Ground-air heterogeneous cluster formation control method and system based on adjustable funnel algorithm

Abstract

The invention discloses a ground-to-ground heterogeneous cluster formation control method and system based on an adjustable funnel algorithm, and relates to the technical field of distributed formation maneuvering control, and the method comprises the steps: building a dynamic model of a ground-to-ground heterogeneous cluster, and building an undirected graph representing an interaction topological structure of the ground-to-ground heterogeneous cluster; modeling a distributed safety critical formation maneuvering control problem of the air-ground heterogeneous cluster; a fully distributed dynamic compensator facing each follower and a formation maneuvering controller based on an adjustable funnel algorithm are designed, and then a safety-critical control framework based on a disturbance observer is adopted to construct a composite controller; and acquiring a virtual navigator signal and inputting the virtual navigator signal to the constructed various controllers to obtain an actual formation control signal of each follower, and executing distributed safety-critical formation maneuvering control on the followers. Through a distributed safety critical formation maneuvering strategy based on an adjustable funnel method, collision / obstacle avoidance and disturbance suppression of an air-ground heterogeneous cluster can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed formation maneuvering control, and in particular to a ground-to-air heterogeneous cluster formation control method and system based on an adjustable funnel algorithm. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In recent years, air-ground heterogeneous swarms, consisting of multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), have attracted widespread attention due to their ability to significantly expand search radius and service coverage through air-ground collaboration. Air-ground heterogeneous swarms are highly complementary and show great potential in a wide range of application scenarios, including collaborative surveillance, three-dimensional mapping, and hybrid path planning. To achieve these complex tasks, UAVs and UGVs must collaborate both in the air and on the ground, achieving efficient collaboration by forming three-dimensional geometric formations. Therefore, the main challenge of the current task lies in designing a distributed formation control strategy that enables the air-ground heterogeneous swarm to establish and maintain the target geometric configuration.

[0004] Numerous research results have been widely reported on the formation control problem. These studies typically directly couple neighbor coordination with individual regulation. Specifically, distributed formation control is designed based directly on the dynamic characteristics of the agents, leveraging the formation error, which includes variables related to individual positions, neighbor positions, and formation configuration. However, as the dynamic complexity or heterogeneity of the agents increases, the design complexity increases significantly, especially for highly nonlinear and fully heterogeneous air-ground cluster systems. In contrast, a hierarchical design framework provides greater flexibility. It consists of two levels: distributed dynamic compensator design and agent tracking control design. Through these two levels, the formation control problem is solved in two steps: first, a dynamic compensator is designed for each agent so that the outputs of all compensators achieve formation; second, a tracking controller is designed so that the agents track the compensator outputs. This hierarchical design framework achieves fully distributed control by simplifying the distributed control design and decoupling the formation error from global information.

[0005] Currently, various hierarchical control strategies have been proposed for heterogeneous multi-agent systems, in which the leader signal is generated by an external system and its state is accessible only to its neighbors. However, all agents in these scenarios must understand the dynamic characteristics of the external system, especially the system matrix. This condition implies direct communication between each agent and the external system, which contradicts the principle of distribution. Therefore, many studies have focused on relaxing these conditions. For example, the system matrix is ​​accessible only to the neighbors of the leader signal, but the external system matrix is ​​required to be marginally stable; or the constraints on the external system matrix are removed, but its estimation error still depends on global information. Therefore, designing a compensator that neither uses global information nor imposes constraints on the external system matrix becomes a more ideal option.

[0006] Furthermore, in actual formation control scenarios, each vehicle has its own geometric dimensions, and obstacles exist in the external environment. Heterogeneous air-ground swarms need to maintain their target geometric configuration, which can lead to conflicting objectives. This means that in complex environments, it is not feasible to simultaneously achieve collision / obstacle avoidance and maintain the target geometric configuration. Furthermore, actual systems are inevitably subject to a range of disturbances, including external disturbances and model uncertainties. These disturbances can lead to unsafe or dangerous behavior. Currently, a disturbance observer-based CBFs (Control Barrier Function) strategy has been proposed to ensure system safety and achieve disturbance suppression. However, the presence of disturbances and their estimation errors will affect the formation performance of heterogeneous air-ground swarms. Summary of the Invention

[0007] To address the deficiencies of the above-mentioned prior art, the present invention provides a ground-to-air heterogeneous cluster formation control method and system based on an adjustable funnel algorithm, designs a distributed safety-critical formation maneuvering strategy based on the adjustable funnel method, realizes collision / obstacle avoidance and disturbance suppression of the air-to-ground heterogeneous cluster, and ensures the formation control performance of the air-to-ground heterogeneous cluster.

[0008] In a first aspect, the present invention provides a ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm.

[0009] A ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm, comprising:

[0010] Build a dynamic model of an air-ground heterogeneous cluster and construct an undirected graph representing the interactive topology of the air-ground heterogeneous cluster. The air-ground heterogeneous cluster consists of several two-dimensional unmanned ground vehicles and several three-dimensional unmanned aerial vehicles. A virtual leader is set, and each individual in the air-ground heterogeneous cluster is a follower.

[0011] Based on dynamic models and undirected graphs, the distributed safety-critical formation maneuvering control problem of heterogeneous air-ground clusters is modeled.

[0012] Based on the modeling problem, a fully distributed dynamic compensator for each follower and a formation maneuver controller based on an adjustable funnel algorithm are designed. Then, a composite controller is constructed using a safety-critical control framework based on a disturbance observer.

[0013] The virtual leader signal is acquired and input into various controllers to obtain the actual formation control signal of each follower, and distributed safety-critical formation maneuver control is performed on the followers.

[0014] A further technical solution is to obtain the virtual leader signal and input it into the constructed multiple controllers to obtain the final actual formation control signal for each follower, including:

[0015] Obtain the virtual leader signal and use a fully distributed dynamic compensator to estimate the leader's estimated state for each follower.

[0016] Based on the leader's estimated state, a formation maneuver controller based on an adjustable funnel algorithm is used to output initial control signals for collision / obstacle avoidance.

[0017] Based on the initial control signal and the rated control input signal, the actual formation maneuver control signal is obtained by solving the QP problem;

[0018] Based on the actual formation maneuver control signal, a composite controller is used to output the final actual formation control signal through a safety-critical control framework based on a disturbance observer. The disturbance observer outputs a disturbance estimate based on the control signal output by the composite controller and the state after follower control execution. The composite controller adjusts the actual formation maneuver control signal based on the disturbance estimate and outputs the final actual formation control signal.

