技术领域technical field
本发明涉及一种无人机着陆引导方法，特别涉及一种风扰环境下无人机着陆引导方 法，属于无人机着陆控制领域。The invention relates to a landing guidance method of an unmanned aerial vehicle, in particular to a landing guidance method of an unmanned aerial vehicle in a wind disturbance environment, and belongs to the field of unmanned aerial vehicle landing control.
背景技术Background technique
随着航空母舰、战列舰、驱逐舰、护卫舰和两栖舰等军舰装备舰载无人机日益增加， 无人机在信息化武器和智能化武器为主导的“非接触战争”中发挥着重要作用。伴随着现代 海战向立体化、多层次的发展，利用排水量小的舰船搭载无人机，到达某些特殊作战区域 执行战场侦察、反潜反舰、两栖突击、空中预警等危险任务，掌握未来战争中的制海权、 制空权，从而增强国家国防实力，也是国际普遍关注的重要问题。With the increasing number of aircraft carriers, battleships, destroyers, frigates and amphibious ships equipped with UAVs, UAVs play an important role in "non-contact warfare" dominated by information-based weapons and intelligent weapons. With the development of modern naval warfare to three-dimensional and multi-level, ships with small displacement are used to carry drones to reach certain special combat areas to perform battlefield reconnaissance, anti-submarine and anti-ship, amphibious assault, air warning and other dangerous tasks, and to master future wars It is also an important issue of international concern to enhance the national defense strength.
风扰环境下无人机(UAV)在小型移动平台上着陆时，需要在无人机与着陆装置对接时刻满足给定的状态向量的边界(终端)条件。现有的风扰环境下无人机着陆引导方法存在引导精度不高的问题。When an unmanned aerial vehicle (UAV) lands on a small mobile platform in a wind disturbance environment, the boundary (terminal) condition of a given state vector needs to be satisfied at the moment of docking between the UAV and the landing device. The existing UAV landing guidance methods in the wind disturbance environment have the problem of low guidance accuracy.
发明内容SUMMARY OF THE INVENTION
针对现有的风扰环境下无人机着陆引导方法存在引导精度不高的问题，本发明提供一 种风扰环境下无人机着陆引导方法。Aiming at the problem of low guidance accuracy in the existing UAV landing guidance methods in a wind disturbance environment, the present invention provides a UAV landing guidance method in a wind disturbance environment.
本发明的风扰环境下无人机着陆引导方法，所述方法包括：The UAV landing guidance method in the wind disturbance environment of the present invention, the method includes:
S1、在控制约束条件和无风的条件下，求解将无人机从任意初始位置转移到最终位 置的辅助最优控制问题，计算得到无人机的着陆运动轨迹，即：导向运动轨迹；S1. Under the condition of control constraints and no wind, solve the auxiliary optimal control problem of transferring the UAV from any initial position to the final position, and calculate the landing motion trajectory of the UAV, that is, the guiding motion trajectory;
所述控制约束条件为：0＜ρ≤1，α(t)表示无人机的攻角，αM表 示α(t)的最大允许值，R(t)表示无人机的电动螺旋桨拉力，RM表示R(t)的最大允许值；The control constraints are: 0<ρ≤1, α(t) represents the angle of attack of the drone, αM represents the maximum allowable value of α(t), R(t) represents the electric propeller pulling force of the drone, and RM represents R(t) the maximum allowable value;
风速的随机分量允许范围内，在给定的风速常值分量下，ρ使判据J的数学期望J小于设定的允许值ε；Within the allowable range of the random component of wind speed, under the given constant component of wind speed, ρ makes the mathematical expectation J of the criterion J less than the set allowable value ε;
所述判据J为：The criterion J is:
V、θ、x和y分别表示无人机的飞行速度、飞行速度矢量的倾角、地面直角坐标 系ox0y0中的无人机质心x轴坐标和y轴坐标，和表示给定边界值，tF表示终端位置对应的时刻；V, θ, x, and y represent the UAV's flight speed, the inclination of the flight speed vector, the x-axis coordinate and the y-axis coordinate of the UAV's center of mass in the ground Cartesian coordinate system ox0 y0 , respectively. and represents the given boundary value, and tF represents the time corresponding to the terminal position;
S2、求解在给定风的随机分量条件下的无人机运动轨迹与导向运动轨迹最大逼近问 题，确定无人机控制律；S2. Solve the maximum approximation problem of the UAV motion trajectory and the guided motion trajectory under the condition of the random component of the given wind, and determine the UAV control law;
所述风速的随机分量为具有给定统计特性的随机函数，0≤σW≤|σW|M，σW表示风速的随机分量均方根，|σW|M表示σW的最大允许值；The random component of the wind speed is a random function with a given statistical characteristic, 0≤σW ≤ |σW |M , σW represents the root mean square of the random component of the wind speed, and |σW |M represents the maximum allowable value of σW ;
S3、利用所述无人机控制律实现无人机着陆引导。S3. Utilizing the UAV control law to realize the UAV landing guidance.
