Rope system multi-unmanned aerial vehicle rapid formation control method based on energy constraint

Abstract

The invention particularly relates to a rope-tied multi-unmanned aerial vehicle rapid formation control method based on energy constraint, and the method comprises the steps: designing a sliding mode surface for a navigator and a plurality of followers in a formation; cooperative gain and neighbor unmanned aerial vehicle information are introduced into follower sliding mode surface design; designing an online nonlinear disturbance observer based on the sliding mode surface to obtain a disturbance estimation value, and applying the disturbance estimation value to feed-forward compensation; designing a dip angle constraint term based on a barrier Lyapunov function, and introducing the dip angle constraint term into the sliding mode surface; designing an additional compensation item based on energy constraint, and introducing the additional compensation item into the sliding mode surface; and designing a sliding mode control law based on the sliding mode surface and the disturbance estimation value which introduce the inclination angle constraint term and the inclination angle constraint term. According to the method, a piloting-following structure is adopted, and sliding mode control, a nonlinear disturbance observer, a barrier type Lyapunov function constraint and an energy constraint method are combined, so that the outer ring position and the inner ring attitude of the unmanned aerial vehicle formation are accurately controlled.

Description

Technical Field

[0001] The present invention relates to the technical field of UAV formation control, and in particular to a tethered multi-UAV rapid formation control method based on energy constraints. Background Art

[0002] UAV formation control technology is the core research direction of UAV collaborative operations and is widely used in disaster relief, agricultural plant protection, logistics and distribution and other fields. The existing mainstream formation control methods include the pilot-follower method, the virtual structure method and the behavior-based method. Among them, the pilot-follower method is widely used because of its simple structure and easy implementation, but its dynamic response speed and anti-interference ability are limited in complex environments. In recent years, with the large-scale application of multi-UAV systems, sliding film control (SMC) and potential field method (PFM) have been introduced into formation control to improve robustness, but the existing methods still have deficiencies in fast convergence, energy optimization and collaborative design of safety constraints. In the field of tethered multi-UAV formation control, existing technologies mainly achieve formation stability by combining dynamic modeling with sliding film control. However, existing methods also have some limitations:

[0003] 1. Weak anti-interference capability: Traditional sliding membrane control relies on fixed gains and lacks a dynamic disturbance observation mechanism, resulting in poor formation stability in strong winds.

[0004] 2. Insufficient attitude safety: Existing methods do not strictly constrain the drone's attitude angles. Exceeding the roll or pitch angle limit may cause hardware damage or mission failure.

[0005] 3. Low convergence efficiency: The formation coordination gain design does not incorporate the energy method, and the convergence speed of multi-aircraft position errors is insufficient to meet the requirements of rapid formation adjustment.

[0006] 4. Obstacle avoidance calculations are complex: The existing potential field method requires independent design of the repulsive field and control law. The system's real-time performance is limited and it is difficult to adapt to high-density formation scenarios.

[0007] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0008] The present invention provides a tethered multi-UAV rapid formation control method based on energy constraints, which is used to solve the problems of insufficient anti-external interference ability, lack of attitude safety, slow formation convergence speed and complex collision avoidance calculation in the prior art.

[0009] Other features and advantages of the present invention will become apparent from the following detailed description, or may be learned in part by practice of the present invention.

[0010] According to a first aspect of the present invention, a method for rapid formation control of multiple UAVs using a tethered system based on energy constraints is provided, which adopts a leader-follower structure. The method comprises:

[0011] For the leader and multiple followers in the formation, sliding surfaces are designed separately. The design of the follower sliding surface incorporates cooperative gain and neighboring drone information.

[0012] An online nonlinear disturbance observer is designed based on the sliding membrane surface to obtain the disturbance estimation value, which is then used for feedforward compensation.

[0013] The inclination angle constraint term is designed based on the barrier Lyapunov function and introduced into the sliding surface;

[0014] Design additional compensation items based on energy constraints and introduce them into the synovial surface;

[0015] The sliding membrane control law is designed based on the sliding membrane surface with the introduction of the tilt angle constraint term and the disturbance estimation value.