[0019] In a second aspect, the present invention provides a ground-to-air heterogeneous cluster formation control system based on an adjustable funnel algorithm.

[0020] A ground-to-air heterogeneous cluster formation control system based on an adjustable funnel algorithm, comprising:

[0021] The air-ground heterogeneous cluster modeling module is used to build a dynamic model of the air-ground heterogeneous cluster and construct an undirected graph that represents the interactive topology of the air-ground heterogeneous cluster. The air-ground heterogeneous cluster includes several two-dimensional unmanned ground vehicles and several three-dimensional unmanned aerial vehicles. A virtual leader is set, and each individual in the air-ground heterogeneous cluster is a follower.

[0022] Formation maneuver control problem modeling module, which is used to model the distributed safety-critical formation maneuver control problem of air-ground heterogeneous clusters based on dynamic models and undirected graphs;

[0023] The controller design module is used to design a fully distributed dynamic compensator for each follower based on the modeling problem, a formation maneuver controller based on a tunable funnel algorithm, and then a composite controller using a safety-critical control framework based on a disturbance observer;

[0024] The formation maneuver control module is used to obtain the virtual leader signal and input it into the various controllers constructed to obtain the actual formation control signal of each follower and perform distributed safety-critical formation maneuver control on the followers.

[0025] In a third aspect, the present invention also provides an electronic device, comprising: a memory for storing executable instructions; and a processor for implementing the above-mentioned ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm when executing the executable instructions stored in the memory.

[0026] In a fourth aspect, the present invention also provides a computer-readable storage medium storing executable instructions for causing a processor to execute the executable instructions to implement the above-mentioned ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm.

[0027] In a fifth aspect, the present invention also provides a computer program product, which includes executable instructions, and the executable instructions are stored in a computer-readable storage medium; wherein, when the processor of the electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the above-mentioned ground-to-air heterogeneous cluster formation control method based on the adjustable funnel algorithm is implemented.

[0028] One or more of the above technical solutions have the following beneficial effects:

[0029] 1. This invention proposes a ground-to-air heterogeneous cluster formation control method and system based on an adjustable funnel algorithm. A fully distributed compensator is constructed for each vehicle in the cluster to estimate the leader signal. The compensator output is used to design a formation maneuver controller based on an adjustable funnel. This controller provides a flexible performance boundary for the funnel function, supporting formation maneuvers while allowing potential collision / obstacle avoidance actions. By developing a safety-critical control framework based on a disturbance observer and combining it with inequality constraints solved and derived using quadratic programming (QP), the actual formation maneuver control input is given. Finally, by combining this input with the disturbance compensation term, a composite controller is constructed to effectively suppress the impact of disturbances on safety and formation control performance. This invention achieves collision / obstacle avoidance and disturbance suppression for ground-to-air heterogeneous clusters by designing the above-mentioned distributed safety-critical formation maneuvering strategy based on the adjustable funnel method.

[0030] 2. The proposed method effectively solves the fully distributed formation maneuvering problem of heterogeneous air-ground swarm systems with cross-domain platform dynamics. Compared to existing hierarchical approaches, which require global knowledge of the leader's dynamics for the entire swarm, the proposed strategy only requires the leader's dynamic information to be locally accessible to its immediate neighbors. Furthermore, this method imposes no constraints on the external system matrix, and the control gain of each vehicle is determined independently, without leveraging global information. Compared to conventional approaches where tracking error depends on global information, the proposed strategy converges to a user-defined tight set.

[0031] 3. This invention constructs a tunable funnel-based formation maneuver controller by introducing a dynamic component capable of expanding the funnel boundary and a nonlinear transformation that inherently satisfies the initial constraints. When collision / obstacle avoidance behavior is activated, the funnel boundary dynamically adjusts to meet performance requirements, thereby achieving the control objective. When collision / obstacle avoidance behavior is inactive, the adjusted funnel boundary reverts to its original form at a specified exponential rate, thereby re-satisfying the original performance requirement. Compared to existing solutions, the proposed controller does not require modification to the control strategy, and the error of interest is constrained within the funnel performance bounds in all time intervals.

[0032] 4. Unlike existing robust safety-critical control methods based on CBFs, which rely on worst-case disturbances, the proposed safety-critical control framework based on a disturbance observer actively suppresses the effects of disturbances, significantly reducing the conservatism of the set of permissible safety inputs. Furthermore, compared with safety-critical control methods with disturbance compensation, the proposed safety-critical control framework based on a disturbance observer does not require precise knowledge of the initial estimation error and the dynamic characteristics of the disturbance, making it computationally simpler.

[0033] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0035] Figure 1 This is an overall flow chart of a ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm in an embodiment of the present invention;

[0036] Figure 2 Schematic diagram of air-ground heterogeneous cluster configuration and obstacle configuration in an embodiment of the present invention;

[0037] Figure 3 1 is a flowchart of a ground-to-air heterogeneous cluster formation control strategy according to an embodiment of the present invention;

[0038] Figure 4 Schematic diagram of the interaction topology and target formation configuration of the air-ground swarm in an embodiment of the present invention; (a) is the interaction topology of the air-ground swarm, and (b) is the target formation configuration;

[0039] Figure 5 Schematic diagram of the three-dimensional trajectory of the air-ground swarm formation movement in an embodiment of the present invention;

[0040] Figure 6 Schematic diagram of the two-dimensional trajectory of the air-ground swarm formation movement in an embodiment of the present invention;

[0041] Figure 7 is the error h after transformation in the embodiment of the present invention i,k (t) and its funnel boundary diagram; where h i,k (t),

[0042] Figure 8 Schematic diagram of the control obstacle function for all vehicles under different strategies in an embodiment of the present invention;

[0043] Figure 9 These are the example simulation results under different control strategies in the embodiments of the present invention; among them, (a) is the traditional funnel control strategy with a fixed funnel boundary; (b) is the traditional funnel control strategy when the initial value does not meet the funnel boundary conditions; (c) is the traditional safety critical control strategy; and (d) is the safety key control strategy. DETAILED DESCRIPTION

[0044] It should be noted that the following detailed descriptions are exemplary only and are intended to describe specific embodiments and provide further explanation of the present invention, and are not intended to limit the exemplary embodiments according to the present invention. Unless otherwise indicated, all technical and scientific terms used herein have the same meanings as those commonly understood by those of ordinary skill in the art to which the present invention belongs. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0045] The problem of formation maneuvering in heterogeneous air-ground swarms is to flexibly adjust the platoon configuration to meet collision / obstacle avoidance requirements when encountering an obstacle or when two vehicles approach each other. After passing the obstacle, all vehicles in the swarm will restore the target formation configuration. In this context, collision / obstacle avoidance becomes a key objective. Existing technologies to achieve this goal include potential function methods, model predictive control (MPC), and control barrier functions (CBFs). Potential function methods are limited by local minima caused by conflicting objectives, while MPC faces difficulties due to the high computational cost of predicting system dynamics. Therefore, to ensure collision / obstacle avoidance while balancing computational efficiency, we propose combining CBFs with quadratic programming (QP) for optimal control synthesis.

