Helicopter safe flight boundary determination method, apparatus, device, medium and product

Abstract

The application discloses a kind of helicopter safety flight boundary determination method, device, equipment, medium and product, it is related to helicopter technical field, the method includes obtaining the mass center speed vector of helicopter, attitude angle vector and angular velocity vector;According to mass center speed vector, attitude angle vector and angular velocity vector utilize helicopter dynamics characteristics to construct helicopter nonlinear model and constraint range;According to the helicopter nonlinear model and the constraint range utilize alpha shape method and heuristic algorithm to determine helicopter attitude angle rate safety boundary;According to the helicopter attitude angle rate safety boundary utilizes DFoG method to determine helicopter attitude angle safety boundary;According to helicopter nonlinear model, the helicopter attitude angle rate safety boundary, the helicopter attitude angle safety boundary and the constraint range determine helicopter speed safety boundary, the application can improve the accuracy of helicopter safety flight boundary.

Description

Technical Field

[0001] This application relates to the field of helicopter technology, and in particular to a method, apparatus, equipment, medium and product for determining the safe flight boundary of a helicopter. Background Technology

[0002] Helicopters are controllable during normal flight. However, due to factors such as weather, signal interference, and the aircraft's own maneuverability, a helicopter's flight attitude may exceed a predetermined threshold and fail to return to a safe range. This situation can cause the helicopter to lose control, seriously endangering flight safety and potentially leading to a major flight accident. Safe flight boundary protection is an important way to mitigate the hazards of flight loss of control. Safe flight boundary protection aims to prevent aircraft from exceeding their ultimate safe flight boundaries. The prerequisite for designing a safe flight boundary protection system is to determine the corresponding safe flight boundaries.

[0003] Studies have shown that changes in the state parameters of a helicopter during flight are closely related to its flight safety. Flight loss of control is a dangerous flight condition where the aircraft's state parameters are out of control. During this process, the aircraft experiences severe, irregular shaking and its next flight state is unpredictable. Most major helicopter accidents are caused by this, and solving this problem requires considering all aspects of the flight process, making it an extremely complex issue. Therefore, it is crucial to find the controllable threshold for helicopter flight and limit its flight state within a safe range to ensure safe and stable flight. However, once the helicopter exceeds this safe threshold, numerous state parameters of the helicopter change rapidly, exhibiting irregular interactions, and the intensity of these interactions varies among different parameters. Therefore, determining the boundary values ​​of the safe state parameters is particularly important. If the boundary values ​​are too small, the aircraft's flight performance cannot be fully utilized; if the boundary values ​​are too large, the aircraft may already be in a dangerous state within the boundaries. Therefore, it is necessary to accurately determine the safe flight boundaries of helicopters to fully utilize their flight performance while ensuring flight safety. Summary of the Invention

[0004] The purpose of this application is to provide a method, apparatus, equipment, medium, and product for determining the safe flight boundary of a helicopter, which can improve the accuracy of the safe flight boundary of a helicopter.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] Firstly, this application provides a method for determining the safe flight boundary of a helicopter, including:

[0007] Obtain the helicopter's center of mass velocity vector, attitude angle vector, and angular velocity vector;

[0008] Based on the centroid velocity vector, attitude angle vector, and angular velocity vector, a nonlinear model and constraint range for the helicopter are constructed using the helicopter's dynamic characteristics.

[0009] Based on the helicopter nonlinear model and the constraint range, the helicopter attitude angular rate safety boundary is determined using the alpha shape method and heuristic algorithm.

[0010] The helicopter attitude angle safety boundary is determined using the DFoG method based on the aforementioned helicopter attitude angular rate safety boundary.

[0011] The helicopter speed safety boundary is determined based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range.

[0012] In one embodiment, the helicopter attitude angular rate safety boundary is determined using the alpha shape method and heuristic algorithm based on the helicopter nonlinear model and the constraint range, specifically including:

[0013] The achievable equilibrium set of attitude angular rate is obtained by solving the nonlinear model of the helicopter and the constraint range.

[0014] The boundary of the 3D point set is calculated using the alpha shape method based on the reachable equilibrium set of the attitude angular rate;

[0015] Determine the inscribed cuboid within the boundary of the point set based on the boundary of the three-dimensional point set;

[0016] The attitude angular rate optimization problem is constructed based on the inscribed cuboid of the point set boundary.

[0017] Based on the attitude angular rate optimization problem, a heuristic algorithm is used to determine the safe boundary of the helicopter attitude angular rate.

[0018] In one embodiment, the heuristic algorithm is a particle swarm optimization algorithm.

[0019] In one embodiment, the helicopter attitude angle safety boundary is determined using the DFoG method based on the helicopter attitude angular rate safety boundary, specifically including:

[0020] The forward reachable set and the backward reachable set of attitude angles are determined based on the aforementioned helicopter attitude angular rate safety boundary;

[0021] The DFoG method is used to solve for the forward reachable set and the backward reachable set of the attitude angle, resulting in the discretized estimated forward reachable set and the discretized estimated backward reachable set of the attitude angle.

[0022] The boundaries of the discretized estimated attitude angle forward reachable set and the discretized estimated attitude angle backward reachable set are calculated using the alpha shape method;

[0023] Based on the boundaries of the discretized estimated attitude angle forward reachable set and the discretized estimated attitude angle backward reachable set, a heuristic algorithm is used to solve the problem, resulting in the first attitude angle inscribed cuboid and the second attitude angle inscribed cuboid.

[0024] The intersection of the cuboid inscribed in the first attitude angle and the cuboid inscribed in the second attitude angle is taken as the safety boundary of the helicopter attitude angle.

[0025] In one embodiment, a heuristic algorithm is used to solve for the boundaries of the discretized estimated attitude angle forward reachable set and the discretized estimated attitude angle backward reachable set, resulting in a first attitude angle inscribed cuboid and a second attitude angle inscribed cuboid, specifically including:

[0026] The first boundary is calculated using the alpha shape method based on the discretized estimated attitude angle forward reachable set;

[0027] The inscribed cuboid of the forward boundary is determined based on the first boundary.

