A method and system for jointly determining flight trajectories and launch power of multiple unmanned aerial vehicles

Abstract

The application discloses a kind of multi-unmanned aerial vehicle flight trajectory and launch power joint determination method and system, the method considers unmanned aerial vehicle to ground node carries out the scene of wireless energy transmission, to maximize the minimum collection energy in single ground node as target, constructs multi-unmanned aerial vehicle flight trajectory and launch power joint optimization model, the scene includes multiple unmanned aerial vehicles flying at fixed height, corresponding to each unmanned aerial vehicle fixed nest and multiple ground nodes receiving wireless energy;And by solving multi-unmanned aerial vehicle flight trajectory and launch power joint optimization model, obtain the optimal flight trajectory set and optimal launch power set of multiple unmanned aerial vehicles.The application considers the existence of nonlinear element in actual ground energy collection node circuit, while being equipped with special fixed nest for unmanned aerial vehicle to charge, the flight trajectory and launch power of multiple unmanned aerial vehicles are optimized jointly, while realizing the maximum minimum collection energy in single ground node, the energy collection efficiency of ground node is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of unmanned aerial vehicle assisted wireless energy transmission, and particularly relates to a multi-unmanned aerial vehicle flight trajectory and transmission power joint determination method and system. BACKGROUND

[0002] With the rapid development of mobile energy storage technology and wireless energy transmission technology, unmanned aerial vehicles have gradually become important energy supplement equipment in modern power systems. In some remote areas where power grids are difficult to cover or emergency places where disasters occur, traditional power generation infrastructure is often difficult to quickly deploy, limiting the timely supply of electricity. As a mobile energy storage device, unmanned aerial vehicles can provide efficient power transmission with their flexible flight capabilities, making up for the shortcomings of traditional power generation.

[0003] Through the high mobility of unmanned aerial vehicles, different regional and time period power demands can be flexibly responded to. In particular, in the case of power grid outage or power scheduling difficulty, unmanned aerial vehicles can serve as temporary power supply stations to maintain the operational stability of the power grid system, which makes unmanned aerial vehicles a key component in scenarios such as smart cities, distributed energy management, disaster recovery, etc., improving the flexibility and energy utilization efficiency of modern power grids.

[0004] Currently, in order to improve the energy transmission efficiency of mobile energy supply equipment, designing unmanned aerial vehicle trajectories and resource allocation is considered an effective approach. Traditional unmanned aerial vehicle design methods include optimizing one-dimensional unmanned aerial vehicle trajectories in wireless energy transmission scenarios, where unmanned aerial vehicles transmit energy to two ground nodes, the flight of unmanned aerial vehicles is limited by the maximum speed, and in the scenario of double unmanned aerial vehicles assisting a single receiver for wireless energy transmission, the optimal trajectory of unmanned aerial vehicles should be evenly distributed on a circle. In these design methods, linear energy harvesting models are considered, however, in actual RF-DC circuits, due to the presence of nonlinear elements such as diodes, there is a nonlinear relationship between the radio frequency power received by the ground equipment and the energy collected, so a nonlinear energy harvesting model is more in line with reality. SUMMARY

[0005] The purpose of the present application is to provide a multi-unmanned aerial vehicle flight trajectory and transmission power joint determination method and system to solve the above problems existing in the prior art.

[0006] To achieve the above purpose, the technical solution of the present application is as follows:

[0007] In a first aspect, the present application provides a multi-unmanned aerial vehicle flight trajectory and transmission power joint determination method, comprising:

[0008] S1. Considering the scenario of UAVs transmitting wireless energy to ground nodes, with the goal of maximizing the minimum collected energy in a single ground node, a joint optimization model of multi-UAV flight trajectory and transmission power is constructed. The scenario includes multiple UAVs flying at a fixed altitude, corresponding to a fixed nest for each UAV and multiple ground nodes receiving wireless energy.

[0009] S2. Solve the joint optimization model of flight trajectory and transmission power of multiple UAVs to obtain the optimal set of flight trajectories and optimal set of transmission power for multiple UAVs.

[0010] In S1, the objective function of the joint optimization model of multi-UAV flight trajectory and transmission power includes:

[0011]

[0012] In the above formula, E k ({q m [n]},{P m [n]}) represents the energy collected by the k-th ground node from all UAVs, which is a multi-source nonlinear energy harvesting model. m [n] represents the flight trajectory of the m-th UAV within the n-th time slot, P m [n] represents the transmit power of the m-th UAV in the n-th time slot, P dc，k (Q k [n]) represents the DC signal power received by the k-th ground node from all UAVs within the n-th time slot, Q. k [n] = {Q k，1 [n],...,Q k，m [n],...,Q k，M [n]} represents the radio frequency signal power received by the k-th ground node from all UAVs within the n-th time slot, where Δ is the length of each time slot, and I... out，k R is the output current of the rectifier circuit of the k-th ground node in the n-th time slot. L Let be the resistance of the energy storage device, 'a' be a parameter related to the physical characteristics of the energy harvesting circuit, 'W0(·)' be the Lambert W function, and 'I' be the resistance of the energy storage device. S It is the reverse saturation current. β represents the impact of the received power at the k-th ground node within the n-th time slot. n For positive integers, To meet A sequence of non-negative integers, Here, M is the combination coefficient, and M is the total number of fixed nests. For the first Within each time slot, the power received by the k-th ground node from the m-th UAV. It is a non-negative integer. For constant waveform coefficients.

[0013] In the S1, the constraint condition of the multi-unmanned aerial vehicle flight trajectory and launch power joint optimization model includes a start and end point constraint of the unmanned aerial vehicle flight trajectory, a maximum flight speed constraint of the unmanned aerial vehicle, a launch power constraint of the unmanned aerial vehicle, and a multi-unmanned aerial vehicle anti-collision constraint.

[0014] The start and end point constraint of the unmanned aerial vehicle flight trajectory is:

[0015] q m [0]=q m [N]=w c,m ;

[0016] The maximum flight speed constraint of the unmanned aerial vehicle is:

[0017]

[0018] The launch power constraint of the unmanned aerial vehicle is:

[0019]

[0020] 0≤P m [n]≤P max ;

[0021] The multi-unmanned aerial vehicle anti-collision constraint is:

[0022]

[0023] In the above formula, q m [0] is the flight start point of the mth unmanned aerial vehicle, q m [N] is the flight end point of the mth unmanned aerial vehicle, w c，m is the position of the fixed nest of the mth unmanned aerial vehicle, q m [n-1] is the flight trajectory of the mth unmanned aerial vehicle in the n-1th time slot, V max is the maximum flight speed of the unmanned aerial vehicle, and Δ is the length of each time slot, is the average launch power, P max is the peak value of the launch power, q v [n] is the flight trajectory of the vth unmanned aerial vehicle in the nth time slot, q w [n] is the flight trajectory of the wth unmanned aerial vehicle in the nth time slot, d min is the minimum safety distance between two unmanned aerial vehicles.

