CN117250859B - Multi-aircraft collaborative search algorithm under communication constraint - Google Patents
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Abstract
The invention discloses a multi-aircraft collaborative search algorithm under communication constraint, which relates to the technical field of aircraft search and constructs a multi-aircraft collaborative search algorithm model based on communication topology according to an environment model, an aircraft sensor detection model, an aircraft platform model, a target model and constraint conditions and in combination with a search performance index function. The invention considers the problem of collaborative searching of multiple aircrafts under the communication constraint, has the function of collaborative searching of dynamic targets of a target area by the multiple aircrafts under the limited communication distance constraint, and simultaneously utilizes a distributed MPC algorithm to carry out distributed track planning on each aircrafts so as to meet the requirement of online calculation.
Description
Technical Field
The invention relates to the technical field of aircraft searching, in particular to a multi-aircraft collaborative searching algorithm under communication constraint.
Background
The distributed method has the advantages of high operation speed, high instantaneity and high cluster fault tolerance, so that the problem of collaborative search of multiple aircrafts is solved at present, and the distributed method is mostly adopted.
Currently, peng Hui et al propose a multi-unmanned aerial vehicle collaborative search algorithm based on distributed model predictive control and solve a single optimization problem by particle swarm optimization. Hou Yueji et al designed an objective function with coverage as real-time search benefits, solving the problem of low coverage of the general search algorithm. However, the two methods adopt an intelligent algorithm based on evolution to solve the optimization problem, so that the requirements of online track planning are difficult to meet.
Dai Jian et al divide the target area, change the multi-machine collaborative search problem into a single-machine search problem, the advantage of this method is that can effectively avoid the problem that the multi-machine constraint coupling causes to be difficult to solve, but in each subregion, the single aircraft adopts the parallel search mode to carry on the coverage search to the area, the search efficiency is low.
The three prior arts solve the problem of collaborative searching of multiple aircrafts to a certain extent, but do not consider the problem of communication topology change caused by dynamic characteristics of enemy targets and limited actual aircraft communication conditions.
Disclosure of Invention
In order to solve the problems, the invention provides a multi-aircraft collaborative search algorithm based on distributed model predictive control (Distributed Model Predictive Control, DMPC), which aims at a scene of collaborative search of a plurality of dynamic targets of an enemy under the constraint of a limited communication distance, and performs track planning for each aircraft.
The technical scheme adopted by the invention is as follows:
a multi-aircraft collaborative search algorithm under communication constraints, comprising the steps of:
s1, constructing an environment model according to the speed of an aircraft and a communication range threshold value, wherein the environment model comprises a task area model and an inter-aircraft communication topology model;
s2, constructing an aircraft sensor detection model according to the detection probability, the identification probability, the false alarm probability and the detectable area range;
s3, constructing an aircraft platform model;
s4, constructing a target model according to the target movement speed;
s5, constructing constraint conditions, including environmental constraint, collision avoidance constraint and aircraft performance constraint;
s6, constructing a search performance index function according to the environmental reconnaissance income and the task execution cost;
s7, constructing a multi-aircraft collaborative search algorithm model based on the communication topology according to the environment model, the aircraft sensor detection model, the aircraft platform model, the target model and the constraint condition and combining the search performance index function.
Specifically, in step S1, the task area model is:
c＝m+(n-1)×L x ，
c∈{1,2,…,L x ×L y }
wherein, (L) x ×L y ) Representing the task area is discretized into (L x ×L y ) The grid, c, represents the grid of the rasterized task area, m represents the mth row of the rasterized task area, and n represents the nth column of the rasterized task area; the length and width of grid c are Δx and Δy, respectively, and may be selected as the average flight distance of the aircraft per unit time step.
The inter-machine communication topology model is as follows:
wherein r (t) is a communication range threshold, N v For the total number of aircraft clusters, if h ij =1 and h ji =1, then this indicates that aircraft a i Can be connected with aircraft A j The communication is enabled, and the matrix C (t) represents the real-time communication topology of the cluster of aircraft at the current moment t.
More specifically, in step S2, the detection probability is the probability that the sensor on the aircraft finds the target, the recognition probability is the probability that the sensor on the aircraft recognizes the target, the false alarm probability is the probability that the sensor on the aircraft erroneously recognizes the target, the detectable area range is a sector area, and the central angle of the sector area is the maximum coverage angle of the aircraft radar on the azimuth plane.
