CN113175930B - MMEA-based multi-unmanned aerial vehicle collaborative track planning method - Google Patents
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Abstract
The invention discloses a multi-unmanned aerial vehicle collaborative track planning method based on MMEA, which is implemented according to the following steps: step 1, establishing a track cost model; step 2, establishing a flight path collaborative space-time constraint model; step 3, establishing a multi-unmanned aerial vehicle collaborative track planning multi-target optimization model according to the track cost model established in the step 1 and the track collaborative space-time constraint model established in the step 2; and 4, solving the multi-unmanned aerial vehicle collaborative track planning multi-target optimization model established in the step 3 to obtain multi-unmanned aerial vehicle collaborative track planning. The MMEA-based multi-unmanned aerial vehicle collaborative track planning method can find all optimal tracks meeting constraint conditions for each unmanned aerial vehicle.
Description
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle track planning methods, and relates to a multi-unmanned aerial vehicle collaborative track planning method based on MMEA.
Background
The existing multimode multi-objective evolution algorithm (MMEA) has achieved good results in solving the multimode multi-objective problem (MMOP). However, these algorithms typically integrate distance indicators of different spaces into new distance indicators to maintain diversity of the population. Such integration techniques typically require the construction of a complex function that is not conducive to application and popularization. In addition, in the multimode and multi-target optimization algorithm, the diversity in the target space is improved so that the obtained Pareto solution sets are uniformly distributed on the Pareto optimal front, and the diversity in the decision space is improved so that the most possible Pareto optimal solution sets can be obtained. How to efficiently and effectively balance the distance indexes in the decision space and the target space is not fully paid attention to and effectively solved in the existing MMEA.
Disclosure of Invention
The invention aims to provide a multi-unmanned aerial vehicle collaborative track planning method based on MMEA, which can find all optimal tracks meeting constraint conditions for each unmanned aerial vehicle.
The technical scheme adopted by the invention is that the multi-unmanned aerial vehicle collaborative track planning method based on MMEA is implemented according to the following steps:
step 1, establishing a track cost model;
step 2, establishing a flight path collaborative space-time constraint model;
step 3, establishing a multi-unmanned aerial vehicle collaborative track planning multi-target optimization model according to the track cost model established in the step 1 and the track collaborative space-time constraint model established in the step 2;
And 4, solving the multi-unmanned aerial vehicle collaborative track planning multi-target optimization model established in the step 3 to obtain multi-unmanned aerial vehicle collaborative track planning.
The present invention is also characterized in that,
The track cost model in the step1 comprises a track distance cost model and a track safety cost model; the track distance cost model is expressed by a formula (1):
Wherein f K is the track distance of the track route K, l i is the length of the ith track segment, and n is the number of unmanned aerial vehicles;
knowing that one track route is K, when the unmanned aerial vehicle navigates along the track route, if the distance from the threat point to the edge is smaller than the threat radius corresponding to the threat point, setting the threat cost of the edge to be infinity, otherwise, the total threat cost of the path K is the sum of the threat costs from all the threat points to the path K, namely, the track safety cost model is expressed as:
Wherein f S represents the track safety of the track route K, w k represents the threat cost of the kth threat point to the path K, and m represents the number of threat points.
The calculation method of the K threat point to the path K threat cost w k is as follows:
Dividing each path into 10 sections, taking the points at the two ends as a starting point and a target point of the unmanned aerial vehicle respectively, taking 5 points in the middle to calculate threat cost suffered by the path, and calculating threat cost of each threat point by the formula (3):
Wherein K ij is the length of path K; d 0.1,k represents the 1/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.3,k represents the 3/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.5,k represents the 5/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.7,k represents the 7/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.9,k represents the 9/10 th minute distance of the center of the kth threat zone on the K ij side, and t k is the threat level of the kth threat source.
