Unmanned aerial vehicle formation path convergence and change method based on reachable set

Abstract

The application provides a kind of based on reachable set UAV formation path convergence and change method, comprising: when UAV formation path needs to converge or change, the flight state information, control information and disturbance quantity information of interferer UAV and evader UAV are obtained;According to the above information, system dynamic data group is constructed;According to the game strategy of evader UAV and interferer UAV, determine the safety area, and the zero sub-level set of the implicit surface function of the safety area is used as the target set;According to the cost value function of the current state reaching the target set and the system dynamic data group defined in advance, Hamilton-Jacobi partial differential equation is constructed, the implicit surface function of the safety area is used as the termination condition, Hamilton-Jacobi partial differential equation is solved, and the optimal control strategy is obtained. Through the implementation of the above method, the optimal control strategy is calculated in real time, the environmental changes and obstacles are quickly adapted, and the safety of UAV formation path convergence and change is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned aerial vehicle formation, and particularly relates to a method for path convergence and change of unmanned aerial vehicle formation based on reachable set. BACKGROUND

[0002] Unmanned aerial vehicle formation flight has a wide range of applications in military, commercial, scientific research and entertainment fields. The leader-follower method is a common method for controlling unmanned aerial vehicle formation, which sets one unmanned aerial vehicle as a leader unmanned aerial vehicle, and other unmanned aerial vehicles follow the leader to move. The leader unmanned aerial vehicle is responsible for guiding the direction and speed of the entire formation, and the follower unmanned aerial vehicle adjusts its position and speed according to the state of the leader to maintain the shape and formation of the formation. This method mainly includes the following key steps:

[0003] 1) Selection of the leader. Select one unmanned aerial vehicle as the leader in the formation. The principle of selecting the leader can be based on its position, speed, ability and other factors. The leader unmanned aerial vehicle can be set by artificial or selected by autonomous algorithm.

[0004] 2) Method for followers to follow the leader. The follower unmanned aerial vehicle follows the leader according to the position and speed information of the leader. The communication system between unmanned aerial vehicles can be used to realize the information exchange between the leader and the follower. The follower moves according to the instructions or predetermined trajectory of the leader. The follower unmanned aerial vehicle needs to adjust in real time according to the movement of the leader, which can obtain the information of the surrounding environment such as relative position, speed, etc. through sensors, and then adjust itself through formation control algorithm.

[0005] 3) Formation maintenance strategy. The leader and the follower need to maintain a certain relative position and distance to ensure the overall stability of the unmanned aerial vehicle formation. In the movement process of the formation, tracking algorithm can be used to adjust the position and speed of the unmanned aerial vehicle to ensure the shape and structure of the formation.

[0006] The leader-follower method has the advantages of simplicity, strong adaptability and good scalability in unmanned aerial vehicle formation control, but also has the disadvantages of information transmission delay and dependence on the leader. In the field of unmanned aerial vehicle formation flight, unmanned aerial vehicles need to safely converge and change paths under the complex air traffic management system. Each unmanned aerial vehicle is an independent flight body and also a part of the entire formation, which needs to work with other unmanned aerial vehicles to complete complex tasks. The related technology does not analyze the path convergence and change process of unmanned aerial vehicle formation under the leader-follower framework, and cannot guarantee the safety of path convergence and change of unmanned aerial vehicle formation. SUMMARY

[0007] In view of this, the purpose of the present application is to provide a kind of based on reachable set UAV formation path convergence and change method to meet the needs of improving UAV formation path convergence and change security.

[0008] To achieve the above object, the present application provides the following technical solutions:

[0009] The present application provides a kind of based on reachable set UAV formation path convergence and change method, including: when UAV formation path needs to converge or change, the flight state information, control information and disturbance amount information of interferer UAV and evader UAV are obtained;According to the state information, control information and disturbance amount information of interferer UAV and evader UAV, system dynamic data group is constructed;According to the game strategy of evader UAV and interferer UAV, determine the safety area, and the zero sub-level set of implicit surface function of safety area is as target set;According to the cost value function of pre-defined current state to target set and system dynamic data group, Hamilton-Jacobi partial differential equation is constructed;Implicit surface function of safety area is as termination condition, Hamilton-Jacobi partial differential equation is solved, and optimal control strategy is obtained;Optimal control strategy is issued to UAV that needs to converge or change in formation path.