More specifically, in step S3, the aircraft platform model is:
x i (k+j|k)＝f(x i (t+j-1|t),u i (t+j-1|t)),i＝1,2,…,N v ,j＝1,2,…,T p
x i (t)＝[x i (t),y i (t),φ i (t)]
wherein f (·) is the aircraft state update equation, u i (k)＝Δφ i (k),T p To predict time domain, i is aircraft sequence number, x i ，y i Respectively aircraft A i In the x-axis and y-axis positions, V i (t) aircraft A i Is phi, the flying speed of the aircraft i (t) aircraft A i Included angle between speed direction and positive half axis of x-axis, mu i (t) is the roll of the aircraftAngle, g is a gravitational constant, n z,i Is a normal overload of the aircraft.
More specifically, in step S4, the target model is
Wherein V is target (t) is the speed of the target aircraft, x target And (t) is the position of the target aircraft.
More specifically, in step S5,
the environmental constraints are:
x min ≤x i (t)≤x max
y min ≤y i (t)≤y max
wherein x is min ，x max Respectively represent the map range in the x direction, y min ，y max Respectively representing map ranges in the y direction;
the collision prevention constraint is as follows:
||x i (t)-x j (t)||≥2R
wherein x is i (t)，x j (t) respectively represent the first aircraft A i ，A j At the position of time t, 2R represents the safe distance between machines;
aircraft performance constraints are:
-φ i,max ≤u i (t)≤φ i,max
wherein u is i (t) is the control quantity of the aircraft, phi i,max For aircraft A i Maximum included angle between speed direction and positive half axis of x-axis, -phi i,max For aircraft A i The maximum angle between the speed direction and the negative half axis of the x axis.
More specifically, in step S6, specifically including:
s61, defining an aircraft A i Is a scout path P of (1) i l (t)＝{P i l (t+1|t),…,P i l (t+q|t),…,P i l (t+T p Environment scout on t)Beneficial effects are that
Wherein P is i l (t+q|t),i＝q,…,T p Representing aircraft A i The q-th track point on the first path predicted at the time t, phi i (c) Representing when aircraft A i When being positioned at the grid path point c, the sensor detects the target surface set phi i (c) Determined by a sensor detection model, eta i,c,t An uncertainty size within the mesh path point c;
defined within grid path point c, the probability of target existence is p c (k)∈[0,1]I.e. p c (k) =0 indicates that there is no target within the mesh path point, p c (k) =1 indicates that there is a target in the mesh waypoint. Uncertainty η of grid path point c i,c,t The updated formula of (2) is:
wherein K is γ > 0, || represents taking absolute values;
defining τ=1 to indicate that there is a target in grid path point c, τ=0 to indicate that there is no target in grid path point c, Ω i,c,t =1 indicates that at time k, unmanned plane a i It is searched that a target exists in the mesh path point c,
constructing a probability map linear updating formula:
Π c,t ＝Π c,t-1 +λ c,t
wherein,
p d ，p f the detection probability and false alarm probability of the sensor, i.e. p d ＝p(Ω i,c,t ＝1∣τ c ＝1),p f ＝p(Ω i,c,t ＝1∣τ c =0), uncertainty η i,c,t The updating is as follows:
s62, constructing an aircraft A i Is a scout path P of (1) i l (t)＝{P i l (t+1|t),…,P i l (t+q|t),…,P i l (t+T p The task execution cost on t) is:
wherein u is i (P i l (t+q+ 1|t) represents aircraft A i At the path point P i l Heading at (t+q|t);
s63, constructing an aircraft A i Is a scout path P of (1) i l Search performance index function above:
wherein the weight k 1 ，k 2 Satisfy k 1 +k 2 ＝1。
More specifically, the multi-aircraft collaborative search algorithm model based on the communication topology is:
wherein J is i Representing aircraft A i In the rolling time domain T p An index function of the internal optimization,and U i (t) aircraft A respectively i In the rolling time domain T p Internal state [ t+1; t+T p ]The prediction sequence and the control input sequence, f represents the motion equation of the aircraft, xi, and Θ represent the aircraft A respectively i The state constraint set comprises environment constraint and collision avoidance constraint, and the control constraint set is aircraft performance constraint; />Respectively A i Other aircrafts outside the rolling time domain t epsilon [ t+1; t+T p ]Intra state prediction sequence and control input prediction sequence,/->The transmission of the aircraft is dependent on an inter-aircraft communication network, but due to the limitation of the actual communication range of a battlefield, part of aircrafts may not have communication conditions at the moment t, so the invention is based on an inter-aircraft communication topology model and will be +.>The update of (2) is divided into the following two cases:
i.e. if at time t, aircraft a i And A is a j Can communicate with each other, i.e. the corresponding element C in the cluster communication connectivity matrix C (t) ij (t) 1 or more, aircraft A i Can utilize A j A latest state prediction sequence; conversely, if aircraft A i And A is a j Is unable to communicate with each other, i.e. the corresponding element C in the cluster communication connectivity matrix C (t) ij (t) < 1, aircraft A i And calculating a multi-aircraft collaborative search algorithm model by using the state prediction sequence obtained at the last moment.
