively.

[0141] Step 2: Design a preset time consistency cooperative formation control method based on preset performance.

[0142] To achieve coordinated formation control of multiple gliders in both altitude and lateral directions, this invention designs a pre-set time-consistent coordinated formation control method based on preset performance. Specifically, a second-order pre-set time convergence controller based on preset performance is designed. Then, this controller is applied to multi-vehicle coordinated formation tasks to achieve efficient computation of coordinated formation commands for each vehicle.

[0143] 2.1 Design of a Second-Order Preset Time-Convergence Controller Based on Preset Performance

[0144] This invention applies a preset time control algorithm based on preset performance to a second-order leader-follower multi-agent system by introducing a backstepping method. A time gain function is selected. Specifically as follows:

[0145] (7)

[0146] In the formula, , , This is the gain coefficient. For time, for Reference value; To preset the stabilization time, For the shortest time of signal transmission and processing in a real physical system, the matrix ,in Laplace matrix ,at the same time

[0147] (8)

[0148] but The first derivative with respect to time can be expressed as:

[0149] (9)

[0150] Based on the above, the specific preset time performance function is selected as follows:

[0151] (10)

[0152] Solving equation (10) with respect to time, we can obtain...

[0153] (11)

[0154] In the formula, For positive integers, , These are the initial value and convergence value of the performance function, respectively. Further, we can obtain... The first derivative with respect to time is

[0155] (12)

[0156] If the performance function of a multi-agent system satisfies:

[0157] (13)

[0158] In the formula, It is a constant. , If the function is monotonically decreasing, then the multi-agent system is said to satisfy the preset performance conditions.

[0159] Define the following error transformation function to transform the error Limited to a preset range:

[0160] (14)

[0161] Further consideration about The first derivative of is then:

[0162] (15)

[0163] In the formula,

[0164] (16)

[0165] (17)

[0166] Theorem 1: Consider a second-order multi-agent system, and design the tracking control law as follows:

[0167] (18)

[0168] In the formula, , , .at the same time,

[0169] (19)

[0170] In the formula, , and The definitions are shown in equations (14) and (7) respectively. Then, consensus can be reached among the followers, and each follower can achieve consensus within a preset time. Internally, it enables the tracking of leaders, while the tracking error is within... Equation (13) is always satisfied.

[0171] 2.2 Solving Cooperative Formation Instructions

[0172] This invention sets up a leader missile to generate formation control commands by tracking preset altitude-velocity and heading angle-velocity profiles. Follower missiles generate formation control commands based on the leader missile's state and a preset time consistency control method based on preset performance. It is worth noting that while the leader missile's reentry command can be solved using methods such as reference trajectory tracking and prediction correction, this invention, without loss of generality, selects the method of generating the leader missile's formation control commands by tracking preset altitude-velocity and heading angle-velocity profiles.

[0173] (1) Solving for the missile lead coordination formation command:

[0174] Set the tracking altitude-velocity profile and heading angle-velocity profile for the missile leader:

[0175] (20)

[0176] (twenty one)

[0177] The leader missile tracks the preset altitude-velocity profile and heading angle-velocity profile using a fixed-time consistency control method, thereby generating formation control commands.

[0178] (2) Solving from missile coordination formation commands

[0179] First, based on , The guidance commands for each aircraft during coordinated formation are solved using a dynamic model, while virtual control variables in two directions are introduced. A control model is constructed by combining the dynamic model with the control model. Based on this, a second-order preset time-converged tracking control law based on preset performance is applied to obtain the control equations.

[0180] (twenty two)

[0181] Thus, under the action of the control law, each aircraft achieves synchronized timing, forming... , Towards the formation.

[0182] To avoid due to Implicit and and The inability to display the solution in the numerical iterative method results in a long computation time, which is utilized up to the period angle of attack. calculate and through calculate The display expression, the specific process is as follows:

[0183] (twenty three)

[0184] Based on the inherent properties of reentry gliding, the actual control input of the aircraft can be obtained as follows:

[0185] (twenty four)

[0186] Step 3: Design a cooperative formation longitudinal configuration preservation strategy

[0187] Under the formation control method in step 2, each aircraft can achieve preset performance convergence in altitude and lateral position within a preset time. Based on this, to further achieve longitudinal formation configuration control of multiple gliders, this invention designs a cooperative formation longitudinal configuration maintenance strategy. Specifically: First, this invention, combining the preset time characteristics of the control algorithm, designs a longitudinal configuration maintenance strategy based on task condition correction to reduce longitudinal position and velocity errors of the formation from the task setting level; second, for cooperative formation mission scenarios in different altitude planes, a longitudinal configuration maintenance strategy based on the cooperative control of leader and follower aircraft is designed to reduce longitudinal position and velocity errors of the formation from the control algorithm level.

