CN115291622A - A Fractional-Order Sliding Mode Control Method for Distributed Formation of Obstacle Avoidance UAVs - Google Patents

A Fractional-Order Sliding Mode Control Method for Distributed Formation of Obstacle Avoidance UAVs Download PDF

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CN115291622A
CN115291622A CN202210595527.8A CN202210595527A CN115291622A CN 115291622 A CN115291622 A CN 115291622A CN 202210595527 A CN202210595527 A CN 202210595527A CN 115291622 A CN115291622 A CN 115291622A
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unmanned aerial
aerial vehicle
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钱默抒
吴柱
刘国勇
展凤江
马传焱
葛贤坤
诸庆生
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Nanjing Tech University
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Abstract

本发明公开一种基于人工势场法和小脑模型神经网络的避障无人机分布式编队分数阶滑模控制方法，用于无人机编队避障控制和处理外部干扰和内部参数不确定性的影响。通过引入小脑模型神经网络来近似估计和补偿集总干扰的不利影响，并基于人工势场法设计出一种自适应分数阶滑模控制器。本发明实现了无人机编队闭环跟踪控制系统的稳定性和良好的避障性能，通过仿真实例验证了该方法具有一定的有效性和良好性能。

Figure 202210595527

The invention discloses a fractional-order sliding mode control method for obstacle avoidance UAV distributed formation based on artificial potential field method and cerebellar model neural network, which is used for UAV formation obstacle avoidance control and processing external disturbance and internal parameter uncertainty Impact. The adverse effects of lumped disturbances are approximately estimated and compensated by introducing a cerebellar model neural network, and an adaptive fractional-order sliding mode controller is designed based on the artificial potential field method. The invention realizes the stability and good obstacle avoidance performance of the UAV formation closed-loop tracking control system, and the simulation example verifies that the method has certain validity and good performance.

Figure 202210595527

Description

一种避障无人机分布式编队分数阶滑模控制方法A Fractional Order Sliding Mode Control Method for Distributed Formation of Unmanned Aerial Vehicles for Obstacle Avoidance

技术领域technical field

本发明涉及航空无人机控制领域，具体涉及一种考虑集总干扰影响的避障无人机分布式编队分数阶滑模控制的问题。The invention relates to the field of control of aviation unmanned aerial vehicles, in particular to a problem of fractional-order sliding mode control of distributed formations of obstacle-avoiding unmanned aerial vehicles considering the influence of lumped interference.

背景技术Background technique

近年来，随着无人机发展的日趋成熟，单架无人机已逐渐不能满足一些复杂任务的需要，研究人员开始对多无人机编队协同控制展开研究。和单无人机相比，无人机编队在装载运输、野火监控、灾难救援、战场侦察和打击等军事或民用领域具有巨大的优势。由于存在外部干扰、障碍物和内部参数不确定性等复杂因素影响，无人机编队协同控制也变得更加复杂和困难。因此，在外部干扰、内部参数不确定性和障碍物存在的情况下，无人机编队快速跟踪控制与避障问题引起了学者的广泛关注。In recent years, with the development of UAVs becoming more and more mature, a single UAV can no longer meet the needs of some complex tasks. Researchers have begun to study the cooperative control of multi-UAV formations. Compared with single drones, drone formations have huge advantages in military or civilian fields such as loading and transportation, wildfire monitoring, disaster relief, battlefield reconnaissance and strikes. Due to the influence of complex factors such as external interference, obstacles and internal parameter uncertainties, the coordinated control of UAV formations has become more complicated and difficult. Therefore, in the presence of external interference, internal parameter uncertainty and obstacles, the problem of UAV formation fast tracking control and obstacle avoidance has attracted extensive attention of scholars.