[0016] In some exemplary embodiments, the synovial surface of the navigator is specifically:

[0017]

[0018] Among them, x1 refers to the error e between the navigator's expected position and actual position, and x2 is the derivative of the error p,q,g,h are odd numbers and satisfy a, b are odd numbers.

[0019] In some exemplary embodiments, the synovial surface of the i-th follower is specifically:

[0020]

[0021] Among them, x 1,i It refers to the error e between the expected position and the actual position of the i-th follower i , x 2,i is the error e i The derivative of , γ>0 is the formation coordination gain, N i Assemble for the neighbor drone, x 1,j It refers to the error e between the expected position and the actual position of the j-th follower j .

[0022] In some exemplary embodiments, the nonlinear disturbance observer is designed as follows:

[0023]

[0024] Where s is the sliding surface, k is the observer gain, is the disturbance estimate.

[0025] In some exemplary embodiments, the design of the inclination angle constraint term based on the obstacle Lyapunov function introduces the inclination angle constraint term into the synovial surface; specifically:

[0026] Define the inclination constraint |φ|≤φ max ,|θ|≤θ max , design barrier Lyapunov function

[0027]

[0028] Introduce constraints into the sliding surface and modify the attitude control law:

[0029]

[0030] Among them, λ>0 is the constraint gain to ensure that φ does not exceed the limit, φ is the roll angle, φ max <15°;

[0031] Similarly,

[0032]

[0033] Among them, θ>0 is the constraint gain to ensure that θ does not exceed the limit, θ is the pitch angle, θ max <15°.

[0034] In some exemplary embodiments, the design is based on an additional compensation term of energy constraint, and the additional compensation term is introduced into the synovial surface, specifically:

[0035] The designed potential function is as follows:

[0036]

[0037] Potential function for x i The partial derivative of is:

[0038]

[0039] Introduced into the synovial surface

[0040]

[0041] Among them, x i , x j are the actual positions of UAV i and UAV j respectively, α>0 is the potential field coupling coefficient, and the sliding mode error is balanced with the minimum distance constraint.

[0042] In some exemplary embodiments, the design of the synovial control law based on the synovial surface with the tilt angle constraint term introduced and the tilt angle constraint term and the disturbance estimation value is specifically as follows:

[0043] The synovial control law includes the inner loop attitude control law and the outer loop position control law. The outer loop control is tracked by the inner loop attitude control.

[0044] The inner loop attitude control law:

[0045]

[0046] Among them, u 2,i 、u 3,i 、u 4,i are the control laws for roll angle, pitch angle and yaw angle respectively, I xx , I yy , I zz They represent the principal moments of inertia, are the disturbance estimates of the roll angle, pitch angle and yaw angle of the i-th UAV, are the angle errors of the roll angle, pitch angle and yaw angle of the i-th UAV, s φ,i 、s θ,i 、s ψ,i are the angular sliding membrane surfaces of the roll angle, pitch angle, and yaw angle of the i-th UAV, respectively;

[0047] The outer loop position control law:

[0048]

[0049] Among them, u 1,i 、u x,i 、u y,i They are the position control laws of the three axes, g represents the gravity vector, f z,i represents the z-axis component of the tension of the tether connected to drone i, f x,i represents the component of the tension of the tether connected to drone i on the x-axis, f y,i It represents the component of the tension of the tether connected to drone i on the y-axis.

[0050] According to a second aspect of the present invention, a storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method for rapidly controlling a tethered multi-UAV formation based on energy constraints described in the first aspect is implemented.

[0051] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored. When the computer program is executed by a processor, the energy constraint-based tethered multi-UAV rapid formation control method described in the first aspect is implemented.

