A trajectory planning method for multi-target coordinated strike by low-cost patrol aircraft

Abstract

The present invention discloses a collaborative trajectory planning method for low-cost patrol aircraft to arrive at multiple strike targets at intervals. Based on the Dubins curve, combined with the initial state of the aircraft, the target strike state, and the target strike accuracy, and considering the interval arrival and maximum sinking rate constraints of the "man-in-the-loop" constraints of the low-cost patrol aircraft, a fast trajectory real-time generation method with the circling radius as the optimization variable is designed. On the basis of ensuring the existence of a feasible solution, multiple patrol aircraft can be quickly and spaced to reach the preset strike targets, thereby improving the accuracy and efficiency of the multiple patrol aircraft in striking multiple targets.

Description

Technical Field

[0001] The present invention relates to the fields of patrol aircraft trajectory planning, multi-target asynchronous strike control, and in particular to a low-cost patrol aircraft multi-target coordinated strike trajectory planning method. Background Art

[0002] In recent years, coordinated strikes by low-cost loitering aircraft have been widely used in various complex military missions. Trajectory planning for loitering aircraft involves comprehensively considering factors such as trajectory length, environmental data, and dynamic constraints, while specifying their starting and ending locations. This approach constructs an optimal trajectory suitable for the current scenario. This is crucial for ensuring that loitering aircraft can quickly complete their strike missions and determines the proper allocation of tasks and the flight paths of each aircraft. While well-established methods exist for trajectory planning for single targets, research on trajectory planning for multi-target, asynchronous strikes by multiple aircraft is limited, resulting in weak coordinated strike capabilities and the inability to meet "man-in-the-loop" control requirements. This method, based on the Dubins curve, combines the initial state of the aircraft, the target strike state, and target strike accuracy. Furthermore, it considers the "man-in-the-loop" constraints of low-cost loitering aircraft, such as arrival interval and maximum sink rate. A rapid real-time trajectory generation method is designed, using the circling radius as the optimization variable. This method ensures the existence of a feasible solution, enabling multiple loitering aircraft to quickly and spaced apart from each other to reach their designated strike targets, thereby improving the precision and effectiveness of multiple loitering aircraft strikes against multiple targets. Summary of the Invention

[0003] The present invention aims to provide a trajectory planning method for coordinated multi-target strike by a low-cost patrol aircraft to solve the problems raised in the above background technology.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] A low-cost patrol aircraft multi-target coordinated strike trajectory planning method includes the following steps:

[0006] S1. Determine the starting state X of the patrol aircraft trajectory planning in the two-dimensional plane according to the flight state of the patrol aircraft, the position of the strike target, and the strike azimuth requirements. s With the target state X f ;

[0007] S2, consider the minimum turning radius r of the patrol aircraft min Constraint, based on the Dubins curve, calculate the s To the target state X f The optimal path S min ;

[0008] S3. Adjust the two-dimensional plane curve to a three-dimensional flight trajectory based on the strike height difference and the maximum sinking rate constraint of the patrol aircraft;

[0009] S4. Using turning radius as a variable, collaboratively optimize the three-dimensional trajectory of multiple patrol aircraft to meet strike time interval requirements and achieve real-time monitoring and auxiliary operations with "man in the loop".

[0010] Preferably, in step S1, the starting state X of the patrol aircraft trajectory planning in the two-dimensional plane is determined according to the flight state of the patrol aircraft, the position of the strike target and the strike azimuth requirement. s With the target state X f , specifically:

[0011] S11, the position of the patrol aircraft is X P =(x p ,y p ,z p ), the flight azimuth is θ s , then the initial state X of the trajectory planning of the patrol aircraft in the two-dimensional plane is s For X s =(x s ,y s ,θ s )=(x p ,y p ,θ s );

[0012] S12. To ensure that the cruise aircraft does not have a large roll angle within a certain period of time or distance before reaching the target, thereby improving the accuracy of the terminal target strike, the terminal straight-line flight distance of the cruise aircraft is set to d.

[0013] S13, according to the target position X g =(x g ,y g ,z g ), strike azimuth θ g The requirements and the terminal straight flight distance d are set to calculate the target state X of the patrol aircraft trajectory planning in the two-dimensional plane. f =(x f ,y f ,θ f )=(x g -d·cosθ g ,y g -d·sinθ g ,θ g ).

[0014] Preferably, in step S2, the minimum turning radius r of the patrol aircraft is considered. minConstraint, based on the Dubins curve, calculate the s To the target state X f The optimal path S min , specifically:

[0015] S21, calculate from the starting state X s To the target state X f The CSC type Dubins curve and the corresponding curve length, CSC types include RSR, RSL, LSR, LSL; where R represents the minimum turning radius r of the cruise aircraft min Right dial, S means going straight, L means the minimum turning radius r of the patrol aircraft min On the left panel, for the four CSC types of Dubins curves, RSR, RSL, LSR, and LSL, the corresponding curve length is calculated and expressed as L RSR , L RSL , L LSR and L LSL ;

[0016] S22, calculate from the starting state X s To the target state X f The CCC type Dubins curve and the corresponding curve length. The CCC types include: RLR, LRL. The meanings of R and L are consistent with those in S21. For the RLR and LRL CCC types of Dubins curves, the corresponding curve length is calculated and expressed as L RLR and L LRL ;

[0017] S23, select L RSR , L RSL , L LSR ,L LSL and L RLR ,L LRL The smallest value L min and the corresponding Dubins curve as the two-dimensional optimal path S min .

