Method and system for jointly determining flight paths and transmitting power of multiple unmanned aerial vehicles

Abstract

The invention discloses a multi-unmanned aerial vehicle flight path and transmitting power joint determination method and system, and the method comprises the steps: taking a scene in which unmanned aerial vehicles carry out wireless energy transmission to ground nodes into consideration, taking the maximization of the minimum collected energy in a single ground node as a target, and constructing a multi-unmanned aerial vehicle flight path and transmitting power joint optimization model; the scene comprises a plurality of unmanned aerial vehicles flying at a fixed height, a fixed nest corresponding to each unmanned aerial vehicle and a plurality of ground nodes for receiving wireless energy; and obtaining an optimal flight path set and an optimal transmitting power set of the multiple unmanned aerial vehicles by solving the flight path and transmitting power joint optimization model of the multiple unmanned aerial vehicles. According to the invention, existence of a nonlinear element in an actual ground energy collection node circuit is considered, a special fixed nest is arranged to charge the unmanned aerial vehicles, flight paths and transmitting power of the multiple unmanned aerial vehicles are jointly optimized, and while the minimum collected energy in a single ground node is maximized, the energy collection efficiency of the unmanned aerial vehicles is improved. And the energy collection efficiency of the ground node is improved.

Description

Technical Field

[0001] The present invention belongs to the field of unmanned aerial vehicle (UAV) assisted wireless energy transmission, and in particular relates to a method and system for jointly determining flight trajectories and transmission powers of multiple UAVs. Background Art

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

[0003] The high maneuverability of drones can flexibly respond to electricity demand in different regions and at different time periods. Especially in the event of a power outage or difficulty in power dispatch, drones can serve as temporary power supply stations to maintain the operational stability of the power grid system. This makes drones a key component in scenarios such as smart cities, distributed energy management, and disaster recovery, improving the resilience and energy efficiency of modern power grids.

[0004] At present, in order to improve the energy transmission efficiency of mobile energy supply equipment, designing drone trajectories and resource allocation is regarded as an effective way. Traditional drone design methods include considering the optimization of one-dimensional drone trajectories in wireless energy transmission scenarios, in which drones transmit energy to two ground nodes, and the flight of drones is limited by maximum speed. In the scenario where dual drones assist a single receiver in wireless energy transmission, the optimal trajectory of the drone should be evenly distributed on the circumference. These design methods all consider linear energy harvesting models. However, in actual RF-DC circuits, due to the presence of nonlinear elements such as diodes, there is a nonlinear relationship between the RF power received by the ground equipment and the collected energy. Therefore, the use of a nonlinear energy harvesting model is more practical. Summary of the invention

[0005] The purpose of the present invention is to provide a method and system for jointly determining the flight trajectories and transmission powers of multiple UAVs in view of the above-mentioned problems existing in the prior art.

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

[0007] In a first aspect, the present invention proposes a method for jointly determining flight trajectories and transmission powers of multiple UAVs, comprising:

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

[0009] S2. Solve the joint optimization model of multi-UAV flight trajectory and transmission power to obtain the optimal flight trajectory set and optimal transmission power set of 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]}) is the energy collected by the kth ground node from all drones. It is a multi-source nonlinear energy collection model. 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, P dc，k (Q k [n]) is the DC signal power received by the kth ground node from all drones in the nth time slot, Q k [n] = {Q k，1 [n], ..., Q k，m [n], ..., Q k，M [n]} is the RF signal power received by the kth ground node from all drones in the nth time slot, 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, a is the parameter related to the physical characteristics of the energy harvesting circuit, W0(·) is the Lambert W function, I S is the reverse saturation current, is the impact of the kth ground node receiving power in the nth time slot, β n is a normal number, To satisfy A sequence of non-negative integers, is the combination coefficient, M is the total number of fixed nests, For the The power received by the kth ground node from the mth UAV in the time slot is: is a non-negative integer, is a constant waveform factor.

[0013] In S1, the constraints of the joint optimization model of multi-UAV flight trajectory and transmission power 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 multiple UAVs;

[0014] The starting and ending point constraints of the UAV flight trajectory are:

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

[0016] The maximum flight speed constraint of the UAV is:

[0017]

[0018] The transmission power constraint of the UAV is:

[0019]

[0020] 0≤P m [n]≤P max ;

[0021] The anti-collision constraints of the multiple UAVs are:

[0022]

[0023] In the above formula, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 average transmission power, P max is the peak value of the transmitted power, q v [n] is the flight trajectory of the vth UAV in the nth time slot, q w [n] The flight trajectory of the w-th UAV in the n-th time slot, d min is the minimum safe distance between two drones.