Compared with the prior art, the invention has the beneficial effects that:
the invention considers the problem of collaborative searching of multiple aircrafts under the communication constraint, has the function of collaborative searching of dynamic targets of a target area by the multiple aircrafts under the limited communication distance constraint, and simultaneously utilizes a distributed MPC algorithm to carry out distributed track planning on each aircrafts so as to meet the requirement of online calculation.
In order to make the above objects, features and advantages of the present invention more comprehensible, embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a rasterized map of a task area in accordance with the present invention;
FIG. 2 is a schematic representation of radar detection ranges in an aircraft sensor detection model of the present invention;
FIG. 3 is a graph of an aircraft search trajectory obtained by the algorithm of the present invention during simulation.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention.
Description of the problem: the multi-aircraft cooperative target reconnaissance scene is described as follows, N v N in unknown region omega for a frame aircraft T The individual targets perform a scout task. FlyingWith the number A i (i＝1,2,3…N v ) Number T for adversary target i (i＝1,2,3…N T ) To represent. The task of collaborative searching of the aircraft is that the aircraft detects a target area omega through an airborne sensor to detect, and information such as the number of targets, the position distribution and the like is acquired in real time. The invention considers the scene that a plurality of subsonic aircrafts carry out collaborative search on a plurality of sea surface low-dynamic ship targets under communication constraint.
The invention provides a multi-aircraft collaborative search algorithm under communication constraint, which aims at the requirements of aircraft collaborative search, and establishes an environment model, an aircraft sensor detection model, an aircraft platform model and a target model, further considers environment constraint, collision prevention constraint and aircraft performance constraint, and combines search performance indexes to construct collaborative search optimization.
1. Reconnaissance situation modeling
1. Environmental modeling
1) Task area modeling
The invention rasterizes the task area omega by known geographic location and environmental boundary information and defines an environmental matrix. Each aircraft obtains known prior information and stores a known map prior to performing the mission.
The task area Ω is discretized into (L) x ×L y ) And (3) a grid, and constructing an environment map shown in fig. 1. Wherein the number of the mesh (m, n) of the mth row and the nth column is denoted by c, c=m+ (n-1) ×l x And c.epsilon. {1,2, …, L x ×L y }. The length and width of grid c are deltax and deltay, and can be chosen as the average flight distance of the aircraft per time step. Thus, a task area model is obtained.
Before the reconnaissance starts, the environmental information of the whole task area omega is completely unknown, and coverage reconnaissance is required to be developed for the task area omega. With the reconnaissance, the map information changes in real time, the coverage distribution map is updated in real time and shared in the multi-cluster communication network, and environmental information is provided for real-time decision making of the aircraft. The mission area is not considered to be the change of the topography, namely the reconnaissance mission area omega is regarded as a horizontal plane, and the altitude coordinate only considers the flying altitude of the aircraft in the three-dimensional coordinate system.
2) Inter-machine communication topology modeling
The communication condition is a very important ring in the cooperative work of multiple aircrafts, and the quality of the communication condition directly influences the cooperative effect of the multiple aircrafts. The invention does not consider the relative position relation between aircrafts during modeling, and only uses the set inter-aircraft communication distance as the only standard for judging whether the aircrafts can communicate or not. When the distance between two aircrafts is within the inter-aircraft communication distance, it is considered that error-free real-time communication can be performed, and information is exchanged, including: self coordinates, direction of movement, speed of movement, whether the target is identified. When the distance between two aircrafts exceeds the communication distance between aircrafts, real-time communication is considered to be impossible, and the two aircrafts cannot cooperate.