[0046] However, in safety-critical control using CBFs, disturbances can lead to unsafe or dangerous behaviors due to their strong dependence on accurate models. While robust CBFs have been proposed to address the impact of disturbances by considering worst-case disturbance scenarios to ensure safety, this design leads to a conservative set of safety inputs and can cause the QP infeasibility problem when the disturbance exceeds a certain level. To address this issue, CBFs based on disturbance observers have been widely used as an effective tool to ensure system safety and achieve disturbance rejection. However, their ultimate performance is affected by the initial magnitude and upper bound of the disturbance estimation error. Furthermore, the presence of disturbances and their estimation errors can affect the formation performance of heterogeneous air-ground swarms. To address this issue, funnel control has been widely used due to its ability to predetermine control performance under unknown disturbances. However, when vehicles need to achieve collision or obstacle avoidance, the global funnel performance cannot always be met. To this end, the funnel controller is often used as the nominal input to the QP to obtain a safety input signal. However, this safety input signal can be considered an input constraint, which can lead to non-fulfillment of the funnel performance.

[0047] To address the above issues, this paper proposes a ground-to-air heterogeneous swarm formation control method and system based on an adjustable funnel algorithm. First, a fully distributed compensator is constructed for each vehicle in the swarm (including both vehicles and aircraft) to estimate the leader signal. Second, a tunable funnel-based formation maneuver controller is designed using the compensator output. This controller provides flexible performance bounds for the funnel function, supporting formation maneuvers while allowing for potential collision / obstacle avoidance. Next, a safety-critical control framework based on a disturbance observer is developed, combined with quadratic programming (QP) solution and derived inequality constraints to provide the actual formation maneuver control input. Finally, this input is combined with a disturbance compensation term to construct a composite controller that effectively suppresses the impact of disturbances on safety and formation control performance. By designing this distributed safety-critical formation maneuver strategy based on the adjustable funnel method, collision / obstacle avoidance and disturbance suppression are achieved for air-to-ground heterogeneous swarms.

[0048] Example 1

[0049] This embodiment provides a ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm, such as Figure 1 As shown, the specific steps include:

[0050] Step S1: Construct a dynamic model of an air-ground heterogeneous cluster, building an undirected graph representing the interactive topology of the air-ground heterogeneous cluster. The air-ground heterogeneous cluster includes several two-dimensional unmanned ground vehicles and several three-dimensional unmanned aerial vehicles. A virtual leader is set, and each individual in the air-ground heterogeneous cluster is a follower.

[0051] In this embodiment, the meanings of the following symbols are clarified before modeling: R, R n 、R n×n and R ≥0 They represent the set of real numbers, the set of n-dimensional real vectors, the set of n×n-dimensional real matrices and the set of non-negative real numbers respectively; Z represents the set of integers; 1 N =[1,…,1] T ∈R N , while I N is the N×N dimensional identity matrix; represents the set {1,…,n}; ‖·‖ represents the Euclidean norm of a vector or the induced 2-norm of a matrix; L ∞ Represents the space of essentially bounded functions; square integrable functions are represented by L2; represents a stacked vector; [·] and vec{·} represent the ceiling operator and vectorization operator, respectively.

[0052] Firstly, the space-land heterogeneous cluster is modeled and a dynamic model of the space-land heterogeneous cluster is constructed.

[0053] In this embodiment, the air-ground heterogeneous cluster consists of multiple two-dimensional (2D) unmanned ground vehicles (UGVs) and multiple three-dimensional (3D) unmanned aerial vehicles (UAVs). a and M g Denote the set of UAVs and UGVs respectively. The construction of vehicle dynamic model is as follows: let the i-th (∈M a ) UAV's location is Its Euler angle is Then the dynamic model of the i-th UAV can be described as:

[0054]

[0055] In the above formula, o3=[0,0,1] T , represents angular velocity, g represents gravitational acceleration, Indicates its quality, Represents the rotation matrix, where SO(3): = {Y∈R 3×3 :YY T =I3,det(Y)=1}, is with The corresponding skew-symmetric matrix is, represents the inertia matrix, u z,i ∈R and Represent the control thrust and torque respectively, Indicates an unknown disturbance.

[0056] Furthermore, by establishing a virtual position control input Model (1) can be restated as:

[0057]

[0058] It should be noted that this embodiment mainly focuses on the formation maneuvering control of the UAV position, and attitude tracking is not considered.

[0059] For the construction of the UAV dynamic model, the i(∈M g The dynamic model of a UGV is:

[0060]

[0061] In the above formula, are position and direction vectors, are the translation and angular velocity vectors, in and denote the mass and moment of inertia of the i-th UGV, is the constant damping matrix, is the torque control input, is an unknown external disturbance signal, and Define the sensor location as where d i >0, the dynamic model of the i-th UGV can be rewritten as:

[0062]

[0063] in, and

[0064] Furthermore, for the sake of simplicity, for the i-th (∈M a ) UAV location system selects the following variables:

[0065] and

[0066] i(∈M g The variables of each UGV are defined as:

[0067]

[0068] Then, the dynamic model of the space-land heterogeneous cluster is expressed as:

[0069]

[0070] in, is the position of the i-th vehicle, if i∈M a Then n i =3, if i∈M g Then n i =2. i ∈R 3 is the position of the i-th vehicle, and i∈M g , p i =x i,1 ,i∈M a .

[0071] Secondly, an undirected graph is constructed to represent the topological structure of the interaction between air-ground heterogeneous clusters.