[0024] The S2 includes:

[0025] S21. Define the flight trajectory point set and transmission power set of the initial iteration of the UAV as;

[0026]

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

[0028] S22. Based on the flight trajectory set and transmission power set of the initial iteration of the UAV, a convex objective function and convex constraints of the joint optimization model of the flight trajectory and transmission power of multiple UAVs are constructed to obtain the optimization solution convex problem for each iteration;

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

[0030]

[0031]

[0032] 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 approximate function of the energy collected by the kth ground node from all drones in the rth iteration, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 approximate function of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration, d min is the minimum safe distance between two drones, is the average transmission power, P max is the peak value of the transmitted power;

[0033] S23. Solve the optimization problem of each iteration and obtain the optimal solution of the UAV flight trajectory and transmission power for each iteration: in, 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. It is determined whether the change of the auxiliary variable in the optimization solution of the convex problem in each iteration is less than the iteration threshold ε, that is, it satisfies E(r) -E (r-1) <ε, if it is satisfied, the iterative algorithm ends, and the optimal flight trajectory set and optimal transmission power set of multiple UAVs are output as If not, set r=r+1 and return to step S22 to reconstruct the iterative optimization solution of the convex problem to obtain the optimal flight trajectory and optimal transmission power of the r+1th iteration.

[0034] In S22, a convex objective function of a joint optimization model of multi-UAV flight trajectory and transmission power is constructed, including:

[0035] A. Due to E k ({q m [n]}, {P m [n]}) is The convex function of , and then the following convex approximation:

[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 drones, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the RF signal power received by 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;

[0038] B. Due to d k 2 (q m [n]) and P m [n] coupling, the objective function of the joint optimization model of multi-UAV flight trajectory and transmission power is further convexly approximated:

[0039]

[0040] In the above formula, The approximate coefficients for the rth iteration, is the lower bound concave approximate function of the energy collected by the kth ground node from all UAVs in the rth iteration;

[0041] Convex constraints are used to construct a joint optimization model of multi-UAV flight trajectory and transmission power, including:

[0042] The anti-collision constraints of multiple UAVs in each iteration are 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 w-th UAV in the n-th time slot in the r-th iteration, is the concave approximate function of the lower bound of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration.

[0045] In a second aspect, the present invention proposes a system for jointly determining flight trajectories and transmission powers of multiple UAVs, including a joint optimization model building module and a joint optimization model solving module;

[0046] The joint optimization model building module is used to consider the scenario of wireless energy transmission from a UAV to a ground node, and to build a joint optimization model of multi-UAV flight trajectory and transmission power with the goal of maximizing the minimum collected energy within a single ground node. 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 joint optimization model of multi-UAV flight trajectory and transmission power to obtain the optimal flight trajectory set and optimal transmission power set of the multi-UAV.

[0048] The joint optimization model construction module includes an objective function construction unit;

[0049] The objective function construction unit is used to construct the objective function of the following multi-UAV flight trajectory and transmission 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 drones. It is a multi-source nonlinear energy collection model. 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, P dc，k (Q k[n]) is the DC signal power received by the kth ground node from all drones in the nth time slot, Q k [n] = {Q k，1 [n], ..., Q k，m [n], ..., Q k，M [n]} is the RF signal power received by the kth ground node from all drones in the nth time slot, 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, a is the parameter related to the physical characteristics of the energy harvesting circuit, W0(·) is the Lambert W function, I S is the reverse saturation current, is the impact of the kth ground node receiving power in the nth time slot, β n is a normal number, To satisfy A sequence of non-negative integers, is the combination coefficient, M is the total number of fixed nests, For the The power received by the kth ground node from the mth UAV in the time slot is: is a non-negative integer, is a constant waveform factor.