Thus, the present invention utilizes a directed graph g= < U, D > representing the communication links between the aircraft, where U represents the set of aircraft, D represents the euclidean distance between the aircraft, then the adjacency communication matrix H is represented as:
wherein r (t) is a communication range threshold, N v For the total number of aircraft clusters. The adjacent communication matrix H can clearly express the real-time communication topological relation among all aircrafts, if H ij =1 and h ji =1, then this indicates that aircraft a i Can be connected with aircraft A j And communicate with each other, and can transmit and receive information such as position. The adjacency matrix H (G, t) is asymmetric in view of the limited environment of battlefield real-time communication. The overall communication topology matrix for the aircraft cluster at time t may be calculated as:
matrix C (t) represents the real-time communication topology of the cluster of aircraft at the current moment t. The cluster communication connectivity matrix C (t) at each moment can be calculated according to the effective communication distance and (2) according to the battlefield environment under different communication interference intensities
Wherein, c ij (t) represents connectivity between aircraft i, j, c if effective communication between aircraft i to j is possible ij Not less than 1, otherwise c ij =0. At the current moment, if the whole communication topology matrix of the unmanned aerial vehicle cluster meets the full communication condition, namelyThe aircraft cluster satisfies the global communication condition.
2. Aircraft sensor detection model
When the aircraft performs a reconnaissance task, unknown information is acquired through the sensor of the aircraft, and the reconnaissance capability of the sensor directly influences the cooperative reconnaissance effect of the aircraft. The present invention considers the following four things when modeling a sensor:
1) Probability of detection
Detection probability, i.e. probability p that a sensor on board an aircraft finds an object d I.e. the probability that the aircraft finds the target when the target is within the detectable range of the aircraft.
2) Identification probability
The probability of recognition, i.e. the probability p of a sensor on board an aircraft recognizing an object c I.e. after the target is found, the aircraft can correctly identify the probability of the mission to be scouted.
3) False alarm probability
False alarm probability, i.e. probability p of false recognition of a target by a sensor on board an aircraft f I.e. the probability that the current area does not have a target, but the aircraft detects the event that the area has a target.
4) Detectable area range
The maximum coverage angle of the radar on the azimuth plane is set asUnder the aircraft there is a detection blind zone with radius d min . The projection of the search range of the aircraft radar on the ground is then a sector as shown in fig. 2, i.e. a grey area.
3. Aircraft platform model
Since the flying height during the reconnaissance of the aircraft needs to be set in advance according to a plurality of restrictions such as the view angle of the sensor, the resolution of the camera, and the like, the flying height and the speed are not generally changed when the mission is executed. Thus, the motion model of the aircraft can be simplified as follows:
wherein x is i ，y i Respectively aircraft A i In the x-axis and y-axis positions, V i (t) aircraft A i Is phi, the flying speed of the aircraft i (t) aircraft A i Included angle between speed direction and positive half axis of x-axis, mu i (t) is the roll angle of the aircraft, g is the gravitational constant, n z,i Is a normal overload of the aircraft. In the case of uniform and uniform flight of all aircraft, the control quantity of the aircraft platform is reduced to the change quantity of the direction angle, namely delta phi i (t)。
The state quantity of the recording subsystem i is x i (t)＝[x i (t),y i (t),φ i (t)]Thus, according to the above equation, a predictive equation for subsystem i (i.e., an aircraft platform model) can be established as:
x i (k+j|k)＝f(x i (t+j-1|t),u i (t+j-1|t)),i＝1,2,…,N v ,j＝1,2,…,T p (5)
wherein f (·) is the aircraft state update equation, u i (k)＝Δφ i (k),T p To predict the time domain.
4. Target model
The enemy object is modeled as follows, taking into account its dynamic characteristics:
wherein V is target (t) velocity of enemy target, x target (t) is the location of the enemy object.
2. Constraint conditions
1. Environmental constraints
Since the search area has boundaries, when the aircraft performs the search task, the constraint of the boundaries of the task area Ω needs to be considered, namely:
wherein x is min ，x max Respectively represent the map range in the x direction, y min ，y max Respectively representing the map range in the y-direction.