The step 2 is specifically as follows:
step 2.1, a space cooperative constraint model is established, and the space cooperative constraint model is specifically expressed according to a formula (4):
||Pu(t)-Pj(t)||≥dSafe，u≠j (4)
Wherein, P u (t) is the position of the ith unmanned aerial vehicle at the time t, P j (t) is the position of the jth unmanned aerial vehicle at the time t, and d Safe is the safety interval between the unmanned aerial vehicles;
step 2.2, establishing a time cooperative constraint model, which specifically comprises the following steps:
if the navigation time interval of each unmanned plane contains intersections, the possibility that multiple unmanned planes arrive at the same time is considered, the speed interval of unmanned plane i is v i＝[vimin,vimax],vimin、vimax, which is the minimum speed and the maximum speed of unmanned plane i respectively, the path length of unmanned plane i is L i, the speed interval of unmanned plane j is v= [ v jmin,vjmax],vjmin、vjmax, which is the minimum speed and the maximum speed of unmanned plane j respectively, and the path length of unmanned plane j is L j;
the arrival time of the unmanned aerial vehicle i is:
Ti＝[Timin,Timax]＝[Li/vimax,Li/vimin] (6)
Wherein, T imin is the earliest arrival time of unmanned plane i, and T imax is the latest arrival time of unmanned plane i;
The arrival time of the drone j is:
Tj＝[Tjmin,Tjmax]＝[Lj/vjmax,Lj/vjmin] (7)
wherein, T jmin is the earliest arrival time of unmanned aerial vehicle j, and T jmax is the latest arrival time of unmanned aerial vehicle j;
If the time cooperativity is satisfied between the two machines, then the requirement is that
max[Timin,Tjmin]<min[Timax,Tjmax] (8)。
The safety interval d Safe between each unmanned aerial vehicle is determined according to formula (5):
wherein T is 80% of the time consumed by the unmanned aerial vehicle with the shortest time, T is the time duration from the starting point to the end point of each unmanned aerial vehicle, d is the safety distance between each unmanned aerial vehicle and the target point, and R is the distance between each unmanned aerial vehicle and other unmanned aerial vehicles within 80% of the time consumed by each unmanned aerial vehicle.
The multi-unmanned aerial vehicle collaborative track planning multi-target optimization model in the step 3 is expressed as:
Wherein, |X i(t)-Xj (t) | represents the distance between unmanned plane i and unmanned plane j at time t, f K (X) is the track distance of unmanned plane individual X at track route K, and f S (X) is the track safety of unmanned plane individual X at track route K.
The step 4 is specifically as follows:
And taking the connecting line from the starting point of each unmanned aerial vehicle to the target point as the transverse axis of the new coordinate system, and rotating the original terrain coordinate system to enable the transverse axis of the original terrain coordinate system to coincide with the transverse axis and the starting point of the new coordinate system, so as to obtain a new rotating coordinate system as follows:
Wherein, (x, y) is an original terrain coordinate system, (x ', y') is a new rotation coordinate system, and θ is a rotation angle; wherein x 1、y1 is the horizontal and vertical coordinate value of each unmanned aerial vehicle in the in-situ terrain coordinate system, The distance between each unmanned aerial vehicle and the intersection point of the vertical direction new coordinate system transverse axis and the new coordinate system transverse axis of the unmanned aerial vehicle;
D equally dividing the abscissa x' of each unmanned aerial vehicle in a rotating coordinate system, calculating the corresponding ordinate on the vertical line of each equally divided point to obtain a group of point columns consisting of the longitudinal coordinates of D points, sequentially connecting the points in the point columns to obtain a path connecting a starting point and a finishing point, converting the route planning problem into a D-dimensional function optimization problem, optimizing a multi-target constraint model of multi-unmanned aerial vehicle collaborative route planning built by a formula (9) by utilizing a multi-mode multi-target differential evolution algorithm under the built rotating coordinate system, and finally outputting an optimal route.
The beneficial effects of the invention are as follows:
According to the invention, in the problem of multi-unmanned aerial vehicle collaborative track planning, all optimal paths meeting the conditions can be planned for each unmanned aerial vehicle.