[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 transmission power constraint construction unit, and an anti-collision constraint construction unit;

[0053] The start-end point constraint construction unit is used to construct the start-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 following maximum flight speed constraint of the UAV:

[0056]

[0057] The transmission power constraint construction unit is used to construct the following transmission power constraint of the UAV:

[0058]

[0059] 0≤P m [n]≤P max ;

[0060] The anti-collision constraint construction unit is used to construct the following anti-collision constraints for multiple UAVs:

[0061]

[0062] In the above formula, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 average transmission power, P max is the peak value of the transmitted power, q v [n] is the flight trajectory of the vth UAV in the nth time slot, q w [n] The flight trajectory of the w-th UAV in the n-th time slot, d min is the minimum safe distance between two drones.

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

[0064] The initial iteration definition unit is used to define the flight trajectory point set and the transmission power set of the initial iteration of the UAV as;

[0065]

[0066] In the above formula, is the flight trajectory set of the initial iteration of the mth UAV, is the transmission power set of the initial iteration of the mth UAV, (0) is the initial iteration;

[0067] The optimization solution convex problem construction unit is used to construct a convex objective function and convex constraints of a multi-UAV flight trajectory and transmission power joint optimization model based on the flight trajectory set and transmission power set of the initial iteration of the UAV, and obtain the optimization solution convex problem for each iteration;

[0068] The optimization solution of each iteration of the convex problem is:

[0069]

[0070]

[0071] 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 approximate function of the energy collected by the kth ground node from all drones in the rth iteration, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 approximate function of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration, d min is the minimum safe distance between two drones, is the average transmission power, P max is the peak value of the transmitted power;

[0072] The loop iteration unit is used to solve the optimization solution convex problem of each iteration, and the optimal solution of the UAV flight trajectory and transmission power of each iteration is obtained as follows: in, 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. It is determined whether the change of the auxiliary variable in the optimization solution of the convex problem in each iteration is less than the iteration threshold ε, that is, it satisfies E (r) -E (r-1) <ε, if it is satisfied, the iterative algorithm ends, and the optimal flight trajectory set and optimal transmission power set of multiple UAVs are output as If not, set r=r+1, return to the optimization solution convex problem construction unit to reconstruct the iterative optimization solution convex problem, and obtain the optimal flight trajectory and optimal transmission power of the r+1th iteration.

[0073] In the optimization solution convex problem construction unit, a convex objective function of a joint optimization model of multi-UAV flight trajectory and transmission power is constructed, including:

[0074] A. Due to E k ({q m [n]}, {P m [n]}) is The convex function of , and then the following convex approximation:

[0075]

[0076] In the above formula, E k ({q m [n]}, {P m [n]}) is the energy collected by the kth ground node from all drones, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the RF signal power received by 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;

[0077] B. Due to d k 2 (q m [n]) and P m [n] coupling, the objective function of the joint optimization model of multi-UAV flight trajectory and transmission power is further convexly approximated:

[0078]

[0079] In the above formula, is the approximate coefficient of the rth iteration, is the lower bound concave approximate function of the energy collected by the kth ground node from all UAVs in the rth iteration;

[0080] Convex constraints are used to construct a joint optimization model of multi-UAV flight trajectory and transmission power, including:

[0081] The anti-collision constraints of multiple UAVs in each iteration are convexly approximated as:

[0082]

[0083] 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 w-th UAV in the n-th time slot in the r-th iteration, is the concave approximate function of the lower bound of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration.

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] The present invention proposes a method and system for jointly determining the flight trajectory and transmission power of multiple unmanned aerial vehicles. The method considers the scenario of wireless energy transmission from unmanned aerial vehicles to ground nodes, and aims to maximize the minimum collected energy in a single ground node, and constructs a joint optimization model of flight trajectory and transmission power of multiple unmanned aerial vehicles. The scenario includes multiple unmanned aerial vehicles flying at a fixed altitude, a fixed machine nest corresponding to each unmanned aerial vehicle, and multiple ground nodes receiving wireless energy; and by solving the joint optimization model of flight trajectory and transmission power of multiple unmanned aerial vehicles, the optimal flight trajectory set and the optimal transmission power set of multiple unmanned aerial vehicles are obtained. On the one hand, the method considers the existence of nonlinear components in the actual ground energy collection node circuit, constructs a multi-source nonlinear joint optimization model of flight trajectory and transmission power of multiple unmanned aerial vehicles, and jointly optimizes the flight trajectory and transmission power of multiple unmanned aerial vehicles, so as to maximize the minimum collected energy in a single ground node and maintain the operation stability of the power grid system; on the other hand, the method is equipped with a special fixed machine nest to charge the unmanned aerial vehicle, so as to ensure that the unmanned aerial vehicle can continuously provide energy transmission services to the ground node during the mission, and significantly improve the energy collection efficiency of the ground node. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 The figure is an overall flow chart of the method of the present invention.