[0024] The S2 includes:

[0025] S21, defining an initial iteration flight trajectory point set and a launch power set of the unmanned aerial vehicle as:

[0026]

[0027] In the above formula, is the flight trajectory set of the mth unmanned aerial vehicle in the initial iteration, is the transmission power set of the mth unmanned aerial vehicle in the initial iteration, (0) is the initial iteration;

[0028] S22, based on the flight trajectory set and the transmission power set of the unmanned aerial vehicle in the initial iteration, a convex objective function and a convex constraint of a multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model are constructed, and an optimization solving convex problem of each iteration is obtained;

[0029] The optimization solving convex problem of each iteration is:

[0030]

[0031]

[0032] In the above formula, E (r) is an auxiliary variable introduced in the rth iteration, q m [n] is the flight trajectory of the mth unmanned aerial vehicle in the nth time slot, P m [n] is the transmission power of the mth unmanned aerial vehicle in the nth time slot, is the rth iteration, and q m [0] is the flight starting point of the mth unmanned aerial vehicle, q m [N] is the flight termination point of the mth unmanned aerial vehicle, w c，m is the position of the fixed nest of the mth unmanned aerial vehicle, q m [n-1] is the flight trajectory of the mth unmanned aerial vehicle in the n-1th time slot, V max is the maximum flight speed of the unmanned aerial vehicle, and Δ is the length of each time slot, is the rth iteration, and d min is the lower bound of the distance between the vth unmanned aerial vehicle and the wth unmanned aerial vehicle in the nth time slot, is the average transmission power, P max is the peak value of the transmission power;

[0033] S23, solving the optimization solving convex problem of each iteration, the optimization solution of the unmanned aerial vehicle flight trajectory and the transmission power of each iteration is wherein, is the optimal flight trajectory of the mth unmanned aerial vehicle in the nth time slot in the rth iteration, is the optimal transmission power of the mth unmanned aerial vehicle in the nth time slot in the rth iteration, and the change amount of the auxiliary variable in the optimization solving convex problem of each iteration is determined whether it is less than the iteration threshold ε, that is, E(r) -E (r-1) <ε, if satisfied, the iterative algorithm ends, and the optimal flight trajectory set of multiple unmanned aerial vehicles and the optimal launch power set are output If not satisfied, let r=r+1, return to step S22 to re-construct the convex optimization problem of iteration to obtain the optimal flight trajectory and the optimal launch power of the r+1th iteration.

[0034] In the S22, the convex objective function of the joint optimization model of the flight trajectory and the launch power of the multiple unmanned aerial vehicles is constructed, including:

[0035] A, since E k ({q m [n]},{P m [n]}) is a convex function, and the following convex approximation is obtained:

[0036]

[0037] In the above formula, E k ({q m [n]},{P m [n]}) is the energy collected by the kth ground node from all unmanned aerial vehicles, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the received radio frequency signal power of the kth ground node from the mth unmanned aerial vehicle in the nth time slot, and Δ is the length of each time slot, d k 2 (q m [n]) is the distance between the mth unmanned aerial vehicle and the kth ground node in the nth time slot, q m [n] is the flight trajectory of the mth unmanned aerial vehicle in the nth time slot, β0 is the channel gain per unit distance, P m [n] is the launch power of the mth unmanned aerial vehicle in the nth time slot;

[0038] B, since d k 2 (q m [n]) and P m [n] are coupled, the objective function of the joint optimization model of the flight trajectory and the launch power of the multiple unmanned aerial vehicles is further convex approximated:

[0039]

[0040] In the above formula, the approximation coefficient of the rth iteration, is the lower bound concave approximation function of the energy collected by the kth ground node from all unmanned aerial vehicles in the rth iteration;

[0041] The convex constraint of the multi-UAV flight trajectory and launch power joint optimization model is constructed, including:

[0042] The anti-collision constraint of the multi-UAV in each iteration is convexly approximated as:

[0043]

[0044] In the above formula, is the flight trajectory of the vth UAV in the nth time slot in the rth iteration, is the flight trajectory of the wth UAV in the nth time slot in the rth iteration, is the lower bound concave approximation function of the distance between the vth UAV and the wth UAV in the nth time slot in the rth iteration.

[0045] In a second aspect, the present application provides a multi-UAV flight trajectory and launch power joint determination system, comprising a joint optimization model construction module and a joint optimization model solving module;

[0046] The joint optimization model construction module is used to consider the scenario of wireless energy transmission from the UAV to the ground node, and to construct a multi-UAV flight trajectory and launch power joint optimization model with the objective of maximizing the minimum collected energy in a single ground node, wherein the scenario includes multiple UAVs flying at a fixed altitude, a fixed nest corresponding to each UAV, and multiple ground nodes receiving wireless energy;

[0047] The joint optimization model solving module is used to solve the multi-UAV flight trajectory and launch power joint optimization model to obtain an optimal flight trajectory set and an optimal launch power set of the multi-UAV.

[0048] The joint optimization model construction module comprises a target function construction unit.

[0049] The target function construction unit is used to construct the following target function of the multi-UAV flight trajectory and launch power joint optimization model:

[0050]

[0051] In the above formula, E k ({q m [n]},{P m [n]}) is the energy collected by the kth ground node from all UAVs, which is a multi-source nonlinear energy collection model, q m [n] is the flight trajectory of the mth UAV in the nth time slot, P m [n] is the launch power of the mth UAV in the nth time slot, P dc，k (Q k[n]) represents the DC signal power received by the k-th ground node from all UAVs within the n-th time slot, Q. k [n]={Q k，1 [n], ..., Q k，m [n], ..., Q k，M [n]} represents the radio frequency signal power received by the k-th ground node from all UAVs within the n-th time slot, where Δ is the length of each time slot, and I... out，k R is the output current of the rectifier circuit of the k-th ground node in the n-th time slot. L Let be the resistance of the energy storage device, 'a' be a parameter related to the physical characteristics of the energy harvesting circuit, 'W0(·)' be the Lambert W function, and 'I' be the resistance of the energy storage device. S It is the reverse saturation current. β represents the impact of the received power at the k-th ground node within the n-th time slot. n For positive integers, To meet A sequence of non-negative integers, Here, M is the combination coefficient, and M is the total number of fixed nests. For the first Within each time slot, the power received by the k-th ground node from the m-th UAV. It is a non-negative integer. These are constant waveform coefficients.