[0188] 3.1 Vertical Configuration Preservation Strategy Based on Task Condition Modification

[0189] According to the dynamic equations, if we expect all aircraft to have the same longitudinal position during formation, the necessary condition is that, under the action of the formation control method, each aircraft... At any given moment within the time interval, they possess the same longitudinal position and velocity. For gliders performing coordinated formation missions within the same altitude plane, if each glider... If each aircraft has the same longitudinal position and velocity at any given time, then under the action of equation (22), each aircraft will... The force patterns within the time interval are basically consistent, meaning that they can... The longitudinal formation configuration is maintained during the time interval. To this end, based on the preset time characteristics of the formation control method (22), this invention designs a longitudinal configuration maintenance strategy specifically for collaborative formation tasks within the same height plane, as follows:

[0190] First, by analyzing the dynamic equations, under the action of the control law, the initial local tilt angle and heading angle of each aircraft are consistent. Therefore, each aircraft... Vertical position at any moment ,speed Only relative to the initial longitudinal position of each aircraft ,speed Correlation leads to the following prediction formula:

[0191] (25)

[0192] In the formula, and All are the initial longitudinal positions of each aircraft. ,speed The function. Based on this, further consideration... At any given moment, the position and velocity of each aircraft should be consistent with the lead missile, where the lead missile's information can be obtained by integrating the dynamic equations. This allows us to construct a... and A system of two nonlinear equations:

[0193] (26)

[0194] The above equation can be solved quickly using Newton's iteration method. The iteration stops when the error between the position and velocity of the follower and the leader is less than the allowable error.

[0195] At this point, the design of the longitudinal configuration retention strategy based on mission condition adjustments has been completed. This strategy adjusts the initial longitudinal position and velocity of each aircraft to ensure that each aircraft maintains its longitudinal configuration within the mission conditions. They always have the same longitudinal state, thus ensuring that the longitudinal configuration of cooperative formation tasks in the same height plane is maintained.

[0196] 3.2 Longitudinal Configuration Maintenance Strategy Based on Coordinated Control of Leader and Slave Aircraft

[0197] As can be seen from the analysis in Section 3.1, the longitudinal configuration preservation strategy based on mission condition modification is limited by its principle and can only be used for cooperative formation missions within the same altitude plane. It cannot effectively solve the problem of longitudinal configuration preservation for cooperative formations within different altitude planes.

[0198] For cooperative formation missions in different altitude planes, the following speed control rules for the lead and follower aircraft can be designed: if the lead aircraft is ahead in both position and speed, it decelerates; if the lead aircraft is ahead in both position and speed, it predicts a given time using numerical integration. If the average longitudinal position of the inner missile can catch up with that of the lead missile, the lead missile should decelerate if it cannot; otherwise, no adjustments should be made to the aircraft. If the lead missile lags behind in position but leads in speed, a given time should be predicted through numerical integration. If the leading missile can catch up with the average longitudinal position of the trailing missiles, the trailing missiles will decelerate; otherwise, no adjustments will be made to the aircraft. If the leading missile lags behind in both position and speed, the trailing missiles will decelerate. Furthermore, the activation condition for the longitudinal configuration maintenance strategy is that the longitudinal position error between the leading missile and a certain trailing missile exceeds a preset value.

[0199] (27)

[0200] In the formula, This is the threshold for longitudinal position error.

[0201] Secondly, deceleration maneuver methods are designed for both the lead missile deceleration and follow missile deceleration scenarios, as detailed below.

[0202] (1) Method of decelerating maneuvering with lead ammunition

[0203] The longitudinal velocity component of the missile is reduced by inducing additional lateral maneuvers within a small range, thus achieving longitudinal deceleration. The additional lateral force of the missile is designed to be...

[0204] (28)

[0205] In the formula, The direction of the lateral force applied to the missile leader can be determined by the boundary of the missile leader's lateral maneuver distance. The magnitude of the lateral force added to the missile can be calculated using the following formula.

[0206] (29)

[0207] In the formula, This represents the average lateral position of the projectile.