[0018] Preferably, in step S21, the calculation from the initial state X s To the target state X s The CSC type Dubins curve and the corresponding curve length are as follows:

[0019] S211. Calculate the center coordinates of the starting circle of the CSC type Dubins curve:

[0020] X i =(x i ,y i )=(x s +rmin ·i·sinθ s ,y s -r min ·i·cosθ s ), where i is the starting circle direction, i=1 when the wheel is right-handed and i=-1 when the wheel is left-handed;

[0021] S212. Calculate the coordinates of the center of the CSC type Dubins curve termination circle:

[0022] X o =(x o ,y o )=(x f +r min ·j·sinθ f ,y f -r min ·j·cosθ f ), where j is the direction of the end circle, j = 1 when the disk is right-handed, and j = -1 when the disk is left-handed;

[0023] S213, calculate the vector V obtained by connecting the centers of the starting circle and the ending circle oi =(x o -x i ,y o -y i ), and convert it into V l =(v lx ,v ly )=V oi / ||V oi ||;

[0024] S214. Calculate the tangent normal vectors of the starting circle and the ending circle:

[0025]

[0026] Where c = (i·j-1)r min / ||V oi ||;

[0027] S215. Calculate the tangent point between the straight line segment of the Dubins curve and the starting circle:

[0028] X it =(x i +i·j·r min ·v nx ,y i +i·j·r min ·v ny );

[0029] S216. Calculate the tangent point between the straight line segment of the Dubins curve and the terminal circle:

[0030] X ot =(x o +r min ·v nx ,y o +r min ·v ny );

[0031] S217. Calculate the length of the Dubins curve in, is the starting state X s The position (x s ,y s ) to the tangent point X it The length of the arc, is the tangent point X it To the tangent point X ot The straight line length, is the tangent point X ot To the target state X f The position (x f ,y f )’s arc length.

[0032] Preferably, in step S217, the length of the Dubins curve is calculated Specifically:

[0033] S2171, calculate the starting state X s To the tangent point X it The arc length Calculate the starting position X s To the tangent point position X it Angle difference where 0≤θ it ,θ is <2π; According to the circling direction of the patrol aircraft, determine whether the circling path is a superior arc or an inferior arc, and calculate the circling angle of the patrol aircraft within the starting circle:

[0034] if(Δθ i <0&i=-1),then(Δθ i =2π+Δθ i ),

[0035] if(Δθ i >0&i=1),then(Δθ i =2π-Δθ i ); thereby calculating the arc length of the spiral

[0036] r min is the circling radius;

[0037] S2172, calculate the tangent point Xit To the tangent point X ot The formula for calculating the length of a straight line is:

[0038]

[0039] S2173, calculate the tangent point X ot To the target state X f The arc length Calculate the tangent point X ot To target state X f Angle difference where 0≤θ ot ,θ of <2π; According to the circling direction of the patrol aircraft, determine whether the circling path is a superior arc or an inferior arc, and calculate the angle value of the patrol aircraft circling within the termination circle:

[0040] if(Δθ o <0&j=-1),then(Δθ o =2π+Δθ o ),

[0041] if(Δθ o >0&j=1),then(Δθ o =2π-Δθ o ), and thus calculate the arc length of the spiral r min is the circling radius;

[0042] S2174, calculate from the starting state X s To the target state X f Dubins curve length

[0043] Preferably, in step S22, the calculation from X s To X f The length of the CCC type Dubins curve is:

[0044] S221. Calculate the center coordinates of the starting circle of the CCC type Dubins curve:

[0045] X i =(x i ,y i )=(x s +r min ·i·sinθ s ,y s -r min ·i·cosθ s ), where i is the starting circle direction, i=1 when the wheel is right-handed and i=-1 when the wheel is left-handed;

[0046] S222. Calculate the coordinates of the center of the CCC type Dubins curve termination circle:

[0047] X o =(x o ,y o )=(x f +r min ·j·sinθ f ,y f -r min ·j·cosθ f ), where j is the direction of the end circle, j = 1 when the disk is right-handed, and j = -1 when the disk is left-handed;

[0048] S223. Calculate the vector obtained by connecting the centers of the starting circle and the ending circle:

[0049] V oi =(v xoi ,v yoi )=(x o -x i ,y o -y i ), and vector angle: θ oi =arctan(v yoi / v xoi );

[0050] S224. Using the center of the starting circle as the vertex, calculate the interior angle of the triangle formed by the centers of the three circles:

[0051] Among them, the subscript i represents the center of the starting circle, the subscript o represents the center of the ending circle, the subscript m represents the center of the middle circle, and the subscript d represents the center of the middle circle. oi =||V oi || is the modulus of the line vector connecting the center of the starting circle and the center of the ending circle, d im =r min +r mid is the modulus of the line vector connecting the center of the starting circle and the center of the middle circle, r mid =max{r min ,(d oi -2·r min ) / 2} is the radius of the middle circle, d im =d mo is the modulus of the vector connecting the center of the central circle and the center of the end circle;

[0052] S225. Calculate the coordinates of the center of the middle circle:

[0053] X mid =(x mid ,y mid )=(x i +d im ·cos(θoi -θ oim ),y i +d im ·sin(θ oi -θ oim ));

[0054] S226. Calculate the vector V of the line connecting the center of the starting circle and the center of the middle circle im =(x mid -x i ,y mid -y i ), and convert it to V i ' m =(v′ imx ,v′ imy )=V im / ||V im ||;

[0055] S227. Calculate the vector V of the line connecting the center of the end circle and the center of the middle circle mo =(x o -x mid ,y o -y mid ), and normalize it to V m ' o =(v′ mox ,v′ moy )=V mo / ||V mo ||;

[0056] S228, calculate the tangent point X on the starting circle it =(x i +r min ·v′ imx ,y i +r min ·v′ imy ), calculate the tangent point X on the termination circle ot =(x mid +r mid ·v′ mox ,y mid +r mid ·v′ moy );

[0057] S229. Calculate the length of the Dubins curve in, is the starting state X s The position (x s ,y s ) to the tangent point X on the starting circle it The length of the arc, is the tangent point X on the starting circleit To the tangent point X on the end circle ot The length of the arc, is the tangent point X on the ending circle ot To the target state X f The position (x f ,y f )’s arc length.

[0058] Preferably, in step S3, the two-dimensional plane curve is adjusted to a three-dimensional flight trajectory in combination with the strike height difference and the maximum sinking rate constraint of the patrol aircraft, specifically:

[0059] S31, determine whether the two-dimensional optimal Dubins curve meets the maximum sink rate requirement of the cruise aircraft. If it meets the maximum sink rate requirement, that is, L min ≥L load ,L load =(z g -z p ) / tanΥ max , Υ max is the maximum sink rate, then the sink rate of the aircraft is set to Υ=arctan((z g -z p ) / L min ), the patrol aircraft maneuvers and descends according to the sinking rate, and the actual three-dimensional trajectory length

[0060] S32, if the maximum sinking rate requirement is not met, that is, L min <L load , then the circling radius r of the patrol aircraft needs to be adjusted 3D (r 3D ≥r min ), so that the length of the Dubins curve in the two-dimensional plane is L load To simplify the calculation, the radius of the starting circle and the ending circle are adjusted to r 3D In step S217, the length L of the Dubins curve in the two-dimensional plane is expressed as a function of the spiral radius r. According to the functional relationship and L=L load , calculate r 3D , then the actual three-dimensional trajectory length

[0061] S33, according to the calculated r 3D , recalculate the corresponding Dubins curve S, and save L and S to the computer memory.