作为优选，所述S1包括：Preferably, the S1 includes:
在无风的情况下及约束条件下，保证在t＝tF时刻无人机沿着给定单 位矢量l＝[0 0 sinξ cosξ]方向的从任意初始位置到给定边界约束条件的位置的位移最大，确定导向轨迹；ξ表示矢量l与ox0轴间的夹角，，在确定导向轨迹时，利用最大值 原理求解单位矢量l的方向，进而使判据J2＝-lTz(t0)为最大值或判据 J3＝lTz(t0)＝y(t0)sinξ+x(t0)cosξ为最小值；In the absence of wind and constraints , to ensure that the displacement of the UAV along the given unit vector l=[0 0 sinξ cosξ] direction from any initial position to the position of the given boundary constraints is the largest at time t=tF , and the guiding trajectory is determined; ξ represents The angle between the vector l and the ox0 axis, when determining the guide trajectory, the maximum value principle is used to solve the direction of the unit vector l, and then the criterion J2 =-lT z(t0 ) is the maximum value or criterion J3 =lT z(t0 )=y(t0 )sinξ+x(t0 )cosξ is the minimum value;
z(t)＝[V,θ,y,x]T，V、θ、x和y分别表示无人机的飞行速度、飞行速度矢量的 倾角、地面直角坐标系ox0y0中的无人机质心x轴坐标和y轴坐标，tF表示终端位置对应 的时刻，t0表示初始位置的时刻；z(t)=[V, θ, y, x]T , V, θ, x and y represent the flight speed of the UAV, the inclination of the flight speed vector, and the unmanned aerial vehicle in the ground rectangular coordinate system ox0 y0 , respectively. The x-axis and y-axis coordinates of the center of mass of the machine, tF represents the time corresponding to the terminal position, and t0 represents the time of the initial position;
计算导向轨迹的相位矢量为：Calculate the phase vector of the guide trajectory as:
wT(t)＝[wV(t) wθ(t) wy(t) wx(t)]wT (t)=[wV (t) wθ (t) wy (t) wx (t)]
wV(t)、wθ(t)、wy(t)和wx(t)分别表示V、θ、x和y对应的相位矢量。 作为优选，所述S2中的无人机控制律的表示形式为：wV (t), wθ (t), wy (t), and wx (t) represent the phase vectors corresponding to V, θ, x, and y, respectively. Preferably, the representation form of the UAV control law in S2 is:
其中，R(t),α(t),XW(t),YW(t))，表示风扰条件下无人机在垂直平面内的运动；XW(t)表示无人机的正面阻力，YW(t)表示无人机的升力。in, R(t), α(t), XW (t), YW (t)), represents the movement of the UAV in the vertical plane under wind disturbance conditions; XW (t) represents the frontal resistance of the UAV , YW (t) represents the lift of the UAV.
作为优选，所述S2中的无人机控制律的表示形式为：Preferably, the representation form of the UAV control law in S2 is:
其中，R(t),α(t),XW(t),YW(t))，表示风扰条件下无人机在垂直平面内的运动；XW(t)表示无人机的正面阻力，YW(t)表示无人机的升力；in, R(t), α(t), XW (t), YW (t)), represents the movement of the UAV in the vertical plane under wind disturbance conditions; XW (t) represents the frontal resistance of the UAV , YW (t) represents the lift of the UAV;
t*根据计算得到，wy(t*)表示导向运动轨迹上高度最近的点；H表示确定高度最近点的搜索时间间隔。t* according to Calculated, wy (t* ) represents the point with the closest height on the guiding motion trajectory; H represents the search time interval for determining the closest point in height.