Drawings
FIG. 1 is a task scenario diagram of an embodiment of the MMEA-based multi-unmanned collaborative flight path planning method of the present invention;
FIG. 2 is a threat cost calculation diagram in the MMEA-based multi-unmanned aerial vehicle collaborative track planning method of the present invention;
FIG. 3 is a schematic diagram of coordinate transformation in the MMEA-based multi-unmanned aerial vehicle collaborative track planning method of the present invention;
FIG. 4 is a random result diagram (I) of a double unmanned aerial vehicle track planning for NSGAII in an embodiment of a MMEA-based multi-unmanned aerial vehicle collaborative track planning method according to the present invention;
FIG. 5 is a graph (one) of the two unmanned aerial vehicle trajectory planning results extracted from FIG. 4 with the most representative solution;
FIG. 6 is a graph (II) of the dual unmanned aerial vehicle trajectory planning result extracted from FIG. 4 with the most representative solution;
FIG. 7 is a random result diagram (II) of a double unmanned aerial vehicle track planning for NSGAII in an embodiment of a MMEA-based multi-unmanned aerial vehicle collaborative track planning method according to the present invention;
FIG. 8 is a graph (one) of the dual unmanned aerial vehicle trajectory planning results extracted from FIG. 7 with the most representative solution;
FIG. 9 is a diagram of the dual unmanned aerial vehicle trajectory planning result (II) of the most representative solution extracted from FIG. 7;
FIG. 10 is a diagram of simulation results of a set of solutions of SRMMODE algorithm in an embodiment of a multi-unmanned collaborative flight path planning method based on MMEA according to the present invention;
FIG. 11 is a graph (one) of the two unmanned aerial vehicle trajectory planning results extracted from FIG. 10 with the most representative solution;
fig. 12 is a diagram of the two unmanned aerial vehicle trajectory planning result (two) extracted from fig. 10 with the most representative solution.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention discloses a multi-unmanned aerial vehicle collaborative track planning method based on MMEA, which is implemented according to the following steps:
Step 1, establishing a track cost model, wherein the track cost model comprises a track distance cost model and a track safety cost model;
the purpose of designing the track distance cost is to shorten the flight distance of the unmanned aerial vehicle as much as possible, and the flight distance is set to be the sum of the distances of all track sections. The track distance cost model is expressed by a formula (1):
Wherein f K is the track distance of the track route K, l i is the length of the ith track segment, and n is the number of unmanned aerial vehicles;
The effect of designing the track safety cost is to enable the unmanned aerial vehicle to be far away from the threat area as far as possible in the track process. For ease of calculation, the present invention designs all threat zones to be circular. Knowing that one track route is K, when the unmanned aerial vehicle navigates along the track route, if the distance from the threat point to the edge is smaller than the threat radius corresponding to the threat point, setting the threat cost of the edge to be infinity, otherwise, the total threat cost of the path K is the sum of the threat costs from all the threat points to the path K, namely, the track safety cost model is expressed as:
Wherein f S represents the track safety of the track route K, w k is the threat cost of the kth threat point to the path K, and m is the number of threat points, wherein the calculation method of the threat cost w k of the kth threat point to the path K is as follows:
Dividing each path into 10 sections, taking the points at the two ends as a starting point and a target point of the unmanned aerial vehicle respectively, taking 5 points in the middle to calculate threat cost suffered by the path, and calculating threat cost of each threat point by the formula (3):
Wherein K ij is the length of path K; d 0.1,k represents the 1/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.3,k represents the 3/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.5,k represents the 5/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.7,k represents the 7/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.9,k represents the 9/10 th minute distance of the center of the kth threat zone on the K ij side, and t k is the threat level of the kth threat source.