[0208] (2) Method of deceleration maneuvering from the projectile

[0209] The deceleration maneuver of the follower projectile is achieved by constructing a longitudinal velocity error and an additional lateral force from the follower projectile. The additional lateral force from the follower projectile is designed as follows:

[0210] (30)

[0211] In the formula, Let be the longitudinal acceleration of each projectile.

[0212] At this point, the design of a longitudinal configuration maintenance strategy based on the coordinated control of lead and follower aircraft has been completed. This strategy adjusts the lateral maneuvering modes of the lead / follower missiles to keep the longitudinal positional errors between the aircraft within an acceptable range, thereby ensuring the longitudinal configuration maintenance effect of coordinated formation missions in different altitude planes.

[0213] Step 4: Design a cooperative formation collision and obstacle avoidance strategy

[0214] In addition to three-dimensional formation configuration constraints, the multi-aircraft cooperative formation problem should further consider collision and obstacle avoidance constraints to ensure the safety and rationality of the formation mission. To this end, this invention designs a collision and obstacle avoidance strategy based on an improved artificial potential field method to ensure that the distances between aircraft and between aircraft and no-fly zones are within safe ranges.

[0215] During formation flying, to simultaneously avoid collisions and inadvertent entry into no-fly zones, this invention designs collision avoidance repulsion fields and obstacle avoidance repulsion fields to achieve collision avoidance and obstacle avoidance functions during coordinated formation flying. After completing obstacle avoidance maneuvers, to ensure that each aircraft flies along the designated formation direction, this invention further designs a gravitational field at a virtual handover point. The specific forms of the above three artificial potential fields are as follows.

[0216] (1) Collision avoidance and repulsion field design

[0217] During the formation and maintenance of the formation configuration, in order to avoid collisions between the aircraft, the aircraft should exert a certain repulsive force on the surrounding aircraft. Meanwhile, this repulsive force increases as the distance between the aircraft decreases. The aircraft to the first The repulsive potential energy function of the aircraft is:

[0218] (31)

[0219] In the formula, To avoid collision repulsion coefficient, For the first The aircraft and the first The distance between the aircraft To establish a preset safe distance, the collision avoidance repulsion force can be expressed as:

[0220] (32)

[0221] (2) Obstacle avoidance repulsion field design

[0222] During coordinated formation, to prevent aircraft from accidentally entering the no-fly zone's influence area, the no-fly zone should exert a certain repulsive force on surrounding aircraft. Simultaneously, this repulsive force increases as the distance from the aircraft to the center of the no-fly zone decreases. Similarly, the... The obstacle avoidance repulsion force of each aircraft is:

[0223] (33)

[0224] (34)

[0225] In the formula, From the center of the no-fly zone towards the first The direction of the aircraft From the The aircraft is pointing towards the virtual handover point.

[0226] (3) Design of the gravitational field at the virtual handover point

[0227] After each aircraft completes its obstacle avoidance maneuver, a virtual handover point is established to guide the aircraft into formation flight, thus giving their flight direction a certain practical physical meaning. The gravitational pull of the spacecraft is:

[0228] (35)

[0229] In the formula, Here are the coordinates of the virtual handover point. Therefore, the resultant force received by each aircraft is:

[0230] (36)

[0231] The additional lateral forces required by each aircraft to complete collision avoidance, obstacle avoidance, and virtual handover point guidance tasks are as follows:

[0232] (37)

[0233] In the formula, This represents a function that takes the z-component of the independent variable.

[0234] Step 5: Design the methodology and workflow framework

[0235] The overall collaborative formation control method, which integrates formation control, longitudinal configuration maintenance, and collision and obstacle avoidance strategies, follows the following framework:

[0236] Step 1: Input the mission conditions for multi-aircraft cooperative formation;

[0237] Step 2: Iteratively modify the cooperative formation task conditions using equation (26);

[0238] Step 3: Based on the current aircraft status, generate virtual formation commands for forming / maintaining altitude and lateral configurations using equations (20), (21), and (23). , ;

[0239] Step 4: If it is a cooperative formation mission in a plane with different altitudes, then generate additional lateral forces for longitudinal configuration maintenance using equations (28) and (30). If it is a collaborative formation mission within the same altitude plane, proceed to step 5;

[0240] Step 5: Generate additional lateral forces for collision avoidance, obstacle avoidance, and directional guidance using equation (37). ;

[0241] Step 6: Calculate the lift components required for each aircraft , ;

[0242] Step 7: Calculate the actual formation commands for each aircraft. and

[0243]

[0244] Step 8: If the handover condition is met, end the algorithm; otherwise, proceed to step 9.