[0062] Preferably, in step S4, the three-dimensional trajectories of multiple patrol aircraft are collaboratively optimized with the turning radius as a variable to meet the strike time interval requirement and realize real-time monitoring and auxiliary operation of "man in the loop", specifically:

[0063] S41: Determine the three-dimensional trajectory lengths L of N patrol aircraft to N strike targets according to steps S1 to S3. k and S k (1≤k≤N), construct the flight track length array L of multiple patrol aircraft whole =[L1,···L k ···L N ],L1≤···L k ···≤L N ;

[0064] S42, starting from the shortest flight path, i.e. L1, determine in turn whether the strike time between the two patrol aircraft and the corresponding target meets the minimum time interval constraint, i.e. (L j+1 -L j ) / V≥ΔT,j=1,…N-1, V is the flight speed of the patrol aircraft: If it is not satisfied, the turning radius of the j+1th patrol aircraft is adjusted to r' 3D ,r' 3D ≥r 3D , to extend the three-dimensional track length of the j+1th patrol aircraft so that the strike time between the two patrol aircraft and the corresponding target meets the minimum time interval requirement. Repeat this step until the strike time interval between all patrol aircraft meets the requirement;

[0065] S43, according to the calculated r' 3D , recalculate the Dubins curve S of the corresponding patrol aircraft, and save L and S to the computer memory, so as to obtain the strike track of all patrol aircraft.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] This method is based on the Dubins curve. Combining the initial state of the aircraft, the target strike state, and the target strike accuracy, this method considers the "man-in-the-loop" constraints of low-cost patrol aircraft, such as the arrival interval and the maximum sinking rate. A fast track real-time generation method with the circling radius as the optimization variable is designed. On the basis of ensuring the existence of a feasible solution, multiple patrol aircraft can be quickly and spaced to reach the preset strike target, which can effectively improve the accuracy and effectiveness of multiple low-cost patrol aircraft in striking multiple targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A multi-target coordinated strike trajectory planning flow chart for a low-cost loitering aircraft multi-target coordinated strike trajectory planning method;

[0069] Figure 2A schematic diagram of the CSC-type Dubins curve configuration for a low-cost loitering aircraft multi-target coordinated strike trajectory planning method;

[0070] Figure 3 A schematic diagram of the calculation of arc length in the Dubins curve for a trajectory planning method for a low-cost loitering aircraft to coordinate multi-target strikes;

[0071] Figure 4 A schematic diagram of the CCC-type Dubins curve configuration for a low-cost loitering aircraft multi-target coordinated strike trajectory planning method;

[0072] Figure 5 A schematic diagram of the LSR type Dubins curve of target point A for a trajectory planning method of a low-cost loitering aircraft for multi-target coordinated strike;

[0073] Figure 6 A schematic diagram of the LRL-type Dubins curve for target A of a trajectory planning method for a low-cost loitering aircraft to coordinate multi-target strikes;

[0074] Figure 7 A trajectory planning method for low-cost patrol aircraft to coordinate multi-target strike is proposed to adjust the two-dimensional Dubins curve of target A into a three-dimensional trajectory.

[0075] Figure 8 A trajectory planning method for low-cost patrol aircraft to coordinate multi-target strike is proposed to adjust the two-dimensional Dubins curve of target B into a three-dimensional trajectory.

[0076] Figure 9 This is a three-dimensional schematic diagram of multiple targets before and after adjustment of the trajectory planning method for multi-target coordinated attack by a low-cost patrol aircraft. DETAILED DESCRIPTION

[0077] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0078] The reference numerals in the drawings of the specification include:

[0079] like Figure 1-4 As shown, a trajectory planning method for a low-cost patrol aircraft to coordinate a multi-target strike includes the following steps:

[0080] S1. Determine the starting state X of the patrol aircraft trajectory planning in the two-dimensional plane according to the flight state of the patrol aircraft, the position of the strike target, and the strike azimuth requirements. s With the target state X f ;

[0081] S2, consider the minimum turning radius r of the patrol aircraft minConstraint, based on the Dubins curve, calculate the s To the target state X f The optimal path S min ;

[0082] S3. Adjust the two-dimensional plane curve to a three-dimensional flight trajectory based on the strike height difference and the maximum sinking rate constraint of the patrol aircraft;

[0083] S4. Using turning radius as a variable, collaboratively optimize the three-dimensional trajectory of multiple patrol aircraft to meet strike time interval requirements and achieve real-time monitoring and auxiliary operations with "man in the loop".

[0084] In step S1, the starting state X of the patrol aircraft trajectory planning in the two-dimensional plane is determined according to the flight state of the patrol aircraft, the position of the strike target and the strike azimuth requirement. s With the target state X f , specifically:

[0085] S11, the position of the patrol aircraft is X P =(x p ,y p ,z p ), the flight azimuth is θ s , then the initial state X of the trajectory planning of the patrol aircraft in the two-dimensional plane is s For X s =(x s ,y s ,θ s )=(x p ,y p ,θ s );

[0086] S12. To ensure that the cruise aircraft does not have a large roll angle within a certain period of time or distance before reaching the target, thereby improving the accuracy of the terminal target strike, the terminal straight-line flight distance of the cruise aircraft is set to d.

[0087] S13, according to the target position X g =(x g ,y g ,z g ), strike azimuth θ g The requirements and the terminal straight flight distance d are set to calculate the target state X of the patrol aircraft trajectory planning in the two-dimensional plane. f =(x f ,y f ,θ f )=(x g -d·cosθ g ,y g -d·sinθ g,θ g ).