[0028] Construct a forward optimization problem based on the inscribed cuboid of the forward boundary;

[0029] Based on the aforementioned forward optimization problem, a heuristic algorithm is used to determine the inscribed cuboid at the first attitude angle;

[0030] The second boundary is calculated using the alpha shape method based on the discretized estimated attitude angle backward reachable set;

[0031] The cuboid is inscribed within the second boundary based on the boundary.

[0032] Construct a backward optimization problem based on the inscribed cuboid of the backward boundary;

[0033] Based on the aforementioned backward optimization problem, a heuristic algorithm is used to determine the inscribed cuboid at the second attitude angle.

[0034] In one embodiment, the helicopter speed safety boundary is determined based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range, specifically including:

[0035] The forward and backward velocity reachable sets are determined based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range.

[0036] The DFoG method is used to solve for the forward and backward reachable sets of velocity, resulting in discretized estimated forward and backward reachable sets of velocity.

[0037] The boundaries of the forward reachable set and the backward reachable set of the discretized estimated velocity are calculated using the alpha shape method.

[0038] Based on the boundaries of the discretized estimated forward velocity reachable set and the discretized estimated backward velocity reachable set, a heuristic algorithm is used to solve for the first velocity inscribed cuboid and the second velocity inscribed cuboid.

[0039] The intersection of the cuboid inscribed in the first velocity and the cuboid inscribed in the second velocity is taken as the safety boundary for helicopter speed.

[0040] Secondly, this application provides a helicopter safe flight boundary determination device, comprising:

[0041] The acquisition module is used to acquire the helicopter's center of mass velocity vector, attitude angle vector, and angular velocity vector;

[0042] The module is used to construct a nonlinear model and constraint range of a helicopter based on the helicopter's dynamic characteristics using the center of mass velocity vector, attitude angle vector, and angular velocity vector.

[0043] The helicopter attitude angular rate safety boundary determination module is used to determine the helicopter attitude angular rate safety boundary based on the helicopter nonlinear model and the constraint range using the alpha shape method and heuristic algorithm.

[0044] The helicopter attitude angle safety boundary determination module is used to determine the helicopter attitude angle safety boundary using the DFoG method based on the helicopter attitude angular rate safety boundary.

[0045] The helicopter speed safety boundary determination module is used to determine the helicopter speed safety boundary based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range.

[0046] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the helicopter safe flight boundary determination method.

[0047] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the helicopter safe flight boundary determination method.

[0048] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the helicopter safe flight boundary determination method.

[0049] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0050] This application provides a method, apparatus, device, medium, and product for determining the safe flight boundaries of a helicopter. It constructs a nonlinear model and constraint range of the helicopter based on the center-of-mass velocity vector, attitude angle vector, and angular velocity vector using the helicopter's dynamic characteristics. Based on the nonlinear model and the constraint range, it determines the helicopter's attitude angular rate safety boundary using the alpha shape method and heuristic algorithms. Based on the attitude angular rate safety boundary, it determines the helicopter's attitude angle safety boundary using the DFoG method. Finally, it determines the helicopter's velocity safety boundary based on the nonlinear model, the attitude angular rate safety boundary, the attitude angle safety boundary, and the constraint range. By considering the center-of-mass velocity vector, attitude angle vector, and angular velocity vector, the state constraints of the helicopter during flight are determined. First, the helicopter's attitude angular rate safety boundary is determined, then the helicopter's attitude angle safety boundary is determined, and finally the helicopter's velocity safety boundary is determined. This iterative process, layer by layer, improves the accuracy of the helicopter's safe flight boundaries. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is an application environment diagram of a method for determining the safe flight boundary of a helicopter according to an embodiment of this application;

[0053] Figure 2 A flowchart illustrating a method for determining the safe flight boundary of a helicopter, provided in an embodiment of this application;

[0054] Figure 3 for Figure 1 Schematic diagram of the safe flight boundary for helicopters in China;

[0055] Figure 4 A functional module diagram of a helicopter safe flight boundary determination device provided in another embodiment of this application;

[0056] Figure 5 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0057] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0058] Currently, methods for determining the safe flight boundary of helicopters mainly include safe flight boundaries reflecting helicopter maneuverability based on reachable equilibrium sets and safe flight boundaries reflecting helicopter dynamic characteristics based on forward / backward reachable sets. This is also the safe flight boundary that this application focuses on. This application discloses a method for determining the safe flight boundary of helicopters through a layer-by-layer recursive approach, including the following steps: 1. Establishing the nonlinear state equation of the helicopter based on its dynamic characteristics, and giving the constraint range of system state variables and control inputs; 2. Solving for the reachable equilibrium set range of angular rates based on the helicopter dynamic model and the given constraint range, and determining the safe boundary of helicopter attitude angular rates; 3. Solving for the reachable set range of Distance Field on Grid (DFoG) of attitude angles based on helicopter kinematics and attitude angular rate safe boundaries, and determining the safe boundary of helicopter attitude angles; 4. Solving for the reachable set range of linear velocity in DFoG based on helicopter kinematics and attitude angle safe boundaries and thrust constraints, and determining the safe boundary of helicopter velocity. This application addresses helicopter flight safety issues by providing a method for determining helicopter safe flight boundaries through a layer-by-layer recursive approach based on reachable balance sets and DFoG reachability analysis. This method identifies state constraints during helicopter flight, providing a necessary foundation for helicopter safety boundary protection and control.

