CN113552898A - A Robust Trajectory Planning Method for Unmanned Aerial Vehicles in Uncertain Interference Environment - Google Patents

A Robust Trajectory Planning Method for Unmanned Aerial Vehicles in Uncertain Interference Environment Download PDF

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CN113552898A
CN113552898A CN202110775624.0A CN202110775624A CN113552898A CN 113552898 A CN113552898 A CN 113552898A CN 202110775624 A CN202110775624 A CN 202110775624A CN 113552898 A CN113552898 A CN 113552898A
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CN113552898B (en
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周凌云
朱华泽
史清江
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Tongji University
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Abstract

本发明公开了一种非确定干扰环境下的无人机鲁棒轨迹规划方法，包括以下步骤：首先确定无人机的起点终点、授权飞行参数、预估辐射源参数、飞行能耗上限及环境参数；构建该无人机系统的轨迹规划问题；然后采取S‑Procedure和连续凸优化算法迭代优化上述问题，直至算法收敛；基于干扰环境信息，地面控制单元利用上述算法实现在飞行前对无人机进行航迹规划，完成无人机通信的鲁棒轨迹设计。本发明的有益效果是：所发明的无人机鲁棒轨迹规划方法能够在满足约束的前提下，提升了接收信号的质量。

Figure 202110775624

The invention discloses a robust trajectory planning method for an unmanned aerial vehicle under a non-determined interference environment. parameters; construct the trajectory planning problem of the UAV system; then adopt S‑Procedure and continuous convex optimization algorithm to iteratively optimize the above problem until the algorithm converges; The UAV carries out trajectory planning and completes the robust trajectory design of UAV communication. The beneficial effects of the present invention are that the invented robust trajectory planning method for unmanned aerial vehicles can improve the quality of received signals on the premise of satisfying constraints.

Figure 202110775624

Description

Unmanned aerial vehicle robust trajectory planning method under uncertain interference environment
Technical Field
The invention relates to the technical field of unmanned aerial vehicle communication, in particular to a design of a robust trajectory planning method of an unmanned aerial vehicle in a non-deterministic interference environment.
Background
With the rapid development of the unmanned aerial vehicle system, the unmanned aerial vehicle communication technology gradually becomes a research hotspot in academic and industrial fields. Unmanned aerial vehicle has promoted the success rate of task, and the wide application is in fields such as military reconnaissance, battlefield aassessment, communication relay. However, drone communication faces a serious challenge due to the limited network resources available to drones. On one hand, due to the blowout type rising service and the battlefield environment with uncertain height, the unmanned aerial vehicle needs to rapidly make a trajectory plan in a very short time, which tests the timeliness of communication; on the other hand, unmanned aerial vehicle operation data transmission link is very easily influenced by external disturbance in with ground control station communication process, this examination unmanned aerial vehicle's anti-interference characteristic. Therefore, before taking off, it is the core problem of unmanned aerial vehicle operation to plan the flight trajectory of unmanned aerial vehicle in advance.
Through the search of the prior art, the article "Energy-efficiency UAV Communication With route Optimization" published by Zeng Y in IEEE Transactions on Wireless Communications in 2017 proposes the problem of unmanned aerial vehicle Trajectory planning. In actual unmanned aerial vehicle communication, a control signaling received by the unmanned aerial vehicle is not only influenced by a data transmission link from a ground control station, but also influenced by an interference signal from a ground radiation source. In addition, due to the insufficient precision of the existing detection equipment, it is often difficult to obtain accurate radiation source position and power information.
Disclosure of Invention
The invention aims to provide a robust trajectory planning scheme of an unmanned aerial vehicle in a non-deterministic interference environment aiming at the defects of the prior art, so that the unmanned aerial vehicle reduces the interference of an external radiation source on the premise of meeting the flight speed/acceleration constraint and the maximum flight energy consumption constraint, and reasonably plans the flight trajectory of the unmanned aerial vehicle, thereby improving the reliability of received signals.
In order to realize the purpose of the invention, the technical scheme is as follows:
an unmanned aerial vehicle robust trajectory planning method under a non-determined interference environment is characterized by comprising the following steps:
s1: establishing an unmanned aerial vehicle trajectory planning system model;
s2: defining an unmanned aerial vehicle robust trajectory planning problem P1 according to a system model;
s3: introducing base station distance vectors
Figure BDA0003154691540000021
Wherein the nth element represents the distance of the drone from the control station at time n; interference power vector
Figure BDA0003154691540000022
Wherein the nth element represents the total power of the drone interfered by the ground radiation source at time n; interference distance matrix
Figure BDA0003154691540000023
Wherein the (m, n) th element represents the distance of the drone from the mth ground radiation source at time instant n. Problem P1 is transformed into equivalent problem P2;
s4: converting the problem P2 into an equivalent problem P3 by using an S-Procedure algorithm;
s5: converting the problem P3 approximation process into a convex problem P4;
s6: and solving an optimization target based on the unmanned aerial vehicle trajectory planning model P4 to obtain the optimal flight trajectory of the unmanned aerial vehicle.