[0010] Optionally, target set L p Expression is as follows:

[0011]

[0012] Wherein, It is relative to reference UAV, specified certain position, It is relative to reference UAV, specified certain speed, p x,r It is the horizontal coordinate relative position variable of interferer UAV and evader UAV, p x,r =p x,i -p x,j , p x,i It is the horizontal coordinate position of evader UAV, p x,j It is the horizontal coordinate position of interferer UAV, p y,r It is the vertical coordinate relative position variable of interferer UAV and evader UAV, p y,r =p y,i -p y,j , p y,i It is the vertical coordinate position of evader UAV, p y,j It is the vertical coordinate position of interferer UAV, v x,r It indicates the horizontal coordinate relative speed variable of interferer UAV and evader UAV, v x,r =v x,i -v x,j , v x,idenotes the lateral coordinate speed of the evader UAV, v x, j denotes the lateral coordinate speed of the jammer UAV, v y,r denotes the longitudinal coordinate relative speed variable of the jammer UAV and the evader UAV, v y,r = v y,i -v y,j , v y,i denotes the longitudinal coordinate speed of the evader UAV, v y,j denotes the longitudinal coordinate speed of the jammer UAV, r px , r vx , r py , respectively denote the pre-defined minimum safety distance difference of the lateral coordinate relative position variable of the jammer UAV and the evader UAV, the minimum safety speed difference of the lateral coordinate speed variable of the jammer UAV and the evader UAV, the minimum safety distance difference of the longitudinal coordinate relative position variable of the jammer UAV and the evader UAV, and the minimum safety speed difference of the longitudinal coordinate speed variable of the jammer UAV and the evader UAV.

[0013] Optionally, the pre-defined cost value function of the current state reaching the target set is:

[0014]

[0015] wherein V(t, x) is the cost value function, x ∈ R n is the system state variable, R n denotes the state of the UAV in n-dimensional space, μ1(·) is the control function of the evader UAV, γ denotes the unexpected control strategy, Γ denotes the conflict set, U1 denotes the control amount set of the evader UAV, s denotes a specific time within [t, 0], γ[u1](·) denotes the unexpected control strategy of the evader, t denotes time, x denotes the system state, ξ f is the system trajectory satisfying the initial condition ξ f (t; x, t, u1(·), γ[u2](·)) = x, L p is the target set.

[0016] Optionally, a Hamilton-Jacobi partial differential equation is constructed according to the pre-defined cost value function of the current state reaching the target set and the system dynamic data group, including:

[0017]

[0018] V(0, x) = l(x)

[0019] wherein D tV(t,x) is a partial differential equation of the cost value function, f(x, u1, u2) represents a system dynamic data set, wherein x∈R n is a system state variable, R n represents the state of the unmanned aerial vehicle in n-dimensional space, u1 is a control function of the evader unmanned aerial vehicle, u2 is a control function of the disturber unmanned aerial vehicle, V(0,x) represents the cost value function at t=0, and l(x) represents an implicit surface function value.

[0020] Optionally, the optimal control strategy comprises:

[0021]

[0022] wherein, represents the optimal control strategy of the evader unmanned aerial vehicle, represents the optimal control strategy of the disturber unmanned aerial vehicle, D t V(t,x) is a partial differential equation of the cost value function, f(x, u1, u2) represents a system dynamic data set, wherein x∈R n is a system state variable, R n represents the state of the unmanned aerial vehicle in n-dimensional space, u1 is a control function of the evader unmanned aerial vehicle, u2 is a control function of the disturber unmanned aerial vehicle, U1 represents a control set of the evader unmanned aerial vehicle, and U2 represents a control set of the disturber unmanned aerial vehicle.

[0023] Optionally, a safety region is determined according to the game strategy of the evader unmanned aerial vehicle and the disturber unmanned aerial vehicle, and a zero sub-level set of an implicit surface function of the safety region is taken as a target set, comprising:

[0024] Static environment information when the unmanned aerial vehicle formation path needs to be merged or changed is acquired;

[0025] Obstacle elements of the unmanned aerial vehicle when the unmanned aerial vehicle formation path needs to be merged or changed are determined according to the static environment information;

[0026] Geographic information system data of the perceived obstacle elements are converted into a mathematical model;

[0027] The obstacle elements converted into the mathematical model are taken as an obstacle avoidance constraint condition, a safety region is determined according to the game strategy of the evader unmanned aerial vehicle and the disturber unmanned aerial vehicle and the obstacle avoidance constraint condition, and a zero sub-level set of an implicit surface function of the safety region is taken as a target set.

