A return capsule recovery control method based on multi-unmanned aerial vehicle flexible net capture

Abstract

The application discloses a kind of based on the return cabin recovery control method of multi-unmanned aerial vehicle flexible net capture, it is related to aircraft cooperative control and aerospace return cabin recovery technical field.Guarantee the accurate interception and smooth buffer of return cabin.Recovery system includes perception and prediction module, impact strategy management unit, control and calculation module and unmanned aerial vehicle formation, the model predictive controller is contained in the control and calculation module;The model predictive controller uses model predictive control algorithm, receives expected trajectory and difference module stiffness instruction simultaneously, and under the condition of comprehensively considering the physical hard constraint of anti-breaking net and dynamic obstacle avoidance, the required thrust of unmanned aerial vehicle is calculated.The existing air recovery system based on multi-unmanned aerial vehicle is solved when coping with dynamic target and instantaneous impact, the coupling relationship exists between system overall tracking trajectory and flexible net variable stiffness adjustment, and the problem that multiple physical constraints are difficult to handle.

Description

Technical Field

[0001] This invention relates to the field of aircraft cooperative control and space return capsule recovery technology, specifically to a return capsule recovery control method based on multi-UAV flexible net capture. Background Technology

[0002] With the rapid development of aerospace technology, the application of recoverable spacecraft such as miniature return capsules and probe payloads is becoming increasingly widespread. Traditional return capsule landing methods mostly rely on parachutes for deceleration and eventual recovery via ground or sea surface. However, ground recovery carries the risk of hard impact damage in complex terrain, and recovery sites are scattered and difficult to locate quickly; sea recovery increases the risk of water ingress or damage to equipment. Therefore, using multiple UAVs to collaboratively deploy a flexible net in the air for active interception and capture has become a promising non-destructive recovery method in recent years.

[0003] Regarding the aforementioned multi-UAV aerial collaborative recovery system, existing patents have proposed a "common-mode-differential-mode" control architecture. This architecture adjusts the stiffness of the flexible net by changing the relative distance between the UAVs, aiming to absorb the impact energy at the moment of contact. However, further research has revealed that the overall translational tracking of the UAV formation and the contraction of relative distance are not completely independent at the physical level, but rather exhibit strong nonlinear coupling. When the system drastically changes the relative distance to adjust the stiffness of the flexible net, the instantaneous change in the tension of the flexible net can react on the UAV body, easily causing the overall trajectory of the formation to deviate from the predetermined interception point, or even causing system instability.

[0004] Furthermore, when the reentry capsule descends with its parachute, the parachute itself constitutes a dynamic obstacle that drifts with the wind. Conventional control methods struggle to simultaneously address multiple physical constraints within a limited thrust range, including avoiding the dynamic parachute, tracking the reentry capsule's trajectory, and limiting the extreme tension of the flexible net.

[0005] Therefore, there is an urgent need for a collaborative control method that can coordinate the overall movement and formation changes of UAV formations in order to achieve precise tracking and smooth transition during the aerial capture of the return capsule. Summary of the Invention

[0006] To address the above problems, this invention proposes a return capsule recovery control method based on multi-UAV flexible net capture. By introducing a nonlinear spring-damped equivalent model and combining it with the rolling optimization capability of model predictive control, this method enables effective control of the overall movement tracking and formation changes of the UAV formation under complex constraints, thereby ensuring accurate interception and smooth buffering of the return capsule.

[0007] The technical solution of the present invention is as follows: a flight formation of four drones pulls a flexible net to dynamically intercept and capture a return capsule with a parachute falling at high altitude, and the drones suspend the flexible net through a main load-bearing cable;