[0052] The joint optimization model construction module also includes a start and end point constraint construction unit, a maximum flight speed constraint construction unit, a launch power constraint construction unit, and an anti-collision constraint construction unit;

[0053] The start and end point constraint construction unit is used to construct the start and end point constraints of the following UAV flight trajectory:

[0054] q m [0] = q m [N] = w c,m ;

[0055] The maximum flight speed constraint construction unit is used to construct the maximum flight speed constraints for the following UAVs:

[0056]

[0057] The transmit power constraint construction unit is used to construct the transmit power constraints for the following UAVs:

[0058]

[0059] 0≤P m [n]≤P max ;

[0060] The anti-collision constraint construction unit is used to construct the anti-collision constraint of the multi-unmanned aerial vehicle as follows:

[0061]

[0062] In the above formula, q m [0] is a flight starting point of the mth unmanned aerial vehicle, q m [N] is a flight ending point of the mth unmanned aerial vehicle, w c，m is a position of a fixed nest of the mth unmanned aerial vehicle, q m [n-1] is a flight trajectory of the mth unmanned aerial vehicle in the n-1th time slot, V max is a maximum flight speed of the unmanned aerial vehicle, and Δ is a length of each time slot, is an average transmission power, P max is a peak value of the transmission power, q v [n] is a flight trajectory of the vth unmanned aerial vehicle in the n th time slot, q w [n] is a flight trajectory of the wth unmanned aerial vehicle in the n th time slot, d min is a minimum safety distance between the two unmanned aerial vehicles.

[0063] The joint optimization model solving module comprises an initial iteration definition unit, an optimization solving convex problem construction unit, and a loop iteration unit.

[0064] The initial iteration definition unit is configured to define a flight trajectory point set and a transmission power set of initial iteration of the unmanned aerial vehicle as follows:

[0065]

[0066] In the above formula, is a flight trajectory set of initial iteration of the mth unmanned aerial vehicle, is a transmission power set of initial iteration of the mth unmanned aerial vehicle, and (0) is initial iteration.

[0067] The optimization solving convex problem construction unit is configured to construct a convex objective function and a convex constraint of a multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model based on the flight trajectory set and the transmission power set of initial iteration of the unmanned aerial vehicle, to obtain an optimization solving convex problem of each iteration.

[0068] The optimization solving convex problem of each iteration is as follows:

[0069]

[0070]

[0071] In the above formula, E (r) is an auxiliary variable introduced in the rth iteration, q m[n] is the flight trajectory of the mth UAV in the nth time slot, P m (n) is the transmission power of the mth UAV in the nth time slot, is the lower bound concave approximation function of the energy collected by the kth ground node from all UAVs in the rth iteration, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight ending point of the mth UAV, w c，m is the location of the fixed nest of the mth UAV, q m [n-1] is the flight trajectory of the mth UAV in the n-1th time slot, V max is the maximum flight speed of the UAV, and Δ is the length of each time slot, is the lower bound concave approximation function of the distance between the vth UAV and the wth UAV in the nth time slot in the rth iteration, d min is the minimum safe distance between two UAVs, is the average transmission power, P max is the peak value of the transmission power;

[0072] The loop iteration unit is used to solve the optimization solving convex problem of each iteration, and the optimal solution of the UAV flight trajectory and the transmission power of each iteration is obtained as wherein, is the optimal flight trajectory of the mth UAV in the nth time slot in the rth iteration, is the optimal transmission power of the mth UAV in the nth time slot in the rth iteration, and the change of the auxiliary variable in the optimization solving convex problem of each iteration is judged whether it is less than the iteration threshold ε, that is, E (r) -E (r-1) <ε, if it is satisfied, the iteration algorithm ends, and the optimal flight trajectory set and the optimal transmission power set of the multiple UAVs are output as If it is not satisfied, let r=r+1, return to the optimization solving convex problem construction unit to re-construct the optimization solving convex problem of the iteration, and obtain the optimal flight trajectory and the optimal transmission power of the r+1th iteration.

[0073] In the optimization solving convex problem construction unit, the convex objective function of the joint optimization model of the multiple UAV flight trajectories and the transmission power is constructed, including:

[0074] A, since E k ({q m [n]},{P m [n]}) is a convex function, and the following convex approximation is obtained:

[0075]

[0076] In the formula, E k ({q m m [n]},{P k，m [n]) is the energy collected by the kth ground node from all unmanned aerial vehicles, are the convex approximation coefficients of the rth iteration, Q k 2 m [n]) is the distance between the mth unmanned aerial vehicle and the kth ground node in the nth time slot, q m [n] is the flight trajectory of the mth unmanned aerial vehicle in the nth time slot, β0 is the channel gain per unit distance, P m [n] is the transmission power of the mth unmanned aerial vehicle in the nth time slot.

[0077] B, since d k 2 (q m [n]) and P m [n] are coupled, the objective function of the multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model is further convexly approximated:

[0078]

[0079] In the formula, E is the approximation coefficient of the rth iteration, is the lower bound concave approximation function of the energy collected by the kth ground node from all unmanned aerial vehicles in the rth iteration;

[0080] The convex constraint of the multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model is constructed, including:

[0081] The anti-collision constraint of the multi-unmanned aerial vehicle in each iteration is convexly approximated as:

[0082]

[0083] In the formula, E is the flight trajectory of the vth unmanned aerial vehicle in the nth time slot in the rth iteration, is the flight trajectory of the wth unmanned aerial vehicle in the nth time slot in the rth iteration, is the lower bound concave approximation function of the distance between the vth unmanned aerial vehicle and the wth unmanned aerial vehicle in the nth time slot in the rth iteration.

[0084] Compared with the prior art, the beneficial effects of the present application are:

[0085] ​​The application provides a multi-unmanned aerial vehicle flight trajectory and transmission power joint determination method and system, which considers a scenario of energy transmission from unmanned aerial vehicles to ground nodes, aims to maximize the minimum collected energy in a single ground node, constructs a multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model, and obtains an optimal flight trajectory set and an optimal transmission power set of the multi-unmanned aerial vehicles by solving the multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model. In one aspect, the method considers the existence of nonlinear elements in an actual ground energy collection node circuit, constructs a multi-source nonlinear multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model, jointly optimizes the flight trajectory and transmission power of the multi-unmanned aerial vehicles, realizes the purpose of maximizing the minimum collected energy in a single ground node, and maintains the operation stability of the power grid system. In another aspect, the method is equipped with a special fixed nest for charging the unmanned aerial vehicles, ensures that the unmanned aerial vehicles can continuously provide energy transmission services for the ground nodes during the task, and significantly improves the energy collection efficiency of the ground nodes. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 The method is shown in the overall flowchart.