[0087] Figure 2 This is a model diagram of the scenario described in Example 1.

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

[0089] The present invention is further described in detail below in conjunction with specific implementations and drawings.

[0090] The present invention proposes a method and system for jointly determining the flight trajectories and transmission powers of multiple UAVs. When multiple UAVs transmit energy to a ground device, the energy received by the ground device is not a linear sum of the energy transmitted by each UAV, but there is a nonlinear relationship. Based on this nonlinear relationship, a joint optimization model of the flight trajectories and transmission powers of multiple UAVs is constructed, and under the constraints of the start and end points, maximum speed, transmission power and anti-collision of the UAVs, the minimum collected energy of the ground nodes is maximized, which significantly improves the energy collection efficiency of the ground nodes.

[0091] Embodiment 1:

[0092] like Figure 1 As shown, a method for jointly determining the flight trajectory and transmission power of multiple UAVs is performed in the following steps:

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

[0094] In the scenario of wireless energy transmission from drones to ground nodes, M = 2 drones are deployed at a fixed altitude H = 100m to transmit energy to K = 5 ground nodes. At the same time, there are M fixed nests on the ground, so that drones can go back and forth between the nests for charging. Based on this scenario, a three-dimensional Cartesian coordinate system is established, and the starting and ending points of the drones are their respective nests. The flight trajectory of the mth drone is defined as q m =(x m ,y m , H), the position of the mth nest is defined as w c，m =(x c，m ,y c，m , 0), the position of the kth ground node is defined as w k =(w x，k , w y，k , 0);

[0095] The total mission time of wireless energy transmission from the UAV to the ground node is set to T = 150s, and the continuous mission time is discretized into N = 20 time slots of equal length, each time slot is The following formula is used to define the RF signal received by each ground node from each drone in each time slot:

[0096]

[0097] In the above formula, Q k，m [n] is the RF signal received by the kth ground node from the mth UAV in the nth time slot, β0 is the channel gain per unit distance, and β0 is set to -30dBm. m is the energy transmission power of the mth UAV, q m [n] is the flight trajectory of the mth UAV in the nth time slot, w k is the position of the kth ground node, and H is the fixed flight altitude of the UAV;

[0098] Considering the energy collected by a single ground node from all drones during the entire mission period, and considering that the energy collection circuit of the ground equipment is composed of a matching circuit, a rectifier circuit, and a low-pass filter, the objective function of constructing a joint optimization model of multi-drone flight trajectory and transmission 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 drones, which is a multi-source nonlinear energy collection model. 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, P dc，k (Q k [n]) is the DC signal power received by the kth ground node from all drones in the nth time slot, Q k [n] = {Q k，1 [n], ..., Q k，m [n], ..., Q j，M [n]} is the RF signal power received by the kth ground node from all drones in the nth time slot, 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 For the resistance of the energy storage device, set R L =500Ω, a is the parameter related to the physical characteristics of the energy harvesting circuit, W0(·) is the Lambert W function, I S For the reverse saturation current, set I s =5μA, is the impact of the kth ground node receiving power in the nth time slot, n ideal is the ideality factor of the diode, v t is the thermal voltage of the diode, set v t =27.153mV, β n is a normal number, To satisfy A sequence of non-negative integers, is the combination coefficient, M is the total number of fixed nests, For the The power received by the kth ground node from the mth UAV in the time slot is: is a non-negative integer, is a constant waveform factor;

[0102] The constraints of the joint optimization model of multi-UAV flight trajectory and transmission power 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 multiple UAVs;

[0103] The starting and ending 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 transmission power constraint of the UAV is:

[0108]

[0109] 0≤P m [n]≤P max ;

[0110] The anti-collision constraints of the multiple UAVs are:

[0111]

[0112] In the above formula, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 Set V to the maximum flight speed of the drone. max =10m / s, is the average transmit power, set P max For the peak value of the transmission power, set P max =10W, q v [n] is the flight trajectory of the vth UAV in the nth time slot, q w [n] The flight trajectory of the w-th UAV in the n-th time slot, d min Set d as the minimum safe distance between two drones. min =3m;