S1 specifically includes:
s1.1, setting the flying height of the unmanned aerial vehicle as H and the flying time as T, and using a preset starting point { xI,yI,H}(xI,yIAbscissa and ordinate representing start point) to a specified end point { xF,yFH flight (x)F,yFAbscissa and ordinate representing the endpoint); the ground has 1 control station with height of 0 and horizontal position of ws＝[xs,ys](xs,ysHorizontal and vertical coordinates representing a control station); the ground has M radiation sources, the height is 0, and the horizontal position is wj,m＝[xj,m,yj,m](xj,m,yj,mHorizontal and vertical coordinates representing a ground radiation source); the relationship between the estimated position/power and the actual position/power of the radiation source is expressed as:
Figure BDA0003154691540000024
Figure BDA0003154691540000025
Figure BDA0003154691540000026
Figure BDA0003154691540000027
wherein
Figure BDA0003154691540000028
And
Figure BDA0003154691540000029
indicating the estimated position and power of the m-th radiation source, Δ wj,mAnd Δ pj,mRepresenting the estimated error of the mth radiation source position and power,
Figure BDA00031546915400000210
and ximRepresents the upper error bound, A, of the mth radiation sourcej,mAnd psij,mIndicating the error range of the position and power of the mth radiation source.
S1.2, the flight time T is averagely divided into N moments, and the length delta of the adjacent moments is equal to T/N; let the minimum flying speed of the unmanned aerial vehicle be uminMaximum flying speed of umaxMaximum acceleration of amax(ii) a At time n, the horizontal coordinate of the unmanned aerial vehicle is q [ n ]]＝[x[n],y[n]](x[n],y[n]Abscissa and ordinate representing position), and a velocity u [ n ]]＝[ux[n],uy[n]](ux[n],uy[n]Transverse and longitudinal components of velocity), and acceleration is a [ n ]]＝[ax[n],ay[n]](ax[n],ay[n]Is the lateral and longitudinal components of acceleration); the flight constraints of a drone are expressed as:
Figure BDA0003154691540000031
u[n]＝u[n-1]+a[n-1]δ,n＝2,3,...,N, (3b)
Figure BDA0003154691540000032
q[N]＝qF,u[N]＝uF, (3d)
Figure BDA0003154691540000033
Figure BDA0003154691540000034
Figure BDA0003154691540000035
wherein q isI、uIAnd aIRespectively representing the position, the speed and the acceleration of the unmanned aerial vehicle at the initial moment; q. q.sFAnd uFRespectively representing the final position and the final speed of the unmanned aerial vehicle;
s1.3 at the nth moment, the distances from the unmanned aerial vehicle to the control station and the ground radiation source are respectively expressed as
Figure BDA0003154691540000036
Figure BDA0003154691540000037
Then the channel gain from the drone to the ground control station and the ground radiation source is:
Figure BDA0003154691540000038
Figure BDA0003154691540000039
wherein beta is0Expressed as the channel gain when the distance is 1;
s1.4 the total energy consumption required by the unmanned aerial vehicle in the flight process is as follows:
Figure BDA00031546915400000310
wherein c is1And c2Represents the relevant constant of the hardware of the unmanned aerial vehicle, g represents the gravity acceleration,
Figure BDA00031546915400000311
representing the consumption of flight kinetic energy of the drone, J represents the mass of the drone.
S2 specifically includes:
at the nth moment, the received signal-to-noise ratio under the worst condition of the unmanned aerial vehicle is as follows:
Figure BDA00031546915400000312
where M is the number of ground radiation sources, p0Uplink transmission power, sigma, for ground control station to drone2Representing additive white gaussian noise. The method is popularized to the whole flight process, the maximum average signal-to-noise ratio of the unmanned aerial vehicle receiving the worst condition is taken as a target, and the trajectory planning problem is expressed as follows:
P1：
Figure BDA0003154691540000041
s.t.
Figure BDA0003154691540000042
Figure BDA0003154691540000043
u[n]＝u[n-1]+a[n-1]δ,n＝2,3,...,N, (8d)
Figure BDA0003154691540000044
q[N]＝qF,u[N]＝uF, (8f)
Figure BDA0003154691540000045
Figure BDA0003154691540000046
Figure BDA0003154691540000047
wherein Γ is the maximum flight energy consumption constraint of the drone.
S3 specifically includes:
power p of radiation sourcej,mGet
Figure BDA0003154691540000048
To eliminate Δ p in the objective functionj,mAnd (4) variable quantity. Introducing base station distance vector by adopting redundancy variable method
Figure BDA0003154691540000049
Wherein the nth element represents the distance of the drone from the control station at time n; interference power vector
Figure BDA00031546915400000410
Wherein the nth element represents the total power of the drone interfered by the ground radiation source at time n; interference distance matrix
Figure BDA00031546915400000411
Wherein the (m, n) th element represents the distance of the drone from the mth ground radiation source at time instant n. Problem P1 is transformed into equivalent problem P2 as follows:
P2：
Figure BDA00031546915400000412
s.t.
Figure BDA00031546915400000413
Figure BDA0003154691540000051
Figure BDA0003154691540000052
(8b)-(8i) (9e)
s4 specifically includes:
using S-Procedure algorithm (algorithm existing in the field), reference constraint matrix
Figure BDA0003154691540000053
Wherein the (m, n) th element represents the constraint of the drone at time instant n with respect to the mth ground radiation source. The semi-infinite constraint (9d) is equivalently converted into the following constraint:
Figure BDA0003154691540000054
Figure BDA0003154691540000055
wherein
Figure BDA0003154691540000056
And is
Figure BDA0003154691540000057
Wherein
Figure BDA0003154691540000058
And
Figure BDA0003154691540000059
a horizontal and vertical coordinate representing the estimated position of the mth radiation source;
reintroducing n-dimensional velocity vector
Figure BDA00031546915400000510
Wherein the nth element represents the speed of the drone at time n; the trajectory plan P2 translates into an equivalence problem P3 as follows:
P3：
Figure BDA00031546915400000511
s.t.