[0059] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] The helicopter safe flight boundary method provided in this application embodiment can be applied to, for example... Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server. Terminal 102 can send the centroid velocity vector, attitude angle vector, and angular velocity vector to be processed to server 104. After receiving the centroid velocity vector, attitude angle vector, and angular velocity vector, server 104 constructs a helicopter nonlinear model and constraint range based on the helicopter dynamics characteristics using the centroid velocity vector, attitude angle vector, and angular velocity vector; determines the helicopter attitude angular rate safety boundary using the alpha shape method and heuristic algorithm based on the helicopter nonlinear model and the constraint range; determines the helicopter attitude angle safety boundary using the DFoG method based on the helicopter attitude angular rate safety boundary; and determines the helicopter speed safety boundary based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range. Server 104 can feed back the obtained helicopter speed safety boundary to terminal 102. In addition, in some embodiments, the method for determining the safe flight boundary of a helicopter can also be implemented by either the server 104 or the terminal 102. For example, the terminal 102 can directly determine the safe flight boundary of a helicopter based on the centroid velocity vector, attitude angle vector, and angular velocity vector to be processed. Alternatively, the server 104 can obtain the centroid velocity vector, attitude angle vector, and angular velocity vector to be processed from the data storage system and determine the safe flight boundary of a helicopter based on the centroid velocity vector, attitude angle vector, and angular velocity vector to be processed.

[0061] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0062] In one exemplary embodiment, such as Figure 2 As shown, a method for determining the safe flight boundary of a helicopter is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps 201 to 205. Wherein:

[0063] Step 201: Obtain the helicopter's center of mass velocity vector, attitude angle vector, and angular velocity vector.

[0064] Step 202: Construct a nonlinear model and constraint range for the helicopter using the helicopter dynamics characteristics based on the centroid velocity vector, attitude angle vector, and angular velocity vector.

[0065] Step 203: Determine the helicopter attitude angular rate safety boundary using the alpha shape method and heuristic algorithm based on the helicopter nonlinear model and the constraint range.

[0066] Step 204: Determine the helicopter attitude angle safety boundary using the DFoG method based on the helicopter attitude angular rate safety boundary.

[0067] Step 205: Determine the helicopter speed safety boundary based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range.

[0068] Implementing steps 201 to 205 above can improve the accuracy of helicopter safe flight boundaries.

[0069] In an exemplary embodiment, step 202 involves constructing a helicopter nonlinear model. Specifically, to facilitate modeling and subsequent calculations, a general form of the helicopter nonlinear model can be established as follows:

[0070]

[0071] Where V, Λ, and Ω represent the states of the helicopter model system, and V = [u, v, w] T Let be the velocity vector of the helicopter's center of mass in the inertial coordinate system, u be the velocity along the x-axis in the body coordinate system, v be the velocity along the y-axis in the body coordinate system, w be the velocity along the z-axis in the body coordinate system, and T be the matrix transpose. The derivative of V, The derivative of Λ Let Λ = [φ, θ, ψ] be the derivative of Ω, T be the helicopter's attitude angle vector, φ be the roll angle, θ be the pitch angle, ψ be the heading angle, and Ω = [p, q, r]. T Let G be the angular rate vector of the helicopter in the body coordinate system, where p is the roll rate, g is the pitch rate, and r is the yaw rate, and G = [0, 0, mg]. T Let g be the weight of the helicopter, m be the acceleration due to gravity, and m be the mass of the helicopter. J = diag(J / m) xx J yy J zz J is the diagonal inertia matrix of the helicopter. xx Let J be the moment of inertia along the x-axis. yy Let J be the moment of inertia along the y-axis.zz Let F be the moment of inertia along the z-axis, then F = [F x ,F y ,F z ] T and ∑=[Σ x ,Σ y ,Σ z ] T Let these be the net external forces and net external moments acting on the helicopter in the body coordinate system, respectively, and the following constraints apply:

[0072] F i,min ≤F i ≤F i,max

[0073] Σ i,min ≤Σ i ≤∑ i,max

[0074] Among them, F x F y and F z The resultant forces along the x-axis, y-axis, and z-axis are Σ. x , ∑ y , and ∑ z The resultant moments along the x, y, and z axes are respectively, i = x, y, z, and F. i,min and F i,max Representing force F respectively i The upper and lower limits are known. Σ i,min and ∑ i,max Representing torque Σ i The upper and lower limits are known. Ω×JΩ is the angular momentum caused by the rotation of the angular velocity about the center of mass, and × is the cross product. According to the definitions of angular velocity Ω and inertia matrix J, the expansion of this angular momentum is:

[0075]

[0076] The rotation matrix from the body coordinate system to the ground coordinate system can be represented as:

[0077]

[0078] H is the attitude rotation matrix, defined as:

[0079]

[0080] In an exemplary embodiment, step 203 specifically includes: solving the nonlinear model of the helicopter and the constraint range to obtain the reachable equilibrium set of attitude angular rates; calculating the boundary of the three-dimensional point set using the alpha shape method based on the reachable equilibrium set of attitude angular rates; determining the inscribed cuboid of the point set boundary based on the boundary of the three-dimensional point set; constructing the attitude angular rate optimization problem based on the inscribed cuboid of the point set boundary; and determining the safe boundary of the helicopter attitude angular rate using a heuristic algorithm based on the attitude angular rate optimization problem.

[0081] In practical applications, when calculating the attitude angular rate safety boundary, consider the following helicopter attitude angular rate dynamics:

[0082]

[0083] Σ i,min ≤Σ i ≤Σ i,max i = x, y, z

[0084] Ω∈Ξ

[0085] in, Let S be the set of permissible states for attitude angular rate. Based on reachable equilibrium set theory and dynamic balancing, by selecting different attitude angular rates within the permissible set and solving the nonlinear equations, the reachable equilibrium set S of the attitude angular rate can be obtained. Ω for:

[0086] S Ω ={Ω∈Ξ:J -1 Ω×JΩ+J -1 ∑=0,Σ i,min ≤Σ i ≤Σ i,max ,i=x,y,z}

[0087] As can be seen from the above formula, the reachable equilibrium set of attitude angular rate is a finite three-dimensional point set. Next, we consider obtaining a regular attitude angular safety boundary based on this three-dimensional point set.