[0245] Step 9: Perform trajectory integration using equation (1) to obtain the state of each aircraft at the next moment, and then proceed to step 3.

[0246] Simulation condition settings

[0247] Using CAV-H as the simulation verification object, its quality is The reference area is Considering the limitations of the aircraft's actuators, the control constraints are set as follows: , , , Set the number of aircraft. Each slave missile can receive status information from the leader missile and the other slave missiles, while the leader missile does not receive status information from any aircraft. Furthermore, in altitude and lateral formation control, the formation controller gain coefficient is set to [value missing]. The terminal performance values ​​in the height direction and lateral position are In the longitudinal configuration maintenance strategy, the upper limits for the longitudinal position and velocity errors of the aircraft are set as follows: , The longitudinal error threshold is Set a safe collision avoidance distance in the collision avoidance strategy. The obstacle avoidance safety distance, i.e., the radius of the no-fly zone, is The collision avoidance repulsion coefficient is The obstacle avoidance repulsion coefficient is The gravitational coefficient of the virtual handover point is .

[0248] Simulation results

[0249] To verify the cooperative formation framework proposed in this invention, a cooperative formation scenario in the same altitude plane is considered, where the formation configuration shrinks from a wide formation configuration to a narrow formation configuration. The initial positions of the mission vehicles and the preset formation configurations are shown in Tables 1 and 2, respectively.

[0250] Table 1 Initial position of the aircraft

[0251]

[0252] Table 2 Preset Formation Configurations

[0253]

[0254] Figure 2-5Simulation results curves are presented. The proposed cooperative formation framework enables each aircraft to contract to form a preset formation configuration at a preset convergence time and maintain this three-dimensional configuration until the handover conditions are met. Simultaneously, during cooperative formation, the altitude and lateral configuration error curves of each aircraft remain within a preset performance envelope; the longitudinal configuration error is consistently maintained within 5m through the proposed mission-condition-based longitudinal configuration maintenance strategy.

[0255] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for cooperative formation control of multiple gliders, characterized in that, Includes the following steps: S1. Description of the cooperative formation problem: The mission scenario, motion model and constraint model of multi-gliding aircraft cooperative formation are clearly defined. The mission scenario is set as having a small degree of initial configuration mismatch, and each gliding aircraft actively controls its flight state using aerodynamics to achieve time and position state consistency convergence and rapid formation of the preset formation configuration and long-range maintenance. The motion model is based on the assumptions that the Earth is a sphere and does not consider the Earth's curvature and rotation, and that all aircraft models are the same. The three-degree-of-freedom center-of-mass dynamic equations of each aircraft are established. The constraint model includes three-dimensional formation configuration constraints, collision avoidance and obstacle avoidance constraints, and control constraints. The three-dimensional formation configuration constraints transform the multi-glider formation control problem into a consistent control problem of the coordinated variables of each aircraft. The collision avoidance constraints limit the spatial distance between each aircraft to no less than the preset collision avoidance safety distance. The obstacle avoidance constraints limit the distance between the aircraft and the center of the no-fly zone to no less than the radius of the no-fly zone. The control constraints limit the amplitude of the angle of attack and the roll angle. S2. Design of a pre-set time consistency cooperative formation control method based on preset performance: First, a second-order preset time convergence controller based on preset performance is designed. Then, the backstepping method is introduced and applied to a second-order leader-follower multi-agent system. The time gain function H and the preset time performance function are selected, the error transformation function is defined, and the tracking control law is designed so that each follower can reach consensus and track the leader within a preset time while the tracking error meets the preset performance conditions. Next, the coordinated formation command is solved. The lead missile generates formation control commands by tracking the preset altitude and velocity profiles and heading angle and velocity profiles, and adopts a fixed-time consistency control method. The follow missiles are based on the lead missile's state and the preset time consistency control method based on preset performance. Combined with the introduction of virtual control quantities into the dynamic model, a control model is constructed. The tracking control law is applied and the actual control input is obtained by using the angle of attack calculation and display expression of the previous cycle to generate formation control commands, thereby realizing coordinated formation control in altitude and lateral directions. S3, Cooperative Formation Vertical Configuration Preservation Strategy Design: For collaborative formation missions within the same altitude plane, a longitudinal configuration maintenance strategy based on mission condition modification is designed. The dynamic equations are analyzed to obtain the relationship between the longitudinal position and velocity of each aircraft at any time and the initial longitudinal position and velocity. A set of two nonlinear equations about the initial longitudinal position and velocity is constructed and solved using the Newton-Raphson iteration method. The initial longitudinal position and velocity of each aircraft are adjusted so that each aircraft has the same longitudinal state at any time to maintain the longitudinal configuration. For cooperative formation mission scenarios in different altitude planes, a longitudinal configuration maintenance strategy based on the coordinated control of leader and follower aircraft is designed. The speed control rules of leader and follower aircraft and the activation conditions of the longitudinal configuration maintenance strategy are set. The deceleration maneuver methods of leader and follower missiles are designed respectively, and the lateral maneuver modes of leader and follower missiles are adjusted to keep the longitudinal position error between each aircraft within the allowable range. S4. Cooperative Formation Collision and Obstacle Avoidance Strategy Design: Based on the improved artificial potential field method, collision avoidance repulsion field, obstacle avoidance repulsion field, and virtual handover point gravitational field are designed respectively. In the collision avoidance repulsion field, the first... The aircraft to the first The repulsive force between two aircraft increases as the distance between them decreases. In the obstacle avoidance repulsive field, the repulsive force of the no-fly zone on an aircraft increases as the distance from the aircraft to the center of the no-fly zone decreases. The virtual handover point gravitational field is used to guide aircraft that have completed obstacle avoidance maneuvers to fly along the designated formation direction. Calculate the resultant force on each aircraft to obtain the additional lateral force required to complete the collision avoidance, obstacle avoidance, and virtual handover point guidance tasks; S5. Cooperative formation control method execution process: Input the mission conditions for multi-aircraft cooperative formation and iteratively correct the mission conditions; Generate virtual formation commands based on the current aircraft status to maintain altitude and lateral configuration; Determine the type of the cooperative formation mission. If it is a mission in a different altitude plane, generate additional lateral forces to maintain the longitudinal configuration. If it is a mission in the same altitude plane, proceed directly to the next step. Generate additional lateral forces for collision avoidance, obstacle avoidance, and directional guidance; Calculate the lift component required by each aircraft and solve the actual formation commands; Determine whether the handover conditions have been met. If they have, end the algorithm. If not, obtain the status of each aircraft at the next moment through trajectory integration and return to the virtual formation generation instruction step for repeated execution.