[0088] In step S2, the minimum turning radius r of the patrol aircraft is considered. min Constraint, based on the Dubins curve, calculate the s To the target state X f The optimal path S min , specifically:

[0089] S21, calculate from the starting state X s To the target state X f The CSC type Dubins curve and the corresponding curve length, CSC types include RSR, RSL, LSR, LSL; where R represents the minimum turning radius r of the cruise aircraft min Right dial, S means going straight, L means the minimum turning radius r of the patrol aircraft min On the left panel, for the four CSC types of Dubins curves, RSR, RSL, LSR, and LSL, the corresponding curve length is calculated and expressed as L RSR , L RSL , L LSR and L LSL ;

[0090] S22, calculate from the starting state X s To the target state X f The CCC type Dubins curve and the corresponding curve length. The CCC types include: RLR, LRL. The meanings of R and L are consistent with those in S21. For the RLR and LRL CCC types of Dubins curves, the corresponding curve length is calculated and expressed as L RLR and L LRL ;

[0091] S23, select L RSR , L RSL , L LSR ,L LSL and L RLR ,L LRL The smallest value L min and the corresponding Dubins curve as the two-dimensional optimal path S min .

[0092] In step S21, the calculation starts from the initial state X s To the target state X s The CSC type Dubins curve and the corresponding curve length are as follows:

[0093] S211. Calculate the center coordinates of the starting circle of the CSC type Dubins curve:

[0094] X i =(x i ,y i )=(x s +r min ·i·sinθ s ,y s -r min ·i·cosθ s ), where i is the starting circle direction, i=1 when the wheel is right-handed and i=-1 when the wheel is left-handed;

[0095] S212. Calculate the coordinates of the center of the CSC type Dubins curve termination circle:

[0096] X o =(x o ,y o )=(x f +r min ·j·sinθ f ,y f -r min ·j·cosθ f ), where j is the direction of the end circle, j = 1 when the disk is right-handed, and j = -1 when the disk is left-handed;

[0097] S213, calculate the vector V obtained by connecting the centers of the starting circle and the ending circle oi =(x o -x i ,y o -y i ), and convert it into V l =(v lx ,v ly )=V oi / ||V oi ||;

[0098] S214. Calculate the tangent normal vectors of the starting circle and the ending circle:

[0099]

[0100] Where c = (i·j-1)r min / ||V oi ||;

[0101] S215. Calculate the tangent point between the straight line segment of the Dubins curve and the starting circle:

[0102] X it =(x i +i·j·r min ·v nx ,y i +i·j·r min ·vny );

[0103] S216. Calculate the tangent point between the straight line segment of the Dubins curve and the terminal circle:

[0104] X ot =(x o +r min ·v nx ,y o +r min ·v ny );

[0105] S217. Calculate the length of the Dubins curve in, is the starting state X s The position (x s ,y s ) to the tangent point X it The length of the arc, is the tangent point X it To the tangent point X ot The straight line length, is the tangent point X ot To the target state X f The position (x f ,y f )’s arc length.

[0106] In step S217, the length of the Dubins curve is calculated Specifically:

[0107] S2171, calculate the starting state X s To the tangent point X it The arc length Calculate the starting position X s To the tangent point position X it Angle difference where 0≤θ it ,θ is <2π,θ it ,θ is like Figure 3 As shown; according to the circling direction of the patrol aircraft, determine whether the circling path is a superior arc or an inferior arc, and calculate the angle value of the patrol aircraft circling within the starting circle:

[0108] if(Δθ i <0&i=-1),then(Δθ i =2π+Δθ i ),

[0109] if(Δθ i >0&i=1),then(Δθ i =2π-Δθi ); thereby calculating the arc length of the spiral

[0110] r min is the circling radius;

[0111] S2172, calculate the tangent point X it To the tangent point X ot The formula for calculating the length of a straight line is:

[0112]

[0113] S2173, calculate the tangent point X ot To the target state X f The arc length Calculate the tangent point X ot To target state X f Angle difference where 0≤θ ot ,θ of <2π; According to the circling direction of the patrol aircraft, determine whether the circling path is a superior arc or an inferior arc, and calculate the angle value of the patrol aircraft circling within the termination circle:

[0114] if(Δθ o <0&j=-1),then(Δθ o =2π+Δθ o ),

[0115] if(Δθ o >0&j=1),then(Δθ o =2π-Δθ o ), and thus calculate the arc length of the spiral r min is the circling radius;

[0116] S2174, calculate from the starting state X s To the target state X f Dubins curve length

[0117] In step S22, calculate from X s To X f The length of the CCC type Dubins curve is:

[0118] S221. Calculate the center coordinates of the starting circle of the CCC type Dubins curve:

[0119] X i =(x i ,y i )=(x s +r min ·i·sinθs ,y s -r min ·i·cosθ s ), where i is the starting circle direction, i=1 when the wheel is right-handed and i=-1 when the wheel is left-handed;

[0120] S222. Calculate the coordinates of the center of the CCC type Dubins curve termination circle:

[0121] X o =(x o ,y o )=(x f +r min ·j·sinθ f ,y f -r min ·j·cosθ f ), where j is the direction of the end circle, j = 1 when the disk is right-handed, and j = -1 when the disk is left-handed;

[0122] S223. Calculate the vector obtained by connecting the centers of the starting circle and the ending circle:

[0123] V oi =(v xoi ,v yoi )=(x o -x i ,y o -y i ), and vector angle: θ oi =arctan(v yoi / v xoi );

[0124] S224. Using the center of the starting circle as the vertex, calculate the interior angle of the triangle formed by the centers of the three circles:

[0125] Among them, the subscript i represents the center of the starting circle, the subscript o represents the center of the ending circle, the subscript m represents the center of the middle circle, and the subscript d represents the center of the middle circle. oi =||V oi || is the modulus of the line vector connecting the center of the starting circle and the center of the ending circle, d im =r min +r mid is the modulus of the line vector connecting the center of the starting circle and the center of the middle circle, r mid =max{r min ,(d oi -2·r min ) / 2} is the radius of the middle circle, d im =d mo is the modulus of the vector connecting the center of the central circle and the center of the end circle;

[0126] S225. Calculate the coordinates of the center of the middle circle:

[0127] X mid =(x mid ,y mid )=(x i +d im ·cos(θ oi -θ oim ),y i +d im ·sin(θ oi -θ oim ));

[0128] S226. Calculate the vector V of the line connecting the center of the starting circle and the center of the middle circle im =(x mid -x i ,y mid -y i ), and normalize it to V i ' m =(v′ imx ,v′ imy )=V im / ||V im ||;

[0129] S227. Calculate the vector V of the line connecting the center of the end circle and the center of the middle circle mo =(x o -x mid ,y o -y mid ), and normalize it to V m ' o =(v′ mox ,v′ moy )=V mo / ||V mo ||;

[0130] S228, calculate the tangent point X on the starting circle it =(x i +r min ·v′ imx ,y i +r min ·v′ imy ), calculate the tangent point X on the termination circle ot =(x mid +r mid ·v′ mox ,y mid +r mid ·v′ moy );

[0131] S229. Calculate the length of the Dubins curve in, is the starting state X s The position (x s ,y s ) to the tangent point X on the starting circle it The length of the arc, is the tangent point X on the starting circle it To the tangent point X on the end circle ot The length of the arc, is the tangent point X on the ending circle ot To the target state X f The position (x f ,y f )’s arc length.