[0008] The return capsule recovery control method is implemented by a recovery system, which includes a perception and prediction module, an impact strategy management unit, a control and calculation module, and a UAV formation. The perception and prediction module acquires real-time three-dimensional spatial state data of the return capsule and its parachute and predicts its descent trajectory. The impact strategy management unit is an upper-level strategy scheduling submodule located within or connected to the control and calculation module. It determines the capture phase of the system based on the predicted contact time, predicted landing point of the return capsule, current network area, current differential distance, safe distance between UAVs, and estimated tension of the main support cable, and generates corresponding differential distance reference commands. The control and calculation module includes a model predictive controller. The model predictive controller uses a model predictive control algorithm, simultaneously receiving the desired trajectory and the differential distance reference commands from the impact strategy management unit, and calculates the required thrust for the UAVs under the condition of comprehensively considering the physical constraints of network disconnection prevention and dynamic obstacle avoidance. During command execution, the UAV formation feeds back the current system state to the model predictive controller in real time, forming a closed-loop rolling optimization control. The current system state includes the common-mode position representing the overall translation of the system. Differential distance representing the degree of formation contraction and the depth of descent during the impact of the reentry capsule. This includes the following steps:

[0009] S1. Obtain the three-dimensional spatial state data of the return capsule and its parachute, predict the expected trajectory of the return capsule's descent, and model the area where the parachute is located as a dynamic no-fly zone that updates dynamically over time.

[0010] In step S1, the area where the parachute is located is modeled as a no-fly zone that is dynamically updated over time. Specifically, this includes: equating the physical envelope of the parachute to a dynamic no-fly cylinder in three-dimensional space; the central axis of the dynamic no-fly cylinder coincides with the parachute's descent trajectory, and its radius is greater than the maximum physical radius of the parachute canopy; using the dynamic no-fly cylinder, the three-dimensional obstacle avoidance constraint is reduced to a distance inequality constraint on a two-dimensional horizontal plane to avoid the risk of parachute rope entanglement.

[0011] S2. Construct a state-space prediction model that includes drone formations and return capsules;

[0012] In step S2, the physical system consisting of the flexible net and cables is equivalent to a virtual spring-damped model connecting each UAV and the return capsule.

[0013] S3. Design the cost function in the prediction time domain of the model predictive controller;

[0014] In step S3, the cost function is a weighted sum of multiple penalty terms in the prediction time domain, specifically including: the trajectory tracking term, used to penalize the three-dimensional position error and velocity error between the geometric center of the UAV formation and the expected landing trajectory of the return capsule in the prediction time domain; the stiffness adjustment term, used to penalize the deviation between the current horizontal relative distance of the UAV and the expected distance required for the target buffer stiffness in the prediction time domain; and the thrust increment term, used to penalize the increment of thrust command in adjacent control cycles to suppress high-frequency oscillations of the multi-UAV actuators.

[0015] S4. Transform the flight safety constraints during the capture process into inequality constraints of the model prediction controller;

[0016] In step S4, the inequality constraints specifically include: requiring that at any time in the prediction time domain, the distance from the projected coordinates of each UAV on the horizontal plane to the central axis of the dynamic no-fly cylinder is strictly greater than the sum of the radius of the cylinder and the preset safety margin; limiting the horizontal relative distance of the UAV formation to between the limit breakage distance and the minimum relaxation distance of the flexible net; and limiting the thrust command sequence to not exceed the maximum physical output thrust limit of a single UAV motor.

[0017] S5. In each control cycle, the model predictive controller, under the premise of strictly satisfying the above inequality constraints, adopts real-time iterative sequential quadratic programming to solve the cost function, obtains the optimal thrust control sequence, takes the first thrust control quantity and sends it to each UAV for execution, driving the UAV formation to perform cooperative capture actions.

[0018] First, the drones are modeled, with each drone treated as a controllable point mass. The state variables of the drone are:

[0019] (1)

[0020] No. The discrete-time kinematics of the UAV is described as follows:

[0021] (2)

[0022] (3)

[0023] No. The dynamic equations of an unmanned aerial vehicle in an inertial coordinate system:

[0024] (4)

[0025] At the same time, define the center position of the drone formation, i.e., the common mode position. for:

[0026] (5)

[0027] Define the distance from each drone in a drone swarm to the common-mode position, i.e., the differential-mode distance. for:

[0028] (6)

[0029] in, For the number of drones, and ; The sampling period; For the first The quality of the drone; For the first The position vector of the UAV in the inertial coordinate system; For the first The velocity vector of the drone in the inertial coordinate system; For the first The acceleration vector of the UAV in the inertial coordinate system; For the first The thrust vector of the drone's motors; The vector of gravitational acceleration. The tension vector exerted on the UAV by the main load-bearing cable;

[0030] During the period when the return capsule did not come into contact with the flexible net, The model predictive controller aims to maintain the large mesh openings of the flexible net and track the desired trajectory of the return capsule, based solely on the tension of the flexible net itself.