2. The method for cooperative formation control of multiple gliders according to claim 1, characterized in that, The equation of motion for the three-degree-of-freedom center of mass in S1 is expressed as follows: ， In the formula, the subscript The aircraft is numbered, among which For the bullet number, Assign a serial number to the ammunition; For the first The position of each aircraft in the formation coordinate system For speed, and These are the track angle and the heading angle, respectively. The tilt angle, It is the acceleration due to gravity. and These are acceleration due to lift and acceleration due to drag, respectively.

3. The method for cooperative formation control of multiple gliders according to claim 1, characterized in that, The specific three-dimensional formation configuration constraints in S1 are as follows: One aircraft satisfies: ， In the formula, , , For the first Coordination variables for each aircraft , , For the first The aircraft along , , The direction is relative to the reference point, and this distance is determined by the preset formation configuration; The formation control objective is described as follows: .

4. The method for cooperative formation control of multiple gliders according to claim 1, characterized in that, The specific form of the collision avoidance constraint in S1 is as follows: ， In the formula, For the first The spatial position vector of an aircraft; Representing the With the The spatial distance between the aircraft; The safe distance for collision avoidance of each aircraft is given according to the formation requirements; The specific form of obstacle avoidance constraints is as follows: , In the formula, The coordinates of the center of the no-fly zone This is the radius of the no-fly zone, and this distance is given according to the formation mission requirements. The specific form of control constraints is: , In the formula, , , , These are the upper and lower limits of the amplitude of the angle of attack and the tilt angle, respectively.