[0087] Figure 2 The model diagram of the scenario is shown in Example 1.

[0088] Figure 3 The structure diagram of the system is shown in the application. DETAILED DESCRIPTION

[0089] The application will be further described in detail in combination with the specific embodiments and the drawings.

[0090] The application provides a multi-unmanned aerial vehicle flight trajectory and transmission power joint determination method and system, which considers that when multiple unmanned aerial vehicles transmit energy to a ground device, the energy received by the ground device is not a linear sum of the energy transmitted by each unmanned aerial vehicle, but there is a nonlinear relationship. Based on the nonlinear relationship, a multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model is constructed, and under the constraints of the start and end points of the unmanned aerial vehicles, the maximum speed, the transmission power and the anti-collision, the minimum collected energy of the ground node is maximized, and the energy collection efficiency of the ground node is significantly improved.

[0091] Example 1

[0092] As shown in Figure 1 A multi-unmanned aerial vehicle flight trajectory and transmission power joint determination method is performed in the following steps:

[0093] 1. Consider a scenario where a drone performs wireless power transfer to a ground node, as described in the following example: Figure 2 As shown, a joint optimization model of multi-UAV flight trajectory and transmission power is constructed with the goal of maximizing the minimum collected energy within a single ground node;

[0094] In a scenario where drones wirelessly transfer energy to ground nodes, M=2 drones flying at a fixed altitude H=100m transmit energy to K=5 ground nodes. Simultaneously, there are M fixed drone nests on the ground, allowing the drones to recharge by traveling to and from the nests. Based on this scenario, a three-dimensional Cartesian coordinate system is established, where the starting and ending points of the drones are their respective nests. The flight trajectory of the m-th drone is defined as q. m =(x m y m The position of the m-th nest is defined as w. c，m =(x c，m y c，m The position of the kth ground node is defined as w (0, 0). k =(w x，k w y，k ,0);

[0095] The total mission time for the UAV to wirelessly transfer energy to the ground node is set to T = 150 seconds. This continuous mission time is discretized into N = 20 time slots of equal length, each time slot being [length missing]. The following formula is used to define the radio frequency signal received by each ground node from each drone within each time slot:

[0096]

[0097] In the above formula, Q k，m [n] represents the radio frequency signal received by the k-th ground node from the m-th UAV within the n-th time slot, and β0 is the channel gain per unit distance, set to -30dBm. m Let q be the energy transfer power of the m-th UAV. m [n] represents the flight trajectory of the m-th UAV within the n-th time slot, w k Let H be the position of the kth ground node, and H be the fixed flight altitude of the UAV.

[0098] Considering the energy collected by a single ground node from all UAVs throughout the entire mission duration, and taking into account that the energy harvesting circuit of the ground equipment consists of a matching circuit, a rectifier circuit, and a low-pass filter, the objective function for constructing a joint optimization model of multi-UAV flight trajectories and transmit power includes:

[0099]

[0100]

[0101] In the above formula, E k ({q m [n]},{P m [n]}) is the energy collected by the jth ground node from all UAVs, which is a multi-source nonlinear energy collection model, q m [n] is the flight trajectory of the nth time slot of the mth UAV, P m [n] is the transmission power of the nth time slot of the mth UAV, P dc，k (Q k [n]) is the received DC signal power of the nth time slot of the kth ground node from all UAVs, Q k [n]={Q k，1 [n],...,Q k，m [n],...,Q j，M [n]} is the received RF signal power of the nth time slot of the kth ground node from all UAVs, Δ is the length of each time slot, I out，k is the output current of the rectifier circuit of the kth ground node in the nth time slot, R L is the resistance of the energy storage device, R L =500Ω, a is a parameter related to the physical characteristics of the energy collection circuit, W0(·) is the Lambert W function, I S is the reverse saturation current, I s =5μA, is the impact received by the kth ground node when receiving power in the nth time slot, n ideal is the ideal factor of the diode, v t is the thermal voltage of the diode, v t =27.153mV, β n is a positive number, is a non-negative integer sequence satisfying , is a combination coefficient, M is the total number of fixed nests, is the power received by the kth ground node from the mth UAV in the nth time slot, is a non-negative integer, is a constant waveform coefficient.

[0102] The constraint conditions of the multi-UAV flight trajectory and transmission power joint optimization model include the start and end point constraints of the UAV flight trajectory, the maximum flight speed constraints of the UAV, the transmission power constraints of the UAV, and the anti-collision constraints of the multi-UAV.

[0103] The start and end point constraints of the UAV flight trajectory are: ​

[0104] q m [0]=q m [N]=w c，m ;

[0105] The maximum flight speed constraint of the UAV is:

[0106]

[0107] The launch power constraint of the UAV is:

[0108]

[0109] 0≤P m [n]≤P max ;

[0110] The anti-collision constraint of the multi-UAV is:

[0111]

[0112] In the above formula, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight termination point of the mth UAV, w c，m is the position of the fixed nest of the mth UAV, q m [n-1] is the flight trajectory of the mth UAV in the n-1th time slot, V max is the maximum flight speed of the UAV, V max = 10 m / s, is the average launch power, P = 10 W, max is the peak value of the launch power, P max = 10 W, q v [n] is the flight trajectory of the vth UAV in the nth time slot, q w [n] is the flight trajectory of the wth UAV in the nth time slot, d min is the minimum safety distance between two UAVs, d min = 3 m;

[0113] In order to facilitate model solving, auxiliary variables E are introduced, and the objective function of the joint optimization model of multi-UAV flight trajectory and launch power is converted to:

[0114]

[0115] Add constraint condition: E k ({q m [n]},{P m [n]})≥E.