[0088] In computational geometry, the alpha shape method describes a set of piecewise linear simple curves that describe the shape of a finite set of points in the Euclidean plane. The alpha shape method can be used to extract edges from an unordered set of points. For a 3D point set, the steps for obtaining the boundary using the alpha shape derived from triangulation are as follows:

[0089] 1) Input 3D point set: Given a discrete point set in 3D space;

[0090] 2) Delaunay triangulation: The Delaunay triangulation algorithm is used to triangulate the 3D point set, generating a series of non-overlapping tetrahedral elements. A key property of Delaunay triangulation is that the circumsphere of any tetrahedron does not contain points from any other point set. This property ensures the stability and sparsity of the partitioning.

[0091] 3) Choosing the alpha value: Based on the characteristics of the point set and the requirements for boundary extraction, select an appropriate alpha value. The alpha value controls the "thickness" or "convexity" of the generated boundary contour. A larger alpha value will generate a convex hull that is closer to the point set, ignoring details. A smaller alpha value will retain more details, allowing for the formation of concave boundaries. Choosing the alpha value is usually a trial-and-error process; try multiple values ​​and observe the resulting boundary effects until a suitable alpha value is found.

[0092] 4) Traverse and filter tetrahedrons: Traverse all generated tetrahedrons. For each tetrahedron, calculate the radius of its circumsphere. Filter tetrahedrons based on the alpha value. If the radius of the circumsphere of a tetrahedron is less than or equal to the alpha value, keep the tetrahedron. If the radius of the circumsphere of a tetrahedron is greater than the alpha value, delete the tetrahedron. The result of this step is: only tetrahedrons that satisfy the alpha value condition are retained; these tetrahedrons will be used to generate the boundary of the point set.

[0093] 5) Generating Boundary Surfaces: Extracting boundary surfaces from the selected tetrahedron set. Boundary surfaces are patches composed of triangles. The method for extracting boundary surfaces is as follows: For each selected tetrahedron, examine each of its four faces (a tetrahedron has four faces) to determine if the face belongs to any other tetrahedron. If a face is isolated (i.e., it does not belong to any other tetrahedron), then that face is considered a boundary surface. This yields the alpha-shaped boundary surfaces, which are composed of triangular patches.

[0094] For a three-dimensional point set S Ω Using the alpha shape method described above, the boundary of this 3D point set is obtained. Because this boundary is typically irregular, it cannot be directly used for calculating the outer safety boundary of a helicopter or designing a boundary protection controller. Therefore, a boundary method using a three-dimensional point set is proposed below. The basic security boundary rule-making method mainly aims to obtain an inner boundary through an optimization algorithm. The largest cuboid within Ω, and the three axes of the cuboid are parallel to the three axes of Ω.

[0095] Define a 6-dimensional vector s = [C p C q C r ,Lp ,L q ,L r ] T , of which (C p C q C r ) represents the center point of the inscribed cuboid, L p L q and L r These represent the length, width, and height of the inscribed cuboid, respectively. Based on the optimization variable s, the set of feature points of the cuboid can be calculated. in These are the feature points of an inscribed cuboid, such as the eight vertices of the cuboid, the center point of each face, the points that halve or quarter-bisect each edge, etc. The selection of feature points will be based on... Select features when When the set is convex, only 8 vertices need to be taken as feature points. In other cases, the remaining feature points need to be extracted to ensure that the cuboid is inscribed in the set. Construct the following optimization problem:

[0096] max L p L q L r

[0097]

[0098] The optimization problem above is not a continuous optimization problem and can be solved using heuristic algorithms such as particle swarm optimization to obtain the inner infinity. The largest possible cuboid is used as the safety boundary for the attitude angular rate, which can be expressed as:

[0099] Ω min ≤Ω≤Ω max

[0100] Among them, [Ω min =(C p -L p / 2,C q -L q / 2,C r -L r / 2) T [Ω] represents the lower bound of the attitude angular rate safety boundary. max =(C p +L p / 2,C q +L q / 2,C r +L r / 2) T [] represents the upper bound of the attitude angular rate safety boundary.

[0101] In one exemplary embodiment, the heuristic algorithm is a particle swarm optimization algorithm.

[0102] In an exemplary embodiment, step 204 specifically includes: determining the forward reachable set and the backward reachable set of attitude angles based on the helicopter attitude angular rate safety boundary; solving the forward reachable set and the backward reachable set of attitude angles using the DFoG method to obtain the discretized estimated forward reachable set and the discretized estimated backward reachable set of attitude angles; calculating the boundary of the discretized estimated forward reachable set and the discretized estimated backward reachable set of attitude angles using the alphashape method; solving the boundary of the discretized estimated forward reachable set and the discretized estimated backward reachable set of attitude angles using a heuristic algorithm to obtain the first inscribed cuboid and the second inscribed cuboid of attitude angles; and taking the intersection of the first inscribed cuboid of attitude angles and the second inscribed cuboid of attitude angles as the helicopter attitude angle safety boundary.

[0103] In practical applications, a heuristic algorithm is used to solve the boundary problems of the discretized estimated attitude angle forward reachable set and the discretized estimated attitude angle backward reachable set to obtain the first and second attitude angle inscribed cuboids. Specifically, this includes: calculating the first boundary using the alpha shape method based on the discretized estimated attitude angle forward reachable set; determining the forward boundary inscribed cuboid based on the first boundary; constructing a forward optimization problem based on the forward boundary inscribed cuboid; determining the first attitude angle inscribed cuboid based on the forward optimization problem using a heuristic algorithm; calculating the second boundary using the alpha shape method based on the discretized estimated attitude angle backward reachable set; determining the backward boundary inscribed cuboid based on the second boundary; constructing a backward optimization problem based on the backward boundary inscribed cuboid; and determining the second attitude angle inscribed cuboid based on the backward optimization problem using a heuristic algorithm.