[0132] In step S3, the two-dimensional plane curve is adjusted to a three-dimensional flight trajectory by combining the strike height difference and the maximum sinking rate constraint of the patrol aircraft, specifically:

[0133] S31, determine whether the two-dimensional optimal Dubins curve meets the maximum sink rate requirement of the cruise aircraft. If it meets the maximum sink rate requirement, that is, L min ≥L load ,L load =(z g -z p ) / tanΥ max , Υ max is the maximum sink rate, then the sink rate of the aircraft is set to Υ=arctan((z g -z p ) / L min ), the patrol aircraft maneuvers and descends according to the sinking rate, and the actual three-dimensional trajectory length

[0134] S32, if the maximum sinking rate requirement is not met, that is, L min <L load , then the circling radius r of the patrol aircraft needs to be adjusted 3D (r 3D ≥r min ), so that the length of the Dubins curve in the two-dimensional plane is L load To simplify the calculation, the radius of the starting circle and the ending circle are adjusted to r 3D In step S217, the length L of the Dubins curve in the two-dimensional plane is expressed as a function of the spiral radius r. According to the functional relationship and L=L load , calculate r 3D , then the actual three-dimensional trajectory length

[0135] S33, according to the calculated r 3D, recalculate the corresponding Dubins curve S, and save L and S to the computer memory.

[0136] In step S4, the three-dimensional trajectories of multiple patrol aircraft are collaboratively optimized with the turning radius as a variable to meet the strike time interval requirements and achieve real-time monitoring and auxiliary operations with "man in the loop". Specifically:

[0137] S41: Determine the three-dimensional trajectory lengths L of N patrol aircraft to N strike targets according to steps S1 to S3. k and S k (1≤k≤N), construct the flight track length array L of multiple patrol aircraft whole =[L1,···L k ···L N ],L1≤···L k ···≤L N ;

[0138] S42, starting from the shortest flight path, i.e. L1, determine in turn whether the strike time between the two patrol aircraft and the corresponding target meets the minimum time interval constraint, i.e. (L j+1 -L j ) / V≥ΔT,j=1,…N-1, V is the flight speed of the patrol aircraft: If it is not satisfied, the turning radius of the j+1th patrol aircraft is adjusted to r' 3D ,r' 3D ≥r 3D , to extend the three-dimensional track length of the j+1th patrol aircraft so that the strike time between the two patrol aircraft and the corresponding target meets the minimum time interval requirement. Repeat this step until the strike time interval between all patrol aircraft meets the requirement;

[0139] S43, according to the calculated r' 3D , recalculate the Dubins curve S of the corresponding patrol aircraft, and save L and S to the computer memory, so as to obtain the strike track of all patrol aircraft.

[0140] The specific implementation process is as follows:

[0141] The following embodiments of the present invention are further described in detail with reference to the accompanying drawings and example diagrams. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0142] In this embodiment, a low-cost patrol aircraft multi-target coordinated strike trajectory planning method is provided. Figure 1 As shown in Table 1, set the flight status, target position and azimuth, minimum turning radius, flight speed and other parameters of the patrol aircraft as shown in Table 1:

[0143] Table 1 Simulation parameter settings

[0144]

[0145] S1. To ensure that the patrol aircraft does not have a large roll angle before reaching the target, so as to improve the accuracy of the terminal target strike, the terminal straight flight distance d of the patrol aircraft is set to 100m. The starting state X of the patrol aircraft trajectory planning in the two-dimensional plane is s With the target state X f As shown in the following table:

[0146] Table 2 Starting state and target state of two-dimensional plane

[0147]

[0148] S2, consider the minimum turning radius r of the patrol aircraft min = 100m constraint, based on the Dubins curve, calculate the two-dimensional plane from the initial state X s To the target state X f The optimal path S min ;

[0149] S21, taking target A as an example, the CSC type Dubins curve from the starting state to the trajectory planning target state in the two-dimensional plane and the corresponding curve length calculation steps are as follows:

[0150] S211-S212, taking the LSR type Dubins curve in CSC as an example, where i = -1, j = 1, the coordinates of the center of the starting circle and the center of the ending circle are as follows:

[0151] X i =(x i ,y i )=(x s +r min ·i·sinθ s ,y s -r min ·i·cosθ s )=(-71,71)

[0152] X o =(x o ,y o )=(x f +r min ·j·sinθ f ,y f -r min ·j·cosθ f )=(-941,-1300)

[0153] S213. Calculate the vector obtained by connecting the centers of the starting circle and the ending circle:

[0154] V oi =(x o -x i ,y o -y i )=(-870,-1375),

[0155] And convert it into units:

[0156] V l =(v lx ,v ly )=V oi / ||V oi || = (-0.535, -0.845);

[0157] S214, tangent normal vectors of the starting and ending circles:

[0158]

[0159] The tangent points of the S215-S216 and Dubins curve straight line segments with the starting and ending circles are:

[0160] X it =(x i +i·j·r min ·v nx ,y i +i·j·r min ·v ny )=(-166,166)

[0161] X ot =(x o +r min ·v nx ,y o +r min ·v ny )=(-850,1346)S217、Calculate the length of Dubins curve in, is the starting state X s The position (x s ,y s ) to the tangent point X it The length of the arc, is the tangent point X it To the tangent point X ot The straight line length, is the tangent point X ot To the target state X f The position (x f ,y fThe specific calculation process is as follows:

[0162] S2171, calculate the starting state X s To the tangent point X it The arc length Calculate the starting position X s To the tangent point position X it Angle difference where 0≤θ it ,θ is <2π, where θ it ,θ is like Figure 3 As shown; according to the circling direction of the patrol aircraft, the circling path is judged to be a good arc or a bad arc, and the angle value of the patrol aircraft circling within the starting circle is calculated: if(Δθ i <0&i=-1),then(Δθ i =2π+Δθ i ),