Figure BDA00031546915400000512
Figure BDA00031546915400000513
Figure BDA00031546915400000514
Figure BDA00031546915400000515
(8c)-(8h),(9b),(9c),(10),(11)(12f)
s5 specifically includes:
at a given kth iteration point (I [ n ])](k),L[n](k)) And (3) performing first-order Taylor expansion on the non-convex function to obtain a global lower boundary value:
Figure BDA0003154691540000061
at a given kth iteration point u n](k)In the non-convex constraint (12c), (12d) | | u [ n |)]||2The first order Taylor expansion is used as follows:
Figure BDA0003154691540000069
at a given kth iteration point (x n)](k),y[n](k))，Non-linear term c in non-convex constraint (10)m[n]The first order Taylor expansion is used as follows:
Figure BDA0003154691540000062
the trajectory plan P3 translates into an approximately convex problem P4 as follows:
P4：
Figure BDA0003154691540000063
s.t.
Figure BDA0003154691540000064
Figure BDA0003154691540000065
Figure BDA0003154691540000066
(8c)-(8h),(9b),(9c)，(11),(12b),(12e) (13e)
wherein
Figure BDA0003154691540000067
At this point, the optimal solution for the trajectory is solved by the CVX toolset.
S6 specifically includes the following steps:
s6.1, initializing the position, the speed and the acceleration of the unmanned aerial vehicle to be q respectively(0)、u(0)And a(0)The objective function is
Figure BDA0003154691540000068
The iteration number K is 0, and the maximum iteration number K is setmaxIterative precision threshold θ1；
S6.2, giving the position, the speed and the acceleration of the k-th iteration unmanned aerial vehicleDegree q of(k)、u(k)And a(k)Substituting the optimal solution into a trajectory planning optimization model P1 to solve to obtain the optimal solution q of the position, the speed and the acceleration of the unmanned aerial vehicle after the k +1 iteration(k+1)、u(k +1)And a(k+1)；
S6.3, judging whether K is more than or equal to KmaxOr is or
Figure BDA0003154691540000071
If yes, obtaining optimized position, speed and acceleration q(*)、u(*)And a(*)(ii) a If not, the number of iterations k is updated to k +1 and steps S6.2 and S6.3 are repeated.
The invention provides a robust trajectory planning method for an unmanned aerial vehicle under a non-deterministic interference environment, which is used for maximizing the average signal-to-noise ratio under the worst condition in the flight process, thereby realizing reasonable planning of the flight trajectory of the unmanned aerial vehicle.
The invention has the beneficial effects that: the robust trajectory planning method for the unmanned aerial vehicle comprises the steps of firstly constructing an optimization model about the flight trajectory of the unmanned aerial vehicle in a non-determined interference environment, then introducing a redundancy variable based on model characteristics, and iteratively solving the problems by adopting an S-Procedure algorithm and a continuous convex optimization algorithm until the algorithms are converged. The method realizes reasonable planning of the flight trajectory on the premise of improving the reliability of the control signal received by the unmanned aerial vehicle and meeting the system flight speed/acceleration constraint and the maximum flight energy consumption constraint.
Drawings
FIG. 1 is a system model diagram of the embodiment of the present invention.
Fig. 2 is a flow chart of an algorithm employing the method according to the embodiment of the present invention.
Fig. 3 is a diagram of the flight trajectory of the unmanned aerial vehicle in the embodiment of the invention.
Fig. 4 is a diagram of communication performance of the drone in the embodiment of the present invention.
Detailed Description
The objects and effects of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.
The embodiment provides an unmanned aerial vehicle robust trajectory planning method under a non-deterministic interference environment, which comprises the following steps:
s1: establishing an unmanned aerial vehicle trajectory planning system model;
as shown in fig. 1, consider a three-dimensional coordinate system. Let the flying height of the unmanned aerial vehicle be H and the flying time be T, and use a preset starting point { xI,yI,H}(xI,yIAbscissa and ordinate representing start point) to a specified end point { xF,yFH flight (x)F,yFAbscissa and ordinate representing the endpoint); the ground has 1 control station with height of 0 and horizontal position of ws＝[xs,ys](xs,ysHorizontal and vertical coordinates representing a control station); the ground has M radiation sources, the height is 0, and the horizontal position is wj,m＝[xj,m,yj,m](xj,m,yj,mHorizontal and vertical coordinates representing a ground radiation source); the relationship between the estimated position/power and the actual position/power of the radiation source is expressed as:
Figure BDA0003154691540000072
Figure BDA0003154691540000081
Figure BDA0003154691540000082
Figure BDA0003154691540000083
wherein
Figure BDA0003154691540000084
And
Figure BDA0003154691540000085
denotes the m-thPosition and power, Δ w, of individual radiation source estimatesj,mAnd Δ pj,mRepresenting the estimated error of the mth radiation source position and power,
Figure BDA0003154691540000086
and ximRepresents the upper error bound, A, of the mth radiation sourcej,mAnd psij,mIndicating the error range of the position and power of the mth radiation source.