针对无人机编队避障问题，国内外众多学者提出了多种算法。专利CN112180954A发明了一种基于人工势场的无人机避障方法，主要贡献为提出额外设置横向避障控制力，从而解决了局部最小值对无人机避障的不良影响，但该方法不能使无人机在避开障碍物后立刻回到期望位置。专利CN111290429A发明了一种基于一致性算法和人工势场法的无人机编队及其避障控制方法，通过引入与障碍物移动方向垂直的辅助牵引加速度信息，可消除局部最小值的影响。然而，在避障过程中，基于该方法的无人机位置跟踪误差和速度跟踪误差波动较大，影响编队的稳定性。此外，上述两种方法均未考虑集总干扰(外部干扰和内部参数不确定性)对编队控制系统的影响。Aiming at the problem of UAV formation obstacle avoidance, many scholars at home and abroad have proposed a variety of algorithms. Patent CN112180954A invented a UAV obstacle avoidance method based on an artificial potential field. The main contribution is to propose an additional lateral obstacle avoidance control force, thereby solving the adverse effects of local minima on UAV obstacle avoidance, but this method cannot Make the drone return to the desired position immediately after avoiding the obstacle. Patent CN111290429A invented a UAV formation and its obstacle avoidance control method based on consensus algorithm and artificial potential field method. By introducing auxiliary traction acceleration information perpendicular to the moving direction of obstacles, the influence of local minimum can be eliminated. However, in the process of obstacle avoidance, the position tracking error and velocity tracking error of the UAV based on this method fluctuate greatly, which affects the stability of the formation. In addition, the above two methods do not consider the impact of aggregate disturbance (external disturbance and internal parameter uncertainty) on the formation control system.

针对外部干扰和参数不确定性影响非线性系统的控制性能的问题，众多学者已经进行了大量的研究，研究结果表明神经网络可以很好的估计和补偿外部干扰和参数不确定性。同时，改进的人工势场法能够解决局部极小值问题并实现了编队协同避障。此外，设计的分数阶滑模控制器可以保证闭环编队控制系统的稳定性和全局鲁棒性，并解决了传统避障算法在避开障碍物后不能立刻回到期望位置的问题。Aiming at the problem that external disturbance and parameter uncertainty affect the control performance of nonlinear systems, many scholars have done a lot of research. The research results show that neural network can estimate and compensate external disturbance and parameter uncertainty very well. At the same time, the improved artificial potential field method can solve the local minimum problem and realize the cooperative obstacle avoidance of the formation. In addition, the designed fractional-order sliding mode controller can ensure the stability and global robustness of the closed-loop formation control system, and solve the problem that the traditional obstacle avoidance algorithm cannot return to the desired position immediately after avoiding obstacles.

发明内容Contents of the invention

鉴于上述现有技术中的不足，本发明提出一种避障无人机分布式编队分数阶滑模控制方法，主要由以下步骤组成：In view of the deficiencies in the above-mentioned prior art, the present invention proposes a fractional-order sliding mode control method for obstacle avoidance UAV distributed formation, which mainly consists of the following steps:

步骤1、建立第i架无人机动力学模型如下所示：Step 1. Establish the i-th UAV dynamics model as follows:

Figure BSA0000273886590000011
Figure BSA0000273886590000011

其中，i为编队中无人机的编号，i＝1，...，n，n为编队中无人机的数量，Vi，ψi，

Figure BSA0000273886590000012
分别表示无人机的空速、俯仰角、航向角，xi，yi和zi为无人机的三维坐标，mi是机身质量，g是重力加速度，系统的控制输入为
Figure BSA0000273886590000021
θi表示滚转角，Ti是发动机推力，uxi，uyi，uzi分别是X轴，Y轴，Z轴方向的控制输入，ni是动载荷系数，Di是阻力；Among them, i is the number of UAVs in the formation, i=1,...,n, n is the number of UAVs in the formation, V i , ψ i ,
Figure BSA0000273886590000012
respectively represent the airspeed, pitch angle, and heading angle of the UAV, x i , y i and zi are the three-dimensional coordinates of the UAV, m i is the mass of the fuselage, g is the acceleration of gravity, and the control input of the system is
Figure BSA0000273886590000021
θ i represents the roll angle, T i is the engine thrust, u xi , u yi , u zi are the control inputs of the X-axis, Y-axis, and Z-axis directions respectively, n i is the dynamic load coefficient, and D i is the resistance;

步骤2、将步骤1中的无人机动力学模型转化为状态空间方程，同时考虑集总干扰的非线性模型可描述为：Step 2. Transform the UAV dynamics model in step 1 into a state space equation, and consider the nonlinear model of lumped disturbance as follows:

Figure BSA0000273886590000022
Figure BSA0000273886590000022

其中，pi＝[xi，yi，zi]T为位置向量，

Figure BSA0000273886590000023
为速度向量，dsi为集总干扰，G和Ri可由下式所得：Among them, p i =[x i , y i , zi ] T is the position vector,
Figure BSA0000273886590000023
is the velocity vector, d si is the lumped disturbance, G and R i can be obtained by the following formula:

G＝[0 0 -g]T G＝[0 0 -g] T

Figure BSA0000273886590000024
Figure BSA0000273886590000024

步骤3、利用小脑模型神经网络实现对集总干扰的在线估计，具体过程如下：Step 3. Use the cerebellar model neural network to realize online estimation of lumped interference. The specific process is as follows:

小脑模型神经网络的结构体系包括输入空间、联想记忆空间、接收域空间、权重记忆空间和输出空间。具体介绍如下：The structural system of the cerebellum model neural network includes input space, associative memory space, receptive field space, weight memory space and output space. The details are as follows:

(1)输入空间：对于输入I＝[I1，I2，...，Iq]T∈Rq，I为连续且q维的输入空间；(1) Input space: For the input I=[I 1 , I 2 ,...,I q ] T ∈ R q , I is a continuous and q-dimensional input space;

(2)联想记忆空间：几个不同的元素堆积成一个区块，每个区块执行一个接受域基函数，这里采用高斯函数作为基函数，可以表示为：(2) Associative memory space: Several different elements are piled up into a block, and each block executes a receptive field basis function. Here, the Gaussian function is used as the basis function, which can be expressed as:

Figure BSA0000273886590000025
Figure BSA0000273886590000025

其中，

Figure BSA0000273886590000026
为第j个输入Ij对应到第k个区块的高斯函数，
Figure BSA0000273886590000027
和σjk分别为对应的高斯函数均值和方差，M为区块数；in,
Figure BSA0000273886590000026
is the Gaussian function of the jth input I j corresponding to the kth block,
Figure BSA0000273886590000027
and σ jk are the mean and variance of the corresponding Gaussian function respectively, and M is the number of blocks;

(3)接收域空间：在此空间内，多维接收域基函数定义为：(3) Receiving domain space: In this space, the multidimensional receiving domain basis function is defined as:

Figure BSA0000273886590000028
Figure BSA0000273886590000028

其中，L表示第L个接收域基函数，N为接收域基函数的个数，多维接收域基函数用向量表示为：Among them, L represents the L-th receiving domain basis function, N is the number of receiving domain basis functions, and the multidimensional receiving domain basis function is expressed as:

Figure BSA0000273886590000029
Figure BSA0000273886590000029

其中，

Figure BSA00002738865900000210
和σ可由下列向量表示：in,
Figure BSA00002738865900000210
and σ can be represented by the following vectors:

Figure BSA00002738865900000211
Figure BSA00002738865900000211

σ＝[σ11，...，σq1，σ12，...，σq2，...，σ1M，...，σqM]T σ=[σ 11 ,...,σ q1 , σ 12 ,...,σ q2 ,...,σ 1M ,...,σ qM ] T

(4)权重记忆空间：接收域空间的每个位置到一个特定可调值的权重记忆空间的N个分量可以表示为：(4) Weight memory space: N components of the weight memory space from each position of the receiving domain space to a specific adjustable value can be expressed as:

W＝[w1，...，wL，...，wN]T W=[w 1 , . . . , w L , . . . , w N ] T

其中，wL表示第L个接收域基函数的连接权值；Among them, w L represents the connection weight of the L-th receiving field basis function;

(5)输出空间：整个小脑模型神经网络的输出可以表示为：(5) Output space: the output of the neural network of the whole cerebellum model can be expressed as:

Figure BSA0000273886590000031
Figure BSA0000273886590000031

小脑模型神经网络的输出用向量可以表示为：The output of the cerebellum model neural network can be expressed as a vector:

Figure BSA0000273886590000032
Figure BSA0000273886590000032

小脑模型神经网络在线逼近集总干扰dsi的表达式为：The expression of the online approximation of the lumped disturbance d si by the neural network of the cerebellum model is:

Figure BSA0000273886590000033
Figure BSA0000273886590000033

其中，ε为逼近误差，

Figure BSA0000273886590000034
W*T和φ*分别为W和φ的最优参数向量，
Figure BSA0000273886590000035
和σ*分别为
Figure BSA0000273886590000036
和σ的最优参数向量，dsi *为dsi的最优向量；where ε is the approximation error,
Figure BSA0000273886590000034
W *T and φ * are the optimal parameter vectors of W and φ respectively,
Figure BSA0000273886590000035
and σ * are respectively
Figure BSA0000273886590000036
and the optimal parameter vector of σ, d si * is the optimal vector of d si ;

小脑模型神经网络估计误差可以表示为：The cerebellar model neural network estimation error can be expressed as:

Figure BSA0000273886590000037
Figure BSA0000273886590000037

其中，

Figure BSA0000273886590000038
Figure BSA0000273886590000039
和
Figure BSA00002738865900000310
分别为W和φ的估计值；in,
Figure BSA0000273886590000038
Figure BSA0000273886590000039
and
Figure BSA00002738865900000310
are the estimated values of W and φ, respectively;