[0072] Specifically, by N a (≥1) UAV and N g The interactive topology of an air-ground heterogeneous cluster consisting of (≥1) UGVs is formally represented by an undirected graph G = (V, E), where V = {1,…,N} is N (=N a +N g ) a collection of vehicles, is a set of edges, and the adjacency matrix of graph G is A=[α il ] N×N, if l∈N i , then α il =1, otherwise α il =0, the Laplace matrix of graph G is L=[L il ] N×N , for i≠l, i,l∈V,L il =-α il ,and For the air-ground heterogeneous cluster, a virtual leader is set, and each individual in the air-ground heterogeneous cluster is a follower (the followers in the cluster are the N vehicles mentioned above). In order to formalize the information exchange topology between the virtual leader and other vehicles (i.e., follower individuals), define B = diag{α 10 ,…,α N0}, where α i0 =1 means the i-th vehicle can access the navigator information, α i0 = 0 means no access, the neighbors of the i-th car are represented as

[0073] Step S2: Based on the dynamic model and undirected graph, the distributed safety-critical formation maneuvering control problem of the air-ground heterogeneous cluster is modeled.

[0074] This example focuses on the distributed formation maneuvering control of air-ground heterogeneous swarms in an obstacle-dense environment. The target formation configuration is specified as follows based on the relative positions of the vehicles:

[0075] F={(p1,p0)∈R 3N+3 :p i -p l =s il , },

[0076] Where p1=col{p1,…,p N}∈R n Represents the position vector of all vehicles; s il ∈R 3 It represents the expected position deviation between the i-th vehicle and the l-th vehicle, and its calculation formula is s {il} =s {i0} -s {l0} ;s i0 ∈R 3 represents the expected position deviation between the leader and the i-th vehicle; p0∈R 3 Represents the pilot signal, which is generated as follows:

[0077]

[0078] in, represents the state vector of the navigator; F T=[13,0 3×1 ] T ∈R 6 is a constant matrix; A∈R 6×6 is a constant matrix.

[0079] like Figure 2 The heterogeneous clusters and obstacle configurations shown in the figure are: x ,I y ,I z} represents the inertial coordinate system, each vehicle has a safety radius r i >0, and the area radius R (>r i ).set up Assume that there is N o ≥0 obstacles, each obstacle is represented by a The Euclidean region centered at in The boundary of Indicates. Figure 2 As shown, the obstacle is modeled as a sphere with a boundary of in Indicates its radius. In addition, they are x OI y The projection on the plane also constitutes an obstacle, prohibiting any vehicle from passing. Therefore, for physical safety reasons, each vehicle must maintain a safe distance from other vehicles and external obstacles. and satisfy and Then the space-ground heterogeneous cluster is called safe. a , For i∈M g , yes The projection of r ij =max{r i ,r j},and

[0080] For the distributed safety-critical formation maneuvering control problem of heterogeneous air-ground clusters (i.e., Problem 1), the task is to find the control input u in a distributed manner. i (t), so that: all UAVs and unmanned vehicles can be guided to the leader signal p0(t); when encountering an obstacle or two vehicles approaching each other, the formation configuration can be dynamically adjusted to meet the collision / obstacle avoidance criteria; once the obstacle is passed, all vehicles in the air-ground heterogeneous cluster will return to the target formation configuration F.

[0081] Modeling the above problem 1 is equivalent to:

[0082]

[0083] as well as:

[0084]

[0085] If the collision / obstacle avoidance behavior is not activated, for all t≥0, and where p′0(t)=p0(t), for i∈M a , s′ i =s i For i∈M g and s′ i =col{s i,1 ,s i,2},in is the projection of p0, is an arbitrarily preset constant.

[0086] To solve the above problem 1, the following standard assumptions are required:

[0087] Assumption 1: Assume that there is a spanning tree in G, with root vehicle i r Can access the information of the navigator, i.e. α ir,0 >0.

[0088] Assumption 2: The initial position of each vehicle is outside the obstacle area and will not collide with other vehicles, that is, for all and There is ‖x i,1 (0)-p′ o,l ‖>r iol and ‖p i -p j ‖>r ij In addition, the target formation configuration F is feasible, that is, for all There are ‖s ij ‖>r ij .

[0089] Assumption 3: Perturbation is Lipschitz continuous in t, with a Lipschitz constant δ for all t ≥ 0 i >0.

[0090] To explain the above assumptions, note 1: Assumption 1 is a standard condition that makes the realization of formation control possible; Assumption 2 ensures that each vehicle maintains a safe distance from other vehicles and external obstacles at the initial position; Assumption 3 is an existing conventional assumption used to ensure that the instantaneous change of interference is not too large. In addition, it should be emphasized that δ can be estimated by applying existing reasoning techniques. i ,This technique utilizes a limited dataset collected from the system.

[0091] Step S3: Based on the modeling problem, a fully distributed dynamic compensator for each follower and a formation maneuver controller based on an adjustable funnel algorithm are designed. Then, a safety-critical control framework based on a disturbance observer is adopted to construct a composite controller.

[0092] In this embodiment, a distributed safety-critical formation maneuvering control strategy based on an adjustable funnel is proposed. This strategy constructs a composite controller for air-ground heterogeneous clusters by designing a fully distributed dynamic compensator, a formation maneuvering controller based on an adjustable funnel, and applying a safety-critical control method based on a disturbance observer.

[0093] Step S3.1: Design a fully distributed dynamic compensator.

[0094] In order to estimate the leader information, a fully distributed dynamic compensator is constructed for the i-th vehicle as:

[0095]

[0096] in, represents the estimated value of v; represents the estimated value of A; Express estimated value of; is a gain parameter. c i,1 and c i,2 is an adaptive parameter with a positive initial value, and its law is given by:

[0097]

[0098] in, is the gain parameter, κ i ∈R represents the estimated value of κ0: κ0: = min{a∈Z:a>‖A‖}, only when α i0 It is only applicable when > 0. The following theorem holds.

[0099] Based on the above fully distributed dynamic compensator, Theorem 1 is clearly stated: If Assumption 1 holds, then the compensator state converges asymptotically to the corresponding estimated value through the fully distributed dynamic compensator (9) with the parameter update rule (10), that is,

[0100] The stability of the fully distributed dynamic compensator is proved by the following parts:

[0101] Part 1: First, let Then, according to (9) and (10), and The error dynamics can be expressed as From this we get and converges asymptotically to zero with a convergence rate of at least Under Assumption 1, since L+B is positive definite, there exists a finite time T such that -∈<κ for all t>T and ò<0.5 i (t)-κ0<∈. From κ0, It can be concluded that That is, all agents obtain the same upper bound of ‖A‖ after time T.

[0102] Part II: We only consider the evolution of the compensator on [T,∞), since all values ​​of the compensator and parameters are bounded on [0,T].