[0163] if(Δθ i >0&i=1),then(Δθ i =2π-Δθ i ), then Δθ i =3.5; thus calculate the arc length r min is the circling radius;

[0164] S2172, calculate the tangent point X it To the tangent point X ot The formula for calculating the length of a straight line is:

[0165]

[0166] S2173, calculate the tangent point X ot To the target state X f The position (x f ,y f ) arc length

[0167] S22, taking target A as an example, the steps for calculating the CCC-type Dubins curve from the initial state to the trajectory planning target state in the two-dimensional plane and the corresponding curve length are as follows:

[0168] S221-S222, taking the LRL type Dubins curve in CCC as an example, where i = -1, the coordinates of the center of the starting circle and the center of the ending circle are as follows:

[0169] X i =(x i ,y i )=(xs +r min ·i·sinθ s ,y s -r min ·i·cosθ s )=(-70,70)

[0170] X o =(x o ,y o )=(x f +r min ·j·sinθ f ,y f -r min ·j·cosθ f )=(-800,-1159)

[0171] S223, calculate the vector V obtained by connecting the centers of the starting circle and the ending circle oi =(v xoi ,v yoi )=(x o -x i ,y o -y i )=(-729,-1229) and vector angle θ oi =arctan(V ot )=1.03;

[0172] S224. Using the center of the starting circle as the vertex, calculate the interior angle of the triangle formed by the centers of the three circles: Among them, the subscript i represents the center of the starting circle, the subscript o represents the center of the ending circle, the subscript m represents the center of the middle circle, and the subscript d represents the center of the middle circle. oi =||V oi ||=1429 is the modulus of the line vector connecting the center of the starting circle and the center of the ending circle, d im =r im +r mid =715 is the modulus length of the line vector connecting the center of the starting circle and the center of the middle circle, r mid =max{r min ,(d oi -2·r min ) / 2}=614 is the radius of the middle circle, d mo =d im =715 is the modulus length of the line vector connecting the center of the middle circle and the center of the end circle;

[0173] S225. Calculate the coordinates of the center of the middle circle:

[0174] X mid =(x mid ,y mid )=(xi +d im ·cos(θ oi -θ oim ),y i +d im ·sin(θ oi -θ oim ))=(-435,-544);

[0175] S226. Calculate the vector of the line connecting the center of the starting circle and the center of the middle circle:

[0176] V im =(x mid -x i ,y mid -y i )=(-365,-615),

[0177] And unitize it V i ' m =(v′ imx ,v′ imy )=V im / ||V im || = (-0.51, -0.86);

[0178] S227. Calculate the vector of the line connecting the center of the end circle and the center of the middle circle:

[0179] V mo =(x o -x mid ,y o -y mid )=(-365,-615),

[0180] And unitize it V m ' o =(v′ mox ,v′ moy )=V mo / ||V mo || = (-0.51, -0.86);

[0181] S228, calculate the tangent point X on the starting circle it =(x i +r min ·v′ imx ,y i +r min ·v′ imy )=(-122,-15), calculate the tangent point X on the termination circle ot =(x mid +r mid ·v′ mox ,y mid+r mid ·v′ moy ) = (-749, -1073);

[0182] S229. Calculate the length of the Dubins curve in, is the starting state X s The position (x s ,y s ) to the tangent point X on the starting circle it The length of the arc, is the tangent point X on the starting circle it To the tangent point X on the end circle ot The length of the arc, is the tangent point X on the ending circle ot To the target state X f The position (x f ,y f ), the calculation steps are similar to those in step S217.

[0183] According to step S2, the Dubins curve lengths and optimal curves of each strike target are shown in the following table:

[0184]

[0185] S3. Combine the strike altitude difference and the maximum sink rate constraint of the patrol aircraft to adjust the two-dimensional plane curve to a three-dimensional flight trajectory. The specific process is as follows:

[0186] S31. Taking the attack target A as an example, determine whether the two-dimensional optimal Dubins curve meets the maximum sinking rate requirement of the patrol aircraft. If it meets the maximum sinking rate requirement, that is, L min ≥L load ,L load =(z g -z p ) / tanΥ max , Υ max is the maximum sink rate, then the sink rate of the aircraft is set to Υ=arctan((z g -z p ) / L min ), the patrol aircraft maneuvers and descends according to the sinking rate, and the actual three-dimensional trajectory length like Figure 7 As shown:

[0187] S32. If the maximum sinking rate requirement is not met, taking the attack on target B as an example, that is, L min <L load ,L load =(z g -z p) / tanΥ max , Υ max For the maximum sinking rate, the circling radius r of the patrol aircraft needs to be adjusted 3D (r 3D ≥r min ), so that the length of the Dubins curve in the two-dimensional plane is L load To simplify the calculation, the radius of the starting circle and the ending circle are adjusted to r 3D , the cruising radius calculation step S217 and its detailed steps are as follows, the actual three-dimensional trajectory length like Figure 8 As shown;

[0188] S33, according to the calculated r 3D , recalculate the corresponding Dubins curve S, and save L and S to the computer memory.

[0189] According to step S3, the table of each strike target adjusted from a two-dimensional plane curve to a three-dimensional flight trajectory is as follows:

[0190]

[0191] S4. Using turning radius as a variable, coordinately optimize the three-dimensional trajectory of multiple patrol aircraft to meet strike interval requirements and achieve real-time monitoring and auxiliary operations with "man in the loop." Specifically:

[0192] S41: Determine the three-dimensional trajectory lengths L of N patrol aircraft to N strike targets according to steps S1 to S3. k and S k (1≤k≤N), construct the flight track length array L of multiple patrol aircraft whole =[L D ,L B , L E , L C , L A , L F ],L D ≤···L C ···≤L F ;

[0193] S42, starting from the shortest flight path, i.e. L1, determine in turn whether the strike time between the two patrol aircraft and the corresponding target meets the minimum time interval constraint, i.e. (L j+1 -L j ) / V≥ΔT,j=1,…N-1, V is the flight speed of the patrol aircraft: If it is not satisfied, the turning radius of the j+1th patrol aircraft is adjusted to r' 3D ,r' 3D ≥r 3D, to extend the three-dimensional track length of the j+1th patrol aircraft so that the strike time between the two patrol aircraft and the corresponding target meets the minimum time interval requirement. Repeat this step until the strike time interval between all patrol aircraft meets the requirement;

[0194] S43, according to the calculated r' 3D , recalculate the Dubins curve S of the corresponding patrol aircraft, and save L and S to the computer memory, so as to obtain the strike track of all patrol aircraft.