[0052] According to a fourth aspect of the present invention, there is provided an electronic device, comprising:

[0053] processor; and

[0054] a memory for storing executable instructions of the processor;

[0055] Wherein, the processor is configured to implement the energy constraint-based tethered multi-UAV rapid formation control method described in the first aspect above by executing the executable instructions.

[0056] The energy-constrained, tethered multi-UAV rapid formation control method provided by the embodiments of the present invention effectively reduces overall energy consumption by introducing an energy constraint mechanism, and ensures that all UAV motion parameters remain within a safe operating range during mission execution. It can also achieve rapid convergence and safe and stable operation of the UAV formation under various complex interference conditions. This is specifically reflected in the following aspects:

[0057] 1. Significantly Enhanced Interference Resistance: An integrated nonlinear disturbance observer (DOB) estimates and compensates for external disturbances in real time. Traditional methods rely on fixed gain compensation and are unable to adapt to dynamic changes such as wind disturbances. Using a sign function and adaptive gain algorithm, the DOB generates interference estimates in real time and directly feeds them into control commands, counteracting the impact of disturbances on the formation's trajectory.

[0058] 2. Comprehensively Improved Attitude Safety: A Barrier Lyapunov Function (BLF) is used to constrain roll and pitch angles. By dynamically adding a penalty term to the sliding surface, when the attitude angle approaches the safety threshold, the penalty term increases exponentially with the degree of deviation, forcing the drone to automatically adjust its attitude to reduce the probability of crossing the threshold. This allows the drone to maintain attitude stability in sudden strong crosswinds or sharp turns, preventing hardware damage or mission failure caused by roll / pitch angle violations.

[0059] 3. Collision avoidance mechanism with low computational load and fast formation convergence: This invention directly embeds the energy-constrained potential field gradient into the control law, shortening obstacle avoidance calculation time and making it suitable for high-density formation scenarios. When the distance between UAVs falls below the safe distance, the potential field gradient always points away from the neighboring UAV, and the repulsive force increases dynamically with decreasing distance, ensuring rapid obstacle avoidance response.

[0060] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The accompanying drawings are incorporated into and constitute a part of this specification, illustrate embodiments consistent with the present invention, and together with the description, serve to explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and it is clear that those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0062] Figure 1 A diagram showing the control structure of a quadrotor drone according to an exemplary embodiment of the present invention;

[0063] Figure 2 Schematic diagram of the process of a tethered multi-UAV rapid formation control method based on energy constraints according to an exemplary embodiment of the present invention;

[0064] Figure 3 A comparison diagram of three-axis position coordinates of a MATLAB numerical simulation of a three-UAV formation according to an exemplary embodiment of the present invention;

[0065] Figure 4 A schematic diagram of three-axis position coordinates of a MATLAB numerical simulation of a three-UAV formation according to an exemplary embodiment of the present invention;

[0066] Figure 5 Schematic diagram of Mujoco physical simulation of a three-UAV formation according to an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0067] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0068] In addition, the accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the blocks shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0069] The present invention establishes a complete UAV dynamics model, designs a two-layer control structure, and introduces energy constraints and barrier Lyapunov functions (BLFs) to achieve rapid formation convergence, optimize energy utilization, and balance system safety and robustness, thereby meeting the requirements of multi-UAV collaborative transportation in complex mission environments.

[0070] like Figure 1As shown, the double-layer control structure designed by the present invention includes an outer loop position sub-control and an inner loop attitude sub-control, which output two control commands, the position desired value and the attitude desired value, to the position subsystem controller and the attitude subsystem controller respectively. Among them, the position subsystem controller outputs the control law u1 to the position subsystem, and the position subsystem outputs the z-axis position of the drone. At the same time, the position subsystem controller outputs the control law u x 、u y To the attitude subsystem, it is used to calculate the expected roll angle and yaw angle; the attitude subsystem controller outputs the control laws u2, u3, and u4 to the attitude subsystem, and the attitude subsystem outputs the UAV attitude. The UAV attitude includes roll angle, pitch angle, and yaw angle. The UAV x-axis and y-axis positions are controlled by the changes in roll angle and pitch angle. At the same time, the roll angle and pitch angle in the UAV attitude are output to the position subsystem controller for calculating u1 and u x 、u y .