[0104] Specifically, in the calculation of the attitude angle safety boundary, for the following helicopter attitude angle dynamics:

[0105]

[0106] Ω min ≤Ω≤Ω max

[0107] Λ∈Υ

[0108] in, This is the set of permissible states for the attitude angle. For the above dynamics, given an initial set... and target set The definitions of forward reachable sets and backward reachable sets are given below. Given an initial set Λ0 and a dynamic system, when the initial conditions Λ(0) of the dynamic system satisfy Λ(0)∈Λ0, and the control input is taken from the admissible control set, the system reaches its maximum reachability at time t. f The set of all possible states at time t is called the forward reachable set, which can be represented as:

[0109]

[0110] Among them, R f (t f ,Λ0) represents the system at t f The forward reachable set at time t. Given the target set Λ f And dynamic systems, when the system's terminal state Λ(t) f ) satisfies Λ(t) f )∈Λ f The control input is taken from the admissible control set. The set of all possible initial states of the system is called the backward reachable set, which can be represented as:

[0111]

[0112] Among them, R b (t f ,Λ f ) indicates that the system at time t f The backward reachable set at time.

[0113] Given an initial set Λ0∈R n and target set Λ f ∈R n At the final time t f Define helicopter in t f The dynamic safe flight boundary at any given time is:

[0114] R(t f ) = R f (t f ,Λ0)∩R b (t f ,Λ f )

[0115] Wherein, R(t) f ) for helicopters in t f Dynamic safe flight boundaries at all times.

[0116] Forward / backward reachability sets can be solved using the DFoG method, which approximates the reachability set through optimal control. Taking the forward reachability set as an example, it first selects an initial set containing the reachability set, such as a subset of the reachable equilibrium set. Then, a grid is constructed on this subset of the reachable equilibrium set, and each grid point is projected onto the reachable set according to DFoG. The DFoG projection minimizes the distance between the grid point and the trajectory terminal point. The trajectory terminal point is the system state at the terminal time starting from the initial set. Since the calculated trajectory terminal point is reachable, it can be considered as a discrete estimate of the reachability set at the final time. Similarly, the backward reachability set can also be calculated using the DFoG method.

[0117] First, create a mesh G in the permissible set X of the state. δ For each grid point g δ Project it onto the reachable set. The definition of DFoG projection is given below. Given a closed, nonempty closed set... And a point Define the DFoG distance between point g and set S as:

[0118]

[0119] Based on the defined DFoG distance, the DFoG projection of point g onto set S can be defined as:

[0120] Π S (g):={s∈S:‖gs‖=dist(g,S)}

[0121] According to the above definition, the DFoG projection of point g onto set S is the point in set S that is the shortest distance from point g.

[0122] For reachable sets, we can consider constructing a grid G ​​within the state space enclosing the reachable sets of the system. r For each grid point g located within the reachable set... δ ∈G r The DFoG projection of a point onto the reachable set is itself. For every grid point outside the reachable set, its DFoG projection onto the reachable set lies on the boundary of the reachable set. The set of all projected points constitutes a discrete estimate of the reachable set, which is the basic principle of the DFoG method for calculating reachable sets.

[0123] For attitude angles, given an initial set and target set For different terminal times t f The forward reachability set R of the attitude angles is calculated using reachability set theory. f (t f ,Λ0) and backward reachable set R b(t f ,Λ f Based on the DFoG method, its discretized estimated forward reachable set is calculated. Discretization estimation of backward reachable set As can be seen from the DFoG calculation process, both of these discretization estimates are three-dimensional discrete point sets. The calculation is shown in the following formula:

[0124]

[0125] Similarly, The calculation is shown in the following formula:

[0126]

[0127] Similar to the previous step, the discretized estimates of the forward and backward reachable sets of the attitude angles are obtained using the alpha shape method of triangulation. and The boundaries are respectively denoted as and This boundary is typically irregular and cannot be directly used in the design of boundary protection controllers. Therefore, optimization methods are used to find two boundaries that are respectively inscribed within the boundary. and The largest possible cuboid. Define two 6-dimensional vectors s. Λf =[C φf C θf C ψf ,L φf ,L θf ,L ψf ] T and s Λb =[C φb C θb C ψb ,L φb ,L θb ,L ψb ] T , among which, (C φf C θf C ψf ) represents the center point of the inscribed cuboid, L φf L θf and L ψf These represent the length, width, and height of the inscribed cuboid, respectively. φb C θb C ψb ) represents the center point of the inscribed cuboid, L φb L θb and L ψb Let represent the length, width, and height of the inscribed cuboid, respectively. Construct two optimization problems as follows:

[0128] max L φf L θf L ψf

[0129]

[0130] max L φb L θb L ψb

[0131]

[0132] in, and They are respectively inscribed in and The feature points of the cuboid. The above optimization problem can be solved using the particle swarm optimization algorithm, obtaining the features inscribed in the cuboid. and The largest cuboid in volume is used as the intersection of these two cuboids as the safety boundary for attitude angles. The safety boundary for attitude angular rate can be expressed as:

[0133] Λ min (t f )≤Λ(t f )≤Λ max (t f )

[0134] in,

[0135] Λ min (t f ) = max(Λ min,f (t f ),Λ min,b (t f ))

[0136] Λ max (t f )=min(Λ max,f (t f ),Λ max,b (t f ))

[0137] Λ min,f (t f )=(C φf -L φf / 2,C θf -L θf / 2,C ψf -L ψf / 2) T

[0138] Λ max,f (tf )=(C φf +L φf / 2,C θf +L θf / 2,C ψf +L ψf / 2) T

[0139] Λ min,b (t f )=(C φb -L φb / 2,C θb -L θb / 2,C ψb -L ψb / 2) T

[0140] Λ max,b (t f )=(C φb +L φb / 2,C θb +L θb / 2,C ψb +L ψb / 2) T

[0141] Λ min,f (t f ) represents the lower bound of the attitude angles determined by the forward reachability set, Λ max,f (t f The upper bound of the attitude angles determined by the forward reachable set, Λ min,b (t f ) represents the lower bound of the attitude angle determined by the backward reachable set, Λ max,b (t f ) represents the upper bound of the attitude angles determined by the backward reachable set, Λ min (t f ) represents the lower bound of the attitude angle safety boundary being the larger of the lower bounds of the forward reachable set and the backward reachable set, Λ max (t f The upper bound of the attitude angle safety boundary is the smaller of the upper bounds of the forward reachable set and the backward reachable set.