[0116] 2. solve the multi-UAV flight trajectory and launch power joint optimization model to obtain the optimal flight trajectory set and the optimal launch power set of the multi-UAV;

[0117] define the initial iteration flight trajectory point set and launch power set of the UAV as

[0118]

[0119] In the above formula, is the initial iteration flight trajectory set of the mth UAV, is the initial iteration launch power set of the mth UAV, and (0) is the initial iteration;

[0120] Based on the initial iteration flight trajectory set and launch power set of the UAV, the convex problem of each iteration is constructed;

[0121] First, the continuous convex optimization technique is adopted, that is, in each iteration, the convex objective function of the multi-UAV flight trajectory and launch power joint optimization model is obtained by the convex approximation method, including:

[0122] Since E k ({q m [n]},{P m [n]}) is a convex function of , the following convex approximation is obtained:

[0123]

[0124] In the above formula, E k ({q m [n]},{P m [n]}) is the energy collected by the kth ground node from all UAVs, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the received radio frequency signal power of the kth ground node from the mth UAV in the nth time slot, Δ is the length of each time slot, d k 2 (q m [n]) is the distance between the mth UAV and the kth ground node in the nth time slot, q m [n] is the flight trajectory of the mth UAV in the nth time slot, β0 is the channel gain per unit distance, P m [n] is the launch power of the mth UAV in the nth time slot;

[0125] Since d k 2 (q m [n]) and P m[n] coupling, the objective function of the multi-UAV flight trajectory and launch power joint optimization model is further convexly approximated:

[0126]

[0127] In the above formula, is the approximation coefficient of the rth iteration, is the lower bound concave approximation function of the energy collected by the kth ground node from all UAVs in the rth iteration;

[0128] Then the convex constraint of the multi-UAV flight trajectory and launch power joint optimization model is constructed;

[0129] The anti-collision constraint of the multi-UAV in each iteration is convexly approximated as:

[0130]

[0131] In the above formula, is the flight trajectory of the vth UAV in the nth time slot in the rth iteration, is the flight trajectory of the wth UAV in the nth time slot in the rth iteration, is the lower bound concave approximation function of the distance between the vth UAV and the wth UAV in the nth time slot in the rth iteration;

[0132] Finally, combining the convex objective function and the convex constraint of the multi-UAV flight trajectory and launch power joint optimization model, the optimization solving convex problem of each iteration is constructed as:

[0133]

[0134]

[0135] In the above formula, E (r) is an auxiliary variable introduced in the rth iteration;

[0136] Solving the optimization solving convex problem of each iteration, the optimal solution of the flight trajectory and the launch power of each iteration is obtained as wherein, is the optimal flight trajectory of the mth UAV in the nth time slot in the rth iteration, is the optimal launch power of the mth UAV in the nth time slot in the rth iteration, and the change of the auxiliary variable in the optimization solving convex problem of each iteration is judged whether it is less than the iteration threshold ε, that is, E (r) -E (r-1) <ε, if it is satisfied, the iteration algorithm ends, and the optimal flight trajectory point set and the optimal launch power set of the multi-UAV are output as If the condition is not met, let r = r + 1, reconstruct the iterative optimization solution to the convex problem, and obtain the optimal flight trajectory and optimal transmission power for the (r+1)th iteration.

[0137] Example 2:

[0138] like Figure 3 As shown, a system for jointly determining the flight trajectory and transmission power of multiple UAVs includes a joint optimization model construction module and a joint optimization model solving module.

[0139] The joint optimization model construction module is used to consider the scenario of UAVs transmitting wireless energy to ground nodes. With the goal of maximizing the minimum collected energy in a single ground node, it constructs a joint optimization model of multi-UAV flight trajectory and transmission power. The scenario includes multiple UAVs flying at a fixed altitude, corresponding to a fixed nest for each UAV and multiple ground nodes receiving wireless energy.

[0140] The joint optimization model solving module is used to solve the joint optimization model of multi-UAV flight trajectory and transmission power, and obtain the optimal flight trajectory set and optimal transmission power set of multi-UAV.

[0141] The joint optimization model construction module includes an objective function construction unit;

[0142] The objective function construction unit is used to construct the objective function of the following joint optimization model of multi-UAV flight trajectory and transmit power:

[0143]

[0144] In the above formula, E k ({q m [n]},{P m [n]}) represents the energy collected by the k-th ground node from all UAVs, which is a multi-source nonlinear energy harvesting model. m [n] represents the flight trajectory of the m-th UAV within the n-th time slot, P m [n] represents the transmit power of the m-th UAV in the n-th time slot, P dc，k (Q k [n]) represents the DC signal power received by the k-th ground node from all UAVs within the n-th time slot, Q. k [n]={Q k，1 [n], ..., Q k，m [n], ..., Q k，M [n]} represents the radio frequency signal power received by the k-th ground node from all UAVs within the n-th time slot, where Δ is the length of each time slot, and I... out，k R is the output current of the rectifier circuit of the k-th ground node in the n-th time slot.L Let be the resistance of the energy storage device, 'a' be a parameter related to the physical characteristics of the energy harvesting circuit, 'W0(·)' be the Lambert W function, and 'I' be the resistance of the energy storage device. S It is the reverse saturation current. β represents the impact of the received power at the k-th ground node within the n-th time slot. n For positive integers, To meet A sequence of non-negative integers, Here, M is the combination coefficient, and M is the total number of fixed nests. For the first Within each time slot, the power received by the k-th ground node from the m-th UAV. It is a non-negative integer. These are constant waveform coefficients.

[0145] The joint optimization model construction module also includes a start and end point constraint construction unit, a maximum flight speed constraint construction unit, a launch power constraint construction unit, and an anti-collision constraint construction unit;

[0146] The start and end point constraint construction unit is used to construct the start and end point constraints of the following UAV flight trajectory:

[0147] q m [0] = q m [N] = w c,m ;

[0148] The maximum flight speed constraint construction unit is used to construct the maximum flight speed constraints for the following UAVs:

[0149]

[0150] The transmit power constraint construction unit is used to construct the transmit power constraints for the following UAVs:

[0151]

[0152] 0≤P m [≤P max ;

[0153] The anti-collision constraint building unit is used to build the following anti-collision constraints for multiple UAVs:

[0154]

[0155] In the above formula, q m [0] is the starting point of the m-th UAV, q m [N] represents the flight termination point of the m-th UAV, w c，m To determine the location of the fixed nest of the m-th UAV, q m[n-1] is the flight trajectory of the mth unmanned aerial vehicle in the n-1th time slot, V max is the maximum flight speed of the unmanned aerial vehicle, and Δ is the length of each time slot, is the average transmission power, P max is the peak value of the transmission power, q v [n] is the flight trajectory of the vth unmanned aerial vehicle in the n th time slot, q w [n] is the flight trajectory of the wth unmanned aerial vehicle in the n th time slot, d min is the minimum safety distance between the two unmanned aerial vehicles.