[0103] For convenience, it is recorded as And C2=diag{c 1,2 ,…,c N,2}. Then, from (9) and (10) we can derive:

[0104]

[0105] The candidate Lyapunov function is chosen as:

[0106]

[0107] Wherein, c2>0 is a constant to be specified.

[0108] Taking its time derivative along (12), we have:

[0109]

[0110] On this basis, we choose c2≥κ0λ max {(L+B) -1}+1 to get Furthermore, there are and ζ∈L2, because By definition Existence limit lim t→∞ f(t). Due to ζ, is also bounded. Using Barbara's lemma, we have lim t→∞ ζ=0 6×1 ,this means There is a limit

[0111] Part III: To express and From (9) and (10) we can see that:

[0112]

[0113] set up C1=diag{c 1,1 ,…,c N,1}, we can get the following compact form:

[0114]

[0115] Additionally, choose a candidate Lyapunov function:

[0116]

[0117] in, is a constant, c1>0 is a constant to be specified.

[0118] The time derivative is obtained according to formula (16):

[0119]

[0120] According to Young's inequality, we have:

[0121]

[0122] because And κ0>‖A‖, so we can get:

[0123]

[0124] For two constants By combining (20) and (21) into (19), we obtain

[0125]

[0126] Depend on It can be concluded that:

[0127]

[0128] choose get Similar to the second part, we can derive

[0129] Remark 2: The assumption that the matrix A in (6) is marginally stable is mitigated by using to estimate an upper bound on ‖A‖ such that all vehicles reach the same upper bound in finite time. Subsequently, the adaptation law can be formulated to eliminate the need for global information. Importantly, κ0 is only accessible to neighbors outside the system, which indicates that the proposed compensator (9) is fully distributed.

[0130] Step S3.2: Design a formation maneuver controller based on an adjustable funnel.

[0131] Based on the obtained compensator status This embodiment mainly seeks to drive x i,1 To track At the same time, the interference is canceled, and for F i T =[12,0 4×1 ] T ∈R 6 , i∈M g , and F i T =F,i∈M a , first define the error variable Its dynamics is Then the adjustable funnel formation maneuver controller is designed as:

[0132]

[0133] Among them, α i is the intermediate controller, i =‖z i,2 ‖ / ρ i (t), z i,2 =x i,2 -α i ,λ i ,l i ,ν i , is the design parameter, ρ i (t) is the funnel function, is the actual input for handling collision / obstacle avoidance, which will be designed later; the initial value ρ i (0) is chosen large enough so that ρ i (0)>‖z i,2 (0)‖, to ensure that the variable ξ i (0) is well defined.

[0134] Based on the above controller, Theorem 2 is formulated: Considering the air-ground swarm (4) and the virtual leader (6), and assuming that Assumptions 1–3 are satisfied, if a fully distributed dynamic compensator (9) and controller (24) are implemented, then all states are uniformly bounded, and when the collision / obstacle avoidance behavior is inactive, the limit

[0135] Proof: From (24), z i,1 The derivative of is:

[0136]

[0137] By solving (25), we can get By taking the induced 2-norm yield, we get:

[0138]

[0139] in, Is used to ensure i ∈(-1,1), where It is given later. Through the following content, it is proved that It can be guaranteed i (t)∈(-1,1).

[0140] First, the existence of a unique (local) solution is established. Consider the following open set:

[0141]

[0142] Among them, x i =col{x i,1 ,x i,2}. From (4) and (24) we can conclude that:

[0143]

[0144] because By the condition ρ i (0)>‖z i,2 (0)‖derived, and Φ i (x i ,ρ i ) is measurable in t, in col{x i ,ρ i} is locally Lipschitz continuous, t M ∈(0,∞] when the maximum solution In addition, It is certain. i ,ρ i ) is not a closure is a compact subset of . Therefore, we can get From (4), we can derive:

[0145]

[0146] in, because If it holds, then ρ i >0, which results in Therefore, when hour,

[0147] Secondly, explain ‖z i,2 (t)‖≤ε i ρ i (t), Some of these i ∈(0,1) satisfies:

[0148]

[0149] in, And σ i ,ι i >0 is and The upper bound of , that is, because and The local Lipschitz continuity of will be given in the following.

[0150] Assume there is a time t1∈(0,t M ) satisfies ‖z i,2 (t1)‖>ε i ρ i (t1), where ε i ∈(0,1). From ‖z i,2 (0)‖≤ε i ρ i (0), the following definition is clear:

[0151] t0:=max{t∈[0,t1):‖z i,2 (t)‖≤ε i ρ i (t)}.(30)

[0152] Therefore, it produces ‖z i,2 (t)‖≥ε i ρ i (t) and For t∈[t0,t1]). By Taking the time derivative, we get:

[0153]

[0154] Therefore, from (24) we can conclude that: Then you can get:

[0155]

[0156] Based on (29), it produces And when integrating, we get:

[0157]

[0158] This leads to a contradiction:

[0159] 0=ε i ρ i (t0)-‖z i,2 (t0)‖≤ε i ρ i (t1)-‖z i,2 (t1)‖<0(34)

[0160] Finally, assuming t M <∞, from the above analysis we can get ‖z i,2 (t)‖≤ε i ρ i (t), because is closest to u i signal, and satisfying the collision / obstacle avoidance constraints shown in the next subsection, for the constant have according to when Therefore, there is a constant Make

[0161] make:

[0162]

[0163] Since for all [0,t M ) This leads to a contradiction. Therefore, we get t M =∞. Therefore, it produces ξ i (t)∈(-1,1), This means, According to the definition of z i,1 and z i,2 , we can conclude that all states are uniformly bounded if but That is, the collision / obstacle avoidance behavior is not active.

[0164] Remark 3: The key feature of the controller (24) is its feasibility in an environment with obstacles. The controller (24) always ensures that z is within the performance funnel. i,2 The evolution of the dynamic component OK. i In the differential equation, the term Determines the activation state of the collision / obstacle avoidance behavior, where It is active when If the collision / obstacle avoidance behavior is inactive, then Conversely, when the collision / obstacle avoidance behavior is active, right Make positive contributions, thereby expanding the funnel. The larger the deviation between the two, the greater the widening effect. Once the collision / obstacle avoidance behavior is completed, the boundary will expand exponentially. Return to the specified shape.