[0031] At the instant the return capsule contacts the flexible net, equation (4) states... The terms changed; to handle the nonlinear dynamics of the flexible net being impacted by the return capsule, the four main load-bearing cables and the flexible net were treated as a virtual spring-damped model, such as... Figure 3 As shown, the equivalent tensile force of a single virtual connection. The calculation formula is as follows:

[0032] (7)

[0033] in The stiffness of the virtual spring-damped model varies with A changing function, The damping of the virtual spring damping model varies with A changing function, The elongation of the virtual spring-damped model can be obtained based on the geometric relationships in three-dimensional space:

[0034] (8)

[0035] in, The depth to which the center of the flexible net sinks as the return capsule descends after contact with it. This is the initial length of the virtual spring-damped model.

[0036] Substituting the equivalent tension equation into the dynamic equation of the UAV, we can obtain a state-space prediction model that includes differential mode distance: , where input quantity For the first The model visually reflects the thrust of the drone's motors when the drone formation actively reduces the differential mode distance. At the same time, it can reduce the stiffness coefficient of the virtual spring damping model, thereby achieving a reduction The aim is to mitigate the impact on drones.

[0037] Within each control cycle, the model predictive controller solves the following finite-time optimization problem:

[0038] (9)

[0039] The prediction time domain length is Cost function Defined as:

[0040] (10)

[0041] in, For the prediction step number, ; To predict the first in the time domain The center position of the drone formation. To predict the first in the time domain The reference trajectory position of the step; To predict the first in the time domain The difference in mode distance of the step, To predict the first in the time domain The step is the expected differential distance determined by the impact strategy management unit; To predict the first in the time domain The thrust control increment of the step, and ;when When =0, This refers to the thrust control vector of the UAV formation that was executed in the previous control cycle; To predict the center position of the drone formation at the time-domain terminal, To predict the reference trajectory position at the time-domain terminal moment; , , , All are positive definite weight matrices; Denotes a weighted quadratic form, and .

[0042] The optimization solution process must satisfy the following constraints:

[0043] (11)

[0044] (12)

[0045] (13)

[0046] Formula (11) represents the anti-network breakage and anti-collision constraints, which limit the differential mode distance. The extreme values ​​are used to prevent the flexible net from breaking and colliding with the drone. This is the critical value for the breakage of the flexible mesh. is the collision avoidance limit between UAVs; formula (12) is the obstacle avoidance constraint for dynamic no-fly zones, where, and For the first The horizontal and vertical coordinates of the UAV's projected coordinates; and The x and y coordinates of the projection of the central axis of the dynamically restricted-fly zone cylinder onto the horizontal plane are given. The safety radius of the dynamic no-fly cylinder includes the maximum physical radius of the parachute canopy and a preset safety margin; Formula (13) is the thrust constraint, used to limit the motor thrust from exceeding the thrust limit. .

[0047] This invention addresses the problem in existing multi-UAV-based aerial recovery systems where the overall tracking trajectory and the flexible net's variable stiffness adjustment are coupled when dealing with dynamic targets and sudden impacts, and where multiple physical constraints are difficult to handle. It provides a return capsule recovery control method based on multi-UAV flexible net capture. Compared with existing technologies, this invention has the following advantages:

[0048] I. The equivalent dynamic model of the flexible net proposed in this invention enables the system to automatically and smoothly transition from high stiffness to low stiffness and actively sink, effectively absorbing instantaneous impacts and preventing cable breakage.