为了实现对集总干扰的良好估计，采用泰勒展开线性化技术将非线性函数转化为部分线性形式，即：In order to achieve a good estimate of the lumped interference, the nonlinear function is transformed into a partially linear form using Taylor expansion linearization technique, namely:

Figure BSA00002738865900000311
Figure BSA00002738865900000311

其中，

Figure BSA00002738865900000312
Figure BSA00002738865900000313
和
Figure BSA00002738865900000314
分别为
Figure BSA00002738865900000315
和σ的估计值，H是高阶项，并有：in,
Figure BSA00002738865900000312
Figure BSA00002738865900000313
and
Figure BSA00002738865900000314
respectively
Figure BSA00002738865900000315
and estimates of σ, H is a higher-order term, and has:

Figure BSA00002738865900000316
Figure BSA00002738865900000316

Figure BSA00002738865900000317
Figure BSA00002738865900000317

并且

Figure BSA00002738865900000318
和
Figure BSA00002738865900000319
被定义为：and
Figure BSA00002738865900000318
and
Figure BSA00002738865900000319
is defined as:

Figure BSA00002738865900000320
Figure BSA00002738865900000320

Figure BSA00002738865900000321
Figure BSA00002738865900000321

根据以上公式得：According to the above formula:

Figure BSA00002738865900000322
Figure BSA00002738865900000322

其中，不确定项

Figure BSA00002738865900000323
表示逼近误差项，并假设其有界，即||Δ||≤δ，δ为正的常数，||Δ||为Δ的欧几里得范数；Among them, the uncertain
Figure BSA00002738865900000323
Represents the approximation error term, and assumes that it is bounded, that is, ||Δ||≤δ, δ is a positive constant, and ||Δ|| is the Euclidean norm of Δ;

通过李雅普诺夫稳定性分析方法，得出小脑模型神经网络自适应律如下：Through the Lyapunov stability analysis method, the adaptive law of the neural network of the cerebellum model is obtained as follows:

Figure BSA0000273886590000041
Figure BSA0000273886590000041

Figure BSA0000273886590000042
Figure BSA0000273886590000042

Figure BSA0000273886590000043
Figure BSA0000273886590000043

其中，λmax为矩阵

Figure BSA0000273886590000044
的最大特征值，L为拉普拉斯矩阵，Λ为领导者的邻接矩阵，
Figure BSA0000273886590000045
为克罗内克积，I3为3×3的单位矩阵，s为本文所设计的分数阶全局积分滑模，
Figure BSA0000273886590000046
ησ，ζ1，ζ2和ζ3都为正常数，W0，
Figure BSA0000273886590000047
σ0分别为W*，
Figure BSA0000273886590000048
σ*的初始估计值；where λ max is the matrix
Figure BSA0000273886590000044
The largest eigenvalue of , L is the Laplacian matrix, Λ is the adjacency matrix of the leader,
Figure BSA0000273886590000045
is the Kronecker product, I 3 is a 3×3 identity matrix, s is the fractional-order global integral sliding mode designed in this paper,
Figure BSA0000273886590000046
η σ , ζ 1 , ζ 2 and ζ 3 are all positive constants, W 0 ,
Figure BSA0000273886590000047
σ0 are respectively W * ,
Figure BSA0000273886590000048
initial estimate of σ * ;

步骤4、基于人工势场法设计出一种自适应分数阶滑模控制器；Step 4, designing an adaptive fractional-order sliding mode controller based on the artificial potential field method;

首先需要说明本发明控制系统的实现要求无人机编队在飞行过程中满足所设计的编队构型，因此，第i架无人机的期望位置应该满足：First of all, it needs to be explained that the realization of the control system of the present invention requires the UAV formation to meet the designed formation configuration during flight. Therefore, the expected position of the i-th UAV should satisfy:

Figure BSA0000273886590000049
Figure BSA0000273886590000049

其中

Figure BSA00002738865900000410
表示虚拟领导者位置，
Figure BSA00002738865900000411
表示每个无人机相对于虚拟领导者的期望位置；in
Figure BSA00002738865900000410
denotes the virtual leader position,
Figure BSA00002738865900000411
represents the desired position of each UAV relative to the virtual leader;