作为优选，所述S1中，风速的随机分量允许范围和η的获取方法为：Preferably, in the S1, the allowable range of the random component of the wind speed and the method for obtaining η are:
在满足0≤σW≤|σW|M、0＜ρ≤1的同时，单一改变σW或η，重新计算，获得小于设定的允许值ε时的所有σW和η的对应关系，根据对应关系确定风速的随机分量允 许范围。While satisfying 0≤σW ≤|σW |M , 0<ρ≤1, change σW or η single, and recalculate ,get The corresponding relationship between all σW and η when it is less than the set allowable value ε, and the allowable range of the random component of the wind speed is determined according to the corresponding relationship.
本发明的有益效果，本发明针对存在风力扰动的情况下，在满足给定终端约束的前提 下，将无人机在指定时间内引导至船载着陆装置的问题进行了研究，提出了一种风力扰动 环境下的具有终端约束的无人机在小型移动平台上着陆的引导方法，其中，风的统计特性 是未知的，但是有限的。将该问题看作是对抗微分博弈问题，使用导向控制法来解决该问 题。仿真结果证明了本发明的方法的误差非常小，提高了引导的精度。The beneficial effect of the present invention is that in the presence of wind disturbance, the present invention studies the problem of guiding the drone to the shipborne landing device within a specified time under the premise of satisfying a given terminal constraint, and proposes a Guidance method for UAV landing on a small mobile platform with terminal constraints in a wind-turbulent environment, where the statistical properties of the wind are unknown but limited. Treat the problem as an adversarial differential game problem and use directed control to solve it. The simulation result proves that the error of the method of the present invention is very small, and the guidance accuracy is improved.
附图说明Description of drawings
图1为本发明的流程示意图。FIG. 1 is a schematic flow chart of the present invention.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地 描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本 发明中的实施例，本领域普通技术人员在没有作出创造性劳动的前提下所获得的所有其他 实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present invention.
需要说明的是，在不冲突的情况下，本发明中的实施例及实施例中的特征可以相互组 合。It should be noted that the embodiments of the present invention and the features of the embodiments may be combined with each other under the condition of no conflict.
下面结合附图和具体实施例对本发明作进一步说明，但不作为本发明的限定。The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but it is not intended to limit the present invention.
风扰条件下无人机在垂直平面内的运动可以表示为下面的矢量微分方程形式：The motion of the UAV in the vertical plane under wind disturbance conditions can be expressed in the form of the following vector differential equation:
其中，z＝[V,θ,y,x]T；V表示无人机的飞行速度；θ表示飞行速度矢量的倾角；x， y表示地面直角坐标系ox0y0中的无人机质心坐标；R表示电动螺旋桨拉力；m表示无人机质量；α表示攻角；g表示重力加速度；表示正面阻力；表示升力；表示无人机空速；Wx和Wy表示风速矢量在速度坐标系内的投 影；Cx(α+△αW)＝Cx0+A(α+△αW)2表示正面阻力系数；表示升力系数；Cx0，A，表示无量纲的空气动力 学系数；△αW表示风力扰动引起的攻角附加值，ρ表示空气密度，忽略其随高度的变化； S表示最大截面积。Among them, z=[V, θ, y, x]T ; V represents the flight speed of the drone; θ represents the inclination of the flight speed vector; x, y represent the center of mass of the drone in the ground rectangular coordinate system ox0 y0 coordinate; R represents the pulling force of the electric propeller; m represents the mass of the drone; α represents the angle of attack; g represents the acceleration of gravity; Indicates positive resistance; means lift; represents the UAV airspeed; Wx and Wy represent the projection of the wind speed vector in the speed coordinate system; Cx (α+△αW )=Cx0 +A(α+△αW )2 represents the frontal drag coefficient; represents the lift coefficient; Cx0 , A, represents the dimensionless aerodynamic coefficient; ΔαW represents the additional value of the angle of attack caused by wind disturbance, ρ is the air density, ignoring its change with height; S is the maximum cross-sectional area.