Step 2, establishing a flight path collaborative space-time constraint model; the method comprises the following steps:
Step 2.1, in the navigation process of the unmanned aerial vehicle, in order to ensure the safety of the unmanned aerial vehicle, a certain safety interval d Safe is needed between each unmanned aerial vehicle, a space cooperative constraint model is established, and the space cooperative constraint model is specifically expressed according to a formula (4):
||Pu(t)-Pj(t)||≥dSafe，u≠j (4)
Wherein, P u (t) is the position of the ith unmanned aerial vehicle at the time t, P j (t) is the position of the jth unmanned aerial vehicle at the time t, and d Safe is the safety interval between the unmanned aerial vehicles;
Wherein the safety interval d Safe between each unmanned aerial vehicle is determined according to formula (5):
Wherein T is 80% of the time consumed by the unmanned aerial vehicle with the shortest time, T is the time duration from the starting point to the end point of each unmanned aerial vehicle, d is the safety distance between each unmanned aerial vehicle and the target point, and R is the distance between each unmanned aerial vehicle and other unmanned aerial vehicles within 80% of the time consumed by each unmanned aerial vehicle;
step 2.2, establishing a time cooperative constraint model, which specifically comprises the following steps:
The time coordination means that when a plurality of unmanned aerial vehicles are coordinated to combat, each unmanned aerial vehicle should arrive at a target point at the same time. That is, considering the speed change range of each unmanned aerial vehicle and the track distance of each unmanned aerial vehicle, if the navigation time interval of each unmanned aerial vehicle contains intersections, then the possibility that multiple unmanned aerial vehicles arrive at the same time is considered, the speed interval of unmanned aerial vehicle i is v i＝[vimin,vimax],vimin、vimax, which is the minimum speed and the maximum speed of unmanned aerial vehicle i respectively, the path length of unmanned aerial vehicle i is L i, the speed interval of unmanned aerial vehicle j is v= [ v jmin,vjmax],vjmin、vjmax, which is the minimum speed and the maximum speed of unmanned aerial vehicle j respectively, and the path length of unmanned aerial vehicle j is L j;
the arrival time of the unmanned aerial vehicle i is:
Ti＝[Timin,Timax]＝[Li/vimax,Li/vimin] (6)
Wherein, T imin is the earliest arrival time of unmanned plane i, and T imax is the latest arrival time of unmanned plane i;
The arrival time of the drone j is:
Tj＝[Tjmin,Tjmax]＝[Lj/vjmax,Lj/vjmin] (7)
wherein, T jmin is the earliest arrival time of unmanned aerial vehicle j, and T jmax is the latest arrival time of unmanned aerial vehicle j;
If the time cooperativity is satisfied between the two machines, then the requirement is that
max[Timin,Tjmin]<min[Timax,Tjmax] (8)。
Step 3, establishing a multi-unmanned aerial vehicle collaborative track planning multi-target optimization model according to the track cost model established in the step 1 and the track collaborative space-time constraint model established in the step 2; the multi-unmanned aerial vehicle collaborative track planning multi-target optimization model is expressed as:
Wherein, I X i(t)-Xj (t) I represents the distance between unmanned plane i and unmanned plane j at t, f K (X) is the track distance of unmanned plane individual X in track route K, and f S (X) is the track safety of unmanned plane individual X in track route K;
step 4, solving the multi-unmanned aerial vehicle collaborative track planning multi-target optimization model established in the step 3 to obtain multi-unmanned aerial vehicle collaborative track planning, wherein the multi-unmanned aerial vehicle collaborative track planning is specifically as follows:
And taking the connecting line from the starting point of each unmanned aerial vehicle to the target point as the transverse axis of the new coordinate system, and rotating the original terrain coordinate system to enable the transverse axis of the original terrain coordinate system to coincide with the transverse axis and the starting point of the new coordinate system, so as to obtain a new rotating coordinate system as follows:
Wherein, (x, y) is an original terrain coordinate system, (x ', y') is a new rotation coordinate system, and θ is a rotation angle; wherein x 1、y1 is the horizontal and vertical coordinate value of each unmanned aerial vehicle in the in-situ terrain coordinate system, The distance between each unmanned aerial vehicle and the intersection point of the vertical direction new coordinate system transverse axis and the new coordinate system transverse axis of the unmanned aerial vehicle;
D equally dividing the abscissa x' of each unmanned aerial vehicle in a rotating coordinate system, calculating the corresponding ordinate on the vertical line of each equally divided point to obtain a group of point columns consisting of the longitudinal coordinates of D points, sequentially connecting the points in the point columns to obtain a path connecting a starting point and a finishing point, converting the route planning problem into a D-dimensional function optimization problem, optimizing a multi-target constraint model of multi-unmanned aerial vehicle collaborative route planning built by a formula (9) by utilizing a multi-mode multi-target differential evolution algorithm under the built rotating coordinate system, and finally outputting an optimal route.
Scenario description:
It is assumed that in a certain battle, n (n > 1) unmanned aerial vehicles are required to cooperatively perform a secret task. The unmanned aerial vehicle takes off from different areas and goes to the same destination point. Before the task is executed, the topography threat, such as radar detection, air defense missile, no-fly zone and the like, needs to be comprehensively considered, and a feasible track is planned for the unmanned aerial vehicle. And for unmanned aerial vehicle navigation's safety, need keep certain safe distance between each unmanned aerial vehicle.