图论是编队飞行中重要的组成部分之一，本发明采用无向图

Figure BSA00002738865900000412
其中
Figure BSA00002738865900000413
表示图G的节点集，
Figure BSA00002738865900000414
表示边集，
Figure BSA00002738865900000415
表示邻接矩阵；在无向图中，我们可以得到：
Figure BSA00002738865900000416
Figure BSA00002738865900000417
和aij＝aji；当第i架无人机可以接收第j架无人机的信息时，有(j，i)∈ε，并有aij＝1，否则，aij＝0；定义
Figure BSA00002738865900000418
为度矩阵，其中
Figure BSA00002738865900000419
因此，Laplacian矩阵为
Figure BSA00002738865900000420
Figure BSA00002738865900000421
对于具有一个领导者0和n个跟随者的通信拓扑图可以表示为：
Figure BSA00002738865900000422
其中
Figure BSA00002738865900000423
表示节点集；领导者的邻接矩阵为Λ＝diag{λ1，...，λn}。如果第i个跟随者可以接收领导者的信息，则λi＞0，否则，λi＝0；Graph theory is one of important components in formation flight, and the present invention adopts undirected graph
Figure BSA00002738865900000412
in
Figure BSA00002738865900000413
Represents the node set of graph G,
Figure BSA00002738865900000414
represents an edge set,
Figure BSA00002738865900000415
Represents the adjacency matrix; in an undirected graph, we can get:
Figure BSA00002738865900000416
Figure BSA00002738865900000417
and a ij = a ji ; when the i-th UAV can receive the information of the j-th UAV, there is (j, i)∈ε, and a ij = 1, otherwise, a ij = 0; define
Figure BSA00002738865900000418
is a degree matrix, where
Figure BSA00002738865900000419
Therefore, the Laplacian matrix is
Figure BSA00002738865900000420
Figure BSA00002738865900000421
For a communication topology graph with one leader 0 and n followers can be expressed as:
Figure BSA00002738865900000422
in
Figure BSA00002738865900000423
Denotes a node set; the adjacency matrix of the leader is Λ=diag{λ 1 , . . . , λ n }. If the i-th follower can receive the information from the leader, then λ i >0, otherwise, λ i =0;

基于人工势场法设计的一种自适应分数阶滑模控制器u由轨迹跟踪控制器和协同避障控制器两部分组成，即：An adaptive fractional-order sliding mode controller u designed based on the artificial potential field method is composed of two parts: a trajectory tracking controller and a cooperative obstacle avoidance controller, namely:

u＝uα+uβ u＝u α +u β

其中，u为自适应分数阶滑模控制器，uα为轨迹跟踪控制器，uβ为协同避障控制器；Among them, u is an adaptive fractional sliding mode controller, u α is a trajectory tracking controller, and u β is a cooperative obstacle avoidance controller;

(1)轨迹跟踪控制器设计(1) Design of trajectory tracking controller

第i架无人机的位置跟踪误差向量ei(t)和速度跟踪误差向量

Figure BSA00002738865900000424
为：The position tracking error vector e i (t) and velocity tracking error vector of the i-th UAV
Figure BSA00002738865900000424
for:

Figure BSA00002738865900000425
Figure BSA00002738865900000425

其中pi(t)和

Figure BSA00002738865900000426
分别为无人机实际位置向量和期望位置向量，vi(t)和
Figure BSA00002738865900000427
分别为无人机实际速度向量和期望速度向量，t为时间；where p i (t) and
Figure BSA00002738865900000426
are the actual position vector and expected position vector of the UAV, v i (t) and
Figure BSA00002738865900000427
are the actual velocity vector and the expected velocity vector of the UAV, respectively, and t is time;

无人机编队的分布式耦合位置跟踪误差

Figure BSA00002738865900000428
可以描述为：Distributed Coupled Position Tracking Errors for UAV Formation
Figure BSA00002738865900000428
Can be described as:

Figure BSA00002738865900000429
Figure BSA00002738865900000429

其中λi为领导者的邻接矩阵Λ的元素，aij为邻接矩阵

Figure BSA00002738865900000430
的元素，ej(t)为第j架无人机的位置跟踪误差向量，j为无人机的编号，j＝1，...，n；Where λ i is the element of the leader's adjacency matrix Λ, and a ij is the adjacency matrix
Figure BSA00002738865900000430
element, e j (t) is the position tracking error vector of the jth UAV, j is the serial number of the UAV, j=1,...,n;

上式可以重写为：The above formula can be rewritten as:

Figure BSA0000273886590000051
Figure BSA0000273886590000051

其中，lii和lij都为拉普拉斯矩阵L的元素；Among them, both l ii and l ij are elements of the Laplacian matrix L;

因此，分布式耦合位置跟踪误差向量为：Therefore, the distributed coupling position tracking error vector is:

Figure BSA0000273886590000052
Figure BSA0000273886590000052

其中，

Figure BSA0000273886590000053
in,
Figure BSA0000273886590000053

由上式得分布式耦合速度跟踪误差向量

Figure BSA0000273886590000054
为：The distributed coupling speed tracking error vector is obtained from the above formula
Figure BSA0000273886590000054
for:

Figure BSA0000273886590000055
Figure BSA0000273886590000055

对分布式耦合速度跟踪误差向量

Figure BSA0000273886590000056
设计一个分数阶全局积分滑模：Tracking Error Vectors for Distributed Coupled Velocities
Figure BSA0000273886590000056
Design a fractional-order global integral sliding mode:

Figure BSA0000273886590000057
Figure BSA0000273886590000057

其中，s为分数阶全局积分滑模，D-α表示分布式耦合速度跟踪误差矢量

Figure BSA0000273886590000058
的分数积分，α∈(0，1)为分数阶阶次，c为正常数，h(t)可以表示为：Among them, s is the fractional order global integral sliding mode, and D -α represents the distributed coupling velocity tracking error vector
Figure BSA0000273886590000058
The fractional integral of , α∈(0,1) is a fractional order, c is a normal constant, h(t) can be expressed as:

Figure BSA0000273886590000059
Figure BSA0000273886590000059

这里k为正常数，

Figure BSA00002738865900000510
h(0)为h(t)的初始值，
Figure BSA00002738865900000511
是初始分布式耦合速度跟踪误差向量，
Figure BSA00002738865900000512
是在t＝0时刻的分数阶积分值；Here k is a constant,
Figure BSA00002738865900000510
h(0) is the initial value of h(t),
Figure BSA00002738865900000511
is the initial distributed coupling velocity tracking error vector,
Figure BSA00002738865900000512
is the fractional integral value at time t=0;

对s求导，得：Taking the derivative of s, we get:

Figure BSA00002738865900000513
Figure BSA00002738865900000513

为了有效减小滑模控制中的抖振问题，提高跟踪误差收敛的速率，本文使用的趋近律为：In order to effectively reduce the chattering problem in sliding mode control and improve the rate of tracking error convergence, the reaching law used in this paper is:

Figure BSA00002738865900000514
Figure BSA00002738865900000514

其中η1，η2，

Figure BSA00002738865900000517
都为设计参数且都是正常数，tanh(·)为双曲正切函数；where η 1 , η 2 ,
Figure BSA00002738865900000517
Both are design parameters and are normal constants, and tanh( ) is a hyperbolic tangent function;

根据上面所述，轨迹跟踪控制器设计为：According to the above, the trajectory tracking controller is designed as:

Figure BSA00002738865900000515
Figure BSA00002738865900000515

其中，

Figure BSA00002738865900000516
为小脑模型神经网络所估计出的集总干扰；in,
Figure BSA00002738865900000516
Lumped noise estimated for the neural network of the cerebellar model;

(2)协同避障控制器设计(2) Cooperative obstacle avoidance controller design

与传统的人工势场法不同，本文所提出的控制器通过在障碍物的表面设计一个虚拟智能体β，并使编队中无人机的速度与虚拟智能体β的速度保持一致。此外，在无人机与虚拟智能体β之间设计一个斥力函数，并在控制器中引入避障预测机制和凹凸函数；Different from the traditional artificial potential field method, the controller proposed in this paper designs a virtual agent β on the surface of the obstacle, and keeps the speed of the drones in the formation consistent with the speed of the virtual agent β. In addition, a repulsion function is designed between the UAV and the virtual agent β, and an obstacle avoidance prediction mechanism and a bump function are introduced into the controller;

假设障碍物为一个半径为ro球心为Oβ的球体，因此，虚拟智能体β的状态信息可由下式得出：Assuming that the obstacle is a sphere with a radius r o and a center O β , the state information of the virtual agent β can be obtained by the following formula:

pi，β＝τpi+(I-τ)Oβ，vi，β＝τPvi p i,β =τp i +(I-τ)O β ,v i,β =τPv i

其中，pi，β，vi，β分别为第i架无人机所对应的虚拟智能体β的位置和速度，

Figure BSA0000273886590000061
Figure BSA0000273886590000062
I3为3×3的单位矩阵，||·||为欧几里得范数；Among them, p i, β , v i, β are the position and velocity of the virtual agent β corresponding to the i-th UAV,
Figure BSA0000273886590000061
Figure BSA0000273886590000062
I 3 is a 3×3 identity matrix, and ||·|| is the Euclidean norm;