[0028] Optionally, a method for merging and changing a formation path of unmanned aerial vehicles based on a reachable set further comprises:

[0029] When any unmanned aerial vehicle is in the formation path merging and changing, the position and radius of an obstacle in a motion plane of the obstacle in real-time measured static environment information are detected through a detection and avoidance system on-board sensor;

[0030] According to the position of the obstacle and the position of the unmanned aerial vehicle, it is judged whether the obstacle enters the conflict area, if it enters the conflict area but is not in the backward reachable set, the unmanned aerial vehicle flies according to the first acceleration, the conflict area is the area drawn by taking the position of the unmanned aerial vehicle as the center, connecting the position of the unmanned aerial vehicle to the position of the obstacle by a straight line, and the distance containing the obstacle is the radius.

[0031] When the obstacle enters the backward reachable set of the unmanned aerial vehicle, the unmanned aerial vehicle is controlled to fly according to the second acceleration, the second acceleration is greater than the first acceleration.

[0032] Optionally, the cost value function of the predefined current state to the target set comprises:

[0033] The predefined unmanned aerial vehicle energy consumption cost function and flight time cost function are obtained;

[0034] The energy consumption cost function and the flight time cost function are added in the cost value function of the predefined current state to the target set, and an optimized total cost value function is obtained.

[0035] Optionally, the predefined unmanned aerial vehicle energy consumption cost function C enegy (x, u2) is:

[0036] C enegy (x, u2) = alpha || u2 || 2 ;

[0037] Wherein, alpha is an energy consumption weight coefficient, u2 is a control function of the interferer unmanned aerial vehicle, and x represents a current given state.

[0038] The flight time cost function C time (x) is:

[0039] C time (x) = beta (T-t) ;

[0040] Wherein, beta is a time cost weight coefficient, and T is an expected arrival time.

[0041] The application provides a kind of based on reachable set unmanned aerial vehicle formation path convergence and change method, based on reachable set method allows unmanned aerial vehicle to calculate backward reachable set and optimal control strategy in real time, to quickly adapt to environmental changes and obstacles, improve the real-time performance and adaptability of system, improve the safety of unmanned aerial vehicle formation path convergence and change.

[0042] Additional advantages, objects, and features of the application will be set forth in the descriptions to follow, and in part will become apparent to those skilled in the art upon examination of the following or can be learned from practice of the application. The objects and other advantages of the application can be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings. BRIEF DESCRIPTION OF DRAWINGS

[0043] To make the objectives, technical solutions and beneficial effects of the present application clearer, the present application is described below with the help of the following drawings:

[0044] Figure 1 A specific flowchart of a method for path merging and changing of a UAV formation based on a reachable set;

[0045] Figure 2 A specific schematic diagram of a path intersection scenario. DETAILED DESCRIPTION

[0046] The technical solutions of the present application will be described clearly and completely below with the help of the drawings. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application.

[0047] In the description of the present application, it should be noted that, unless otherwise explicitly specified and limited, the terms “mounting”, “connection”, “linking” should be understood in a broad sense, for example, can be fixed connection, or detachable connection, or integrally connected; can be mechanical connection, or electrical connection; can be directly connected, or indirectly connected through an intermediate medium, or the internal communication of two elements, can be wireless connection, or wired connection. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0048] In addition, the technical features involved in the different embodiments of the present application described below can be combined with each other as long as there is no conflict.

[0049] The present embodiment provides a method for path merging and changing of a UAV formation based on a reachable set, as shown in the accompanying drawings, comprising: Figure 1

[0050] S101, when the path of the UAV formation needs to be merged or changed, the flight state information, control information and disturbance quantity information of the disturber UAV and the evader UAV are obtained;

[0051] S102, according to the state information, control information and disturbance quantity information of the disturber UAV and the evader UAV, a system dynamic data set is constructed;​

[0052] S103, determining a safe area according to the game strategies of the evader UAV and the jammer UAV, and taking the zero sub-level set of the implicit surface function of the safe area as the target set;

[0053] S104, constructing a Hamilton-Jacobi partial differential equation based on a predefined cost-value function of reaching a target set from a current state and a system dynamic data set;

[0054] S105, using the implicit surface function of the safety region as a termination condition, solving the Hamilton-Jacobi partial differential equation to obtain the optimal control strategy;

[0055] S106: Send the optimal control strategy to the UAVs whose formation paths need to be merged or changed.