[0071] Based on the above-mentioned two-layer control structure, this example implementation provides a tethered multi-UAV rapid formation control method based on energy constraints. It adopts a "leader-follower" structure, combined with sliding mode control, nonlinear disturbance observer (DOB), barrier-type Lyapunov function constraints and energy constraint methods to achieve precise control of the outer ring position and inner ring attitude of the UAV formation.

[0072] refer to Figure 2 As shown, the tethered multi-UAV rapid formation control method based on energy constraint may specifically include the following steps:

[0073] Step S11, deriving a dynamic model of the UAV based on Newton's second law;

[0074] Step S12, comprehensively considering the formation requirements, establishing the sliding surface of the UAV;

[0075] Step S13, designing a nonlinear disturbance observer (DOB) to estimate wind disturbances online;

[0076] Step S14, constraining the inclination angle according to the obstacle Lyapunov function;

[0077] Step S15, introducing the energy method into the existing control law to constrain the position of the UAV formation;

[0078] Step S16, adopting a leader-follower structure and designing a formation function;

[0079] Step S17, designing a multi-UAV cooperative formation outer loop position controller;

[0080] Step S18, designing an inner loop attitude tracking controller for a multi-UAV cooperative formation;

[0081] Below, each step in this exemplary implementation will be described in more detail with reference to the accompanying drawings and embodiments.

[0082] In step S11, based on Newton's second law, a dynamic model of the UAV is derived; wherein the UAV dynamic model includes a UAV translation dynamic model and a UAV attitude dynamic model;

[0083] Specifically, Newton's second law is used to construct a UAV translational dynamics model, taking into account the mass, lift, gravity and tension factors related to the rope; at the same time, a UAV attitude dynamics model is established to describe the angular changes such as roll, pitch, yaw and their corresponding control inputs.

[0084] For example, the design of the UAV dynamics equation is as follows:

[0085] Based on Newton's second law, the translational dynamics equation of the UAV is:

[0086]

[0087] Among them, m i , F i denote the mass and lift of UAV i respectively; is the rotation matrix of the drone i’s local system to the inertial system F0; e3 is the identity matrix [0,0,1] T ; g represents the gravity vector [0,0,-9.81] T ms -2 ;T i and t i They represent the magnitude and direction of the tension of the tether connected to UAV i; d i Represents the interference of the external environment on UAV i. The UAV rotates around the system with zyx as the rotation order relative to the inertial system, and the rotation matrix of the system relative to the inertial system is obtained for:

[0088]

[0089] The attitude dynamics of UAV i The attitude dynamics equation of UAV is:

[0090]

[0091] Among them, φ i ,θ i and ψ i Denote the roll, pitch and yaw angles of UAV i respectively; d φi and d θi Represents half of the distance between the roll and pitch motors respectively; u 2i 、u 3i and u4i Represents the roll, pitch and yaw attitude motion control inputs respectively; I xxi , I yyi and I zzi They represent the principal moments of inertia respectively.

[0092] In step S12, the formation requirements are comprehensively considered and the sliding surface of the UAV is established;

[0093] Specifically, sliding surfaces are designed for the leader and multiple followers in the formation respectively, so as to convert the error between the actual motion state and the expected state of the UAV into a controllable error variable.

[0094] For example, the design of the UAV sliding surface is as follows:

[0095] Taking formation requirements into consideration, a sliding film surface is established for the UAVs, utilizing non-singular fast terminal sliding film control. Non-singular fast terminal sliding film control (NFTSMC) is an advanced sliding film control method that combines the fast convergence characteristics of terminal sliding mode control (TSMC) with a non-singular design. Its core goal is to ensure finite-time stability while avoiding the singularity issues inherent in traditional terminal sliding mode control, reducing control chattering and improving dynamic response speed and robustness.