Dividing T into N moments on average, wherein the length delta of adjacent moments is T/N; let the minimum flying speed of the unmanned aerial vehicle be uminMaximum flying speed of umaxMaximum acceleration of amax(ii) a At time n, the horizontal coordinate of the unmanned aerial vehicle is q [ n ]]＝[x[n],y[n]](x[n],y[n]Abscissa and ordinate representing position), and a velocity u [ n ]]＝[ux[n],uy[n]](ux[n],uy[n]Transverse and longitudinal components of velocity), and acceleration is a [ n ]]＝[ax[n],ay[n]](ax[n],ay[n]Is the lateral and longitudinal components of acceleration); the flight constraints of a drone are expressed as:
Figure BDA0003154691540000087
u[n]＝u[n-1]+a[n-1]δ,n＝2,3,...,N, (3b)
Figure BDA0003154691540000088
q[N]＝qF,u[N]＝uF, (3d)
Figure BDA0003154691540000089
Figure BDA00031546915400000810
Figure BDA00031546915400000811
wherein q isI、uIAnd aIRespectively representing the position, the speed and the acceleration of the unmanned aerial vehicle at the initial moment; q. q.sFAnd uFRespectively representing the final position and the final speed of the unmanned aerial vehicle;
at the nth moment, the distances from the unmanned aerial vehicle to the control station and the ground radiation source are respectively expressed as
Figure BDA00031546915400000812
Figure BDA00031546915400000813
Then the channel gain from the drone to the ground control station and the ground radiation source is:
Figure BDA00031546915400000814
Figure BDA00031546915400000815
wherein beta is0Expressed as the channel gain when the distance is 1;
the total energy consumption required by the unmanned aerial vehicle in the flight process is as follows:
Figure BDA0003154691540000091
wherein c is1And c2Represents the relevant constant of the hardware of the unmanned aerial vehicle, g represents the gravity acceleration,
Figure BDA0003154691540000092
representing the consumption of flight kinetic energy of the drone, J represents the mass of the drone.
S2: defining an unmanned aerial vehicle robust trajectory planning problem P1 according to a system model;
at the nth moment, the received signal-to-noise ratio under the worst condition of the unmanned aerial vehicle is as follows:
Figure BDA0003154691540000093
where M is the number of ground radiation sources, p0Uplink transmission power, sigma, for ground control station to drone2Representing additive white gaussian noise. The method is popularized to the whole flight process, the maximum average signal-to-noise ratio of the unmanned aerial vehicle receiving the worst condition is taken as a target, and the trajectory planning problem is expressed as follows:
P1：
Figure BDA0003154691540000094
s.t.
Figure BDA0003154691540000095
Figure BDA0003154691540000096
u[n]＝u[n-1]+a[n-1]δ,n＝2,3,...,N, (8d)
Figure BDA0003154691540000097
q[N]＝qF,u[N]＝uF, (8f)
Figure BDA0003154691540000098
Figure BDA0003154691540000099
Figure BDA00031546915400000910
wherein Γ is the maximum flight energy consumption constraint of the drone.
S3: power p of radiation sourcej,mGet
Figure BDA0003154691540000101
To eliminate Δ p in the objective functionj,mAnd (4) variable quantity. Introducing base station distance vectors
Figure BDA0003154691540000102
Wherein the nth element represents the distance of the drone from the control station at time n; interference power vector
Figure BDA0003154691540000103
Wherein the nth element represents the total power of the drone interfered by the ground radiation source at time n; interference distance matrix
Figure BDA0003154691540000104
Wherein the (m, n) th element represents the distance of the drone from the mth ground radiation source at time instant n. Problem P1 is transformed into equivalent problem P2 as follows:
P2：
Figure BDA0003154691540000105
s.t.
Figure BDA0003154691540000106
Figure BDA0003154691540000107
Figure BDA0003154691540000108
(8b)-(8i) (9e)
s4: converting the problem P2 into an equivalent problem P3 by using an S-Procedure algorithm;
adopting S-Procedure algorithm, and using constraint matrix
Figure BDA0003154691540000109
Wherein the (m, n) th element represents the constraint of the drone at time instant n with respect to the mth ground radiation source. The semi-infinite constraint (9d) is equivalently converted into the following constraint:
Figure BDA00031546915400001010
Figure BDA00031546915400001011
wherein
Figure BDA00031546915400001012
And is
Figure BDA00031546915400001013
Wherein
Figure BDA00031546915400001014
And
Figure BDA00031546915400001015
a horizontal and vertical coordinate representing the estimated position of the mth radiation source;
reintroducing n-dimensional velocity vector
Figure BDA00031546915400001016
Wherein the nth element represents the speed of the drone at time n; the trajectory plan P2 translates into an equivalence problem P3 as follows:
P3：
Figure BDA00031546915400001017
s.t.
Figure BDA0003154691540000111
Figure BDA0003154691540000112
Figure BDA0003154691540000113
Figure BDA0003154691540000114
(8c)-(8h),(9b),(9c),(10),(11) (12f)
s5: converting the problem P3 approximation process into a convex problem P4;
at a given kth iteration point (I [ n ])](k),L[n](k)) And (3) performing first-order Taylor expansion on the non-convex function to obtain a global lower boundary value:
Figure BDA0003154691540000115
at a given kth iteration point u n](k)In the non-convex constraint (12c), (12d) | | u [ n |)]||2The first order Taylor expansion is used as follows:
Figure BDA0003154691540000116
at a given kth iteration point (x n)](k),y[n](k)) The non-linear term c in the non-convex constraint (10)m[n]The first order Taylor expansion is used as follows:
Figure BDA0003154691540000117
the trajectory plan P3 translates into an approximately convex problem P4 as follows:
P4：
Figure BDA0003154691540000118
s.t.