Fig. 1 is a schematic view of a task scenario in which two unmanned aerial vehicles start from different starting points and simultaneously travel to a task area T to perform a cooperative hit task. Four optimal routes are planned for the UAV1 in FIG. 1 (a), wherein the UAVs 1-1 and UAVs 1-2 enable the UAVs 1-1 and UAVs 1-2 to keep high safety in the flight process of the unmanned aerial vehicle, and the routes UAVs 1-1 and UAVs 1-2 are two completely different routes, but have similar performances, namely the safety is similar to the sailing distance between the two routes. The UAVs 1-3 and the UAVs 1-4 enable the unmanned aerial vehicle to have the shortest sailing distance on the premise of keeping certain safety. FIG. 1 (b) shows two satisfactory optimal trajectories for UAV2 planning, where UAV2-1 minimizes voyage distance and UAV2-2 maximizes voyage safety. Finally, in order to ensure the safety of the unmanned aerial vehicle in the flight process, a certain distance is required to be kept between the two unmanned aerial vehicles at any time; in order to complete the combat mission, the two unmanned aerial vehicles also need to meet the time constraint, i.e. reach the target area simultaneously within the required range. And selecting corresponding tracks for each machine according to the requirements, so that the fight plan is successful satisfactorily.
Experimental setup
The unmanned aerial vehicle performs spatial topography setting of tasks. The unmanned aerial vehicle executes the topography space size of the mission to be 200km×200km, there are four threat centers in the space, the central point is C11[50km,150km ], C12[60km,60km ], C13[100km,100km ], C14[150km,150km ], threat radius is 20km,15km,20km and 20km separately, threat parameter is 10. The starting points of the two unmanned aerial vehicles in the terrain are respectively S1[0km,0km ], S2[0km,10km ], and the target points are T [200km,200km ].
Setting experimental parameters: for all evolutionary operators in the comparison algorithm, the scaling factor F takes 0.6, the crossover probability CR takes 0.3, each unmanned aerial vehicle takes 12 track points respectively, the population scale takes 200, the evolutionary algebra takes 200, and the unmanned aerial vehicle flight speeds are 200m/s and 300 m/s.
Setting a comparison algorithm: and respectively planning proper navigation routes for two unmanned aerial vehicles under the same simple terrain environment by using a multimode multi-target evolution algorithm (SRMMODE) and a multi-target evolution algorithm (NSGAII).
Fig. 4-9 are multiple sets of results obtained using SRMMODE for two unmanned aerial vehicle simulations, and fig. 10-12 are NSGAII for two unmanned aerial vehicle simulations. As can be seen from fig. 4-12, NSGAII simulations result in two possible sets of solutions, whereas SRMMODE simulation results have only one set of solutions. The reason is that the conventional multi-objective evolution algorithm only considers the diversity of the objective space due to a simple diversity selection mechanism, and when the objective function values calculated by two different solutions are equal or similar, the two solutions are considered to be repeated, so that one solution is possibly eliminated, and the result of partial Pareto optimal solution set loss is caused. Two possible outcomes occur randomly using the NSGAII algorithm, while all possible solutions can be found simultaneously using the SRMMODE algorithm.
The most representative solutions are extracted in fig. 4 and 7, respectively, as shown in fig. 5, 6, 8 and 9. Wherein, fig. 5 and 8 are the results of taking the shortest track distance of each machine, and fig. 6 and 5 and 7 are the results of taking the highest safety of each machine. Similarly, two sets of most representative solutions are selected from fig. 10 to 12, and as shown in fig. 11 and 12, fig. 11 shows the result of shortest path distance of each machine, and fig. 12 shows the result of optimal path security of each machine.
Table 1 uses the objective function values of the respective machine representative solutions obtained by NSGAII (where S represents the safety factor, D represents the track distance, T represents the arrival time range, NSGAII _uav1_1_l represents the optimal path of UAV1 in fig. 5, and so on). According to the data in the table, the navigation distance of any two unmanned aerial vehicles is intersected, and the simultaneous arrival can be realized. However NSGAII randomly generates two possible results, in the case of fig. 7, the optimal paths of UAV1 and UAV2 overlap, and if the spatial coordination of the drones is considered, two drones cannot reach the destination at the same time. Therefore, a certain defect exists in planning a navigation track for the unmanned aerial vehicle by using a multi-target evolution algorithm.