[0096] Sliding surface of non-singular fast terminal sliding mode

[0097]

[0098] Therefore, the synovial surface of the Navigator is designed

[0099]

[0100] Among them, x1 refers to the error e between the navigator's expected position and actual position, and x2 is the derivative of the error p,q,g,h are odd numbers and satisfy 1 <p / q<2,g / h> p / q, a, b are odd weights.

[0101] Constrain the formation The follower's sliding surface is added, and the cooperative gain (γ) and neighbor drone information are introduced in the sliding surface design, so that the overall formation error can converge quickly within a limited time.

[0102] The synovial surface of the i-th follower

[0103]

[0104] Among them, x 1,i It refers to the error e between the expected position and the actual position of the i-th follower i , x 2,i is the error e iDerivatives, p, q, g, h are odd numbers and satisfy a, b are weights, γ>0 is the formation coordination gain, N i Assemble for the neighbor drone, x 1,j It refers to the error e between the expected position and the actual position of the j-th follower j .

[0105] In step S13, a nonlinear disturbance observer (DOB) is designed to estimate wind disturbances online;

[0106] Specifically, in order to cope with external wind disturbances and other environmental disturbances, the present invention designs an online nonlinear disturbance observer to estimate external disturbances in real time and feed forward the disturbance estimation value to the controller, thereby improving control robustness.

[0107] For example, the design of the nonlinear disturbance observer is as follows:

[0108]

[0109] Where s is the sliding surface and k is the observer gain. Used for feedforward compensation.

[0110] In step S14, the inclination angle is constrained according to the obstacle Lyapunov function;

[0111] Specifically, to prevent the drone from losing control due to excessively large tilt angles, this invention introduces a Barrier Lyapunov Function (BLF) to strictly constrain the tilt angle. By adding a constraint term to the existing sliding mode control law, the BLF ensures that the drone's attitude angles remain within a safe range during control, preventing out-of-bounds errors caused by excessive control inputs.

[0112] Exemplarily, the barrier Lyapunov function is designed as follows:

[0113] The Barrier Lyapunov Function (BLF) is a special Lyapunov function used to ensure that the system state does not exceed the preset safety boundary. Its mathematical definition includes:

[0114] Smooth positive definite: The function is always positive within the domain and is zero only at the origin.

[0115] Boundary approaches infinity: When the system state approaches the safety boundary, the value of BLF tends to infinity, forming a "barrier" effect.

[0116] Derivative constraint: By controlling the derivative of BLF, the system state is ensured to always be within the safe region.

[0117] Define the inclination constraint |φ|≤φ max ,|θ|≤θ max , design BLF

[0118]

[0119] Introduce constraints into the sliding surface and modify the attitude control law:

[0120]

[0121] Among them, λ>0 is the constraint gain to ensure that φ does not exceed the limit, φ is the roll angle, φ max <15°.

[0122] Similarly,

[0123]

[0124] Among them, θ>0 is the constraint gain to ensure that θ does not exceed the limit, θ is the pitch angle, θ max <15°.

[0125] In step S15, in order to meet the formation requirements, a repulsive potential field with a repulsive point potential source is designed to achieve a minimum safe distance between UAVs, and an energy method is introduced into the existing control law to constrain the UAV formation position;

[0126] Specifically, the potential field method is used, treating each drone as a repulsive force source. When the distance between drones is less than a preset minimum safe distance, the repulsive field generates a repulsive force, forcing the drones to move away from each other, thus avoiding collision.

[0127] For example, the potential function is designed as follows:

[0128]

[0129] Potential function for x i The partial derivative of is:

[0130]

[0131] Introduced into the synovial surface

[0132]

[0133] Among them, x i , x j are the actual positions of UAV i and UAV j respectively, α>0 is the potential field coupling coefficient, and the sliding mode error is balanced with the minimum distance constraint.