[0056] For example, the application scenario of this embodiment is as follows Figure 2 The figure shows a path intersection scenario involving disruptor drones and evader drones. A disruptor drone is one that interferes with the intersection of the drone formation's paths. An evader drone is one that wishes to avoid collision, such as one originally in the formation. In this scenario, some drones can switch queues during the path convergence process, while others can switch from master to slave. This embodiment does not limit the switching method, but for both of these switching methods, the reachable set-based method for drone formation path convergence and change is used.

[0057] First, in order to calculate the backward reachable set, the system model is constructed using ordinary differential equations to obtain the system dynamic data set. Specifically,

[0058]

[0059] Where x∈R n is the system state variable; u(t)∈U is the control variable; d(t)∈D is the disturbance variable; τ is a certain moment; t f is the terminal time. f ={x∈R n |T(x)≤0}, T f represents the target set of the system. T(x) can be an implicit surface function that describes certain properties and constraints of the system state x. For fixed u and d, it is assumed that f(·) is uniformly continuous, bounded, and Lipschitz continuous on x; the control functions u1(·)∈U1 and u2(·)∈U2 are drawn from the set of measurable functions.

[0060] The jammer drone is allowed to use an unintended strategy γ, defined as:

[0061] For all For all r ∈ [t, s] ; (2)

[0062] where r represents any time in [t, s], s represents a specific time, N[u1](r) represents the actual state set, represents the estimated state set.

[0063] In differential games, the goal of the aggressor UAV is to make the system enter the target set T f , and the goal of the evader UAV is to make the system away from the target set T f . Set T f is expressed as the zero sub-level set of the bounded Lipschitz continuous function L p : R n → R. L f (·) is called the implicit surface function representing the set T p : L n = {x ∈ R p | l(x) ≤ 0}.

[0064] For a given dynamic, and target set L p , the BRSV(t, x) is calculated as follows:

[0065]

[0066] where V(t, x) is the cost value function, x ∈ R n is the system state variable, R n represents the state of the UAV in n-dimensional space, μ1(·) is the control function of the evader UAV, γ represents the unexpected control strategy, Γ represents the conflict set, U1 represents the control set of the evader UAV, s represents a specific time in [t, 0], γ[u1](·) represents the unexpected control strategy of the evader, t represents time, x represents the system state, L p is the target set, ξ f is the system trajectory satisfying the initial condition ξ f (t; x, t, u1(·), γ[u2](·)) = x and all [-t, 0] intervals in the following differential equation:

[0067]

[0068] γ[u2](·) represents the unexpected control strategy of the aggressor, u1(s) represents the control of the evader at a specific time s, and u2(s) represents the control of the aggressor at a specific time s.

[0069] It is noted that the cost value function V(t, x) defined here is a theoretical construct that represents the expected minimum cumulative cost (or maximum cumulative return) from the current state x at time t following the optimal control policy until the end time T. The specific V(t, x) function is found by solving the Hamilton-Jacobi equation, which is a partial differential equation that describes how the value function changes over time and how it is affected by the system state and control policy. Solving this equation yields a specific function that gives the value for any given time and state.

[0070] Many methods involving solving the Hamilton-Jacobi partial differential equation (HJ PDE) and the Hamilton-Jacobi variational inequality (HJ VI) have been developed for computing the backward reachable set (BRS), which can be solved using well-established numerical methods and are not repeated here.

[0071] For the method described in the embodiments of the present application, using the formula in (1), the boundary of the backward reachable set can be obtained as the zero sublevel set of the value function. In the terminal value problem of the Hamilton-Jacobi partial differential equation, the value function V(x, T) is given at the terminal time T, which is usually referred to as the terminal condition. This condition is a key part of the problem because it defines the state that the system needs to reach at the terminal time.

[0072] According to the pre-defined cost value function of the current state reaching the target set and the system dynamic data set, the Hamilton-Jacobi partial differential equation is constructed, including:

[0073]

[0074] where D t V(t, x) is the partial differential equation of the cost value function, f(x, u1, u2) represents the system dynamic data set, where the disturbance has a small impact and can be ignored here, where x ∈ R n is the system state variable, R n represents the state of the UAV in n-dimensional space, u1 is the control function of the evader UAV, u2 is the control function of the disturber UAV, V(0, x) represents the cost value function at t = 0, and l(x) represents the value of the implicit surface function.