[0142] From the above equation, it can be seen that with the end time t f The difference, Λ min (t f ), Λ max (t f The initial set Λ0 and the target set Λ will change, therefore the attitude angle safety boundary changes over time. In actual calculations, given the initial set Λ0 and the target set Λ... fBy selecting different calculation times t, the following dynamic helicopter attitude angular rate safety boundaries are obtained:

[0143] Λ min (t)≤Λ(t)≤Λ max (t)

[0144] Where Λ(t) represents the safety boundary at time t, Λ min (t) and Λ max (t) represents the lower and upper bounds of the safety boundary, respectively.

[0145] In an exemplary embodiment, step 205 specifically includes: determining the forward reachable set and the backward reachable set of speeds based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range; solving the forward reachable set and the backward reachable set of speeds using the DFoG method to obtain the discretized estimated forward reachable set and the discretized estimated backward reachable set of speeds; calculating the boundaries of the discretized estimated forward reachable set and the discretized estimated backward reachable set of speeds using the alpha shape method; solving the boundaries of the discretized estimated forward reachable set and the discretized estimated backward reachable set of speeds using a heuristic algorithm to obtain the first inscribed cuboid and the second inscribed cuboid of speeds; and taking the intersection of the first inscribed cuboid of speeds and the second inscribed cuboid of speeds as the helicopter speed safety boundary.

[0146] Specifically, in the calculation of the speed safety boundary, the following helicopter speed dynamics are considered:

[0147]

[0148] Ω min ≤Ω≤Ω max

[0149] Λ min (t)≤Λ(t)≤Λ max (t)

[0150] ∑ i,min ≤∑ i ≤Σ i,max i = x, y, z

[0151] V∈Θ

[0152] in, Let this be the set of admissible states for the velocity vector. For the above dynamics, given an initial set... and target set The definitions of forward reachable sets and backward reachable sets are given below. Given an initial set V0 and a dynamic system, when the initial conditions V(0) of the dynamic system satisfy V(0)∈V0, and the control input is taken from the admissible control set, the system reaches its maximum reachability in time t.f The set of all possible states is called the forward reachable set, which can be represented as:

[0153]

[0154] Among them, R f (t f V0) represents the system at time t f The forward reachable set at time V. Given the target set V. f And dynamic systems, when the system's terminal state V(t) f ) satisfies V(t) f )∈V f The control input is taken from the admissible control set. The set of all possible initial states of the system is called the backward reachable set, which can be represented as:

[0155]

[0156] Among them, R b (t f ,Λ f ) indicates that the system at time t f The backward reachable set at time.

[0157] Given an initial set V0∈R 3 and target set V f ∈R 3 At the final time t f Define helicopter in t f The dynamic safe flight boundary at any given time is:

[0158] R(t f ) = R f (t f ,v0)∩R b (t f V f )

[0159] Wherein, R(t) f ) for helicopters in t f Dynamic safe flight boundaries at all times.

[0160] For a velocity vector V, given an initial set and target set For different terminal times t f The forward reachability set R of the velocity is calculated using reachability set theory. f (t f (V0) and R b (t f V f Based on the DFoG method, its discretization estimate is calculated. and As can be seen from the DFoG calculation process, both of these discretization estimates are three-dimensional discrete point sets. The calculation is shown in the following formula:

[0161]

[0162] Wherein, V(t) f ) represents t f Similarly, the velocity vector at time t, The calculation is shown in the following formula:

[0163]

[0164] Here, V(t0) represents the velocity vector at time t0. Similar to the previous step, the discretized estimates of the forward and backward reachable sets of the velocity are obtained using the alpha shape method of triangulation. and The boundaries are respectively denoted as and This boundary is typically irregular and cannot be directly used in the design of boundary protection controllers. Therefore, optimization methods are used to find two boundaries that are respectively inscribed within the boundary. and The largest possible cuboid. Define two 6-dimensional vectors. in, This represents the center point of the inscribed cuboid. and These represent the length, width, and height of the inscribed cuboid, respectively. This represents the center point of the inscribed cuboid. and Let represent the length, width, and height of the inscribed cuboid, respectively. Construct the following two optimization problems:

[0165]

[0166] in, and They are respectively inscribed in and The feature points of the cuboid. The above optimization problem can be solved using the particle swarm optimization algorithm, obtaining the features inscribed in the cuboid. and The largest cuboid is given as the velocity safety boundary, and the intersection of these two cuboids is used as the velocity safety boundary. The velocity safety boundary can be expressed as:

[0167] V min (t f )≤V(t f )≤V max (t f )

[0168] in,

[0169] V min (t f ) = max(V min,f (t f ),V min,b (t f ))

[0170] V max (t f )=min(V max,f (t f ),V max,b (t f ))

[0171]

[0172] V min,f (t f V represents the lower bound of the velocity determined by the forward reachable set. max,f (t f The upper bound of the velocity determined by the forward reachable set, V min,b (t f V represents the lower bound of the velocity determined by the backward reachable set. max,b (t f V represents the upper bound of the velocity determined by the backward reachable set. min (t f The lower bound of the velocity safety boundary is taken as the larger of the lower bounds of the forward reachable set and the backward reachable set, V. max (t f The upper bound of the velocity safety boundary is the smaller of the upper bounds of the forward reachable set and the backward reachable set.