2. Collision prevention constraint
In performing a mission, multiple aircraft collaborative reconnaissance may take into account the problem of inter-aircraft collisions as compared to a single aircraft. Because of the inherent factors such as the drift of the aircrafts, the influence of air flow and the like, the safety distance must be set when a plurality of aircrafts execute tasks, otherwise, the aircrafts are mutually interfered by light aircrafts, and a plurality of crashes crash by heavy aircrafts, thus the safety distance between the aircrafts is necessary to be set, namely
||x i (t)-x j (t)||≥2R (8)
Wherein x is i (t)，x j (t) respectively represent the first aircraft A i ，A j At the position at time t, 2R represents the inter-machine safety distance.
3. Aircraft performance constraints
Due to the limited performance of the aircraft itself, the turning radius of the aircraft is limited during high speed flight. I.e. the control quantity u of the aircraft i (t) the following constraints need to be satisfied:
-φ i,max ≤u i (t)≤φ i,max (9)
u i (t) is the control quantity of the aircraft, phi i,max For aircraft A i Maximum included angle between speed direction and positive half axis of x-axis, -phi i,max For aircraft A i The maximum angle between the speed direction and the negative half axis of the x axis.
3. Distributed cooperative target reconnaissance control for aircraft clusters
1. Aircraft scout performance index function
When designing an aircraft scout performance index function, consideration is needed:
(1) Environmental scout benefits, i.e., how to enable an aircraft to detect as much as possible an unknown region of high uncertainty?
(2) The task execution cost is the cost of how to keep the aircraft in a straight flight state as much as possible, and the turning maneuver times are reduced.
The aircraft scout performance index function is thus a multi-objective function.
1) Environmental investigation benefits
Definition of aircraft A i Is a scout path P of (1) i l (t)＝{P i l (t+1|t),…,P i l (t+q|t),…,P i l (t+T p Environmental scout benefit on t } is
Wherein P is i l (t+q|t),i＝q,…,T p Representing aircraft A i The q-th track point on the first path predicted at the time t, phi i (c) Representing when aircraft A i When being positioned at the grid path point c, the sensor detects the target surface set phi i (c) Determined by a sensor detection model, eta i,c,t Is the uncertainty size within the mesh path point c.
Defined within grid path point c, the probability of target existence is p c (k)∈[0,1]I.e. p c (k) =0 denotes a trellis pathNo targets exist in the dot, p c (k) =1 indicates that there is a target in the mesh waypoint. Uncertainty η of grid path point c i,c,t The updated formula of (2) is:
wherein K is γ > 0, || means taking absolute value.
Definition τ=1 indicates that the event "there is a target in the grid-path point c", τ=0 indicates that the event "there is no target in the grid-path point c", Ω i,c,t =1 indicates that at time k, unmanned plane a i Searching for the existence target in the grid path point c to ensure that the existence probability p of the target c (t) updating the map to define a new variable as a linear update formula:
the probability map linear update formula is therefore:
Π c,t ＝Π c,t-1 +λ c,t (13)
wherein the method comprises the steps of
p d ，p f The detection probability and false alarm probability of the sensor, i.e. p d ＝p(Ω i,c,t ＝1∣τ c ＝1),p f ＝p(Ω i,c,t ＝1∣τ c =0), these two indices describe the performance of the sensor. Uncertainty η i,c,t The updating method can be updated as follows:
2) Cost of task execution
Aircraft A i Is a scout path P of (1) i l (t)＝{P i l (t+1|t),…,P i l (t+q|t),…,P i l (t+T p The task execution cost on t) is:
u i (P i l (t+q+ 1|t) represents aircraft A i At the path point P i l Heading at (t+q|t). As can be seen, task execution cost J c (i, l, t) may enable aircraft A i The number of turning maneuvers is reduced as much as possible to maintain straight flight as much as possible, which is beneficial to reducing fuel consumption.
Thus, aircraft A i Is a scout path P of (1) i l The overall performance index function is a weighted summation of the individual performance indices.
Wherein the weight k 1 ，k 2 Satisfy k 1 +k 2 ＝1。
2. Distributed rolling time domain optimization model for multi-aircraft cooperative target reconnaissance control problem
In order to avoid the problem of dimension disasters caused by the increase of the number of aircrafts in a centralized rolling time domain optimization model, the invention establishes the following distributed rolling time domain optimization problem based on communication topology.
Wherein J is i Representing aircraft A i In the rolling time domain T p An index function (16) of the internal optimization.And U i (t) aircraft A respectively i In the rolling time domain T p Internal state [ t+1; t+T p ]A predicted sequence and a control input sequence, f representing the equation of motion of the aircraft. Xi, Θ represent the set of state constraints and the set of control constraints, respectively, of the aircraft described above.