[0165] Remark 4: Observe that the controller (24) requires the condition ρ i (0)>‖z i,2 (0)‖, which means that the initial error is known or within a known range. Under this condition, the controller is effective and the transient performance of the error (such as overshoot and convergence speed) can be preset. However, when the initial error is unknown, in order to ensure the validity of this condition, it is necessary to i (0) Choose a sufficiently large initial value. Therefore, in order to remove the initial condition, i Redefined as ξ i =‖h i ‖ / ρ i (t), and select in Through nonlinear transformation And ω i >1, Then, the control input is redesigned as:

[0166]

[0167] Because h i,k The definition of h i,k < 1, for any z i,2 (0), which gives That is to say, i (0)∈(-1,1), so this nonlinear transformation inherently satisfies the initial constraint. In addition, similar to the proof in Theorem 2, it can be checked that ξ i (t)∈(-1,1), and |h i,k|≤‖h i ‖<ρ i (t). Then, from h i,k The definition of This gives the limit Therefore, if the collision / obstacle avoidance behavior is not active, the limit is obtained

[0168] Step S3.3: Use the disturbance observer-based safety-critical control framework to construct a composite controller and design a disturbance observer-based safety-critical control method.

[0169] In this embodiment, the CBF method is used to ensure collision-free formation maneuvers. In order to characterize the safety goals between vehicles, Similarly, this embodiment introduces To capture the i-th vehicle and the According to Question 1, all vehicles can achieve collision-free driving if the following conditions are met:

[0170]

[0171] in, Since the relative order of the open-space group is 2 (relative order refers to the minimum number of derivatives required from the control input u to the output y in a control system), the exponential CBF method is used, and the constraint set is then defined as:

[0172]

[0173] in, and μ i,1 >0.

[0174] Assumptions If the collection and is forward-invariant, then C can be guaranteed i,0 and C ij,0 It is worth noting that when the interference When there is a disturbance, the safety characteristics of the system (4) may be destroyed and its control performance may also deteriorate. Therefore, a disturbance observer is constructed for each vehicle to estimate the disturbance It is expressed as:

[0175]

[0176] in, yes The estimated value of It is the auxiliary state. is a diagonally positive definite observer design matrix, and and χ i The initial value of (t) is set to zero.

[0177] Lemma 1: Consider a time-varying signal And satisfy assumption 2 and have Lipschitz constant δ i The error dynamics of the interference observer exist Nearby is the input-state stable.

[0178] Proof: Define the interference estimation error as Then we have:

[0179]

[0180] Consider a candidate Lyapunov function right Taking the derivative along (42), we get Then applying Young's inequality we can get therefore:

[0181]

[0182] in, This formula ensures Input-state stability of the neighborhood.

[0183] Furthermore, based on the above disturbance estimation, the composite controller is designed as follows:

[0184]

[0185] Where, is the state feedback item, is the disturbance compensation term. Under this controller, x i,2 The kinetic equation is:

[0186] make and where μ i and μ j Is a positive constant. Define a new safe set as:

[0187] C ij,2 ={(p i ,p j )∈R 3 ×R 3 :b 2,ij (p i ,p j )≥0}(45)

[0188]

[0189] From this we can see that and The original security set C ij,1 and The forward invariance of is transformed into a new security set C ij,2 and The forward invariance is guaranteed.

[0190] Theorem 3: Under assumptions 2 and 3, for the air-ground system (4) using the composite controller (44) and the disturbance observer (41), if the initial conditions satisfy (x i,1 (0)),b 2,ij (p i (0),p j (0))>0, and satisfies:

[0191]

[0192] in, and Corresponding to i∈M g and v i =x i,2 as well as Corresponding to i∈M a and μ i,2 >0, then the safe set is forward-invariant.

[0193] Proof: From Lemma 1, we can see that to b 2,ij Taking the time derivative, we get:

[0194]

[0195] By completing the square and scaling, we can get:

[0196]

[0197] According to (47), we can conclude that:

[0198]

[0199] Therefore, if b 2,ij (p i (0),p j (0))>0, Then, we can test b 2,ij ≥0. Similarly, take The time derivative of , we can get:

[0200]

[0201] Using (48), we can get This means that the security set It is also forward-looking.

[0202] Note 5: According to (43) and b 2,ij and From the definition of , we can conclude that as time approaches infinity, b 2,ij and will be close to b 1,ij and Therefore, compared to robust safety-critical control methods that rely on worst-case disturbances, the proposed strategy can achieve a wider set of safe inputs while effectively resisting disturbances. Moreover, the conditions derived in (47) and (48) do not depend on the initial estimation error and relax the assumptions, replacing the need for an accurate disturbance model with the requirement of Lipschitz continuity.

[0203] Furthermore, considering that the inequality condition (47) involves It contains the neighbor information of the jth vehicle, so it is non-distributed and difficult to calculate. To solve this problem, the inequality condition (47) is decomposed into two independent conditions, resulting in the following distributed inequality condition:

[0204]

[0205] It can be proved that when inequality condition (53) is satisfied, inequality condition (47) is also satisfied.

[0206] Therefore, the actual formation maneuver control input is determined by solving the following QP problem:

[0207]

[0208] in, represents the nominal control input given in (36). The solution to the optimization problem (54) is to ensure that each vehicle can achieve the funnel formation maneuver as much as possible, that is, to minimize In addition, for x i,1 As for (54), the solution is locally Lipschitz continuous, where Int(·) represents the interior of ·.

[0209] Step S4: Acquire the virtual leader signal and input it into the constructed multiple controllers to obtain the actual formation control signal of each follower, and perform distributed safety-critical formation maneuver control on the followers.

[0210] Based on the above steps, the distributed safety-critical funnel formation manipulation control strategy is implemented as follows: Figure 3 As shown in the figure, a virtual leader signal is acquired and estimated using a fully distributed dynamic compensator to obtain the estimated leader state for each follower. Based on the leader estimated state, a formation maneuver controller based on an adjustable funnel algorithm outputs an initial control signal for handling collision and obstacle avoidance. Based on the initial control signal, combined with the rated control input signal, the actual formation maneuver control signal is obtained by solving the QP problem. Based on the actual formation maneuver control signal, a composite controller is used to output the final actual formation control signal through a safety-critical control framework based on a disturbance observer. The disturbance observer outputs a disturbance estimate based on the control signal output by the composite controller and the state after follower control execution. The composite controller adjusts the actual formation maneuver control signal based on the disturbance estimate and outputs the final actual formation control signal.