在编队飞行中，第i架无人机不仅要共享已探测到的障碍物信息，还会接收来自邻近无人机的障碍物信息。通过将得到的障碍物信息进行比较，选取出一对障碍物信息，具体选择原则如下：In formation flight, the i-th UAV not only shares the detected obstacle information, but also receives obstacle information from neighboring UAVs. By comparing the obtained obstacle information, a pair of obstacle information is selected. The specific selection principles are as follows:

1)当多对障碍物信息的速度值不同时，根据最大速度值max(||vi，β||)来选择对应的障碍物信息；1) When the speed values of multiple pairs of obstacle information are different, select the corresponding obstacle information according to the maximum speed value max(||v i, β ||);

2)当多对障碍物信息的速度值相同时，根据最小距离值min(||pi-pi，β||)来选择对应的障碍物信息；2) When the speed values of multiple pairs of obstacle information are the same, select the corresponding obstacle information according to the minimum distance value min(||p i -p i, β ||);

3)如果上述两个条件都不满足，则随机选择一对障碍物信息；3) If the above two conditions are not met, randomly select a pair of obstacle information;

因此，协同避障控制器设计为：Therefore, the cooperative obstacle avoidance controller is designed as:

Figure BSA0000273886590000063
Figure BSA0000273886590000063

其中，

Figure BSA0000273886590000064
表示协同避障控制器，∈β，cp，cv都是正常数，pγ，β和vγ，β是根据上述原则选择出的虚拟智能体β的位置和速度，kβ为避障预测机制，其决定无人机在探测到障碍物时是否需要避障，
Figure BSA0000273886590000065
是一个连续光滑的凹凸函数，其能改变斥力对无人机的影响程度，kβ和
Figure BSA0000273886590000066
可由下式所得：in,
Figure BSA0000273886590000064
Indicates the cooperative obstacle avoidance controller, ∈ β , c p , c v are all normal numbers, p γ, β and v γ, β is the position and speed of the virtual agent β selected according to the above principles, and k β is the obstacle avoidance Prediction mechanism, which decides whether the UAV needs to avoid obstacles when it detects obstacles,
Figure BSA0000273886590000065
is a continuous smooth concave-convex function, which can change the degree of influence of the repulsive force on the UAV, k β and
Figure BSA0000273886590000066
Can be obtained by the following formula:

Figure BSA0000273886590000067
Figure BSA0000273886590000067

Figure BSA0000273886590000068
Figure BSA0000273886590000068

其中，ri为无人机的半径，rd为无人机的探测半径，ro为障碍物的半径，Oβ为障碍物中心，dio为无人机与障碍物之间的距离，dio＝||pi-Oβ||，

Figure BSA0000273886590000069
Figure BSA00002738865900000610
决定无人机受斥力场影响的最大范围，
Figure BSA00002738865900000611
Among them, ri is the radius of the UAV, rd is the detection radius of the UAV, r o is the radius of the obstacle, O β is the center of the obstacle, and d io is the distance between the UAV and the obstacle, d io =||p i -O β ||,
Figure BSA0000273886590000069
Figure BSA00002738865900000610
Determines the maximum range of drones affected by the repulsion field,
Figure BSA00002738865900000611

步骤5、验证无人机编队闭环控制系统的稳定性。Step 5. Verify the stability of the UAV formation closed-loop control system.

根据所述的一种自适应分数阶滑模控制器，需证明在集总干扰影响下的编队闭环控制系统的稳定性。According to the described adaptive fractional-order sliding mode controller, it is necessary to prove the stability of the formation closed-loop control system under the influence of lumped disturbance.

定义李雅普诺夫函数V：Define the Lyapunov function V:

Figure BSA00002738865900000612
Figure BSA00002738865900000612

对V求导得：Deriving with respect to V gives:

Figure BSA00002738865900000613
Figure BSA00002738865900000613

Figure BSA0000273886590000071
Figure BSA0000273886590000071

等效变换后不难得出：After the equivalent transformation, it is not difficult to get:

Figure BSA0000273886590000072
Figure BSA0000273886590000072

Figure BSA0000273886590000073
Figure BSA0000273886590000073

上式可以被描述为：The above formula can be described as:

Figure BSA0000273886590000074
Figure BSA0000273886590000074

其中，χ和b是正常数，可由下式得到：Among them, χ and b are normal numbers, which can be obtained by the following formula:

Figure BSA0000273886590000075
Figure BSA0000273886590000075

Figure BSA0000273886590000076
Figure BSA0000273886590000076

根据以上式子我们可得：According to the above formula we can get:

Figure BSA0000273886590000077
Figure BSA0000273886590000077

由上式得出：根据李雅普诺夫稳定性条件，所有的误差信号都是有界的，因此上述闭环控制系统是渐进稳定的。From the above formula: according to the Lyapunov stability condition, all error signals are bounded, so the above closed-loop control system is asymptotically stable.