Objective function values of representative solutions for each machine obtained in Table 1 NSGAII
The objective function values for each of the representative solutions obtained by SRMMODE are shown in table 2 (wherein SRMMODE _uav1_l_1 represents the first optimal path for UAV1 in fig. 11, and so on). As can be seen from the data in the table, the safety coefficients of SRMMODE _uav1_l_1 and SRMMODE _uav1_l_2 are lower than those of SRMMODE _uav1_s_1 and SRMMODE _uav1_s_2, and the flight path distances of SRMMODE _uav1_l_1 and SRMMODE _uav1_l_2 are smaller than those of SRMMODE _uav1_s_1 and SRMMODE _uav1_s_2, which is the same as our expected result, i.e. the flight path with a larger safety coefficient would have a larger flight path distance, and vice versa. In addition, the voyage distances of SRMMODE _uav1_l_1 and SRMMODE _uav1_l_2 are relatively close, and the safety coefficient values of SRMMODE _uav1_s_1 and SRMMODE _uav1_s_2 are relatively close, which represents the multi-modal nature of the multi-unmanned aerial vehicle voyage problem. The data in the observation table can show that the arrival time of the optimal paths of the UAV1 and the UAV2 has intersection, namely any two optimal paths of each machine in the table 2 are selected, so that two unmanned aerial vehicles can arrive at the same time. In order to satisfy the spatial cooperativity between the machines, the optimal path for UAV1 should be selected between SRMMODE _UAV1_L_1 and SRMMODE _UAV1_S_1.
Table 2 SRMMODE objective function values of representative solutions for each machine
Summarizing: the multi-unmanned aerial vehicle collaborative track planning problem is modeled as a multi-target optimization problem, multi-mode properties implied in the optimization problem are discussed, and a multi-unmanned aerial vehicle collaborative track planning method based on a multi-mode multi-target evolution algorithm of random sequencing learning is provided for planning the track distance, track safety and time space cooperativity of multiple unmanned aerial vehicles. Compared with the traditional multi-objective planning algorithm, the multi-objective planning algorithm has the advantages that the multi-modal property in the actual optimization problem is considered by the improved algorithm, and meanwhile, a plurality of groups of tracks meeting the condition constraint are planned, so that the time and space synergies can be met, a decision maker can select the tracks according to actual needs, the combination of multi-unmanned-plane synergic track planning and unmanned-plane multi-track planning is realized, and the effectiveness of the algorithm SRMMODE in practical application is verified.
Claims (2)
1. The MMEA-based multi-unmanned aerial vehicle collaborative track planning method is characterized by comprising the following steps of:
step 1, establishing a track cost model;
step 2, establishing a flight path collaborative space-time constraint model;
step 3, establishing a multi-unmanned aerial vehicle collaborative track planning multi-target optimization model according to the track cost model established in the step 1 and the track collaborative space-time constraint model established in the step 2;
Step 4, solving the multi-unmanned aerial vehicle collaborative track planning multi-target optimization model established in the step 3 to obtain multi-unmanned aerial vehicle collaborative track planning;
The track cost model in the step 1 comprises a track distance cost model and a track safety cost model;
The track distance cost model is expressed by adopting a formula (1):
Wherein f K is the track distance of the track route K, l i is the length of the ith track segment, and n is the number of unmanned aerial vehicles;
knowing that one track route is K, when the unmanned aerial vehicle navigates along the track route, if the distance from the threat point to the edge is smaller than the threat radius corresponding to the threat point, setting the threat cost of the edge to be infinity, otherwise, the total threat cost of the path K is the sum of the threat costs from all the threat points to the path K, namely, the track safety cost model is expressed as:
Wherein f S represents the track safety of the track route K, w k represents the threat cost of the kth threat point to the path K, and m represents the number of threat points;
the step 2 specifically comprises the following steps:
step 2.1, a space cooperative constraint model is established, and the space cooperative constraint model is specifically expressed according to a formula (4):
||Pu(t)-Pj(t)||≥dsafe，u≠j(4)
Wherein, P u (t) is the position of the ith unmanned aerial vehicle at the time t, P j (t) is the position of the jth unmanned aerial vehicle at the time t, and d Safe is the safety interval between the unmanned aerial vehicles;
step 2.2, establishing a time cooperative constraint model, which specifically comprises the following steps:
if the navigation time interval of each unmanned plane contains intersections, the possibility that multiple unmanned planes arrive at the same time is considered, the speed interval of unmanned plane i is v i＝[vimin,vimax],vimin、vimax, which is the minimum speed and the maximum speed of unmanned plane i respectively, the path length of unmanned plane i is L i, the speed interval of unmanned plane j is v= [ v jmin,vjmax],vjmin、vjmax, which is the minimum speed and the maximum speed of unmanned plane j respectively, and the path length of unmanned plane j is L j;
the arrival time of the unmanned aerial vehicle i is:
Ti＝[Timin,Timax]＝[Li/vimax,Li/vimin](6)
Wherein, T imin is the earliest arrival time of unmanned plane i, and T imax is the latest arrival time of unmanned plane i;
The arrival time of the drone j is:
Tj＝[Tjmin,Tjmax]＝[Lj/vjmax,Lj/vjmin](7)
wherein, T jmin is the earliest arrival time of unmanned aerial vehicle j, and T jmax is the latest arrival time of unmanned aerial vehicle j;
If the time cooperativity is satisfied between the two machines, then the requirement is that
max[Timin,Tjmin]<min[Timax,Tjmax] (8)；
The safety interval d Safe between each unmanned aerial vehicle is determined according to the formula (5):
Wherein T is 80% of the time consumed by the unmanned aerial vehicle with the shortest time, T is the time duration from the starting point to the end point of each unmanned aerial vehicle, d is the safety distance between each unmanned aerial vehicle and the target point, and R is the distance between each unmanned aerial vehicle and other unmanned aerial vehicles within 80% of the time consumed by each unmanned aerial vehicle;
the multi-unmanned aerial vehicle collaborative track planning multi-target optimization model in the step 3 is expressed as follows:
Wherein, I X i(t)-Xj (t) I represents the distance between unmanned plane i and unmanned plane j at t, f K (X) is the track distance of unmanned plane individual X in track route K, and f S (X) is the track safety of unmanned plane individual X in track route K;
the step 4 specifically comprises the following steps:
And taking the connecting line from the starting point of each unmanned aerial vehicle to the target point as the transverse axis of the new coordinate system, and rotating the original terrain coordinate system to enable the transverse axis of the original terrain coordinate system to coincide with the transverse axis and the starting point of the new coordinate system, so as to obtain a new rotating coordinate system as follows:
Wherein, (x, y) is an original terrain coordinate system, (x ', y') is a new rotation coordinate system, and θ is a rotation angle; wherein x 1、y1 is the horizontal and vertical coordinate value of each unmanned aerial vehicle in the in-situ terrain coordinate system, The distance between each unmanned aerial vehicle and the intersection point of the vertical direction new coordinate system transverse axis and the new coordinate system transverse axis of the unmanned aerial vehicle;
D equally dividing the abscissa x' of each unmanned aerial vehicle in a rotating coordinate system, calculating the corresponding ordinate on the vertical line of each equally divided point to obtain a group of point columns consisting of the longitudinal coordinates of D points, sequentially connecting the points in the point columns to obtain a path connecting a starting point and a finishing point, converting the route planning problem into a D-dimensional function optimization problem, optimizing a multi-target constraint model of multi-unmanned aerial vehicle collaborative route planning built by a formula (9) by utilizing a multi-mode multi-target differential evolution algorithm under the built rotating coordinate system, and finally outputting an optimal route.
2. The multi-unmanned aerial vehicle collaborative flight path planning method based on MMEA according to claim 1, wherein the calculation method of the kth threat point-to-path K threat cost w k is as follows:
Dividing each path into 10 sections, taking the points at the two ends as a starting point and a target point of the unmanned aerial vehicle respectively, taking 5 points in the middle to calculate threat cost suffered by the path, and calculating threat cost of each threat point by the formula (3):
Wherein K ij is the length of path K; d 0.1,k represents the 1/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.3,k represents the 3/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.5,k represents the 5/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.7,k represents the 7/10 th minute distance of the center of the kth threat zone on the K ij side, d 0.9,k represents the 9/10 th minute distance of the center of the kth threat zone on the K ij side, and t k is the threat level of the kth threat source.
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