Figure BDA0003154691540000119
Figure BDA00031546915400001110
Figure BDA00031546915400001111
(8c)-(8h),(9b),(9c)，(11),(12b),(12e) (13e)
wherein
Figure BDA0003154691540000121
At this point, the optimal solution for the trajectory is solved by the CVX toolset.
S6: and solving an optimization target based on the unmanned aerial vehicle trajectory planning model P4 to obtain the optimal flight trajectory of the unmanned aerial vehicle. As shown in fig. 2, the specific steps are as follows:
s6.1, initializing the position, the speed and the acceleration of the unmanned aerial vehicle to be q respectively(0)、u(0)And a(0)The objective function is
Figure BDA0003154691540000122
The iteration number K is 0, and the maximum iteration number K is setmaxIterative precision threshold θ1；
S6.2, giving the position, the speed and the acceleration q of the k iteration unmanned aerial vehicle(k)、u(k)And a(k)Substituting the optimal solution into a trajectory planning optimization model P1 to solve to obtain the optimal solution q of the position, the speed and the acceleration of the unmanned aerial vehicle after the k +1 iteration(k+1)、u(k +1)And a(k+1)；
S6.3, judging whether K is more than or equal to KmaxOr is or
Figure BDA0003154691540000123
If yes, obtaining optimized position, speed and acceleration q(*)、u(*)And a(*)(ii) a If not, the number of iterations k is updated to k +1 and steps S6.2 and S6.3 are repeated.
Fig. 3 compares the performance of the inventive solution with the performance of the reference trajectory planning solution, and simulates the designed solution by Matlab. The parameters are specifically set as: flight height H is 100m, and starting point coordinate is qI(100) m, end point qF(800) m; the coordinate and power of the ground control unit are (0,0,0) m and p respectively010W; 3 radiation sources to
Figure BDA0003154691540000124
Has a power distribution coordinate of
Figure BDA0003154691540000125
On the ground; error of radiation source power is xim0.02W; the total time of flight T is 30 s. Other parameters are shown in table 1:
TABLE 1 simulation parameters
Figure BDA0003154691540000126
Fig. 3 shows a flight trajectory diagram of the drone, wherein the abscissa and ordinate are expressed as flight coordinates of the drone. As can be seen from the figure: for the same network scene, the unmanned aerial vehicle trajectory planning path provided by the method can be skillfully far away from the radiation source, and the distance between the unmanned aerial vehicle trajectory planning path and the radiation source is greater than that of a reference trajectory planning scheme.
Fig. 4 shows the average worst-case signal-to-noise ratio during the flight of the drone, where the abscissa is the flight energy consumption upper limit of the drone and the ordinate is the average worst-case signal-to-noise ratio. It can be seen that for the same network scenario, the system performance of the method of the present invention is superior to that of the reference trajectory planning scheme.
Through the performance simulation comparison, the method of the invention not only can meet the flight speed/acceleration constraint of the system and the maximum flight energy consumption limitation, but also can improve the communication performance of the network so as to realize the reasonable planning of the flight path. The method can be well adapted to the future mobile communication technology based on the unmanned aerial vehicle, so that the performance of the unmanned aerial vehicle is improved.
The present invention is not limited to the above-described embodiments, and those skilled in the art can implement the present invention in other various embodiments based on the disclosure of the present invention. Therefore, the design of the invention is within the scope of protection, with simple changes or modifications, based on the design structure and thought of the invention.