Due to aircraft A i In calculating the local optimization problem (17), the synergy with other aircraft needs to be considered, so the objective function (16) contains the division A i Other aircrafts outside the rolling time domain t epsilon [ t+1; t+T p ]In-phase state prediction sequences and control input prediction sequences, i.e.And-> The transmission of (a) requires reliance on an inter-aircraft communication network, but due to battlefield practical communication range limitations, some aircraft may not have communication conditions at time t. Therefore, the present invention bases the +.>The update of (2) is classified into the following two cases.
That is, if at time t, aircraft A i And A is a j Can communicate with each other, i.e. the corresponding element C in the cluster communication connectivity matrix C (t) ij (t) 1 or more, aircraft A i Can utilize A j A latest state prediction sequence; conversely, if aircraft A i And A is a j Is unable to communicate with each other, i.e. the corresponding element C in the cluster communication connectivity matrix C (t) ij (t) < 1, aircraft A i State prediction order obtained by last momentThe column computes a local optimization problem (17).
4. Simulation results
Simulation is carried out on the multi-aircraft collaborative search algorithm under the communication constraint, the following scenes are considered, the scenes are small-range rectangular areas, three aircraft on the sea search targets of three enemy ships on the sea, and the parameter design is shown in table 1:
TABLE 1
As shown in fig. 3, the five-pointed star is a target position, the target moves at a uniform speed on the sea surface according to a specified navigational speed, the fan-shaped radar detection target surface of the aircraft is represented, and the gray area is the searched area of the aircraft. Under the task scene, under the condition that turning radius constraint and inter-aircraft collision prevention constraint are not violated, all targets are searched by 3 aircrafts through 132s, the average single-step decision time is 0.012s, and the task instantaneity requirement is met.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. A multi-aircraft collaborative search algorithm under communication constraints, comprising the steps of:
s1, constructing an environment model according to the speed of an aircraft and a communication range threshold, wherein the environment model comprises a task area model and an inter-machine communication topology model, and the task area model is as follows:
c＝m+(n-1)×L x ，
c∈{1,2,…,L x ×L y }
wherein, (L) x ×L y ) Representing the task area is discretized into (L x ×L y ) The grid, c, represents the grid of the rasterized task area, m represents the mth row of the rasterized task area, and n represents the nth column of the rasterized task area;
the inter-machine communication topology model is as follows:
wherein r (t) is a communication range threshold, N v For the total number of aircraft clusters, if h ij =1 and h ji =1, then this indicates that aircraft a i Can be connected with aircraft A j The communication can be realized, and a matrix C (t) represents the real-time communication topological relation of the aircraft cluster at the current moment t;
s2, constructing an aircraft sensor detection model according to detection probability, identification probability, false alarm probability and detectable area range, wherein the detection probability is the probability that a sensor on an aircraft finds a target, the identification probability is the probability that the sensor on the aircraft identifies the target, the false alarm probability is the probability that the sensor on the aircraft erroneously identifies the target, the detectable area range is a sector area, and the central angle of the sector area is the maximum coverage angle of an aircraft radar on an azimuth plane;
s3, constructing an aircraft platform model:
x i (k+j|k)＝f(x i (t+j-1|t),u i (t+j-1|t)),i＝1,2,…,N v ,j＝1,2,…,T p
x i (t)＝[x i (t),y i (t),φ i (t)]
wherein f (·) is the aircraft state update equation, u i (k)＝Δφ i (k),T p To predict time domain, i is aircraft sequence number, x i ，y i Respectively aircraft A i In the x-axis and y-axis positions, V i (t) aircraft A i Is phi, the flying speed of the aircraft i (t) aircraft A i Included angle between speed direction and positive half axis of x-axis, mu i (t) is the roll angle of the aircraft, g is the gravitational constant, n z,i Is the normal overload of the aircraft;
s4, constructing a target model according to the target movement speed:
wherein V is target (t) is the speed of the target aircraft, x target (t) is the location of the target aircraft;
s5, constructing constraint conditions, including environmental constraint, collision avoidance constraint and aircraft performance constraint;