在本实施方式中，无人机的一个控制量是攻角，其约束条件为：In this embodiment, one of the control variables of the UAV is the angle of attack, and its constraints are:
|α(t)|≤αM (2)|α(t)|≤αM (2)
无人机的另一个控制量是电动螺旋桨拉力，其约束条件为：Another controlled quantity of the drone is the electric propeller pull, which is constrained by:
0≤R(t)≤RM (3)0≤R(t)≤RM (3)
风速矢量在地面坐标系ox0y0的相应坐标轴上的投影可以表示为：其中，和表示相应坐标轴的单位矢量；和表示风速常值分量在相应坐标轴上的投影；ζx(x0,y0)和 ζy(x0,y0)表示风速随机分量在相应坐标轴上的投影。The projection of the wind speed vector on the corresponding axis of the ground coordinate system ox0 y0 can be expressed as: in, and represents the unit vector of the corresponding coordinate axis; and Represents the projection of the constant wind speed component on the corresponding coordinate axis; ζx (x0 , y0 ) and ζy (x0 , y0 ) represent the projection of the random component of the wind speed on the corresponding coordinate axis.
风速矢量在速度坐标系的相应坐标轴上的投影Wx和Wy通过关系式 Wx＝Wx0cosθ+Wy0sinθ和Wy＝Wx0sinθ+Wy0cosθ与风速矢量在地面坐标系ox0y0的相应坐标轴上的投影相关联。The projections Wx and Wy of the wind speed vector on the corresponding axes of the speed coordinate system are related to the wind speed vector in the ground coordinate system ox by the relations Wx = Wx0 cosθ+Wy0 sinθ and Wy = Wx0 sinθ+Wy0 cosθ The projections on the corresponding axes of0 y0 are associated.
在无人机的着陆过程中，风速的常值分量几乎没有变化，因此，假设风速常值分量的 投影是常值。使用整形滤波器方程将风速的随机分量ζx＝ζx(x0,y0)，ζy＝ζy(x0,y0) 表示为具有给定统计特性的随机函数形式。During the landing of the UAV, the constant component of the wind speed hardly changes, so the projection of the constant component of the wind speed is assumed to be constant. The random components of wind speed ζx = ζx (x0 , y0 ), ζy = ζy (x0 , y0 ) are expressed as random functional forms with given statistical properties using shaping filter equations.
风速的随机分量是未知的，但是有界的。在仿真过程中，风速的随机分量被设置为σW (湍流速度的均方根)，其变化范围为：The random component of wind speed is unknown, but bounded. During the simulation, the random component of wind speed is set to σW (root mean square of turbulent velocity), which varies from:
0≤σW≤|σW|M (4)0≤σW ≤|σW |M (4)
无人机着陆机动的初始时刻t0和完成时刻tF是已知的。在控制约束(2)和(3)的 条件下，考虑风力扰动的影响,恒定分量是已知，随机分量满足约束条件(4))设计无人 机的控制律，保证判据(5)取最小值：The initial time t0 and the completion time tF of the drone landing maneuver are known. Under the conditions of control constraints (2) and (3), considering the influence of wind disturbance, the constant component is known, and the random component satisfies the constraint condition (4)) Design the control law of the UAV, and ensure that the criterion (5) takes Minimum:
其中，表示给定的边界(终端)条件。in, Represents a given boundary (terminal) condition.
由于风的随机分量的存在，所研究的问题包含了不确定性因素。在本实施方式中，将 所要求解的问题看作是有两个玩家参与的对抗性微分博弈问题。其中，第一个玩家按照我 们的利益行事，寻求判据(5)的最小值，第二个玩家的利益相反，寻找判据(5)的最大值。The studied problem contains an element of uncertainty due to the presence of a random component of the wind. In this embodiment, the problem to be solved is regarded as an adversarial differential game problem involving two players. Among them, the first player acts in our interests and seeks the minimum value of criterion (5), and the second player has the opposite interests and seeks the maximum value of criterion (5).