[0156] The joint optimization model solving module comprises an initial iteration definition unit, an optimization solving convex problem construction unit, and a loop iteration unit.

[0157] The initial iteration definition unit is configured to define the flight trajectory point set and the transmission power set of the initial iteration of the unmanned aerial vehicle as follows:

[0158]

[0159] In the above formula, is the flight trajectory set of the mth unmanned aerial vehicle in the initial iteration, is the transmission power set of the mth unmanned aerial vehicle in the initial iteration, and (0) is the initial iteration.

[0160] The optimization solving convex problem construction unit is configured to construct the convex objective function and the convex constraint of the multi-unmanned aerial vehicle flight trajectory and transmission power joint optimization model based on the flight trajectory set and the transmission power set of the initial iteration of the unmanned aerial vehicle, to obtain the optimization solving convex problem of each iteration.

[0161] The optimization solving convex problem of each iteration is as follows:

[0162]

[0163]

[0164] In the above formula, E (r) is an auxiliary variable introduced in the rth iteration, q m [n] is the flight trajectory of the mth unmanned aerial vehicle in the n th time slot, P m [n] is the transmission power of the mth unmanned aerial vehicle in the n th time slot, is the lower bound concave approximation function of the energy collected by the kth ground node from all unmanned aerial vehicles in the rth iteration, q m [0] is the flight starting point of the mth unmanned aerial vehicle, q m [N] is the flight termination point of the mth unmanned aerial vehicle, w c，m is the position of the fixed nest of the mth unmanned aerial vehicle, q m[n-1] is the flight trajectory of the mth UAV in the n-1th time slot, V max is the maximum flight speed of the UAV, and Δ is the length of each time slot, is the lower bound of the concave approximation function of the distance between the vth UAV and the wth UAV in the nth time slot in the rth iteration, d min is the minimum safe distance between the two UAVs, is the average transmission power, P max is the peak value of the transmission power;

[0165] The cyclic iteration unit is used to solve the optimization solving convex problem of each iteration, and the optimization solution of the UAV flight trajectory and the transmission power of each iteration is obtained as wherein, is the optimal flight trajectory of the mth UAV in the nth time slot in the rth iteration, is the optimal transmission power of the mth UAV in the nth time slot in the rth iteration, and the change amount of the auxiliary variable in the optimization solving convex problem of each iteration is judged whether it is less than the iteration threshold ε, that is, E (r) -E (r-1) < ε, if it is satisfied, the iteration algorithm ends, and the optimal flight trajectory set and the optimal transmission power set of the multiple UAVs are output as If it is not satisfied, let r = r + 1, return to the optimization solving convex problem construction unit to re-construct the optimization solving convex problem of the iteration, and obtain the optimal flight trajectory and the optimal transmission power of the r+1th iteration.

[0166] In the optimization solving convex problem construction unit, the convex objective function of the joint optimization model of the multiple UAV flight trajectories and the transmission power is constructed, which includes:

[0167] A, since E k ({q m [n]},{P m [n]}) is a convex function of , and the following convex approximation is obtained:

[0168]

[0169] In the above formula, E k ({q m [n]},{P m [n]}) is the energy collected by the kth ground node from all UAVs, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the received radio frequency signal power of the kth ground node from the mth UAV in the nth time slot, Δ is the length of each time slot, dx 2 (q m[n] is the distance between the mth UAV and the kth ground node in the nth time slot, q m [n] is the flight trajectory of the mth UAV in the nth time slot, β0is the channel gain per unit distance, P m [n] is the flight trajectory of the mth UAV in the nth time slot, β0is the channel gain per unit distance, P

[0170] B, since d k 2 q m [n]) and P m [n] coupling, the objective function of the multi-UAV flight trajectory and transmission power joint optimization model is further convexly approximated:

[0171]

[0172] In the above formula, is the approximation coefficient of the rth iteration, is the lower bound concave approximation function of the energy collected by the kth ground node from all UAVs in the rth iteration;

[0173] The convex constraint of the multi-UAV flight trajectory and transmission power joint optimization model is constructed, including:

[0174] The anti-collision constraint of the multi-UAV in each iteration is convexly approximated as:

[0175]

[0176] In the above formula, is the flight trajectory of the vth UAV in the nth time slot in the rth iteration, is the flight trajectory of the wth UAV in the nth time slot in the rth iteration, is the lower bound concave approximation function of the distance between the bth UAV and the wth UAV in the nth time slot in the rth iteration.