[0075] From which V(t) = {x ∈ R n |V(t, x) ≤ 0}, V(t, x) ≤ 0 means that from the state x, there exists at least one control policy that can make the system reach the target set within a given time with a cost of not more than zero. In many cases, zero cost represents collision-free, safe arrival, or satisfaction of other constraint conditions. According to the target set Lp and the implicit function l(x) from which V(t,x) is solved.

[0076] In this embodiment, the relative dynamics Q i ; Q j between two quadrotors will also be considered i denote the evader drone, Q j denote the jammer drone. These dynamics can be obtained by defining the relevant variables:

[0077] p x,r = p x,i - p x,j ;

[0078] p y,r = p y,i - p y,j ; (6)

[0079] v x,r = v x,i - v x,j ;

[0080] v y,r = v y,i - v y,j ;

[0081] where p x,r is the relative position variable in the lateral direction of the jammer drone and the evader drone, p x,i is the lateral position of the evader drone, p x, j is the lateral position of the jammer drone, p y,r is the relative position variable in the longitudinal direction of the jammer drone and the evader drone, p y,i is the longitudinal position of the evader drone, p y, j is the longitudinal position of the jammer drone, v x,r denotes the relative velocity variable in the lateral direction of the jammer drone and the evader drone, v x,i denotes the lateral velocity of the evader drone, v x, j denotes the lateral velocity of the jammer drone, v y,r denotes the relative velocity variable in the longitudinal direction of the jammer drone and the evader drone, v y,i denotes the longitudinal velocity of the evader drone, v y,j denotes the longitudinal velocity of the jammer drone.

[0082] From the relative variables given in equation (6), it follows that:

[0083]

[0084] where ux,i is the control input of the evader UAV in the lateral coordinate, u x, j is the control input of the jammer UAV in the lateral coordinate, u y,i is the control input of the evader UAV in the longitudinal coordinate, u y, j is the control input of the jammer UAV in the longitudinal coordinate.

[0085] Q is increased i The speed of the evader UAV, to impose a speed limit on the quadrotor UAV:

[0086]

[0087]

[0088] In a formation environment, the ability to enter a state relative to another moving UAV is important for both formation and joining a formation. For example, a free UAV can join an existing UAV formation on a highway and change mode to become a follower.

[0089] In addition, a leader or follower can join another platoon and then enter the follower mode.

[0090] To construct a controller to achieve a state relative to another UAV, the relative dynamics of two UAVs are used, as shown in equation (7). In general, the target state is specified as a certain position and velocity relative to the reference UAV. In the case of a UAV joining a platoon that maintains a single column, the reference UAV will be the platoon leader, i.e., the leader in the UAV formation, and the desired relative position is a certain distance behind the platoon leader, depending on how many other UAVs are already in the platoon, and the desired relative velocity is (0, 0) to maintain the formation.

[0091] Therefore, the safety region is determined according to the game strategy of the evader UAV and the jammer UAV, and the zero sub-level set of the implicit surface function of the safety region is taken as the target set. The target set L p is expressed as follows:

[0092]

[0093] where, is a certain position specified relative to the reference UAV, is a certain velocity specified relative to the reference UAV, p x,r is the relative position variable of the lateral coordinates of the jammer UAV and the evader UAV, p x,r = p x,i -p x,j , p x,iis the horizontal position of the evader drone, p x, j is the horizontal position of the jammer drone, p y,r is the vertical relative position variable of the jammer drone and the evader drone, p y,r = p y,i - p y,j , p y,i is the vertical position of the evader drone, p y,j is the vertical position of the jammer drone, v x,r is the horizontal relative velocity variable of the jammer drone and the evader drone, v x,r = v x,i - v x,j , v x,i is the horizontal velocity of the evader drone, v x, j is the horizontal velocity of the jammer drone, v y,r is the vertical relative velocity variable of the jammer drone and the evader drone, v y,r = v y,i - v y,j , v y,i is the vertical velocity of the evader drone, v y,j is the vertical velocity of the jammer drone, r px , r vx , r py , r vy respectively represent the pre-set minimum safety distance difference of the horizontal relative position variable of the jammer drone and the evader drone, the minimum safety speed difference of the horizontal velocity variable of the jammer drone and the evader drone, the minimum safety distance difference of the vertical relative position variable of the jammer drone and the evader drone, and the minimum safety speed difference of the vertical velocity variable of the jammer drone and the evader drone. The setting of the above minimum safety distance and minimum safety speed is determined according to the actual situation, which is not limited in the embodiment.