第一个玩家的控制集U由满足约束条件(2)和(3)的所有可行控制率组成，将其 分成两个子集U1和U2。子集U1用于求解无风情况下的辅助最优控制问题，将计算得到 的着陆运动轨迹称为导向轨迹。子集U2用于补偿实际运动轨迹与导向轨迹之间的偏差。The first player's control set U consists of all feasible control rates satisfying constraints (2) and (3), which are divided into two subsets U1 and U2 . The subset U1 is used to solve the auxiliary optimal control problem in the case of no wind, and the calculated landing motion trajectory is called the guidance trajectory. The subset U2 is used to compensate for the deviation between the actual motion trajectory and the guide trajectory.
从理论上讲，很难从所研究的问题中分离出一个用于补偿风力扰动作用的子集U2。 为此，本实施方式的本发明的风扰环境下无人机着陆引导方法，包括：Theoretically, it is difficult to separate out a subset U2 for compensating wind disturbance effects from the problem under study. For this reason, the UAV landing guidance method in the wind disturbance environment of the present invention includes:
S1、在控制约束条件和无风的条件下，求解将无人机从任意初始位置转移到最终位 置的辅助最优控制问题，计算得到无人机的着陆运动轨迹，即：导向运动轨迹；S1. Under the condition of control constraints and no wind, solve the auxiliary optimal control problem of transferring the UAV from any initial position to the final position, and calculate the landing motion trajectory of the UAV, that is, the guiding motion trajectory;
本实施方式引入从0到1变化的系数η，即，0＜η≤1，并将无人机控制约束集U1表示为：This embodiment introduces a coefficient η varying from 0 to 1, that is, 0<η≤1, and expresses the UAV control constraint set U1 as:
α(t)表示无人机的攻角，αM表示α(t)的最大允许值，R(t)表示无人机的电动螺旋桨拉力，RM表示R(t)的最大允许值；α(t) represents the angle of attack of the UAV, αM represents the maximum allowable value of α(t), R(t) represents the electric propeller pulling force of the UAV, and RM represents the maximum allowable value of R(t);
风速的随机分量允许范围内，在给定的风速常值分量下，η使判据J的数学期望小 于设定的允许值ε；Within the allowable range of the random component of wind speed, under the given constant component of wind speed, η makes the mathematical expectation of criterion J less than the set allowable value ε;
所述判据J为：The criterion J is:
V、θ、x和y分别表示无人机的飞行速度、飞行速度矢量的倾角、地面直角坐标 系ox0y0中的无人机质心x轴坐标和y轴坐标，和表示给定边界值，tF表示终端位置对应的时刻；V, θ, x, and y represent the UAV's flight speed, the inclination of the flight speed vector, the x-axis coordinate and the y-axis coordinate of the UAV's center of mass in the ground Cartesian coordinate system ox0 y0 , respectively. and represents the given boundary value, and tF represents the time corresponding to the terminal position;
S2、求解在给定风的随机分量条件下的无人机运动轨迹与导向运动轨迹最大逼近问 题，确定无人机控制律；S2. Solve the maximum approximation problem of the UAV motion trajectory and the guided motion trajectory under the condition of the random component of the given wind, and determine the UAV control law;
所述风速的随机分量为具有给定统计特性的随机函数，0≤σW≤|σW|M，σW表示风速的随机分量均方根，|σW|M表示σW的最大允许值；The random component of the wind speed is a random function with a given statistical characteristic, 0≤σW ≤ |σW |M , σW represents the root mean square of the random component of the wind speed, and |σW |M represents the maximum allowable value of σW ;
S3、利用所述无人机控制律实现无人机着陆引导。S3. Utilizing the UAV control law to realize the UAV landing guidance.
本实施方式针对存在风力扰动的情况下，在满足给定终端约束的前提下，将无人机在指 定时间内引导至船载着陆装置的问题进行了研究，其中，风的统计特性是未知的，但是有 限的。将该问题看作是对抗微分博弈问题，引入η使用导向控制法来解决该问题。仿真结 果证明了本发明的方法的误差非常小，提高了引导的精度。This embodiment studies the problem of guiding the UAV to the shipborne landing device within a specified time under the premise of satisfying the given terminal constraints in the presence of wind disturbance, wherein the statistical characteristics of the wind are unknown , but limited. Considering the problem as an adversarial differential game problem, η is introduced to solve the problem using a directed control method. The simulation result proves that the error of the method of the present invention is very small, and the precision of guidance is improved.