Claims (7)

1.一种非确定干扰环境下的无人机鲁棒轨迹规划方法，其特征在于，包括以下步骤：1. an unmanned aerial vehicle robust trajectory planning method under a non-determined interference environment, is characterized in that, comprises the following steps: S1：建立无人机轨迹规划系统模型；S1: Establish the UAV trajectory planning system model; S2：根据系统模型定义无人机鲁棒轨迹规划问题P1；S2: Define the UAV robust trajectory planning problem P1 according to the system model; S3：引入基站距离向量
Figure FDA0003154691530000011
其中第n元素表示无人机在时刻n到控制站的距离；干扰功率向量
Figure FDA0003154691530000012
其中第n元素表示在时刻n无人机受到地面辐射源干扰的总功率；干扰距离矩阵
Figure FDA0003154691530000013
其中第(m,n)个元素表示无人机在时刻n到第m个地面辐射源的距离。将问题P1转化为等价问题P2；S3: Introduce the base station distance vector
Figure FDA0003154691530000011
The nth element represents the distance from the UAV to the control station at time n; the interference power vector
Figure FDA0003154691530000012
The nth element represents the total power of the UAV interfered by the ground radiation source at time n; the interference distance matrix
Figure FDA0003154691530000013
The (m,n)th element represents the distance from the UAV to the mth ground radiation source at time n. Transform problem P1 into an equivalent problem P2; S4：利用S-Procedure算法，将问题P2转化为等价问题P3；S4: Use the S-Procedure algorithm to transform the problem P2 into an equivalent problem P3; S5：将问题P3近似处理转换为凸问题P4；S5: Convert the problem P3 approximation to a convex problem P4; S6：基于所述无人机轨迹规划模型P4，对优化目标进行求解，得到无人机最优飞行轨迹。S6: Based on the UAV trajectory planning model P4, the optimization target is solved to obtain the optimal flight trajectory of the UAV. 2.根据权利要求1所述的非确定干扰环境下无人机轨迹规划方法，其特征在于，S1具体为：2. UAV trajectory planning method under non-determined interference environment according to claim 1, is characterized in that, S1 is specifically: 设无人机飞行高度为H、飞行时间为T，以预设的起点{xI,yI,H}(xI,yI代表起点的横纵坐标)向指定的终点{xF,yF,H}飞行(xF,yF代表终点的横纵坐标)；地面有1个控制站，高度为0，水平位置为ws＝[xs,ys](xs,ys代表控制站的横纵坐标)；地面有M个辐射源，高度为0，水平位置为wj,m＝[xj,m,yj,m](xj,m,yj,m代表地面辐射源的横纵坐标)；辐射源的预估位置/功率与实际位置/功率的关系表示为：Let the flying height of the drone be H and the flight time to be T, and take the preset starting point {x I , y I , H} (x I , y I represent the horizontal and vertical coordinates of the starting point) to the specified end point {x F , y F , H} flight (x F , y F represents the horizontal and vertical coordinates of the end point); there is a control station on the ground, the height is 0, and the horizontal position is ws = [x s , y s ] ( x s , y s represent The horizontal and vertical coordinates of the control station); there are M radiation sources on the ground, the height is 0, and the horizontal position is w j,m =[x j,m ,y j,m ](x j,m ,y j,m represents the ground The horizontal and vertical coordinates of the radiation source); the relationship between the estimated position/power of the radiation source and the actual position/power is expressed as:
Figure FDA0003154691530000014
Figure FDA0003154691530000014
Figure FDA0003154691530000015
Figure FDA0003154691530000015
Figure FDA0003154691530000016
Figure FDA0003154691530000016
Figure FDA0003154691530000017
Figure FDA0003154691530000017
 其中
Figure FDA0003154691530000018
和
Figure FDA0003154691530000019
表示第m个辐射源估计的位置及功率，Δwj,m和Δpj,m表示第m个辐射源位置及功率的估计误差，
Figure FDA00031546915300000110
和ξm表示第m个辐射源的误差上界，Aj,m和ψj,m表示第m个辐射源位置及功率的误差范围。in
Figure FDA0003154691530000018
and
Figure FDA0003154691530000019
represents the estimated position and power of the mth radiation source, Δw j,m and Δp j,m represent the estimated error of the mth radiation source position and power,
Figure FDA00031546915300000110
and ξ m represent the upper bound of the error of the mth radiation source, A j,m and ψ j,m represent the error range of the position and power of the mth radiation source. 将T平均分成N个时刻，相邻时刻的长度δ＝T/N；设无人机最小飞行速度为umin，最大飞行速度为umax，最大加速度为amax；在时刻n，无人机水平坐标为q[n]＝[x[n],y[n]](x[n],y[n]代表位置的横纵坐标)，速度为
Figure FDA00031546915300000212
(ux[n],uy[n]为速度的横纵分量)，加速度为a[n]＝[ax[n],ay[n]](ax[n],ay[n]为加速度的横纵分量)；无人机的飞行约束表示为：Divide T into N moments on average, and the length of adjacent moments δ=T/N; set the minimum flight speed of the UAV as u min , the maximum flight speed as u max , and the maximum acceleration as a max ; at time n, the UAV is The horizontal coordinate is q[n]=[x[n], y[n]] (x[n], y[n] represents the horizontal and vertical coordinates of the position), and the speed is
Figure FDA00031546915300000212
(u x [n], u y [n] are the horizontal and vertical components of velocity), the acceleration is a[n]=[a x [n], a y [n]](a x [n], a y [ n] is the horizontal and vertical components of the acceleration); the flight constraints of the UAV are expressed as:
Figure FDA0003154691530000021
Figure FDA0003154691530000021
 u[n]＝u[n-1]+a[n-1]δ,n＝2,3,...,N, (3b)u[n]=u[n-1]+a[n-1]δ,n=2,3,...,N, (3b)