[0113] In order to facilitate the model solution, the auxiliary variable E is introduced to convert the objective function of the joint optimization model of multi-UAV flight trajectory and transmission power into:

[0114]

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

[0116] 2. Solve the joint optimization model of multi-UAV flight trajectory and transmission power to obtain the optimal flight trajectory set and optimal transmission power set of multiple UAVs;

[0117] The flight trajectory point set and transmission power set of the initial iteration of the UAV are defined as;

[0118]

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

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

[0121] First, the continuous convex optimization technology is used, that is, the convex objective function of the joint optimization model of multi-UAV flight trajectory and transmission power is obtained through the convex approximation method in each iteration, including:

[0122] Due to E k ({q m [n]}, {P m [n]}) is The convex function of , and then the following convex approximation:

[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 drones, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the RF signal power received by 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;

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

[0126]

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

[0128] Then, the convex constraints of the joint optimization model of multi-UAV flight trajectory and transmission power are constructed;

[0129] The anti-collision constraints of multiple UAVs in each iteration are 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 w-th UAV in the n-th time slot in the r-th iteration, is the lower bound concave approximate function of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration;

[0132] Finally, combining the convex objective function and convex constraints of the joint optimization model of multi-UAV flight trajectory and transmission power, the optimization solution of each iteration is constructed as:

[0133]

[0134]

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

[0136] Solve the optimization problem of each iteration and get the optimal solution of flight trajectory and transmission power for each iteration: in, 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. It is determined whether the change of the auxiliary variable in the optimization solution of the convex problem in each iteration is less than the iteration threshold ε, that is, it satisfies E (r) -E (r-1) <ε, if it is satisfied, the iterative algorithm ends, and the optimal flight trajectory point set and optimal transmission power set of multiple UAVs are output as If it is not satisfied, then set r=r+1, reconstruct the iterative optimization to solve the convex problem, and obtain the optimal flight trajectory and optimal transmission power of the r+1th iteration.

[0137] Embodiment 2:

[0138] like Figure 3 As shown, a system for jointly determining flight trajectories and transmission powers of multiple UAVs includes a joint optimization model building module and a joint optimization model solving module;

[0139] The joint optimization model building module is used to consider the scenario of wireless energy transmission from a UAV to a ground node, and to build a joint optimization model of multi-UAV flight trajectory and transmission power with the goal of maximizing the minimum collected energy within a single ground node. The scenario includes multiple UAVs flying at a fixed altitude, a fixed nest corresponding to 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 to obtain the optimal flight trajectory set and optimal transmission power set of the 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 multi-UAV flight trajectory and transmission power joint optimization model:

[0143]

[0144] In the above formula, E k ({q m [n]}, {P m [n]}) is the energy collected by the kth ground node from all drones. It is a multi-source nonlinear energy collection model. 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, P dc，k (Q k [n]) is the DC signal power received by the kth ground node from all drones in the nth time slot, Q k [n] = {Q k，1 [n], ..., Q k，m [n], ..., Q k，M [n]} is the RF signal power received by the kth ground node from all drones in the nth time slot, 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, RL is the resistance of the energy storage device, a is the parameter related to the physical characteristics of the energy harvesting circuit, W0(·) is the Lambert W function, I S is the reverse saturation current, is the impact of the kth ground node receiving power in the nth time slot, β n is a normal number, To satisfy A sequence of non-negative integers, is the combination coefficient, M is the total number of fixed nests, For the The power received by the kth ground node from the mth UAV in the time slot is: is a non-negative integer, is a constant waveform factor.

[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 transmission power constraint construction unit, and an anti-collision constraint construction unit;

[0146] The start-end point constraint construction unit is used to construct the start-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 following maximum flight speed constraint of the UAV:

[0149]

[0150] The transmission power constraint construction unit is used to construct the following transmission power constraint of the UAV:

[0151]

[0152] 0≤P m [≤P max ;

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

[0154]

[0155] In the above formula, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 average transmission power, P max is the peak value of the transmitted power, q v [n] is the flight trajectory of the vth UAV in the nth time slot, q w [n] The flight trajectory of the w-th UAV in the n-th time slot, d min is the minimum safe distance between two drones.