[0094] Target set L p is represented by the zero sub-level set of the implicit surface function l p (x), which specifies the terminal condition (5) of the HJPDE. The zero sub-level set V p (-T, x) of the solution of equation (5) gives the relative state set of the quadcopter drone reaching the relative coordinate target within T duration.

[0095] The optimal control of the evader drone and the jammer drone is obtained by the following method:

[0096]

[0097] In the BRS computation, it is assumed that the reference UAV (the platoon leader) moves at a constant speed, and the control input u j (t) = 0. The following is a suitable algorithm for a UAV to join the platoon leader to follow the platoon leader:

[0098] 1) Move straight to the target point at a certain speed until the value function V p (-T, x) ≤ 0, and stop moving when the value function V p (-T, x) ≤ 0, which means that the UAV can safely reach the target set from the current state x in the remaining time T.

[0099] 2) Apply the optimal control extracted from V p (-T, x) according to equation (10) until the target set L p is reached.

[0100] Further, in the special case where there is only one participant, an optimal control problem for a system with dynamics is obtained. In addition, the leader or follower can join another platoon and then enter the follower mode.

[0101]

[0102] In this case, the backward reachable set (BRS) is given by the Hamilton-Jacobi partial differential equation:

[0103]

[0104] where the optimal control is:

[0105]

[0106] The embodiment provides a UAV platoon path merging and changing method based on a reachable set. The method based on the reachable set allows the UAV to calculate a backward reachable set and an optimal control strategy in real time, thereby quickly adapting to environmental changes and obstacles, improving real-time performance and adaptability of the system, and improving safety of the UAV platoon path merging and changing.

[0107] As an optional implementation, the safety area is determined according to the game strategy of the evader UAV and the disturber UAV, and a zero sub-level set of an implicit surface function of the safety area is taken as a target set, and the method comprises the following steps: acquiring static environmental information when a UAV platoon path needs to be merged or changed; determining obstacle elements of the UAV when the platoon path is merged or changed according to the static environmental information; converting geographic information system data of the perceived obstacle elements into a mathematical model; taking the obstacle elements converted into the mathematical model as an obstacle avoidance constraint condition, determining a safety area according to a game strategy of an evader UAV and a disturber UAV and the obstacle avoidance constraint condition, and taking a zero sub-level set of an implicit surface function of the safety area as a target set.

[0108] Exemplarily, static information of the surrounding environment is acquired using geographic information system (GIS) data and sensors (such as lidar, camera) carried by the UAV, including the positions and shapes of obstacles such as buildings, trees, no-fly zones, and the like. Then, important features in the environment are extracted, such as the height, width, and relative position of the obstacles, and all static obstacles that can affect the merging and path changing of the UAV are identified. The features (such as position, shape, and size) of the obstacles are converted into mathematical models, which can be represented using geometric shapes (such as circles, rectangles, polygons, and the like). An implicit surface function is defined for each obstacle, for example, for a circular obstacle, it can be defined as:

[0109] l(x,y)=(x-x c ) 2 +(y-y c ) 2 -R 2 ;

[0110] where (x c ,y c ) represents the center coordinates of the obstacle, and R represents the radius of the obstacle.

[0111] Then, a safety distance is defined for each obstacle to ensure that the UAV maintains a safe interval from the obstacle, and the implicit surface function of the obstacle is combined with the safety distance to form an obstacle avoidance constraint condition:

[0112]

[0113] This indicates that the UAV must remain within the safety area, which can be represented as the zero sublevel set of the implicit surface function: S safe ={(x,y)|l(x,y)≤0}, which contains all points within the safety area.

[0114] According to the game strategy of the evader UAV and the disturber UAV, the definition of the safety area is adjusted. For example, the evader UAV can need a larger safety area to avoid the approach of the disturber UAV. During real-time flight, the state of the disturber UAV is monitored, and the boundary of the safety area is dynamically adjusted.

[0115] The embodiment provides a UAV formation path merging and changing method based on a reachable set. In the case that static environment information is determined when the UAV formation path needs to be merged or changed, the static environment information is considered in the embodiment, conflicts or collisions caused by static environment obstacles when the UAV formation path is merged and changed are avoided, and the safety of the UAV formation path merging and changing is improved.