[0195] The schematic diagram of judging whether the time interval constraint is satisfied is shown below. The schematic diagram of the multi-target 3D diagram before and after adjustment is shown below. Figure 9 shown.

[0196]

[0197] The above is only an embodiment of the present invention, and the common knowledge such as the specific technical solutions and / or characteristics in the solution are not described in detail here. It should be pointed out that for those skilled in the art, without departing from the technical solution of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the description can be used to interpret the content of the claims.

Claims

1. A low-cost patrol aircraft multi-target coordinated strike trajectory planning method, characterized by: The following steps are involved: S1. Determine the starting state X of the patrol aircraft trajectory planning in the two-dimensional plane according to the flight state of the patrol aircraft, the position of the strike target, and the strike azimuth requirements. s With the target state X f ; S2, consider the minimum turning radius r of the patrol aircraft min Constraint, based on the Dubins curve, calculate the s To the target state X f The optimal path S min ; S3. Adjust the two-dimensional plane curve to a three-dimensional flight trajectory based on the strike height difference and the maximum sinking rate constraint of the patrol aircraft; S4. Using turning radius as a variable, collaboratively optimize the three-dimensional trajectory of multiple patrol aircraft to meet strike time interval requirements and achieve real-time monitoring and auxiliary operations with "man in the loop".

2. The method for trajectory planning of a low-cost patrol aircraft for coordinated multi-target strike according to claim 1, characterized in that: In step S1, the starting state X of the patrol aircraft trajectory planning in the two-dimensional plane is determined according to the flight state of the patrol aircraft, the position of the strike target and the strike azimuth requirement. s With the target state X f , specifically: S11, the position of the patrol aircraft is X P =(x p ,y p ,z p ), the flight azimuth is θ s , then the initial state X of the trajectory planning of the patrol aircraft in the two-dimensional plane is s For X s =(x s ,y s ,θ s )=(x p ,y p ,θ s ); S12. To ensure that the cruise aircraft does not have a large roll angle within a certain period of time or distance before reaching the target, thereby improving the accuracy of the terminal target strike, the terminal straight-line flight distance of the cruise aircraft is set to d. S13, according to the target position X g =(x g ,y g ,z g ), strike azimuth θ g The requirements and the terminal straight flight distance d are set to calculate the target state X of the patrol aircraft trajectory planning in the two-dimensional plane. f =(x f ,y f ,θ f )=(x g -d·cosθ g ,y g -d·sinθ g ,θ g ).

3. The method for trajectory planning of a low-cost patrol aircraft for coordinated multi-target strike according to claim 1, characterized in that: In step S2, the minimum turning radius r of the patrol aircraft is considered. min Constraint, based on the Dubins curve, calculate the s To the target state X f The optimal path S min , specifically: S21, calculate from the starting state X s To the target state X f The CSC type Dubins curve and the corresponding curve length, CSC types include RSR, RSL, LSR, LSL; where R represents the minimum turning radius r of the cruise aircraft min Right dial, S means going straight, L means the minimum turning radius r of the patrol aircraft min On the left panel, for the four CSC types of Dubins curves, RSR, RSL, LSR, and LSL, the corresponding curve length is calculated and expressed as L RSR , L RSL , L LSR and L LSL ; S22, calculate from the starting state X s To the target state X f The CCC type Dubins curve and the corresponding curve length. The CCC types include: RLR, LRL. The meanings of R and L are consistent with those in S21. For the RLR and LRL CCC types of Dubins curves, the corresponding curve length is calculated and expressed as L RLR and L LRL ; S23, select L RSR , L RSL , L LSR ,L LSL and L RLR ,L LRL The smallest value L min and the corresponding Dubins curve as the two-dimensional optimal path S min .

4. The method for trajectory planning of a low-cost patrol aircraft for coordinated multi-target strike according to claim 3, characterized in that: In step S21, the calculation from the initial state X s To the target state X s The CSC type Dubins curve and the corresponding curve length are as follows: S211. Calculate the center coordinates of the starting circle of the CSC type Dubins curve: X i =(x i ,y i )=(x s +r min ·i·sinθ s ,y s -r min ·i·cosθ s ), where i is the starting circle direction, i=1 when the wheel is right-handed and i=-1 when the wheel is left-handed; S212. Calculate the coordinates of the center of the CSC type Dubins curve termination circle: X o =(x o ,y o )=(x f +r min ·j·sinθ f ,y f -r min ·j·cosθ f ), where j is the direction of the end circle, j = 1 when the disk is right-handed, and j = -1 when the disk is left-handed; S213, calculate the vector V obtained by connecting the centers of the starting circle and the ending circle oi =(x o -x i ,y o -y i ), and convert it into V l =(v lx ,v ly )=V oi / ||V oi ||; S214. Calculate the tangent normal vectors of the starting circle and the ending circle: Where c = (i·j-1)r min / ||V oi ||; S215. Calculate the tangent point between the straight line segment of the Dubins curve and the starting circle: X it =(x i +i·j·r min ·v nx ,y i +i·j·r min ·v ny ); S216. Calculate the tangent point between the straight line segment of the Dubins curve and the terminal circle: X ot =(x o +r min ·v nx ,y o +r min ·v ny ); S217. Calculate the length of the Dubins curve in, is the starting state X s The position (x s ,y s ) to the tangent point X it The length of the arc, is the tangent point X it To the tangent point X ot The straight line length, is the tangent point X ot To the target state X f The position (x f ,y f )’s arc length.