本实施方式引入从0到1变化的系数η，即，0＜η≤1，并将无人机控制约束集U1表示为：This embodiment introduces a coefficient η varying from 0 to 1, that is, 0<η≤1, and expresses the UAV control constraint set U1 as:
本实施方式求解辅助最优控制问题，确定算得到无人机的着陆运动轨迹，优选实施例 中，本实施方式的S1包括：This embodiment solves the auxiliary optimal control problem, and determines and calculates the landing motion trajectory of the UAV. In a preferred embodiment, S1 of this embodiment includes:
在无风的情况下，根据矢量方程(1)确定导向运动，控制量满足约束条件(6)。给定受控运动的初始时刻t0和终止时刻tF，以及t＝tF时刻的边界条件保证在t＝tF时刻沿着给定单位矢量l＝[0 0 sinξ cosξ]方向的从任意初始位置(t0时 刻)到最终位置(tF时刻)的位移最大，其中，ξ表示矢量l与ox0轴间的夹角，即，需 要找到判据J1＝lT[z(tF)-z(t0)]的最大值。由于在本文中z(tF)是已知的，所以只需 要找到判据J2＝-lTz(t0)的最大值或判据J3＝lTz(t0)＝y(t0)sinξ+x(t0)cosξ的最 小值。In the case of no wind, the steering motion is determined according to the vector equation (1), and the control quantity satisfies the constraint condition (6). Given the initial time t0 and termination time tF of the controlled motion, and the boundary conditions at time t = tF Ensure that the displacement from any initial position (time t0 ) to the final position (time tF ) along a given unit vector l=[0 0 sinξ cosξ] direction at time t=tF is the largest, where ξ represents vector l The angle with the ox0 axis, that is, the maximum value of the criterion J1 =lT [z(tF )-z(t0 )] needs to be found. Since z(tF ) is known in this paper, it is only necessary to find the maximum value of the criterion J2 =-lT z(t0 ) or the criterion J3 =lT z(t0 )=y( The minimum value of t0 )sinξ+x(t0 )cosξ.
根据初始时刻(t＝t0)无人机的飞行高度设置矢量l的方向。通过庞特里亚金最大值原 理的必要条件来求解矢量l的方向问题，并使用Krylov-Chernousko逐次逼近法求解该边 界问题。The direction of the vector l is set according to the flying height of the UAV at the initial moment (t=t0 ). The orientation problem of the vector l is solved by the necessary conditions of the Pontryagin maximum principle, and the boundary problem is solved using the Krylov-Chernousko successive approximation method.
计算导向轨迹的相位矢量为：Calculate the phase vector of the guide trajectory as:
wT(t)＝[wV(t) wθ(t) wy(t) wx(t)] (7)wT (t)=[wV (t) wθ (t) wy (t) wx (t)] (7)
wV(t)、wθ(t)、wy(t)和wx(t)分别表示V、θ、x和y对应的相位矢量。wV (t), wθ (t), wy (t), and wx (t) represent the phase vectors corresponding to V, θ, x, and y, respectively.
本实施方式给定风速的常值分量和湍流速度的均方根σW；In this embodiment, the constant value component of the wind speed and the root mean square σW of the turbulent speed are given;
本实施方式的S2求解在给定风的随机分量(σW)条件下的无人机运动轨迹与导向运动轨迹最大逼近问题。风的常值分量是不变的。无人机的控制量满足约束条件(2)和(3)，即，使用完全的控制能力。无人机在t0时刻的初始条件对应于通过求解辅助最优控 制问题得到的t0时刻的导向轨迹相位矢量的值。S2 of this embodiment solves the maximum approximation problem of the UAV motion trajectory and the guidance motion trajectory under the condition of a given wind random component (σW ). The constant component of the wind is constant. The amount of control of the UAV satisfies constraints (2) and (3), ie, full control capability is used. The initial condition of the UAV at time t0 corresponds to the value of the phase vector of the guidance trajectory at time t0 obtained by solving the auxiliary optimal control problem.