[0116] As an optional implementation, the UAV formation path merging and changing method based on the reachable set further comprises: when any UAV is in the process of merging and changing the path, the position and radius of the obstacle in the motion plane of the UAV are detected in real time by the on-board sensor of the detection and avoidance system in the static environment information; whether the obstacle enters the conflict region is determined according to the position of the obstacle and the position of the UAV, if the obstacle enters the conflict region but is not in the backward reachable set, the UAV flies at the first acceleration, and the conflict region is a region with the position of the UAV as the center, a straight line connecting the position of the UAV to the position of the obstacle, and a radius containing the position of the obstacle; when the obstacle enters the backward reachable set of the UAV, the UAV flies according to the second acceleration, and the second acceleration is greater than the first acceleration.

[0117] Exemplarily, the obstacle avoidance strategy of the UAV in the process of merging and changing the path in the formation flight generally involves real-time detection of the static environment information by the on-board sensor, including the position and radius of the obstacle. When the obstacle enters a specific region of the UAV, i.e., the conflict region, the UAV will avoid according to the preset algorithm.

[0118] Specifically, the UAV uses the on-board sensor to monitor the obstacle in its motion plane in real time to obtain the position and radius information of the obstacle. Then, whether the obstacle enters the conflict region related to its position is determined, and the conflict region is a region with the UAV as the center, a straight line connecting the position of the UAV to the position of the obstacle, and containing the radius of the obstacle. If the obstacle enters the conflict region but does not enter the backward reachable set of the UAV, the UAV will fly at the first acceleration, wherein the backward reachable set refers to a set of all positions that the UAV can reach within a given time. When the obstacle enters the backward reachable set of the UAV, the UAV will fly according to the second acceleration, which is generally greater than the first acceleration, to achieve faster obstacle avoidance.

[0119] The size of the first acceleration and the second acceleration of the UAV can be determined by using a real-time collision avoidance algorithm based on reachable set analysis, for example, using a level set method and optimal control theory to analyze and calculate the reachable set of the UAV. The size of the first acceleration and the second acceleration can be determined by using a target detection and obstacle avoidance algorithm based on a dynamic vision sensor, which designs a filtering method and a motion compensation algorithm to filter out noise in the event stream, and designs a dynamic target fusion detection algorithm that fuses event images and RGB images to ensure the reliability of detection. In addition to the above methods, the size of the first acceleration and the second acceleration can also be determined by using a reinforcement learning-based obstacle avoidance method, such as the Greedy-DDPG algorithm, which improves the exploration strategy of DDPG through greedy selection, shortens the training time and improves the training effect.

[0120] The embodiment provides a UAV formation path merging and changing method based on a reachable set.

[0121] As an optional implementation, a UAV formation path merging and changing method based on a reachable set, a pre-defined cost value function of a current state reaching a target set comprises the following steps: obtaining a pre-defined UAV energy consumption cost function and a flight time cost function; adding the energy consumption cost function and the flight time cost function in the pre-defined cost value function of the current state reaching the target set, so as to obtain an optimized total cost value function.

[0122] Exemplarily, the pre-defined UAV energy consumption cost function C enegy (x, u2) is C enegy (x, u2) = a||u2|| 2 ; wherein a is an energy consumption weight coefficient, u2 is a control function of an interferer UAV, and x represents a current given state; the flight time cost function C time (x) is C time (x) = b(T-t); wherein b is a time cost weight coefficient, and T is an expected arrival time. By adding the energy consumption cost function and the flight time cost function in the pre-defined cost value function of the current state reaching the target set, the optimized total cost value function can be obtained.

[0123] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present application but not limit the present application, and although the present application has been described in detail through the above preferred embodiments, those skilled in the art should understand that various modifications can be made in form and details without departing from the scope defined by the claims of the present application.