Claims

1.A method for jointly determining flight trajectories and transmission powers of multiple unmanned aerial vehicles (UAVs), comprising: S1. considering a scenario in which multiple UAVs fly at a fixed altitude and transmit wireless energy to multiple ground nodes, and constructing a joint optimization model of flight trajectories and transmission powers of the multiple UAVs, aiming to maximize the minimum collected energy in a single ground node; wherein the joint optimization model of flight trajectories and transmission powers of the multiple UAVs comprises: S2. solving the joint optimization model of flight trajectories and transmission powers of the multiple UAVs to obtain an optimal set of flight trajectories and an optimal set of transmission powers of the multiple UAVs. 2.The method of claim 1, wherein the constraints of the joint optimization model of flight trajectories and transmission powers of the multiple UAVs in S1 comprise start and end point constraints of flight trajectories of the multiple UAVs, maximum flight speed constraints of the multiple UAVs, transmission power constraints of the multiple UAVs, and anti-collision constraints of the multiple UAVs; wherein the start and end point constraints of flight trajectories of the multiple UAVs are: wherein the maximum flight speed constraints of the multiple UAVs are: wherein the transmission power constraints of the multiple UAVs are: wherein the anti-collision constraints of the multiple UAVs are: 3.The method of claim 1, wherein S2 comprises: S21. defining an initial set of flight trajectory points and an initial set of transmission powers of the multiple UAVs in an initial iteration as: S22. constructing a convex objective function and a convex constraint of the joint optimization model of flight trajectories and transmission powers of the multiple UAVs based on the initial set of flight trajectory points and the initial set of transmission powers of the multiple UAVs in the initial iteration to obtain an optimization solving convex problem in each iteration; wherein the optimization solving convex problem in each iteration is: 4.The method of claim 3, wherein the convex objective function of the joint optimization model of flight trajectories and transmission powers of the multiple UAVs in S22 comprises: wherein the convex constraint of the joint optimization model of flight trajectories and transmission powers of the multiple UAVs in S22 comprises: wherein the anti-collision constraints of the multiple UAVs in each iteration are convexly approximated as: In the above formula, E k ({q m [n]},{P m [n]}) represents the energy collected by the k-th ground node from all UAVs, which is a multi-source nonlinear energy harvesting model. m [n] represents the flight trajectory of the m-th UAV within the n-th time slot, P m [n] represents the transmit power of the m-th UAV in the n-th time slot, P dc，k (Q k [n]) represents the DC signal power received by the k-th ground node from all UAVs within the n-th time slot, Ω. k [n]={Q k，1 [n],...,Q k，m [n],...,Q k，M [n]} represents the radio frequency signal power received by the k-th ground node from all UAVs within the n-th time slot, where Δ is the length of each time slot, and I... out，k R is the output current of the rectifier circuit of the k-th ground node in the n-th time slot. L Let be the resistance of the energy storage device, 'a' be a parameter related to the physical characteristics of the energy harvesting circuit, 'W0(·)' be the Lambert W function, and 'I' be the resistance of the energy storage device. S It is the reverse saturation current. β represents the impact of the received power at the k-th ground node within the n-th time slot. n For positive integers, To meet A sequence of non-negative integers, Here, M is the combination coefficient, and M is the total number of fixed nests. For the first Within each time slot, the power received by the k-th ground node from the m-th UAV. It is a non-negative integer. For constant waveform coefficients; 5.A system for jointly determining flight trajectories and transmission powers of multiple unmanned aerial vehicles (UAVs), comprising: a joint optimization model construction module and a joint optimization model solving module; wherein the joint optimization model construction module is configured to consider a scenario in which multiple UAVs fly at a fixed altitude and transmit wireless energy to multiple ground nodes, and construct a joint optimization model of flight trajectories and transmission powers of the multiple UAVs, aiming to maximize the minimum collected energy in a single ground node; wherein the joint optimization model construction module comprises a target function construction unit; and wherein the target function construction unit is configured to construct a target function of the joint optimization model of flight trajectories and transmission powers of the multiple UAVs as follows: ​ ​ ​ q m [0] = q m [N] = w c，m ; ​ ​ 0 < P m [n] < P max ; ​ In the above formula, q m [0] is the flight starting point of the mth unmanned aerial vehicle, q m [N] is the flight termination point of the mth unmanned aerial vehicle, w c,m is the position of the fixed nest of the mth unmanned aerial vehicle, q m [n-1] is the flight trajectory of the mth unmanned aerial vehicle in the n-1th time slot, V max is the maximum flight speed of the unmanned aerial vehicle, Δ is the length of each time slot, is the average transmission power, P max is the peak value of the transmission power, q v [n] is the flight trajectory of the vth unmanned aerial vehicle in the n th time slot, q w [n] is the flight trajectory of the wth unmanned aerial vehicle in the n th time slot, d min is the minimum safety distance between the two unmanned aerial vehicles. ​ ​ ​ In the above formula, is a set of flight trajectories for the mth UAV for the initial iteration, is a set of transmit powers for the mth UAV for the initial iteration, (0) is the initial iteration; ​ ​ In the above formula, E (r) is the auxiliary variable introduced in the rth iteration, q m [n] is the flight trajectory of the mth UAV in the nth time slot, P m [n] is the transmission power of the mth UAV in the nth time slot, is the lower bound concave approximation function of the energy collected by the kth ground node from all UAVs in the rth iteration, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight termination point of the mth UAV, w c，m is the location of the fixed nest of the mth UAV, q m [n-1] is the flight trajectory of the mth UAV in the n-1th time slot, V max is the maximum flight speed of the UAV, Δ is the length of each time slot, is the lower bound concave approximation function of the distance between the vth UAV and the wth UAV in the nth time slot in the rth iteration, d min is the minimum safe distance between two UAVs, is the average transmission power, P max is the peak value of the transmission power; S23, solving the optimization solving convex problem of each iteration, obtaining the optimal solution of the flight trajectory and the transmission power of each iteration of the unmanned aerial vehicle as wherein, is the optimal flight trajectory of the mth unmanned aerial vehicle in the nth time slot in the rth iteration, is the optimal transmission power of the mth unmanned aerial vehicle in the nth time slot in the rth iteration, and the change of the auxiliary variable in the optimization solving convex problem of each iteration is determined whether it is less than the iteration threshold ε, that is, it meets E (r) -E (r-1) <ε, if it meets, the iteration algorithm ends, and the optimal flight trajectory set and the optimal transmission power set of the multiple unmanned aerial vehicles are output as If it does not meet, let r=r+1, return to step S22 to re-construct the optimization solving convex problem of iteration, and obtain the optimal flight trajectory and the optimal transmission power of the r+1th iteration. ​ ​ A, due to E k ({q m [n]},{p m [n]}) is a convex function, and further has the following convex approximation: In the above formula, E k ({q m [n]},{P m [n]}) is the energy collected by the kth ground node from all UAVs, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the received radio frequency signal power of the kth ground node from the mth UAV in the nth time slot, Δ is the length of each time slot, d k 2 (q m [n]) is the distance between the mth UAV and the kth ground node in the nth time slot, q m [n] is the flight trajectory of the mth UAV in the nth time slot, β0 is the channel gain per unit distance, P m [n] is the transmission power of the mth UAV in the nth time slot; B, due to d k 2 (q m [n]) and P m [n] coupling, the objective function of the multi-UAV flight trajectory and launch power joint optimization model is further convexly approximated: In the above formula, is the approximation coefficient for the rth iteration, is the lower bound concave approximation function of the energy collected by the kth ground node from all the UAVs for the rth iteration; ​ ​ In the above formula, is the flight trajectory of the vth UAV in