优选实施例中，本实施方式的S2中的无人机控制律的表示形式为：In a preferred embodiment, the representation of the UAV control law in S2 of this embodiment is:
其中，R(t),α(t),XW(t),YW(t))，表示风扰条件下无人机在垂直平面内的运动；XW(t)表示无人机的正面阻力，YW(t)表示无人机的升力。in, R(t), α(t), XW (t), YW (t)), represents the movement of the UAV in the vertical plane under wind disturbance conditions; XW (t) represents the frontal resistance of the UAV , YW (t) represents the lift of the UAV.
本实施方式中风速的随机分量允许范围和ρ的获取方法为：The method for obtaining the allowable range of the random component of the wind speed and ρ in this embodiment is:
在满足0≤σW≤|σW|M、0＜ρ≤1的同时，单一改变σW或ρ，重新计算，获得小于设定的允许值ε时的所有σW和ρ的对应关系，根据对应关系确定风速的随机分量允 许范围。具体包括：While satisfying 0≤σW ≤|σW |M , 0<ρ≤1, change σW or ρ single, and recalculate ,get The corresponding relationship between all σW and ρ when it is less than the set allowable value ε, and the allowable range of the random component of the wind speed is determined according to the corresponding relationship. Specifically include:
步骤1、求解在给定风的随机分量(σW)条件下的无人机运动轨迹与导向运动轨迹最大逼近问题；Step 1. Solve the maximum approximation problem of the UAV motion trajectory and the guided motion trajectory under the condition of a given wind random component (σW );
步骤2、通关求解该问题，找到了判据(5)的数学期望Step 2. Solve the problem through customs clearance and find the mathematical expectation of criterion (5)
步骤3、如果判据(5)的数学期望小于设定的允许值ε，那么在无人机与着陆装置对接时刻能够完全消除风的随机分量(σW)的影响。将σW的值增加ΔσW，然后转到 步骤1；Step 3. If the mathematical expectation of criterion (5) If it is less than the set allowable value ε, the influence of the random component (σW ) of the wind can be completely eliminated when the UAV is docked with the landing device. Increase the value of σW by ΔσW , then go to step 1;
步骤4、如果判据(5)的数学期望大于设定的允许值ε，那么对于给定的ρ值， 无人机将无法补偿给定的风的随机分量(σW)和恒定分量的影响。Step 4. If the mathematical expectation of criterion (5) greater than the set allowable value ε, then for a given value of ρ, the UAV will not be able to compensate for the effects of the random component (σW ) and the constant component of the given wind.
改变ρ值，并计算对应于每个ρ值的风速随机分量均方差的最大允许值σW，找到风的随机分量允许范围，在该范围内，在给定的风速常值分量下，判据(5)的数学期望小于设定的允许值ε。Change the value of ρ, and calculate the maximum allowable value σW of the mean square error of the random component of the wind speed corresponding to each value of ρ, find the allowable range of the random component of the wind, within this range, under the given constant component of the wind speed, the criterion (5) Mathematical expectations less than the set allowable value ε.
仿真验证：Simulation:
终端约束条件为：tF＝60s；The terminal constraints are: tF =60s;
无人机的参数为：cx0＝0.34；A＝0.01；m＝20kg；S＝0.0357m2； αM＝0.4°；RM＝98N。The parameters of the drone are: cx0 = 0.34; A = 0.01; m=20kg; S=0.0357m2 ; αM =0.4°; RM =98N.
在系数ρ＝0.8的条件下，求解所研究的问题。The problem under study is solved under the condition that the coefficient ρ = 0.8.
在控制约束(6)的条件下，通过求解无人机从任意初始的位置(t＝t0)转移到给定终端约束条件的位置(t＝tF)的辅助方程来确定导向轨迹。在确定导向轨迹时，单位矢 量l的方向根据t＝t0时刻在高度为y(t0)＝y0＝250m处的无人机位置条件确定。Guided trajectories are determined by solving the auxiliary equations for the UAV to transfer from an arbitrary initial position (t=t0 ) to a position (t=tF ) given terminal constraints, subject to control constraints (6). When determining the guidance trajectory, the direction of the unit vector l is determined according to the position condition of the UAV at a height of y(t0 )=y0 =250m at time t=t0 .