Claims

1. A method for UAV formation path merging and changing based on reachable set, characterized in that, The method comprises the following steps: When the UAV formation path needs to be merged or changed, the flight state information, control information and disturbance information of the disturber UAV and the evader UAV are acquired; According to the state information, control information and disturbance information of the disturber UAV and the evader UAV, a system dynamic data group is constructed; According to the game strategy of the evader UAV and the disturber UAV, a safety region is determined, and the zero sub-level set of the implicit surface function of the safety region is taken as a target set; According to the pre-defined cost value function of the current state reaching the target set and the system dynamic data group, a Hamilton-Jacobi partial differential equation is constructed; The implicit surface function of the safety region is taken as a termination condition, and the Hamilton-Jacobi partial differential equation is solved to obtain an optimal control strategy; The optimal control strategy is issued to the UAV whose formation path needs to be merged or changed; Wherein, the target set The expression is as follows: ； wherein, respectively represent a certain position designated with respect to a reference UAV, is a certain speed designated with respect to a reference UAV, is a horizontal coordinate relative position variable of the jammer UAV and the evader UAV, , is a horizontal coordinate position of the evader UAV, is a horizontal coordinate position of the jammer UAV, is a vertical coordinate relative position variable of the jammer UAV and the evader UAV, , is a vertical coordinate position of the evader UAV, is a vertical coordinate position of the jammer UAV, represents a horizontal coordinate relative speed variable of the jammer UAV and the evader UAV, , represents a horizontal coordinate speed of the evader UAV, represents a horizontal coordinate speed of the jammer UAV, represents a vertical coordinate relative speed variable of the jammer UAV and the evader UAV, , represents a vertical coordinate speed of the evader UAV, represents a vertical coordinate speed of the jammer UAV, , , , respectively represent a pre-set minimum safe distance difference of a horizontal coordinate relative position variable of the jammer UAV and the evader UAV, a minimum safe speed difference of a horizontal coordinate speed variable of the jammer UAV and the evader UAV, a minimum safe distance difference of a vertical coordinate relative position variable of the jammer UAV and the evader UAV, and a minimum safe speed difference of a vertical coordinate speed variable of the jammer UAV and the evader UAV. According to the game strategy of the evader UAV and the disturber UAV, a safety region is determined, and the zero sub-level set of the implicit surface function of the safety region is taken as a target set, which comprises the following steps: Static environment information when the UAV formation path needs to be merged or changed is acquired; Obstacle elements when the UAV is merged or changed are determined according to the static environment information; The perceived obstacle element geographic information system data is converted into a mathematical model; The converted obstacle element mathematical model is taken as an obstacle avoidance constraint condition, and a safety region is determined according to the game strategy of the evader UAV and the disturber UAV and the obstacle avoidance constraint condition, and the zero sub-level set of the implicit surface function of the safety region is taken as a target set. 2.The method of claim 1, wherein, The pre-defined cost value function of the current state reaching the target set is: ； wherein, is a cost value function, is a system state variable, denotes the state of the UAV in n-dimensional space, is a control function of the evader UAV, denotes an unintended control strategy, denotes a conflict set, denotes a set of control amounts of the evader UAV, s denotes a specific time within [t,0], denotes an unintended control strategy of the evader, t denotes time, x denotes system state, is a system trajectory satisfying initial conditions , is a target set. 3.The method of claim 2, wherein, Wherein, According to the pre-defined cost value function of the current state reaching the target set and the system dynamic data group, a Hamilton-Jacobi partial differential equation is constructed, which comprises the following steps: wherein is the partial differential equation of the cost value function with respect to t , is the partial differential equation of the cost value function with respect to x , denotes the system dynamic data set, wherein is the system state variable, denotes the state of the UAV in n-dimensional space, is the control function of the evader UAV, is the control function of the disturber UAV, denotes the cost value function at t = 0, denotes the implicit surface function value, denotes the control amount set of the evader UAV, denotes the control amount set of the disturber UAV. 4.The method of claim 3, wherein, The optimal control strategy comprises the following steps: wherein, represents the optimal control strategy of the evader drone, represents the optimal control strategy of the disturber drone.

5. The method of claim 1, wherein, Further comprising: When any UAV is merged and changed in the formation path, the position and radius of the obstacle in the motion plane of the UAV in the real-time measured static environment information are detected through the on-board sensor of the detection and avoidance system; Whether the obstacle enters the conflict region is judged according to the position of the obstacle and the position of the UAV, if the obstacle enters the conflict region but is not in the backward reachable set, the UAV flies according to the first acceleration, and the conflict region is a region defined by taking the position of the UAV as the center, connecting the position of the UAV to the position of the obstacle by a straight line and taking the distance containing the obstacle as the radius; When the obstacle enters the backward reachable set of the UAV, the UAV is controlled to fly according to the second acceleration, and the second acceleration is greater than the first acceleration. 6.The method of claim 1, wherein, The pre-defined cost value function of the current state reaching the target set comprises the following steps: A pre-defined UAV energy consumption cost function and a flight time cost function are acquired; The energy consumption cost function and the flight time cost function are added in the pre-defined cost value function of the current state reaching the target set to obtain an optimized total cost value function.

7. The method of claim 6, wherein, Predefined drone energy consumption cost function is: ； wherein, is an energy consumption weight coefficient, is a control function of the aggressor drone, x denotes the current given state; Time of flight cost function is: ； wherein, is a weight coefficient of the time cost, T is the expected arrival time.

Images