[0134] To meet energy consumption requirements during formation, an additional compensation term based on energy constraints is designed. This uses an energy function to constrain the control inputs of each UAV, reducing energy consumption while ensuring rapid convergence. A repulsive potential field is introduced into the control law to ensure that UAVs maintain a minimum safe distance. Specifically, the gradient of the potential function is used as an additional compensation term to dynamically adjust the interaction force between UAVs to prevent collision risks caused by close proximity.

[0135] In step S16, the formation function is exemplarily designed as follows:

[0136] Adopting the leader-follower structure, designing the formation function,

[0137] Define the expected position of the i-th follower as:

[0138] p d,i =p l +Δp i

[0139] Among them, p d,i is the expected position of the ith follower, p l is the actual position of the pilot, Δp i is the expected relative position offset of follower i relative to the leader.

[0140] In step S17, the outer loop position controller of the multi-UAV cooperative formation is designed as follows:

[0141]

[0142]

[0143] Among them, u 1,i 、u x,i 、u y,i They are the position control laws of the three axes, g represents the gravity vector [0,0,-9.81] T ms -2 , f x,i represents the z-axis component of the tension of the tether connected to drone i, f y,i represents the component of the tension of the tether connected to drone i on the x-axis, f y,i represents the component of the tension of the tether connected to drone i on the y-axis, where g, h, m, and n are all odd numbers satisfying And a, b, ρ1, ρ2 are odd numbers.

[0144] In step S18, the process of designing the inner loop attitude tracking controller of the multi-UAV cooperative formation is as follows:

[0145] The UAV tracks the outer loop control of the UAV by controlling the inner loop attitude. The reference tracking components of the roll angle and pitch angle corresponding to the desired input of the outer loop controller are:

[0146]

[0147] In order to make the roll angle, pitch angle and yaw angle of the UAV track their respective reference tracking components, the control law is designed as follows:

[0148]

[0149] Among them, u 2,i 、u 3,i 、u 4,i are the control laws for roll angle, pitch angle and yaw angle respectively, I xx , I yy and I zz Represent the principal moments of inertia, g, h, m, n are all odd numbers satisfying And a, b, ρ1, ρ2 are odd numbers, are the disturbance estimates of the roll angle, pitch angle and yaw angle of the i-th UAV, are the angle errors of the roll angle, pitch angle and yaw angle of the i-th UAV, s φ,i 、s θ,i 、s ψ,i are the angular sliding surfaces of the roll angle, pitch angle, and yaw angle of the i-th UAV, respectively.

[0150] Theoretical analysis and simulation verification show that the proposed control method can achieve rapid convergence and safe and stable operation of UAV formations under various complex interference conditions. At the same time, the introduction of energy constraint mechanism effectively reduces the overall energy consumption and ensures that the various motion parameters of UAVs are always within the safe working area during the execution of the mission. Figure 3-5 As shown, an embodiment of the present invention consisting of a formation of three UAVs is simulated. It can be seen from the figure that the UAV formation converges quickly and can stably fly to the desired position.

[0151] Furthermore, the above-described figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes illustrated in the above-described figures do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0152] Other embodiments of the present invention will readily occur to those skilled in the art after considering the specification and practicing the invention herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the invention being indicated by the claims.

[0153] It should be understood that the present invention is not limited to the exact construction described above and shown in the drawings and that various modifications and variations can be made without departing from the scope thereof, which is limited only by the appended claims.

Claims

1. A tethered multi-UAV rapid formation control method based on energy constraints, characterized by: Adopting a pilot-follower structure, the method includes: For the leader and multiple followers in the formation, sliding surfaces are designed separately. The collaborative gain and neighboring drone information are introduced into the follower sliding surface design. An online nonlinear disturbance observer is designed based on the sliding membrane surface to obtain the disturbance estimation value, which is then used for feedforward compensation. The inclination angle constraint term is designed based on the obstacle Lyapunov function and introduced into the sliding surface; Design additional compensation items based on energy constraints and introduce them into the synovial surface; The sliding membrane control law is designed based on the sliding membrane surface with the introduction of the tilt angle constraint term and the disturbance estimation value.