5. The method for trajectory planning of a low-cost patrol aircraft for coordinated multi-target strike according to claim 4, characterized in that: In step S217, the length of the Dubins curve is calculated. Specifically: S2171, calculate the starting state X s To the tangent point X it The arc length Calculate the starting position X s To the tangent point position X it Angle difference where 0≤θ it ,θ is <2π; According to the circling direction of the patrol aircraft, determine whether the circling path is a superior arc or an inferior arc, and calculate the circling angle of the patrol aircraft within the starting circle: if(Δθ i <0&i=-1),then(Δθ i =2π+Δθ i ), if(Δθ i >0&i=1),then(Δθ i =2π-Δθ i ); thereby calculating the arc length of the spiral r min is the circling radius; S2172, calculate the tangent point X it To the tangent point X ot The formula for calculating the length of a straight line is: S2173, calculate the tangent point X ot To the target state X f The arc length Calculate the tangent point X ot To target state X f Angle difference where 0≤θ ot ,θ of <2π; According to the circling direction of the patrol aircraft, determine whether the circling path is a superior arc or an inferior arc, and calculate the angle value of the patrol aircraft circling within the termination circle: if(Δθ o <0&j=-1),then(Δθ o =2π+Δθ o ), if(Δθ o >0&j=1),then(Δθ o =2π-Δθ o ), and thus calculate the arc length of the spiral r min is the circling radius; S2174, calculate from the starting state X s To the target state X f Dubins curve length 6. The method for trajectory planning of a low-cost patrol aircraft for coordinated multi-target strike according to claim 3, characterized in that: In step S22, the calculation from X s To X f The length of the CCC type Dubins curve is: S221. Calculate the center coordinates of the starting circle of the CCC type Dubins curve: X i =(x i ,y i )=(x s +r min ·i·sinθ s ,y s -r min ·i·cosθ s ), where i is the starting circle direction, i=1 when the wheel is right-handed and i=-1 when the wheel is left-handed; S222. Calculate the coordinates of the center of the CCC type Dubins curve termination circle: X o =(x o ,y o )=(x f +r min ·j·sinθ f ,y f -r min ·j·cosθ f ), where j is the direction of the end circle, j = 1 when the disk is right-handed, and j = -1 when the disk is left-handed; S223. Calculate the vector obtained by connecting the centers of the starting circle and the ending circle: V oi =(v xoi ,v yoi )=(x o -x i ,y o -y i ), and vector angle: θ oi =arctan(v yoi / v xoi ); S224. Using the center of the starting circle as the vertex, calculate the interior angle of the triangle formed by the centers of the three circles: Among them, the subscript i represents the center of the starting circle, the subscript o represents the center of the ending circle, the subscript m represents the center of the middle circle, and the subscript d represents the center of the middle circle. oi =||V oi || is the modulus of the line vector connecting the center of the starting circle and the center of the ending circle, d im =r min +r mid is the modulus of the line vector connecting the center of the starting circle and the center of the middle circle, r mid =max{r min ,(d oi -2·r min ) / 2} is the radius of the middle circle, d im =d mo is the modulus of the vector connecting the center of the central circle and the center of the end circle; S225. Calculate the coordinates of the center of the middle circle: X mid =(x mid ,y mid )=(x i +d im ·cos(θ oi -θ oim ),y i +d im ·sin(θ oi -θ oim )); S226. Calculate the vector V of the line connecting the center of the starting circle and the center of the middle circle im =(x mid -x i ,y mid -y i ), and normalize it to V′ im =(v′ imx ,v′ imy )=V im / ||V im ||; S227. Calculate the vector V of the line connecting the center of the end circle and the center of the middle circle mo =(x o -x mid ,y o -y mid ), and normalize it to V′ mo =(v′ mox ,v′ moy )=V mo / ||V mo ||; S228, calculate the tangent point X on the starting circle it =(x i +r min ·v′ imx ,y i +r min ·v′ imy ), calculate the tangent point X on the termination circle ot =(x mid +r mid ·v′ mox ,y mid +r mid ·v′ moy ); S229. Calculate the length of the Dubins curve in, is the starting state X s The position (x s ,y s ) to the tangent point X on the starting circle it The length of the arc, is the tangent point X on the starting circle it To the tangent point X on the end circle ot The length of the arc, is the tangent point X on the ending circle ot To the target state X f The position (x f ,y f )’s arc length.

7. The method for trajectory planning of a low-cost patrol aircraft for coordinated multi-target strike according to claim 1, characterized in that: In step S3, the two-dimensional plane curve is adjusted to a three-dimensional flight trajectory in combination with the strike height difference and the maximum sinking rate constraint of the patrol aircraft, specifically: S31, determine whether the two-dimensional optimal Dubins curve meets the maximum sink rate requirement of the cruise aircraft. If it meets the maximum sink rate requirement, that is, L min ≥L load ,L load =(z g -z p ) / tanΥ max , Υ max is the maximum sink rate, then the sink rate of the aircraft is set to Υ=arctan((z g -z p ) / L min ), the patrol aircraft maneuvers and descends according to the sinking rate, and the actual three-dimensional trajectory length S32, if the maximum sinking rate requirement is not met, that is, L min <L load , then the circling radius r of the patrol aircraft needs to be adjusted 3D , that is, r 3D ≥r min , so that the length of the Dubins curve in the two-dimensional plane is L load To simplify the calculation, the radius of the starting circle and the ending circle are adjusted to r 3D In step S217, the length L of the Dubins curve in the two-dimensional plane is expressed as a function of the spiral radius r. According to the functional relationship and L=L load , calculate r 3D , then the actual three-dimensional trajectory length S33, according to the calculated r 3D , recalculate the corresponding Dubins curve S, and save L and S to the computer memory.

8. The method for trajectory planning of a low-cost patrol aircraft for coordinated multi-target strike according to claim 1, characterized in that: In step S4, the three-dimensional flight paths of multiple patrol aircraft are collaboratively optimized with the turning radius as a variable to meet the strike time interval requirement and achieve "man-in-the-loop" real-time monitoring and auxiliary operations, specifically: S41: Determine the three-dimensional trajectory lengths L of N patrol aircraft to N strike targets according to steps S1 to S3. k and S k , and 1≤k≤N, construct the flight track length array L of multiple patrol aircraft whole =[L1,···L k ···L N ],L1≤···L k ···≤L N ; S42, starting from the shortest flight path, i.e. L1, determine in turn whether the strike time between the two patrol aircraft and the corresponding target meets the minimum time interval constraint, i.e. (L j+1 -L j ) / V≥ΔT,j=1,…N-1, V is the flight speed of the patrol aircraft: If it is not satisfied, the turning radius of the j+1th patrol aircraft is adjusted to r' 3D ,r' 3D ≥r 3D , to extend the three-dimensional track length of the j+1th patrol aircraft so that the strike time between the two patrol aircraft and the corresponding target meets the minimum time interval requirement. Repeat this step until the strike time interval between all patrol aircraft meets the requirement; S43, according to the calculated r' 3D , recalculate the Dubins curve S of the corresponding patrol aircraft, and save L and S to the computer memory, so as to obtain the strike track of all patrol aircraft.

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