[0211] The stability results corresponding to the above control strategy can be found in the following theorem, namely:

[0212] Theorem 4: Consider an air-ground swarm (4) with a virtual leader (6) and a distributed safety-critical funnel formation maneuvering control strategy (9), including a fully distributed dynamic compensator with adaptive law (10), an adjustable funnel-based formation maneuvering controller (24), an improved control input (36), a disturbance observer (41), a composite controller (44), and an actual formation maneuvering control input (54). If assumptions 1-3 hold, then all signals are uniformly bounded, inter-vehicle collisions and obstacle collisions are avoided, and the formation error e i :=x i,1 (t)-p′0(t)-s′ i Converges to a predefined set, and converges to t→∞ when the collision / obstacle avoidance behavior is inactive. That is, Problem 1 is solved.

[0213] Proof: First, according to Lemma 1 and Theorems 1-3, all signals are uniformly bounded. Then, by Theorem 3 and the control strategy based on quadratic programming (54), it can be proved that by using and the composite controller (44), since the constraints in (48) and (53) are satisfied, collisions between vehicles and obstacles are avoided. In addition, according to Theorems 1-2 and Remark 4, it can be concluded that: and and The collision / obstacle avoidance behavior of is inactive. It converges to a predefined set at t→∞, namely

[0214] Furthermore, this embodiment uses an air-ground swarm (including three drones and three unmanned underwater vehicles) to conduct numerical simulations to verify the effectiveness of the proposed strategy. The interaction topology and target formation configuration that meet assumption 1 are as follows: Figure 4 As shown, the three drones are indexed 1 to 3, the three UGVs are indexed 4 to 6, and the virtual leader (i.e., the leading aircraft) is indexed 0.

[0215] The virtual leader signal is selected as p0(t) = [0.6t+2.1, 0.72sin(0.2t+1), 0.1t+0.5] T (m), which can be generated by (6), the vehicles need to maintain the formation configuration F as shown in the figure, such as Figure 4 As shown, its shape is two equilateral triangles, and the required position deviations are listed in Table 1 below.

[0216] Table 1 The position deviation required for each individual in the ground-air bee swarm

[0217]

[0218] Among them, the physical parameters of the open space bee colony are set as follows: g=9.81(m / s 2 ), i∈M a :={1,2,3}, d i =0.15(m) and i∈M g :={4,5,6}, where the initial position lists the positions and radii of seven spherical obstacles; the safety distance and detection distance of each vehicle are set to r i =0.2(m) and R=1.5(m); external interference is and

[0219] In the proposed strategy, the parameters of the fully distributed dynamic compensator are The parameters of the funnel forming maneuver controller are set as: i =1,l i =2, ν i =0.5.

[0220] Observer gain matrix L i The diagonal elements of are set to 40, so In addition, select δ i =6,μ i,1 =μ i,2 =3,μ i =1, then γ i =0.45. The initial value is as follows And the initial values ​​of all adaptive laws are set to 1. The simulation results are as follows Figure 5-7 As shown. Figure 5 As shown in Figure 2, under the proposed distributed safety-critical funnel formation maneuvering strategy, the six vehicles can adaptively adjust the formation shape to avoid collision when approaching an obstacle (as shown by the black ball and its projection), and after crossing the obstacle, they will quickly restore the target formation configuration after the leader sends a signal p0. A clearer illustration of the formation configuration change can be found in Figure 2. Figure 6 .like Figure 7 As shown in , the transformed error has been evolving in the funnel. It is worth noting that when the collision / obstacle avoidance behavior is active, the transformed error leaves the initial performance funnel but remains within the expanded funnel. It is also worth noting that after crossing the obstacle, the funnel boundary exponentially converges to The transformation error is therefore again kept within the ideal region. Figure 8 This is a schematic diagram of the control obstacle function of all vehicles under the strategy proposed in this embodiment, which shows the control obstacle function of all vehicles. It can be seen from the figure that all control obstacle functions are greater than zero at all times, which means that the safety goal has been achieved, that is, the strategy proposed in this embodiment can achieve obstacle avoidance.

[0221] In order to illustrate the superiority of the control strategy proposed in this embodiment, the traditional funnel control scheme with fixed funnel boundary, the traditional funnel controller when the initial value does not meet the funnel boundary condition, the traditional safety critical control strategy without disturbance attenuation and the robust safety critical control based on CBF are also applied to this example. The simulation results are shown in Figure 2. Figure 9 As shown, different colors represent the control obstacle functions corresponding to different obstacles. Figure 9 As shown in (a), the traditional funnel control strategy with fixed funnel boundaries cannot keep the transformation error within these boundaries when encountering obstacles, and thus cannot successfully complete the control task; Figure 9 As shown in (b), when the initial transformation error does not satisfy the funnel boundary, the traditional funnel controller is infeasible; Figure 9 As shown in (c), the solid line represents the CBF under this strategy, and the dotted line represents the no-disturbance attenuation. In the case of the traditional safety critical control strategy without disturbance attenuation of the control obstacle function, the CBF will exceed 0, resulting in a collision; Figure 9 As shown in (d), the solid line represents the CBF under the proposed strategy, and the dotted line represents the strategy based on robust CBF. Both strategies can ensure the safety of the system, and the trajectory of the CBF in the proposed strategy evolves almost completely within the constraint tolerance set. This is because the strategy proposed in this embodiment greatly reduces the conservatism of the allowed safe input set. In addition, compared with Figure 9 Compared with the traditional safety-critical control strategy based on robust control barrier function shown in FIG, the strategy proposed in this embodiment ensures excellent control performance while ensuring safety.

[0222] Example 2

[0223] This embodiment provides a ground-to-air heterogeneous cluster formation control system based on an adjustable funnel algorithm, including:

[0224] The air-ground heterogeneous cluster modeling module is used to build a dynamic model of the air-ground heterogeneous cluster and construct an undirected graph that represents the interactive topology of the air-ground heterogeneous cluster. The air-ground heterogeneous cluster includes several two-dimensional unmanned ground vehicles and several three-dimensional unmanned aerial vehicles. A virtual leader is set, and each individual in the air-ground heterogeneous cluster is a follower.

[0225] Formation maneuver control problem modeling module, which is used to model the distributed safety-critical formation maneuver control problem of air-ground heterogeneous clusters based on dynamic models and undirected graphs;

[0226] The controller design module is used to design a fully distributed dynamic compensator for each follower based on the modeling problem, a formation maneuver controller based on a tunable funnel algorithm, and then a composite controller using a safety-critical control framework based on a disturbance observer;

[0227] The formation maneuver control module is used to obtain the virtual leader signal and input it into the various controllers constructed to obtain the actual formation control signal of each follower and perform distributed safety-critical formation maneuver control on the followers.