[0049] Second, in this invention, the parachute is modeled as a dynamic obstacle avoidance constraint, and the motor thrust and cable tension limit are incorporated as hard constraints into the optimization solution, which effectively avoids the risks of collision and cable entanglement.

[0050] Third, this invention relies on model predictive control to coordinate multiple future states, predict the trajectory and tension trend of the return capsule in advance, and achieve active interception. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the overall scene of a multi-drone collaborative capture system;

[0052] Figure 2 A physical model diagram of a multi-UAV collaborative capture system;

[0053] Figure 3 This is a block diagram of the control system architecture based on model predictive control.

[0054] Figure 4 A flowchart illustrating the steps of a multi-UAV collaborative capture method;

[0055] Figure 5 The diagram shows the formation and system stiffness changes during the multi-UAV collaborative capture process. Detailed Implementation

[0056] To clearly illustrate the technical features of this case, the following detailed explanation will be provided through specific implementation methods and in conjunction with the accompanying drawings.

[0057] like Figure 1 As shown, this embodiment provides a return capsule recovery control method based on multi-UAV flexible net capture. At the physical hardware and execution level, it mainly includes: a flight formation composed of multiple UAVs 101, a main support cable 102 connected to each UAV 101, and a flexible net 103 suspended and supported by the main support cable 102. The system of this invention aims to dynamically intercept and capture a return capsule 200 descending with a parachute at high altitude.

[0058] In this embodiment, the number of drones 101 is set to four. The four drones 101 are respectively pulled to the edge nodes of the flexible net 103 by four main load-bearing cables 102. By coordinating their flight, they change the common mode spatial position and differential mode geometry of the entire formation, thereby achieving precise trajectory tracking of the return capsule 200 and safe buffering and capture at the moment of contact.

[0059] like Figure 3 As shown, the recovery system in this case includes: a perception and prediction module, an impact strategy management unit, a control and computing module, and a drone formation.

[0060] The perception and prediction module includes one or more of the following: a visual camera, lidar, satellite locator, inertial measurement unit, and wireless rangefinder. It acquires three-dimensional spatial state data of the return capsule and its parachute using a multi-source data fusion algorithm. Based on this three-dimensional spatial state data, it predicts the expected trajectory of the return capsule's descent, the contact time, and the positional relationship of the return capsule relative to the flexible net, and generates dynamic no-fly zone parameters. Its output serves as the reference trajectory and obstacle avoidance constraint input for the model predictive controller, and also as the basis for the impact strategy management unit to generate differential mode distance reference commands.

[0061] The perception and prediction module acquires real-time three-dimensional spatial state data of the return capsule and its parachute, and predicts their descent trajectory. The impact strategy management unit is an upper-level strategy scheduling submodule located within or connected to the control and calculation module. It determines the system's current capture phase based on the predicted contact time, predicted landing point of the return capsule, current network area, current differential distance, safe distance between UAVs, and estimated tension of the main support cable, and generates corresponding differential distance reference commands. The control and calculation module includes a model prediction controller. The model prediction controller employs a model prediction control algorithm, simultaneously receiving the desired trajectory and the differential distance reference commands from the impact strategy management unit, and calculates the required thrust for the UAVs under the condition of comprehensively considering the physical constraints of network disconnection prevention and dynamic obstacle avoidance. During command execution, the UAV formation feeds back the current system state to the model prediction controller in real time, forming a closed-loop rolling optimization control. The current system state includes the common-mode position representing the overall system translation. Differential distance representing the degree of formation contraction and the depth of descent during the impact of the reentry capsule. .

[0062] like Figure 3 As shown, during the capture mission, the perception and prediction module acquires real-time three-dimensional spatial state data of the return capsule and its parachute, and predicts its descent trajectory. Considering the thin and easily tangled nature of the parachute lines, the UAV needs to avoid the influence range of the return capsule and parachute during flight. Therefore, this embodiment constructs a dynamic no-fly zone for the UAVs to avoid the risk of the UAV formation getting entangled in the parachute lines.