the environmental constraints are:
x min ≤x i (t)≤x max
y min ≤y i (t)≤y max
wherein x is min ，x max Respectively in the x directionMap range, y min ，y max Respectively representing map ranges in the y direction;
the collision prevention constraint is as follows:
||x i (t)-x j (t)||≥2R
wherein x is i (t)，x j (t) respectively represent the first aircraft A i ，A j At the position of time t, 2R represents the safe distance between machines;
aircraft performance constraints are:
-φ i,max ≤u i (t)≤φ i,max
wherein u is i (t) is the control quantity of the aircraft, phi i,max For aircraft A i Maximum included angle between speed direction and positive half axis of x-axis, -phi i,max For aircraft A i Maximum included angle between the speed direction and the negative half axis of the x axis;
s6, constructing a search performance index function according to environmental reconnaissance benefits and task execution costs, wherein the method specifically comprises the following steps:
s61, defining an aircraft A i Is a scout path P of (1) i l (t)＝{P i l (t+1|t),…,P i l (t+q|t),…,P i l (t+T p Environmental scout benefit on t } is
Wherein P is i l (t+q|t),i＝q,…,T p Representing aircraft A i The q-th track point on the first path predicted at the time t, phi i (c) Representing when aircraft A i When being positioned at the grid path point c, the sensor detects the target surface set phi i (c) Determined by a sensor detection model, eta i,c,t An uncertainty size within the mesh path point c;
defined within grid path point c, the probability of target existence is p c (k)∈[0,1]I.e. p c (k) =0 indicates that there is no target within the mesh path point, p c (k) =1 represents a mesh pathThe target exists in the path point, and the uncertainty eta of the grid path point c is determined i,c,t The updated formula of (2) is:
wherein K is γ > 0, |·| represents taking absolute values;
defining τ=1 to indicate that there is a target in grid path point c, τ=0 to indicate that there is no target in grid path point c, Ω i,c,t =1 indicates that at time k, unmanned plane a i It is searched that a target exists in the mesh path point c,
constructing a probability map linear updating formula:
Π c,t ＝Π c,t-1 +λ c,t
wherein,
p d ，p f the detection probability and false alarm probability of the sensor, i.e. p d ＝p(Ω i,c,t ＝1∣τ c ＝1),p f ＝p(Ω i,c,t ＝1∣τ c =0), uncertainty η i,c,t The updating is as follows:
s62, constructing an aircraft A i Is a scout path P of (1) i l (t)＝{P i l (t+1|t),…,P i l (t+q|t),…,P i l (t+T p The task execution cost on t) is:
wherein u is i (P i l (t+q+ 1|t) represents aircraft A i At the path point P i l Heading at (t+q|t);
s63, constructing an aircraft A i Is a scout path P of (1) i l Search performance index function above:
wherein the weight k 1 ，k 2 Satisfy k 1 +k 2 ＝1；
S7, constructing a multi-aircraft collaborative search algorithm model based on communication topology according to an environment model, an aircraft sensor detection model, an aircraft platform model, a target model and constraint conditions and combining a search performance index function:
wherein J is i Representing aircraft A i In the rolling time domain T p An index function of the internal optimization,and U i (t) aircraft A respectively i In the rolling time domain T p Internal state [ t+1; t+T p ]The prediction sequence and the control input sequence, f represents the motion equation of the aircraft, xi, and Θ represent the aircraft A respectively i A set of state constraints and a set of control constraints, the set of state constraints comprising an environment constraint andcollision prevention constraint, wherein the control constraint set is aircraft performance constraint; />Respectively A i Other aircrafts outside the rolling time domain t epsilon [ t+1; t+T p ]Intra state prediction sequence and control input prediction sequence,/->The transmission of (a) is dependent on an inter-aircraft communication network, but due to the limitation of the actual communication range of a battlefield, part of aircrafts may not have communication conditions at the moment t, so based on an inter-aircraft communication topology model, the following is +_>The update of (2) is divided into the following two cases:
i.e. if at time t, aircraft a i And A is a j Can communicate with each other, i.e. the corresponding element C in the cluster communication connectivity matrix C (t) ij (t) 1 or more, aircraft A i Can utilize A j A latest state prediction sequence; conversely, if aircraft A i And A is a j Is unable to communicate with each other, i.e. the corresponding element C in the cluster communication connectivity matrix C (t) ij (t) < 1, aircraft A i And calculating a multi-aircraft collaborative search algorithm model by using the state prediction sequence obtained at the last moment.
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