[0173] From the above equation, it can be seen that with the end time t f The difference, V min (t f V max (t f The initial set V0 and the target set V will change, therefore the velocity safety boundary changes over time. In actual calculations, given the initial set V0 and the target set V... f By selecting different calculation times t, the dynamic safety boundary is obtained as shown below:

[0174] V min (t)≤V(t)≤V max (t)

[0175] Where V(t) represents the safety boundary at time t, V min (t) and V max (t) represents the lower and upper bounds of the safety boundary, respectively.

[0176] Compared with existing methods for calculating helicopter safety boundaries, the safety boundary proposed in this application has the following characteristics. The safety boundary calculation method proposed in this application is a loop-based calculation. First, the boundary of the attitude angular rate is calculated. Then, the safety boundary of the attitude angular rate is calculated. Combined with the torque constraint, the safety boundary of the attitude angle is calculated. Finally, based on the safety boundaries of the attitude angular rate and the attitude angle, combined with the resultant force constraint, the safety boundary of the velocity is calculated. A major advantage of the loop-based calculation is that it can greatly reduce the computational complexity.

[0177] Based on the same inventive concept, this application also provides a helicopter safe flight boundary determination device for implementing the helicopter safe flight boundary determination method described above. The solution provided by this device is similar to the solution described in the above method; therefore, the specific limitations in one or more embodiments of the helicopter safe flight boundary determination device provided below can be found in the limitations of the helicopter safe flight boundary determination method described above, and will not be repeated here.

[0178] like Figure 4 As shown, in one exemplary embodiment, a helicopter safe flight boundary determination device is provided, comprising:

[0179] The acquisition module 401 is used to acquire the helicopter's center of mass velocity vector, attitude angle vector, and angular velocity vector.

[0180] Module 402 is used to construct a nonlinear model and constraint range of a helicopter based on the helicopter's dynamic characteristics using the centroid velocity vector, attitude angle vector, and angular velocity vector.

[0181] The helicopter attitude angular rate safety boundary determination module 403 is used to determine the helicopter attitude angular rate safety boundary based on the helicopter nonlinear model and the constraint range using the alpha shape method and heuristic algorithm.

[0182] The helicopter attitude angle safety boundary determination module 404 is used to determine the helicopter attitude angle safety boundary using the DFoG method based on the helicopter attitude angular rate safety boundary.

[0183] The helicopter speed safety boundary determination module 405 is used to determine the helicopter speed safety boundary based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range.

[0184] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 5As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores helicopter safe flight boundary determination data. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for determining helicopter safe flight boundaries.

[0185] Those skilled in the art will understand that Figure 5 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method embodiments.

[0186] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the above-described method embodiments.

[0187] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the above-described method embodiments.

[0188] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0189] In this application, all actions to acquire signals, information, or data are carried out in compliance with the relevant data protection laws and policies of the country where the location is situated, and with the authorization granted by the owner of the relevant device.

[0190] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0191] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0192] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0193] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for determining the safe flight boundary of a helicopter, characterized in that, The method for determining the safe flight boundary of a helicopter includes: Obtain the helicopter's center of mass velocity vector, attitude angle vector, and angular velocity vector; Based on the centroid velocity vector, attitude angle vector, and angular velocity vector, a nonlinear model and constraint range for the helicopter are constructed using the helicopter's dynamic characteristics. The formula for constructing a nonlinear model of a helicopter is: ； in, Let be the velocity vector of the helicopter's center of mass in the inertial coordinate system. The lower edge of the body coordinate system The speed of the shaft, The lower edge of the body coordinate system The speed of the shaft, The lower edge of the body coordinate system The velocity of the axis, where T is the matrix transpose. for The derivative, for derivative for The derivative, Let be the helicopter's attitude angle vector. For roll angle, The pitch angle, It is the direction angle. This is the angular rate vector of the helicopter in the body coordinate system. For the roll rate, For pitch rate, The yaw rate, For the weight of the helicopter, It is the acceleration due to gravity. For helicopter mass. Here is the diagonal inertia matrix of the helicopter. For along Moment of inertia of the axis, For along Moment of inertia of the axis, For along Moment of inertia of the axis, and Let these be the net external forces and net external moments acting on the helicopter in the body coordinate system, respectively, and the following constraints apply: ； in, , They are respectively axis, shaft and Resultant force in the axial direction , They are respectively axis, shaft and Resultant torque in the axial direction, , and Representing force respectively The upper and lower limits are known, and their values ​​are known. and They represent torque respectively The upper and lower limits are known, and their values ​​are known. The angular momentum caused by the angular velocity of rotation about the center of mass. It is the cross product; based on the angular velocity and inertia matrix From the definition, the expansion of the angular momentum is: ； The rotation matrix from the body coordinate system to the ground coordinate system can be represented as: The attitude rotation matrix is ​​defined as follows: ； Based on the helicopter nonlinear model and the constraint range, the helicopter attitude angular rate safety boundary is determined using the alpha shape method and heuristic algorithm. The helicopter attitude angle safety boundary is determined using the DFoG method based on the aforementioned helicopter attitude angular rate safety boundary. The helicopter speed safety boundary is determined based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range.

2. The method for determining the safe flight boundary of a helicopter according to claim 1, characterized in that, Based on the helicopter nonlinear model and the constraint range, the helicopter attitude angular rate safety boundary is determined using the alpha shape method and heuristic algorithm, specifically including: The achievable equilibrium set of attitude angular rate is obtained by solving the nonlinear model of the helicopter and the constraint range. The boundary of the 3D point set is calculated using the alpha shape method based on the reachable equilibrium set of the attitude angular rate; Determine the inscribed cuboid within the boundary of the point set based on the boundary of the three-dimensional point set; The attitude angular rate optimization problem is constructed based on the inscribed cuboid of the point set boundary. Based on the attitude angular rate optimization problem, a heuristic algorithm is used to determine the safe boundary of the helicopter attitude angular rate.