[0063] like Figure 1 As shown, assume the return capsule is in The horizontal projection coordinates at time are Then, using this coordinate as the axis, a safety isolation radius greater than the maximum physical radius of the parachute canopy is set. A dynamic cylindrical constraint surface is constructed in three-dimensional space. This dynamic cylindrical constraint surface serves as the dynamic no-fly zone for the UAV formation.

[0064] To achieve model predictive control of UAV formations, a state-space predictive model of the system must be established.

[0065] First, the drones are modeled, with each drone treated as a controllable point mass. The state variables of the drone are:

[0066] (1)

[0067] No. The discrete-time kinematics of the UAV is described as follows:

[0068] (2)

[0069] (3)

[0070] No. The dynamic equations of an unmanned aerial vehicle in an inertial coordinate system:

[0071] (4)

[0072] At the same time, define the center position of the drone formation, i.e., the common mode position. for:

[0073] (5)

[0074] Define the distance from each drone in a drone swarm to the common-mode position, i.e., the differential-mode distance. for:

[0075] (6)

[0076] in, For the number of drones, and ; The sampling period; For the first The quality of the drone; For the first The position vector of the UAV in the inertial coordinate system; For the first The velocity vector of the drone in the inertial coordinate system; For the first The acceleration vector of the UAV in the inertial coordinate system; For the first The thrust vector of the drone's motors; The vector of gravitational acceleration. The tension vector exerted on the UAV by the main load-bearing cable;

[0077] During the period when the return capsule did not come into contact with the flexible net, The model predictive controller aims to maintain the large mesh openings of the flexible net and track the desired trajectory of the return capsule, based solely on the tension of the flexible net itself.

[0078] At the instant the return capsule contacts the flexible net, equation (4) states... The terms have changed; to address the nonlinear dynamics of the flexible net being impacted by the return capsule, this embodiment treats the four main load-bearing cables and the flexible net as a virtual spring-damped model, such as... Figure 3 As shown, the equivalent tensile force of a single virtual connection. The calculation formula is as follows:

[0079] (7)

[0080] in The stiffness of the virtual spring-damped model varies with A changing function, The damping of the virtual spring damping model varies with A changing function, The elongation of the virtual spring-damped model can be obtained based on the geometric relationships in three-dimensional space:

[0081] (8)

[0082] in, The depth to which the center of the flexible net sinks as the return capsule descends after contact with it. This is the initial length of the virtual spring-damped model.

[0083] Substituting the equivalent tension equation into the dynamic equation of the UAV, we can obtain a state-space prediction model that includes differential mode distance: , where input quantity For the first The model visually reflects the thrust of the drone's motors when the drone formation actively reduces the differential mode distance. At the same time, it can reduce the stiffness coefficient of the virtual spring damping model, thereby achieving a reduction The aim is to mitigate the impact on drones.

[0084] Within each control cycle, the model predictive controller solves the following finite-time optimization problem:

[0085] (9)

[0086] The prediction time domain length is Cost function Defined as:

[0087] (10)

[0088] in, For the prediction step number, ; To predict the first in the time domain The center position of the drone formation. To predict the first in the time domain The reference trajectory position of the step; To predict the first in the time domain The difference in mode distance of the step, To predict the first in the time domain The step is the expected differential distance determined by the impact strategy management unit; To predict the first in the time domain The thrust control increment of the step, and ;when When =0, This refers to the thrust control vector of the UAV formation that was executed in the previous control cycle; To predict the center position of the drone formation at the time-domain terminal, To predict the reference trajectory position at the time-domain terminal moment; , , , All are positive definite weight matrices; Denotes a weighted quadratic form, and .