the nth time slot for the rth iteration, is the flight trajectory of the wth UAV in the nth time slot for the rth iteration, is the lower bound concave approximation function of the distance between the vth UAV and the wth UAV in the nth time slot for the rth iteration. ​ ​ ​ ​ In the above formula, E k ({q m [n]},{P m [n]}) represents the energy collected by the k-th ground node from all UAVs, which is a multi-source nonlinear energy harvesting model. m [n] represents the flight trajectory of the m-th UAV within the n-th time slot, P m [n] represents the transmit power of the m-th UAV in the n-th time slot, P dc，k (Q k [n]) represents the DC signal power received by the k-th ground node from all UAVs within the n-th time slot, Q. k [n]={Q k，1 [n],...,Q k，m [n], ..., Q k，M [n]} represents the radio frequency signal power received by the k-th ground node from all UAVs within the n-th time slot, where Δ is the length of each time slot, and I... out,k R is the output current of the rectifier circuit of the k-th ground node in the n-th time slot. L Let be the resistance of the energy storage device, 'a' be a parameter related to the physical characteristics of the energy harvesting circuit, 'W0(·)' be the Lambert W function, and 'I' be the resistance of the energy storage device. S It is the reverse saturation current. β represents the impact of the received power at the k-th ground node within the n-th time slot. n For positive integers, To meet A sequence of non-negative integers, Here, M is the combination coefficient, and M is the total number of fixed nests. For the first Within each time slot, the power received by the k-th ground node from the m-th UAV. It is a non-negative integer. For constant waveform coefficients; The joint optimization model solving module is configured to solve the multi-unmanned aerial vehicle flight trajectory and launch power joint optimization model to obtain an optimal flight trajectory set and an optimal launch power set of the multi-unmanned aerial vehicles. 6.The multi-unmanned aerial vehicle flight trajectory and launch power joint determination system according to claim 5, characterized in that, The joint optimization model constructing module further comprises a start and end point constraint constructing unit, a maximum flight speed constraint constructing unit, a launch power constraint constructing unit, and a collision avoidance constraint constructing unit. The start and end point constraint constructing unit is configured to construct the start and end point constraint of the unmanned aerial vehicle flight trajectory as follows: q m [0] = q m [N] = w c，m ; The maximum flight speed constraint constructing unit is configured to construct the maximum flight speed constraint of the unmanned aerial vehicle as follows: The launch power constraint constructing unit is configured to construct the launch power constraint of the unmanned aerial vehicle as follows: 0 < P m [n] < P max ; The collision avoidance constraint constructing unit is configured to construct the collision avoidance constraint of the multi-unmanned aerial vehicles as follows: In the above formula, q m [0] is the flight starting point of the mth unmanned aerial vehicle, q m [N] is the flight termination point of the mth unmanned aerial vehicle, w c，m is the position of the fixed nest of the mth unmanned aerial vehicle, q m [n-1] is the flight trajectory of the mth unmanned aerial vehicle in the n-1th time slot, V max is the maximum flight speed of the unmanned aerial vehicle, Δ is the length of each time slot, is the average transmission power, P max is the peak value of the transmission power, q v [n] is the flight trajectory of the vth unmanned aerial vehicle in the n th time slot, q w [n] is the flight trajectory of the wth unmanned aerial vehicle in the n th time slot, d min is the minimum safety distance between the two unmanned aerial vehicles. 7.The multi-unmanned aerial vehicle flight trajectory and launch power joint determination system according to claim 5, characterized in that, The joint optimization model solving module comprises an initial iteration defining unit, an optimization solving convex problem constructing unit, and a loop iteration unit. The initial iteration defining unit is configured to define the flight trajectory point set and the launch power set of the initial iteration of the unmanned aerial vehicle as follows: In the above formula, is a set of flight trajectories for the mth UAV for the initial iteration, is a set of transmit powers for the mth UAV for the initial iteration, (0) is the initial iteration; The optimization solving convex problem constructing unit is configured to construct a convex objective function and a convex constraint of the multi-unmanned aerial vehicle flight trajectory and launch power joint optimization model based on the flight trajectory set and the launch power set of the initial iteration of the unmanned aerial vehicle to obtain an optimization solving convex problem of each iteration. The optimization solving convex problem of each iteration is as follows: In the above formula, E (r) is the auxiliary variable introduced in the rth iteration, q m [n] is the flight trajectory of the mth UAV in the nth time slot, P m [n] is the transmission power of the mth UAV in the nth time slot, is the lower bound concave approximation function of the energy collected by the kth ground node from all UAVs in the rth iteration, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight termination point of the mth UAV, w c，m is the location of the fixed nest of the mth UAV, q m [n-1] is the flight trajectory of the mth UAV in the n-1th time slot, V max is the maximum flight speed of the UAV, Δ is the length of each time slot, is the lower bound concave approximation function of the distance between the vth UAV and the wth UAV in the nth time slot in the rth iteration, d min is the minimum safe distance between two UAVs, is the average transmission power, P max is the peak value of the transmission power; The cyclic iteration unit is configured to solve the optimization solving convex problem of each iteration to obtain the optimal solution of the flight trajectory and the transmission power of each iteration as wherein, is the optimal flight trajectory of the mth UAV in the nth time slot in the rth iteration, is the optimal transmission power of the mth UAV in the nth time slot in the rth iteration, and the change of the auxiliary variable in the optimization solving convex problem of each iteration is determined to be less than an iteration threshold ε, that is, E (r) -E (r-1) <ε, if the condition is met, the iteration algorithm is ended, and the optimal flight trajectory set and the optimal transmission power set of the multiple UAVs are output as If the condition is not met, r is set to r+1, and the optimization solving convex problem construction unit is returned to re-construct the optimization solving convex problem of the iteration to obtain the optimal flight trajectory and the optimal transmission power of the r+1th iteration. 8.The multi-unmanned aerial vehicle flight trajectory and launch power joint determination system according to claim 7, characterized in that, In the optimization solving convex problem constructing unit, the convex objective function of the multi-unmanned aerial vehicle flight trajectory and launch power joint optimization model comprises: A, due to E k ({q m [n]}, {P m [n]}) is a convex function, and further has the following convex approximation: In the above formula, E k ({q m m [n]} and {P k，m [n]} are the energy collected by the kth ground node from all UAVs, are the convex approximation coefficients of the rth iteration, Q k [n] is the received radio frequency signal power of the kth ground node from the mth UAV in the nth time slot, Δ is the length of each time slot, d 2 m (q m [n]) is the distance between the mth UAV and the kth ground node in the nth time slot, q m [k] is the flight trajectory of the mth UAV in the nth time slot, β0 is the channel gain per unit distance, P[n] is the transmission power of the mth UAV in the nth time slot; B, due to d k 2 (q m [n]) and P m [n] coupling, the objective function of the multi-UAV flight trajectory and launch power joint optimization model is further convexly approximated: In the above formula, is the approximation coefficient for the rth iteration, is the lower bound concave approximation function of the energy collected by the kth ground node from all the UAVs for the rth iteration; The convex constraint of the multi-unmanned aerial vehicle flight trajectory and launch power joint optimization model comprises: The collision avoidance constraint of the multi-unmanned aerial vehicles of each iteration is convexly approximated as follows: In the above formula, is the flight trajectory of the vth UAV in the nth time slot for the rth iteration, is the flight trajectory of the wth UAV in the nth time slot for the rth iteration, is the lower bound concave approximation function of the distance between the vth UAV and the wth UAV in the nth time slot for the rth iteration.

Images