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

[0157] The initial iteration definition unit is used to define the flight trajectory point set and the transmission power set of the initial iteration of the UAV as;

[0158]

[0159] In the above formula, is the flight trajectory set of the initial iteration of the mth UAV, is the transmission power set of the initial iteration of the mth UAV, (0) is the initial iteration;

[0160] The optimization solution convex problem construction unit is used to construct a convex objective function and convex constraints of a multi-UAV flight trajectory and transmission power joint optimization model based on the flight trajectory set and transmission power set of the initial iteration of the UAV, and obtain the optimization solution convex problem for each iteration;

[0161] The optimization solution of each iteration of the convex problem is:

[0162]

[0163]

[0164] 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 approximate function of the energy collected by the kth ground node from all drones in the rth iteration, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 approximate function of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration, d min is the minimum safe distance between two drones, is the average transmission power, P max is the peak value of the transmitted power;

[0165] The loop iteration unit is used to solve the optimization solution convex problem of each iteration, and the optimal solution of the UAV flight trajectory and transmission power of each iteration is obtained as follows: in, 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. It is determined whether the change of the auxiliary variable in the optimization solution of the convex problem in each iteration is less than the iteration threshold ε, that is, it satisfies E (r) -E (r-1) <ε, if it is satisfied, the iterative algorithm ends, and the optimal flight trajectory set and optimal transmission power set of multiple UAVs are output as If not, set r=r+1, return to the optimization solution convex problem construction unit to reconstruct the iterative optimization solution convex problem, and obtain the optimal flight trajectory and optimal transmission power of the r+1th iteration.

[0166] In the optimization solution convex problem construction unit, a convex objective function of a joint optimization model of multi-UAV flight trajectory and transmission power is constructed, including:

[0167] A. Due to E k ({q m [n]}, {P m [n]}) is The convex function of , and then the following convex approximation:

[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 drones, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the RF signal power received by 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, β0 is the channel gain per unit distance, P m [n] is the transmission power of the mth UAV in the nth time slot;

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

[0171]

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

[0173] Convex constraints are used to construct a joint optimization model of multi-UAV flight trajectory and transmission power, including:

[0174] The anti-collision constraints of multiple UAVs in each iteration are 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 w-th UAV in the n-th time slot in the r-th iteration, is the concave approximate function of the lower bound of the distance between the b-th UAV and the w-th UAV in the n-th time slot at the r-th iteration.

Claims

1. A method for jointly determining the flight trajectories and transmission powers of multiple UAVs, characterized in that: The method comprises: S1. Considering the scenario of wireless energy transmission from drones to ground nodes, a joint optimization model of multi-drone flight trajectory and transmission power is constructed with the goal of maximizing the minimum collected energy within a single ground node. The scenario includes multiple drones flying at a fixed altitude, a fixed nest corresponding to each drone, and multiple ground nodes receiving wireless energy. S2. Solve the joint optimization model of multi-UAV flight trajectory and transmission power to obtain the optimal flight trajectory set and optimal transmission power set of multiple UAVs.

2. A method for jointly determining flight trajectories and transmission powers of multiple UAVs according to claim 1, characterized in that: In S1, the objective function of the joint optimization model of multi-UAV flight trajectory and transmission power includes: In the above formula, E k ({q m [n]}, {P m [n]}) is the energy collected by the kth ground node from all drones. It is a multi-source nonlinear energy collection model. 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, P dc，k (Q k [n]) is the DC signal power received by the kth ground node from all drones in the nth time slot, Q k [n] = {Q k，1 [n], ..., Q k，m [n], ..., Q k，M [n]} is the RF signal power received by the kth ground node from all drones in the nth time slot, 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, a is the parameter related to the physical characteristics of the energy harvesting circuit, W0(·) is the Lambert W function, I S is the reverse saturation current, is the impact of the kth ground node receiving power in the nth time slot, β n is a normal number, To satisfy A sequence of non-negative integers, is the combination coefficient, M is the total number of fixed nests, For the The power received by the kth ground node from the mth UAV in the time slot is: is a non-negative integer, is a constant waveform factor.