2. The energy-constrained tethered multi-UAV rapid formation control method according to claim 1 is characterized in that: The synovial surface of the navigator is specifically as follows: Among them, x1 refers to the error e between the navigator's expected position and actual position, and x2 is the derivative of the error p,q,g,h are odd numbers and satisfy a, b are odd numbers.

3. The energy-constrained tethered multi-UAV rapid formation control method according to claim 2 is characterized in that: The synovial surface of the i-th follower is specifically: Among them, x 1,i It refers to the error e between the expected position and the actual position of the i-th follower i , x 2,i is the error e i The derivative of , γ>0 is the formation coordination gain, N i Assemble for the neighbor drone, x 1,j It refers to the error e between the expected position and the actual position of the j-th follower j .

4. The energy-constrained tethered multi-UAV rapid formation control method according to claim 3 is characterized in that: The design of the nonlinear disturbance observer is as follows: Where s is the sliding surface, k is the observer gain, is the disturbance estimate.

5. The energy-constrained tethered multi-UAV rapid formation control method according to claim 4 is characterized in that: The inclination angle constraint term is designed based on the obstacle Lyapunov function, and the inclination angle constraint term is introduced into the synovial surface; specifically: Define the inclination constraint |φ|≤φ max ,|θ|≤θ max , design barrier Lyapunov function Introduce constraints into the sliding surface and modify the attitude control law: Among them, λ>0 is the constraint gain to ensure that φ does not exceed the limit, φ is the roll angle, φ max <15°; Similarly, Among them, θ>0 is the constraint gain to ensure that θ does not exceed the limit, θ is the pitch angle, θ max <15°.

6. The energy-constrained tethered multi-UAV rapid formation control method according to claim 5 is characterized in that: The design is based on an additional compensation term of energy constraint, which is introduced into the synovial surface. Specifically, The designed potential function is as follows: Potential function for x i The partial derivative of is: Introduced into the synovial surface Among them, x i , x j are the actual positions of UAV i and UAV j respectively, α>0 is the potential field coupling coefficient, and the sliding mode error is balanced with the minimum distance constraint.

7. The energy-constrained tethered multi-UAV rapid formation control method according to claim 6 is characterized in that: The synovial control law is designed based on the synovial surface with the inclination constraint term and the disturbance estimation value, specifically: The synovial control law includes the inner loop attitude control law and the outer loop position control law. The outer loop control is tracked by the inner loop attitude control. The inner loop attitude control law: Among them, u 2,i 、u 3,i 、u 4,i are the control laws for roll angle, pitch angle and yaw angle respectively, I xx , I yy , I zz They represent the principal moments of inertia, are the disturbance estimates of the roll angle, pitch angle and yaw angle of the i-th UAV, are the angle errors of the roll angle, pitch angle and yaw angle of the i-th UAV, s φ,i 、s θ,i 、s ψ,i are the angular sliding membrane surfaces of the roll angle, pitch angle, and yaw angle of the i-th UAV, respectively; The outer loop position control law: Among them, u 1,i 、u x,i 、u y,i They are the position control laws of the three axes, g represents the gravity vector, f z,i represents the z-axis component of the tension of the tether connected to drone i, f x,i represents the component of the tension of the tether connected to drone i on the x-axis, f y,i It represents the component of the tension of the tether connected to drone i on the y-axis.

8. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for fast formation control of tethered multi-UAVs based on energy constraints according to any one of claims 1 to 7 is implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the energy-constrained tethered multi-UAV rapid formation control method according to any one of claims 1 to 7 is implemented.

10. An electronic device, characterized in that: include: processor; as well as a memory for storing executable instructions of the processor; The processor is configured to execute the energy constraint-based tethered multi-UAV rapid formation control method according to any one of claims 1 to 7 by executing the executable instructions.

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