3. The method for determining the safe flight boundary of a helicopter according to claim 1, characterized in that, The heuristic algorithm is a particle swarm optimization algorithm.

4. The method for determining the safe flight boundary of a helicopter according to claim 1, characterized in that, The helicopter attitude angle safety boundary is determined using the DFoG method based on the aforementioned helicopter attitude angular rate safety boundary, specifically including: The forward reachable set and the backward reachable set of attitude angles are determined based on the helicopter attitude angular rate safety boundary. The DFoG method is used to solve for the forward reachable set and the backward reachable set of the attitude angle, resulting in the discretized estimated forward reachable set and the discretized estimated backward reachable set of the attitude angle. The boundaries of the discretized estimated attitude angle forward reachable set and the discretized estimated attitude angle backward reachable set are calculated using the alpha shape method; Based on the boundaries of the discretized estimated attitude angle forward reachable set and the discretized estimated attitude angle backward reachable set, a heuristic algorithm is used to solve the problem, resulting in the first attitude angle inscribed cuboid and the second attitude angle inscribed cuboid. The intersection of the cuboid inscribed in the first attitude angle and the cuboid inscribed in the second attitude angle is taken as the safety boundary of the helicopter attitude angle.

5. The method for determining the safe flight boundary of a helicopter according to claim 4, characterized in that, Based on the boundaries of the discretized estimated attitude angle forward reachable set and the discretized estimated attitude angle backward reachable set, a heuristic algorithm is used to solve for the first attitude angle inscribed cuboid and the second attitude angle inscribed cuboid, specifically including: The first boundary is calculated using the alpha shape method based on the discretized estimated attitude angle forward reachable set; The inscribed cuboid of the forward boundary is determined based on the first boundary. Construct a forward optimization problem based on the inscribed cuboid of the forward boundary; Based on the aforementioned forward optimization problem, a heuristic algorithm is used to determine the inscribed cuboid at the first attitude angle; The second boundary is calculated using the alpha shape method based on the discretized estimated attitude angle backward reachable set; The cuboid is inscribed within the second boundary based on the boundary. Construct a backward optimization problem based on the inscribed cuboid of the backward boundary; Based on the aforementioned backward optimization problem, a heuristic algorithm is used to determine the inscribed cuboid at the second attitude angle.

6. The method for determining the safe flight boundary of a helicopter according to claim 1, characterized in that, The helicopter speed safety boundary is determined based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range, specifically including: The forward and backward velocity reachable sets are determined based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range. The DFoG method is used to solve for the forward and backward reachable sets of velocity, resulting in discretized estimated forward and backward reachable sets of velocity. The boundaries of the forward reachable set and the backward reachable set of the discretized estimated velocity are calculated using the alpha shape method. Based on the boundaries of the discretized estimated forward velocity reachable set and the discretized estimated backward velocity reachable set, a heuristic algorithm is used to solve for the first velocity inscribed cuboid and the second velocity inscribed cuboid. The intersection of the cuboid inscribed in the first velocity and the cuboid inscribed in the second velocity is taken as the safety boundary for helicopter speed.

7. A device for determining the safe flight boundary of a helicopter, characterized in that, The helicopter safe flight boundary determination device includes: The acquisition module is used to acquire the helicopter's center of mass velocity vector, attitude angle vector, and angular velocity vector; The module is used to construct a nonlinear model and constraint range for the helicopter based on its center-of-mass velocity vector, attitude angle vector, and angular velocity vector, utilizing the helicopter's dynamic characteristics. The formula for constructing the nonlinear model of the helicopter is as follows: ； in, Let be the velocity vector of the helicopter's center of mass in the inertial coordinate system. The lower edge of the body coordinate system The speed of the shaft, The lower edge of the body coordinate system The speed of the shaft, The lower edge of the body coordinate system The velocity of the axis, where T is the matrix transpose. for The derivative of for derivative for The derivative of Let be the helicopter's attitude angle vector. For roll angle, The pitch angle, It is the direction angle. Let be the angular rate vector of the helicopter in the body coordinate system. For the roll rate, For pitch rate, The yaw rate, For the weight of the helicopter, It is the acceleration due to gravity. For helicopter mass. Here is the diagonal inertia matrix of the helicopter. For along Moment of inertia of the axis, For along Moment of inertia of the axis, For along Moment of inertia of the axis, and Let these be the net external forces and net external moments acting on the helicopter in the body coordinate system, respectively, and the following constraints apply: ； in, , They are respectively axis, shaft and Resultant force in the axial direction , They are respectively axis, shaft and Resultant torque in the axial direction, , and Representing force respectively The upper and lower limits are known, and their values ​​are known. and They represent torque respectively The upper and lower limits are known, and their values ​​are known. The angular momentum caused by the angular velocity of rotation about the center of mass. It is the cross product; based on the angular velocity and inertia matrix From the definition, the expansion of the angular momentum is: ； The rotation matrix from the body coordinate system to the ground coordinate system can be represented as: The attitude rotation matrix is ​​defined as follows: ； The helicopter attitude angular rate safety boundary determination module is used to determine the helicopter attitude angular rate safety boundary based on the helicopter nonlinear model and the constraint range using the alpha shape method and heuristic algorithm. The helicopter attitude angle safety boundary determination module is used to determine the helicopter attitude angle safety boundary using the DFoG method based on the helicopter attitude angular rate safety boundary. The helicopter speed safety boundary determination module is used to determine the helicopter speed safety boundary based on the helicopter nonlinear model, the helicopter attitude angular rate safety boundary, the helicopter attitude angle safety boundary, and the constraint range.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the helicopter safe flight boundary determination method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the helicopter safe flight boundary determination method as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the helicopter safe flight boundary determination method as described in any one of claims 1-6.

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