3. The method for jointly determining the flight trajectories and transmission powers of multiple UAVs according to claim 1, characterized in that: In S1, the constraints of the joint optimization model of multi-UAV flight trajectory and transmission power 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 multiple UAVs; The starting and ending point constraints of the UAV flight trajectory are: q m [0]= m [N]=w c,m ; The maximum flight speed constraint of the UAV is: The transmission power constraint of the UAV is: 0≤P m [n]≤P max ; The anti-collision constraints of the multiple UAVs are: In the above formula, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 average transmission power, P max is the peak value of the transmitted power, q v [n] is the flight trajectory of the vth UAV in the nth time slot, q w [n] The flight trajectory of the w-th UAV in the n-th time slot, d min is the minimum safe distance between two drones.

4. The method for jointly determining the flight trajectories and transmission powers of multiple UAVs according to claim 1, characterized in that: The S2 includes: S21. Define the flight trajectory point set and transmission power set of the initial iteration of the UAV as; In the above formula, is the flight trajectory set of the initial iteration of the mth UAV, is the transmission power set of the initial iteration of the mth UAV, (0) is the initial iteration; S22. Based on the flight trajectory set and transmission power set of the initial iteration of the UAV, a convex objective function and convex constraints of the joint optimization model of the flight trajectory and transmission power of multiple UAVs are constructed to obtain the optimization solution convex problem for each iteration; The optimization solution of each iteration of the convex problem is: 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 approximate function of the energy collected by the kth ground node from all drones in the rth iteration, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 approximate function of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration, d min is the minimum safe distance between two drones, is the average transmission power, P max is the peak value of the transmitted power; S23. Solve the optimization problem of each iteration and obtain the optimal solution of the UAV flight trajectory and transmission power for each iteration: in, 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. It is determined whether the change of the auxiliary variable in the optimization solution of the convex problem in each iteration is less than the iteration threshold ε, that is, it satisfies E (r) -E (r-1) <ε, if it is satisfied, the iterative algorithm ends, and the optimal flight trajectory set and optimal transmission power set of multiple UAVs are output as If not, set r=r+1 and return to step S22 to reconstruct the iterative optimization solution of the convex problem to obtain the optimal flight trajectory and optimal transmission power of the r+1th iteration.

5. A method for jointly determining flight trajectories and transmission powers of multiple UAVs according to claim 4, characterized in that: In S22, a convex objective function of a joint optimization model of multi-UAV flight trajectory and transmission power is constructed, including: A. Due to E k ({q m [n]}, {P m [n]}) is The convex function of , and then 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 drones, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the RF signal power received by 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 joint optimization model of multi-UAV flight trajectory and transmission power is further convexly approximated: In the above formula, is the approximate coefficient of the rth iteration, is the lower bound concave approximate function of the energy collected by the kth ground node from all UAVs in the rth iteration; Convex constraints are used to construct a joint optimization model of multi-UAV flight trajectory and transmission power, including: The anti-collision constraints of multiple UAVs in each iteration are convexly approximated as: 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 w-th UAV in the n-th time slot in the r-th iteration, is the concave approximate function of the lower bound of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration.

6. A system for jointly determining the flight trajectory and transmission power of multiple UAVs, characterized in that: The system includes a joint optimization model building module and a joint optimization model solving module; The joint optimization model building module is used to consider the scenario of wireless energy transmission from a UAV to a ground node, and to build a joint optimization model of multi-UAV flight trajectory and transmission power with the goal of maximizing the minimum collected energy within a single ground node. The scenario includes multiple UAVs flying at a fixed altitude, a fixed nest corresponding to each UAV, and multiple ground nodes receiving wireless energy; The joint optimization model solving module is used to solve the joint optimization model of multi-UAV flight trajectory and transmission power to obtain the optimal flight trajectory set and optimal transmission power set of the multi-UAV.

7. A system for jointly determining flight trajectories and transmission powers of multiple UAVs according to claim 6, characterized in that: The joint optimization model construction module includes an objective function construction unit; The objective function construction unit is used to construct the objective function of the following multi-UAV flight trajectory and transmission power joint optimization model: In the above formula, E k ({q m [n]}, {P m [n]}) is the energy collected by the kth ground node from all drones. It is a multi-source nonlinear energy collection model. 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, P dc，k (Q k [n]) is the DC signal power received by the kth ground node from all drones in the nth time slot, Q k [n] = {Q k，1 [n], ..., Q k，m [n], ..., Q k，M [n]} is the RF signal power received by the kth ground node from all drones in the nth time slot, 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, a is the parameter related to the physical characteristics of the energy harvesting circuit, W0(·) is the Lambert W function, I S is the reverse saturation current, is the impact of the kth ground node receiving power in the nth time slot, β n is a normal number, To satisfy A sequence of non-negative integers, is the combination coefficient, M is the total number of fixed nests, For the The power received by the kth ground node from the mth UAV in the time slot is: is a non-negative integer, is a constant waveform factor.