[0228] Example 3

[0229] This embodiment provides an electronic device, including: a memory for storing executable instructions; and a processor for implementing the above method provided in this embodiment when executing the executable instructions stored in the memory.

[0230] Example 4

[0231] This embodiment further provides a computer-readable storage medium storing executable instructions. When the executable instructions are executed by a processor, the processor will be caused to execute the above method provided in this embodiment.

[0232] Example 5

[0233] This embodiment provides a computer program product including executable instructions, which are computer instructions stored in a computer-readable storage medium. When a processor of an electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the electronic device performs the method provided in this embodiment.

[0234] The steps involved in the above embodiments 2 to 5 correspond to those in embodiment 1. For detailed implementation, please refer to the relevant description of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media that includes one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and cause the processor to perform any method of the present invention.

[0235] Those skilled in the art will appreciate that the modules or steps of the present invention described above can be implemented using a general-purpose computer device. Alternatively, they can be implemented using program code executable by a computing device, which can then be stored in a storage device and executed by the computing device. Alternatively, they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0236] The above description is only a preferred embodiment of the present invention. Although the specific implementation of the present invention is described in conjunction with the accompanying drawings, it does not limit the scope of protection of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present invention.

Claims

1. A ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm, characterized in that: include: Build a dynamic model of an air-ground heterogeneous cluster and construct an undirected graph representing the interactive topology of the air-ground heterogeneous cluster. The air-ground heterogeneous cluster consists of several two-dimensional unmanned ground vehicles and several three-dimensional unmanned aerial vehicles. A virtual leader is set, and each individual in the air-ground heterogeneous cluster is a follower. Based on dynamic models and undirected graphs, the distributed safety-critical formation maneuvering control problem of heterogeneous air-ground clusters is modeled. Based on the modeling problem, a fully distributed dynamic compensator for each follower and a formation maneuver controller based on an adjustable funnel algorithm are designed. Then, a composite controller is constructed using a safety-critical control framework based on a disturbance observer. The virtual leader signal is acquired and input into various controllers to obtain the actual formation control signal of each follower, and distributed safety-critical formation maneuver control is performed on the followers.

2. The ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm according to claim 1, characterized in that: The virtual leader signal is obtained and input into the various controllers constructed to obtain the final actual formation control signal for each follower, including: Obtain the virtual leader signal and use a fully distributed dynamic compensator to estimate the leader's estimated state for each follower. Based on the leader's estimated state, a formation maneuver controller based on an adjustable funnel algorithm is used to output initial control signals for collision / obstacle avoidance. Based on the initial control signal and the rated control input signal, the actual formation maneuver control signal is obtained by solving the QP problem; Based on the actual formation maneuver control signal, a composite controller is used to output the final actual formation control signal through a safety-critical control framework based on a disturbance observer. The disturbance observer outputs a disturbance estimate based on the control signal output by the composite controller and the state after follower control execution. The composite controller adjusts the actual formation maneuver control signal based on the disturbance estimate and outputs the final actual formation control signal.

3. The ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm according to claim 1, characterized in that: The distributed safety-critical formation maneuver control problem is: The formation control input of each follower is sought in a distributed manner so that: the dynamic models of all followers are guided by the leader's signal; when encountering obstacles or two followers approaching each other, the formation configuration can be dynamically adjusted to meet the collision / obstacle avoidance criteria; Once the obstacle is passed, all individuals in the air-ground heterogeneous cluster will return to the target formation configuration.

4. The ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm according to claim 1, characterized in that: The fully distributed dynamic compensator constructed for the i-th vehicle is: in, represents the estimated value of v; represents the estimated value of A; Express estimated value of; is a gain parameter; c i,1 and c i,2 is an adaptive parameter with a positive initial value, and its law is: in, is the gain parameter, κ i ∈R represents the estimated value of κ0: κ0: = min{a∈Z:a>‖A‖}, only when α i0 Available only when >0.

5. The ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm according to claim 1, characterized in that: The formation maneuver controller based on the adjustable funnel algorithm is: Among them, α i is the intermediate controller, i =‖z i,2 ‖ / ρ i (t), z i,2 =x i,2 -α i , is the design parameter, ρ i (t) is the funnel function, is the actual input for processing collision / obstacle avoidance, and the initial value ρ i (0) is chosen large enough so that ρ i (0)>‖z i,2 (0)‖, to ensure that the variable ξ i (0) is well defined; Will i Redefined as ξ i =‖h i ‖ / ρ i (t), and select in Through nonlinear transformation And ω i >1, The transformation error is , then the control input is redesigned as:

6. The ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm according to claim 1, characterized in that: The disturbance observer is: in, yes The estimated value of It is the auxiliary state. is a diagonally positive definite observer design matrix, and and χ i The initial value of (t) is set to zero.

7. A ground-to-air heterogeneous cluster formation control system based on an adjustable funnel algorithm, characterized in that: include: The air-ground heterogeneous cluster modeling module is used to build a dynamic model of the air-ground heterogeneous cluster and construct an undirected graph that represents the interactive topology of the air-ground heterogeneous cluster. The air-ground heterogeneous cluster includes several two-dimensional unmanned ground vehicles and several three-dimensional unmanned aerial vehicles. A virtual leader is set, and each individual in the air-ground heterogeneous cluster is a follower. Formation maneuver control problem modeling module, which is used to model the distributed safety-critical formation maneuver control problem of air-ground heterogeneous clusters based on dynamic models and undirected graphs; The controller design module is used to design a fully distributed dynamic compensator for each follower based on the modeling problem, a formation maneuver controller based on a tunable funnel algorithm, and then a composite controller using a safety-critical control framework based on a disturbance observer; The formation maneuver control module is used to obtain the virtual leader signal and input it into the various controllers constructed to obtain the actual formation control signal of each follower and perform distributed safety-critical formation maneuver control on the followers.

8. An electronic device, characterized in that: include: a memory for storing executable instructions; The processor is configured to implement the ground-to-air heterogeneous cluster formation control method based on an adjustable funnel algorithm as described in any one of claims 1 to 6 when executing the executable instructions stored in the memory.

9. A computer-readable storage medium, characterized in that Executable instructions are stored, which are used to cause the processor to execute the executable instructions to implement the ground-to-air heterogeneous cluster formation control method based on the adjustable funnel algorithm as described in any one of claims 1-6.

10. A computer program product, characterized in that The computer program product includes executable instructions stored in a computer-readable storage medium; When the processor of the electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the ground-to-air heterogeneous cluster formation control method based on the adjustable funnel algorithm described in any one of claims 1 to 6 is implemented.

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