[0089] Meanwhile, optimizing the solution process must satisfy the following constraints:

[0090] (11)

[0091] (12)

[0092] (13)

[0093] Formula (11) represents the anti-network breakage and anti-collision constraints, which limit the differential mode distance. The extreme values ​​are used to prevent the flexible net from breaking and colliding with the drone. This is the critical value for the breakage of the flexible mesh. is the collision avoidance limit between UAVs; formula (12) is the obstacle avoidance constraint for dynamic no-fly zones, where, and For the first The horizontal and vertical coordinates of the UAV's projected coordinates; and The x and y coordinates of the projection of the central axis of the dynamically restricted-fly zone cylinder onto the horizontal plane are given. The safety radius of the dynamic no-fly cylinder includes the maximum physical radius of the parachute canopy and a preset safety margin; Formula (13) is the thrust constraint, used to limit the motor thrust from exceeding the thrust limit. .

[0094] Within each control cycle, the model predictive controller, under the premise of strictly satisfying the above inequality hard constraints, uses real-time iterative sequential quadratic programming to obtain the optimal control sequence, takes the first thrust control quantity and sends it to each UAV for execution, and repeats the above process in the next cycle.

[0095] To further illustrate the execution process and shock resistance effect of the control system described in this invention, the following is combined with... Figure 5 The diagram showing the formation and system stiffness changes during the multi-UAV collaborative capture process provides a detailed explanation of the complete work cycle of the multi-UAV collaborative capture of the return capsule.

[0096] like Figure 5 As shown, during the tracking phase before the return capsule falls into the flexible net, i.e. During this phase, the flexible net is in an unloaded state. To ensure the maximum capture and interception area, the model prediction controller issues a large differential mode distance command, driving the UAV formation to maintain a large horizontal diagonal distance. At this time, the flexible net is fully extended, and the equivalent stiffness of the four main load-bearing cables and the flexible net as a whole is at a high level. The control and calculation module uses common mode trajectory tracking to ensure that the geometric center of the flexible net is precisely aligned with the descent trajectory of the return capsule with a parachute.

[0097] exist At that moment, the return capsule physically contacts and impacts the flexible net. At this time, the impact strategy management unit issues a differential mode stiffness command. The control and calculation module quickly controls the UAV formation to track the desired position at the common mode position while contracting inward, thereby relaxing the flexible net. The equivalent stiffness of the four main load-bearing cables and the flexible net as a whole decreases sharply, thereby reducing the peak impact tensile force on the UAV and alleviating the load on the UAV.

[0098] go through Through brief energy dissipation and dynamic buffering, the enormous impact kinetic energy of the return capsule is largely absorbed by the equivalent damping of the flexible net, at which point the differential mode distance... With stiffness The system stabilized within the pre-defined low-level safety zone. The return capsule was captured by the recovery system, which then returned to a stable state. The model predictive controller continued to drive the drone formation, smoothly transferring the return capsule to the designated recovery area.