Figure FDA0003154691530000022
Figure FDA0003154691530000022
 q[N]＝qF,u[N]＝uF, (3d)q[N]=q F , u[N]=u F , (3d)
Figure FDA0003154691530000023
Figure FDA0003154691530000023
Figure FDA0003154691530000024
Figure FDA0003154691530000024
Figure FDA0003154691530000025
Figure FDA0003154691530000025
 其中qI、uI和aI分别表示无人机初始时刻的位置、速度及加速度；qF和uF分别表示无人机最终的位置及速度；Among them, q I , u I and a I respectively represent the position, velocity and acceleration of the UAV at the initial moment; q F and u F respectively represent the final position and speed of the UAV; 在第n个时刻，无人机到控制站和地面辐射源的距离分别表示为
Figure FDA0003154691530000026
Figure FDA0003154691530000027
则无人机到地面控制站和地面辐射源的信道增益为：At the nth moment, the distance from the UAV to the control station and the ground radiation source is expressed as
Figure FDA0003154691530000026
Figure FDA0003154691530000027
Then the channel gain from the UAV to the ground control station and the ground radiation source is:
Figure FDA0003154691530000028
Figure FDA0003154691530000028
Figure FDA0003154691530000029
Figure FDA0003154691530000029
 其中β0表示为当距离为1时的信道增益；where β 0 represents the channel gain when the distance is 1; 无人机在飞行过程中所需总能耗为：The total energy consumption required by the drone during flight is:
Figure FDA00031546915300000210
Figure FDA00031546915300000210
 其中c1和c2代表无人机自身硬件相关常数，g代表重力加速度，
Figure FDA00031546915300000211
代表无人机飞行动能消耗，J表示无人机的质量。where c 1 and c 2 represent the hardware-related constants of the drone itself, g represents the acceleration of gravity,
Figure FDA00031546915300000211
Represents the kinetic energy consumption of the drone, and J represents the mass of the drone. 3.根据权利要求1所述的非确定干扰环境下无人机轨迹规划方法，其特征在于，S2具体为：3. UAV trajectory planning method under non-determined interference environment according to claim 1, is characterized in that, S2 is specifically: 无人机在第n个时刻，接收到最坏情况下的信噪比如下：At the nth moment, the UAV receives the worst-case signal-to-noise ratio as follows:
Figure FDA0003154691530000031
Figure FDA0003154691530000031
 其中M为地面辐射源的数目，p0为地面控制站对无人机的上行传输功率，σ2表示加性高斯白噪声。推广到整个飞行过程，以最大化无人机接收到最坏情况下的平均信噪比为目标，该轨迹规划问题表示如下：Among them, M is the number of ground radiation sources, p 0 is the uplink transmission power of the ground control station to the UAV, and σ 2 is the additive white Gaussian noise. Generalized to the entire flight process, with the goal of maximizing the worst-case average signal-to-noise ratio received by the UAV, the trajectory planning problem is expressed as follows:
Figure FDA0003154691530000032
Figure FDA0003154691530000032
Figure FDA0003154691530000033
Figure FDA0003154691530000033
Figure FDA0003154691530000034
Figure FDA0003154691530000034
 u[n]＝u[n-1]+a[n-1]δ,n＝2,3,...,N, (8d)u[n]=u[n-1]+a[n-1]δ,n=2,3,...,N, (8d)
Figure FDA0003154691530000035
Figure FDA0003154691530000035
 q[N]＝qF,u[N]＝uF, (8f)q[N]=q F , u[N]=u F , (8f)
Figure FDA0003154691530000036
Figure FDA0003154691530000036
Figure FDA0003154691530000037
Figure FDA0003154691530000037
Figure FDA0003154691530000038
Figure FDA0003154691530000038
 其中Γ为无人机的最大飞行能耗约束。where Γ is the maximum flight energy consumption constraint of the UAV. 4.根据权利要求1所述的非确定干扰环境下无人机轨迹规划方法，其特征在于，所述的S3具体为：4. UAV trajectory planning method under non-determined interference environment according to claim 1, is characterized in that, described S3 is specifically: 将辐射源功率pj,m取
Figure FDA0003154691530000039
以消除目标函数中Δpj,m变量。采用冗余变量法，引入基站距离向量
Figure FDA00031546915300000310
其中第n元素表示无人机在时刻n到控制站的距离；干扰功率向量
Figure FDA00031546915300000311
其中第n元素表示在时刻n无人机受到地面辐射源干扰的总功率；干扰距离矩阵
Figure FDA0003154691530000041
其中第(m,n)个元素表示无人机在时刻n到第m个地面辐射源的距离。将问题P1转化为等价问题P2如下：The radiation source power p j,m is taken as
Figure FDA0003154691530000039
To eliminate the Δp j,m variable in the objective function. Using the redundant variable method, the base station distance vector is introduced
Figure FDA00031546915300000310
The nth element represents the distance from the UAV to the control station at time n; the interference power vector
Figure FDA00031546915300000311
The nth element represents the total power of the UAV interfered by the ground radiation source at time n; the interference distance matrix
Figure FDA0003154691530000041
The (m,n)th element represents the distance from the UAV to the mth ground radiation source at time n. Transforming problem P1 into an equivalent problem P2 is as follows:
Figure FDA0003154691530000042
Figure FDA0003154691530000042
Figure FDA0003154691530000043
Figure FDA0003154691530000043
Figure FDA0003154691530000044
Figure FDA0003154691530000044
Figure FDA0003154691530000045
Figure FDA0003154691530000045
 (8b)-(8i) (9e)(8b)-(8i) (9e) 5.根据权利要求1所述的非确定干扰环境下无人机轨迹规划方法，其特征在于，所述的S4具体为：5. UAV trajectory planning method under non-determined interference environment according to claim 1, is characterized in that, described S4 is specifically: 采用S-Procedure算法，引用约束矩阵