最优攻角是常值，且α(t)＝0.8αM＝0.32°。湍流速度均方根σM的变化范围0.1m/s –30m/s。The optimum angle of attack is constant, and α(t) = 0.8αM = 0.32°. The turbulent velocity root mean square σM varies from 0.1m/s to 30m/s.
在设计无人机控制律时，不使用方程(8)，而使用(x(t)-w(t*))计算无人机与导引轨迹间的偏差，即，使用下面的方程：When designing the UAV control law, instead of using equation (8), use (x(t)-w(t* )) to calculate the deviation between the UAV and the guidance trajectory, that is, use the following equation:
在方程(9)中，t*根据方程(10)计算得到。In equation (9), t* is calculated according to equation (10).
其中，wy(t*)表示导向运动轨迹上高度最近的点；H表示确定高度最近点的搜索 时间间隔。在仿真过程中，选取H＝5s。Among them, wy (t* ) represents the point with the closest height on the guiding motion trajectory; H represents the search time interval for determining the closest point in height. In the simulation process, choose H = 5s.
在这种情况下，当选择无人机控制采样周期Δt＝0.01s且无风条件下，无人机与着陆 装置对接时刻的无人机像坐标与给定的终端条件的偏差最小。其中，飞行速度的偏差–In this case, when the UAV control sampling period Δt=0.01s is selected and there is no wind, the deviation of the UAV image coordinates at the moment of docking between the UAV and the landing device and the given terminal conditions is the smallest. Among them, the deviation of flight speed –
在研究风速随机分量的影响时，改变湍流速度均方根的值σM，风速的恒定分量为零。When studying the effect of the random component of wind speed, change the value σM of the root mean square of the turbulent velocity, and the constant component of the wind speed is zero.
在表1中给出了系数ρ＝0.8，以及ρ＝0.6和ρ＝0.4时，最优判据(5)的数学期 望。表1中给出的数据是根据20次仿真实验结果计算得到。Mathematical expectations of the optimal criterion (5) are given in Table 1 for the coefficient ρ=0.8, and for ρ=0.6 and ρ=0.4. Data given in Table 1 It is calculated based on the results of 20 simulation experiments.
表1判据(5)的数学期望Mathematical expectations of criterion (5) in Table 1
从表1中的实验数据可以看出，如果判据(5)的数学期望允许值的绝对值小于2，那么在ρ＝0.8的条件下风速随机分量均方根的值不应该超过1m/s，在ρ＝0.6的条件下 风速随机分量均方根的值不应该超过5m/s，在ρ＝0.4的条件下风速随机分量均方根的 值不应该超过10m/s。It can be seen from the experimental data in Table 1 that if the absolute value of the mathematical expectation of the criterion (5) is less than 2, then the value of the root mean square of the random component of the wind speed should not exceed 1m/s under the condition of ρ=0.8 , under the condition of ρ = 0.6, the value of the root mean square of the random component of the wind speed should not exceed 5m/s, and under the condition of ρ = 0.4, the value of the root mean square of the random component of the wind speed should not exceed 10m/s.
仿真结果表明，本实施方式提出的基于向导轨迹的控制算法可用于引导无人机在小型 运动平台的着陆装置上回收，并且可以用于评估风力扰动对无人机与着陆收装置对接的引 导精度的影响。The simulation results show that the control algorithm based on the guidance trajectory proposed in this embodiment can be used to guide the UAV to recover on the landing device of the small moving platform, and can be used to evaluate the guidance accuracy of the wind disturbance on the docking of the UAV and the landing device. Impact.
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| CN201910833094.3ACN110487280B (en) | 2019-09-04 | 2019-09-04 | UAV landing guidance method in wind disturbance environment |
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| CN201910833094.3ACN110487280B (en) | 2019-09-04 | 2019-09-04 | UAV landing guidance method in wind disturbance environment |
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