[0099] There are many specific ways to implement this invention. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A return capsule recovery control method based on multi-UAV flexible net capture, characterized in that, A flight formation of four drones pulls a flexible net to dynamically intercept and capture return capsules with parachutes falling at high altitudes. The drones suspend the flexible net through a main load-bearing cable. The return capsule recovery control method is implemented by a recovery system, which includes a perception and prediction module, an impact strategy management unit, a control and calculation module, and a UAV formation. The perception and prediction module acquires real-time three-dimensional spatial state data of the return capsule and its parachute and predicts its descent trajectory. The impact strategy management unit is an upper-level strategy scheduling submodule located within or communicatively connected to the control and calculation module. It generates a differential distance reference command based on the predicted trajectory of the return capsule, the predicted contact time, the return capsule's relative position to the network port, the current differential distance, and the safety constraint status, and inputs the reference command to the model predictive controller. The control and calculation module includes a model predictive controller. The model predictive controller employs a model predictive control algorithm, simultaneously receiving the desired trajectory and the differential distance reference command, and calculates the required thrust for the UAVs under the condition of comprehensively considering the physical hard constraints of preventing network disconnection and dynamic obstacle avoidance. During the execution of commands, the UAV formation feeds back the current system status to the model predictive controller in real time, thus forming a closed-loop rolling optimization control. Includes the following steps: S1. Obtain the three-dimensional spatial state data of the return capsule and its parachute, predict the expected trajectory of the return capsule's descent, and model the area where the parachute is located as a dynamic no-fly zone that updates dynamically over time. S2. Construct a state-space prediction model that includes drone formations and return capsules; S3. Design the cost function in the prediction time domain of the model predictive controller; S4. Transform the flight safety constraints during the capture process into inequality constraints of the model prediction controller; S5. In each control cycle, the model predictive controller, under the premise of strictly satisfying the above inequality constraints, adopts real-time iterative sequential quadratic programming to solve the problem, minimizes the cost function, and obtains the optimal thrust control sequence. The first thrust control quantity is taken and sent to each UAV for execution, driving the UAV formation to perform cooperative capture actions. Within each control cycle, the model predictive controller solves the following finite-time optimization problem: （9） The prediction time domain length is Cost function Defined as: （10） in, For the prediction step number, ; To predict the first in the time domain The center position of the drone formation. To predict the first in the time domain The reference trajectory position of the step; To predict the first in the time domain The difference in mode distance of the step, To predict the first in the time domain The step is the expected differential distance determined by the impact strategy management unit; To predict the first in the time domain The thrust control increment of the step, and ;when When =0, This refers to the thrust control vector of the UAV formation that was executed in the previous control cycle; To predict the center position of the drone formation at the time-domain terminal, To predict the reference trajectory position at the time-domain terminal moment; , , , All are positive definite weight matrices; Denotes a weighted quadratic form, and ; The optimization solution process must satisfy the following constraints: （11） （12） （13） Formula (11) represents the anti-network breakage and anti-collision constraints, which limit the differential mode distance. The extreme values ​​are used to prevent the flexible net from breaking and colliding with the drone. This is the critical value for the breakage of the flexible mesh. is the collision avoidance limit between UAVs; formula (12) is the obstacle avoidance constraint for dynamic no-fly zones, where, and For the first The horizontal and vertical coordinates of the UAV's projected coordinates; and The x and y coordinates of the projection of the central axis of the dynamically restricted-fly zone cylinder onto the horizontal plane are given. The safety radius of the dynamic no-fly cylinder includes the maximum physical radius of the parachute canopy and a preset safety margin; Formula (13) is the thrust constraint, used to limit the motor thrust from exceeding the thrust limit. .

2. The return capsule recovery control method based on multi-UAV flexible net capture according to claim 1, characterized in that, First, the drones are modeled, with each drone treated as a controllable point mass. The state variables of the drone are: （1） No. The discrete-time kinematics of the UAV is described as follows: （2） （3） No. The dynamic equations of a drone in an inertial coordinate system: （4） At the same time, define the center position of the drone formation, i.e., the common mode position. for: （5） Define the distance from each drone in a drone swarm to the common-mode position, i.e., the differential-mode distance. for: （6） in, For the number of drones, and ; The sampling period; For the first The quality of the drone; For the first The position vector of the UAV in the inertial coordinate system; For the first The velocity vector of the drone in the inertial coordinate system; For the first The acceleration vector of the UAV in the inertial coordinate system; For the first The thrust vector of the drone's motors; The vector of gravitational acceleration. The tension vector exerted on the UAV by the main support cable; During the period when the return capsule did not come into contact with the flexible net, The model predictive controller aims to maintain the large mesh openings of the flexible net and track the expected trajectory of the return capsule, based solely on the tension of the flexible net itself. At the instant the return capsule contacts the flexible net, equation (4) states... The terms have changed; the four main load-bearing cables and the flexible net are treated as a virtual spring damping model, and the equivalent tension of a single virtual connection is determined. The calculation formula is as follows: （7） in The stiffness of the virtual spring-damped model varies with A changing function, The damping of the virtual spring damping model varies with A changing function, The elongation of the virtual spring-damped model can be obtained based on the geometric relationships in three-dimensional space: （8） in, The depth to which the center of the flexible net sinks as the return capsule descends after contact with it. This is the initial length of the virtual spring-damped model; Substituting the equivalent tension equation into the dynamic equation of the UAV, we can obtain a state-space prediction model that includes differential mode distance: , where input quantity For the first The thrust of the drone's motor.

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