Figure FDA0003154691530000046
其中第(m,n)个元素表示无人机在时刻n关于第m个地面辐射源的约束。将半无限约束(9d)等价转化为如下约束：Using S-Procedure algorithm, reference constraint matrix
Figure FDA0003154691530000046
The (m,n)th element represents the constraint of the UAV on the mth ground radiation source at time n. The semi-infinite constraint (9d) is equivalently transformed into the following constraint:
Figure FDA0003154691530000047
Figure FDA0003154691530000047
Figure FDA0003154691530000048
Figure FDA0003154691530000048
 其中in
Figure FDA0003154691530000049
Figure FDA0003154691530000049
 且
Figure FDA00031546915300000410
其中
Figure FDA00031546915300000411
和
Figure FDA00031546915300000412
表示第m个辐射源估计位置的横纵坐标；and
Figure FDA00031546915300000410
in
Figure FDA00031546915300000411
and
Figure FDA00031546915300000412
The abscissa and ordinate representing the estimated position of the mth radiation source; 再引入n维速度向量
Figure FDA00031546915300000413
其中第n元素表示在时刻n无人机的速度；轨迹规划P2转化为等价问题P3如下：Reintroduce the n-dimensional velocity vector
Figure FDA00031546915300000413
The nth element represents the speed of the UAV at time n; the trajectory planning P2 is transformed into an equivalent problem P3 as follows:
Figure FDA00031546915300000414
Figure FDA00031546915300000414
Figure FDA00031546915300000415
Figure FDA00031546915300000415
Figure FDA00031546915300000416
Figure FDA00031546915300000416
Figure FDA0003154691530000051
Figure FDA0003154691530000051
Figure FDA0003154691530000052
Figure FDA0003154691530000052
 (8c)-(8h),(9b),(9c),(10),(11) (12f)(8c)-(8h),(9b),(9c),(10),(11) (12f) 6.根据权利要求1所述的非确定干扰环境下无人机轨迹规划方法，其特征在于，所述的S5具体为：6. UAV trajectory planning method under non-determined interference environment according to claim 1, is characterized in that, described S5 is specifically: 在给定的第k次迭代点(I[n](k),L[n](k))，将非凸函数用一阶泰勒展开得到全局下界值：At the given k-th iteration point (I[n] (k) , L[n] (k) ), the non-convex function is expanded by first-order Taylor to obtain the global lower bound value:
Figure FDA0003154691530000053
Figure FDA0003154691530000053
 在给定的第k次迭代点u[n](k)，将非凸约束(12c)、(12d)中||u[n]||2用一阶泰勒展开如下：At the given k-th iteration point u[n] (k) , the non-convex constraints (12c), (12d) in ||u[n]|| 2 are expanded by first-order Taylor as follows:
Figure FDA0003154691530000054
Figure FDA0003154691530000054
 在给定的第k次迭代点(x[n](k),y[n](k))，将非凸约束(10)中非线性项cm[n]用一阶泰勒展开如下：At a given k-th iteration point (x[n] (k) , y[n] (k) ), the nonlinear term c m [n] in the non-convex constraint (10) is expanded by first-order Taylor as follows:
Figure FDA0003154691530000055
Figure FDA0003154691530000055
 轨迹规划P3转化为近似凸问题P4如下：The trajectory planning P3 is transformed into an approximate convex problem P4 as follows:
Figure FDA0003154691530000056
Figure FDA0003154691530000056
Figure FDA0003154691530000057
Figure FDA0003154691530000057
Figure FDA0003154691530000058
Figure FDA0003154691530000058
Figure FDA0003154691530000059
Figure FDA0003154691530000059
 (8c)-(8h),(9b),(9c)，(11),(12b),(12e) (13e)(8c)-(8h),(9b),(9c),(11),(12b),(12e) (13e) 其中in
Figure FDA00031546915300000510
Figure FDA00031546915300000510
 此时，通过CVX工具箱解出轨迹的最优解。At this time, the optimal solution of the trajectory is solved by the CVX toolbox. 7.根据权利要求1所述的非确定干扰环境下无人机轨迹规划方法，其特征在于，所述S6具体包括以下步骤：7. The unmanned aerial vehicle trajectory planning method under non-determined interference environment according to claim 1, is characterized in that, described S6 specifically comprises the following steps: S6.1.初始化无人机的位置、速度、加速度分别为q(0)、u(0)和a(0)，目标函数为
Figure FDA0003154691530000061
迭代次数k＝0，设置最大迭代次数Kmax，迭代精度阈值θ1；S6.1. Initialize the position, velocity and acceleration of the UAV as q (0) , u (0) and a (0) respectively, and the objective function is
Figure FDA0003154691530000061
The number of iterations k=0, the maximum number of iterations K max is set, and the iteration accuracy threshold θ 1 ; S6.2.给定第k次迭代无人机的位置、速度、加速度q(k)、u(k)和a(k)代入轨迹规划优化模型P1进行求解，得到第k+1次迭代后无人机的位置、速度、加速度的最优解为q(k+1)、u(k+1)和a(k+1)；S6.2. Given the position, velocity, acceleration q (k) , u (k) and a (k) of the UAV in the kth iteration, substitute it into the trajectory planning optimization model P1 to solve, and obtain the k+1th iteration after The optimal solutions for the position, velocity, and acceleration of the UAV are q (k+1) , u (k+1) and a (k+1) ; S6.3.判断是否满足k≥Kmax，或
Figure FDA0003154691530000062
如果是，得到优化后的位置、速度、加速度q(*)、u(*)和a(*)；如果否，则更新迭代次数k＝k+1，并重复步骤S6.2和S6.3。S6.3. Determine whether k≥K max is satisfied, or
Figure FDA0003154691530000062
If yes, get the optimized position, velocity, acceleration q (*) , u (*) and a (*) ; if not, update the number of iterations k=k+1, and repeat steps S6.2 and S6.3 .
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