5. The method for cooperative formation control of multiple gliders according to claim 1, characterized in that, The time gain function H in S2 is: ， In the formula, , , This is the gain coefficient. For time, for Reference value; To preset the stabilization time, For the shortest time of signal transmission and processing in a real physical system, the matrix ,in Laplace matrix ,at the same time ， but The first derivative with respect to time is expressed as: ， The preset time performance function is selected as follows: ， Solving for the first derivative of the preset time performance function with respect to time yields: ， In the formula, For positive integers, , These are the initial value and convergence value of the performance function, respectively. Further, we can obtain The first derivative with respect to time is: ， If the performance function of a multi-agent system satisfies: ， In the formula, It is a constant. , If the function is monotonically decreasing, then the multi-agent system is said to satisfy the preset performance conditions. Define the following error transformation function to transform the error Limited to a preset range: ， Further consideration about The first derivative of is then: ， In the formula, ， 。 6. The multi-gliding vehicle cooperative formation control method according to claim 1, characterized in that, The altitude, velocity profile, heading angle, and velocity profile tracked by the missile leader in S2 are as follows: , , From the process of solving the missile coordinated formation command, a second-order preset time-converged tracking control law based on preset performance is applied to obtain the control equation. ， Thus, under the action of the control law, each aircraft achieves synchronized timing, forming... , To the formation, To avoid due to Implicit and and The inability to display the solution in the numerical iterative method results in a long computation time, which is utilized up to the period angle of attack. calculate and through calculate The display expression, the specific process is as follows: ， Based on the inherent properties of reentry gliding, the actual control input of the aircraft can be obtained as follows: 。 7. The method for cooperative formation control of multiple gliders according to claim 1, characterized in that, In the longitudinal configuration preservation strategy based on task condition modification in S3, the prediction formula is: ， In the formula, and All are the initial longitudinal positions of each aircraft. ,speed The function; based on this, further consideration At any given moment, the position and velocity of each aircraft should be consistent with that of the lead missile, where the lead missile's information is obtained by integrating the dynamic equations; thus, a system is constructed regarding... and A system of two nonlinear equations: ， The above formula is solved quickly using Newton's iteration method. The iteration stops when the error between the position and velocity of the follower and the leader is less than the allowable error.

8. The method for cooperative formation control of multiple gliders according to claim 1, characterized in that, In the longitudinal configuration maintenance strategy based on the coordinated control of leader and follower aircraft in S3, the activation condition of the longitudinal configuration maintenance strategy is as follows: In the formula, The longitudinal position error threshold; The additional lateral force design of the missile leader is as follows: In the formula, The direction of the lateral force applied to the missile leader is determined by the boundary of the missile leader's lateral maneuver distance. The magnitude of the lateral force added to the missile leader is calculated using the following formula: ， In the formula, This refers to the average lateral position of the projectile; The additional lateral force from the projectile is designed as follows: ， In the formula, Let be the longitudinal acceleration of each projectile.

9. The method for cooperative formation control of multiple gliders according to claim 1, characterized in that, S4 The aircraft to the first The repulsive potential energy function of the aircraft is: ， In the formula, To avoid collision repulsion coefficient, For the first The aircraft and the first The distance between the aircraft To establish a preset safe distance; The collision avoidance repulsion force is expressed as: ， No. The obstacle avoidance repulsion force of each aircraft is: ， ， In the formula, From the center of the no-fly zone towards the first The direction of the aircraft From the The aircraft is pointing towards the virtual handover point; No. The gravitational pull of the spacecraft is: ， In the formula, Here are the coordinates of the virtual handover point; therefore, the resultant force received by each aircraft is: ， The additional lateral forces required by each aircraft to complete collision avoidance, obstacle avoidance, and virtual handover point guidance tasks are as follows: ， In the formula, This represents a function that takes the z-component of the independent variable.

10. A multi-gliding vehicle cooperative formation control system based on the control method of claim 1, characterized in that, include: Problem description module: used to clarify the mission scenario, motion model and constraint model of multi-gliding aircraft cooperative formation, providing basic information for subsequent control method design; Preset time consistency control module: used to realize coordinated formation control in altitude and lateral directions, including a second-order preset time convergence controller design unit and a coordinated formation command solving unit. The controller design unit designs the tracking control law through backstepping method, time gain function, preset time performance function and error transformation function. The command solving unit generates formation control commands for lead missile and follow missile respectively. The longitudinal configuration maintenance module includes a mission condition correction unit for cooperative formation missions in the same altitude plane and a leader-follower coordination control unit for cooperative formation missions in different altitude planes. The longitudinal configuration is maintained by adjusting the initial longitudinal state and the lateral maneuver mode, respectively. Collision and obstacle avoidance module: Based on the improved artificial potential field method, a collision avoidance repulsion field, an obstacle avoidance repulsion field, and a virtual handover point gravitational field are designed, and additional lateral forces are calculated to realize the collision and obstacle avoidance function; Control Flow Execution Module: Used to execute the overall process of collaborative formation control, including task condition input and correction, virtual formation command generation, additional lateral force generation, required lift component calculation, actual formation command solution and trajectory integral update of aircraft status until the handover conditions are met.

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