8. The system for jointly determining the flight trajectories and transmission powers of multiple UAVs according to claim 6, characterized in that: The joint optimization model construction module also includes a start and end point constraint construction unit, a maximum flight speed constraint construction unit, a transmission power constraint construction unit, and an anti-collision constraint construction unit; The start-end point constraint construction unit is used to construct the start-end point constraints of the following UAV flight trajectory: q m [0]=q m [N]=w c，m ; The maximum flight speed constraint construction unit is used to construct the following maximum flight speed constraint of the UAV: The transmission power constraint construction unit is used to construct the following transmission power constraint of the UAV: 0≤P m [n]≤P max ; The anti-collision constraint construction unit is used to construct the following anti-collision constraints for multiple UAVs: In the above formula, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 average transmission power, P max is the peak value of the transmitted power, q v [n] is the flight trajectory of the vth UAV in the nth time slot, q w [n] The flight trajectory of the w-th UAV in the n-th time slot, d min is the minimum safe distance between two drones.

9. A system for jointly determining flight trajectories and transmission powers of multiple UAVs according to claim 6, characterized in that: The joint optimization model solving module includes an initial iteration definition unit, an optimization solving convex problem construction unit, and a loop iteration unit; The initial iteration definition unit is used to define the flight trajectory point set and the transmission power set of the initial iteration of the UAV as; In the above formula, is the flight trajectory set of the initial iteration of the mth UAV, is the transmission power set of the initial iteration of the mth UAV, (0) is the initial iteration; The optimization solution convex problem construction unit is used to construct a convex objective function and convex constraints of a multi-UAV flight trajectory and transmission power joint optimization model based on the flight trajectory set and transmission power set of the initial iteration of the UAV, and obtain the optimization solution convex problem for each iteration; The optimization solution of each iteration of the convex problem is: 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 approximate function of the energy collected by the kth ground node from all drones in the rth iteration, q m [0] is the flight starting point of the mth UAV, q m [N] is the flight end 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 approximate function of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration, d min is the minimum safe distance between two drones, is the average transmission power, P max is the peak value of the transmitted power; The loop iteration unit is used to solve the optimization solution convex problem of each iteration, and the optimal solution of the UAV flight trajectory and transmission power of each iteration is obtained as follows: in, 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. It is determined whether the change of the auxiliary variable in the optimization solution of the convex problem in each iteration is less than the iteration threshold ε, that is, it satisfies E (r) -E (r-1) <ε, if it is satisfied, the iterative algorithm ends, and the optimal flight trajectory set and optimal transmission power set of multiple UAVs are output as If not, set r=r+1, return to the optimization solution convex problem construction unit to reconstruct the iterative optimization solution convex problem, and obtain the optimal flight trajectory and optimal transmission power of the r+1th iteration.

10. A system for jointly determining flight trajectories and transmission powers of multiple UAVs according to claim 9, characterized in that: In the optimization solution convex problem construction unit, a convex objective function of a joint optimization model of multi-UAV flight trajectory and transmission power is constructed, including: A. Due to E k ({q m [n]}, {P m [n]}) is The convex function of , and then 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 drones, are the convex approximation coefficients of the rth iteration, Q k，m [n] is the RF signal power received by 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 joint optimization model of multi-UAV flight trajectory and transmission power is further convexly approximated: In the above formula, is the approximate coefficient of the rth iteration, is the lower bound concave approximate function of the energy collected by the kth ground node from all UAVs in the rth iteration; Convex constraints are used to construct a joint optimization model of multi-UAV flight trajectory and transmission power, including: The anti-collision constraints of multiple UAVs in each iteration are convexly approximated as: 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 w-th UAV in the n-th time slot in the r-th iteration, is the concave approximate function of the lower bound of the distance between the vth UAV and the wth UAV in the nth time slot at the rth iteration.

Images