与已有技术相比，本发明的有益效果体现在以下方面：Compared with the prior art, the beneficial effects of the present invention are reflected in the following aspects:

(1)根据本发明提出的一种基于人工势场法和小脑模型神经网络的避障无人机分布式编队分数阶滑模控制方法具有跟踪速度快、控制精度高等优点，并保证了编队在避障完成后快速恢复至期望位置；(1) According to the present invention, a distributed formation fractional sliding mode control method based on artificial potential field method and cerebellum model neural network for obstacle avoidance UAVs has the advantages of fast tracking speed and high control precision, and ensures that the formation is Quickly return to the desired position after obstacle avoidance;

(2)根据本发明提出的一种基于人工势场法和小脑模型神经网络避障无人机分布式编队分数阶滑模控制方法考虑了集总干扰的不利影响；(2) a kind of artificial potential field method and cerebellar model neural network obstacle-avoiding unmanned aerial vehicle distributed formation fractional order sliding mode control method based on artificial potential field method proposed by the present invention has considered the adverse effect of lumped interference;

(3)根据本发明提出的一种基于人工势场法和小脑模型神经网络避障无人机分布式编队分数阶滑模控制方法能够解决局部极小值问题并成功实现编队避障。(3) A fractional order sliding mode control method for UAV distributed formation based on artificial potential field method and cerebellum model neural network obstacle avoidance proposed by the present invention can solve the local minimum problem and successfully realize formation obstacle avoidance.

附图说明Description of drawings

为更好地体现本发明所设计方法的优势所在，针对无人机避障问题，选取了一种传统人工势场法的避障方法与本发明所设计的避障无人机分布式编队分数阶滑模控制方法相比较，结果表明本发明所提出的方法具有更好的跟踪性能和避障性能。In order to better reflect the advantages of the method designed in the present invention, for the problem of UAV obstacle avoidance, a traditional artificial potential field method of obstacle avoidance method and the distributed formation score of UAV obstacle avoidance designed in the present invention are selected. Compared with the first-order sliding mode control method, the results show that the method proposed by the present invention has better tracking performance and obstacle avoidance performance.

图1为本发明的无人机编队通信拓扑图；Fig. 1 is the UAV formation communication topological diagram of the present invention;

图2为三维轨迹仿真对比图；Figure 2 is a comparison diagram of three-dimensional trajectory simulation;

图3为x轴的位置跟踪误差仿真对比图；Figure 3 is a comparison diagram of the position tracking error simulation of the x-axis;

图4为y轴的位置跟踪误差仿真对比图；Figure 4 is a comparison diagram of the position tracking error simulation of the y-axis;

图5为z轴的位置跟踪误差仿真对比图。Fig. 5 is a simulation comparison diagram of the position tracking error of the z-axis.

具体实施方式Detailed ways

以下将结合附图及实施方式对本发明进一步详细地解释说明。此处所描述的具体实施例仅用于解释本发明，并不用于限定本发明。The present invention will be explained in further detail below in conjunction with the drawings and embodiments. The specific embodiments described here are only used to explain the present invention, not to limit the present invention.

为了让本研究领域人员可以更好地理解本发明的实施，本发明将运用Matlab2017a软件进行无人机编队跟踪控制与避障的仿真以验证其可靠性。本文给出了由一架虚拟领导者和四架相同无人机组成的编队的仿真结果。无人机编队通信拓扑图的拉普拉斯矩阵L为：In order to allow those in this research field to better understand the implementation of the present invention, the present invention will use Matlab2017a software to carry out the simulation of UAV formation tracking control and obstacle avoidance to verify its reliability. This paper presents the simulation results of a formation consisting of a virtual leader and four identical UAVs. The Laplacian matrix L of the UAV formation communication topology map is:

Figure BSA0000273886590000081
Figure BSA0000273886590000081

在本文中，虚拟领航者的初始速度和位置分别为：vL(0)＝50m/s，

Figure BSA0000273886590000082
飞行路径为[50t，200，400]Tm。无人机最大速度为60m/s，最大加速度为10m/s2，重力加速度g＝9.8m/s2。无人机的初始状态如表1所示，控制器的各设计参数选择为：k＝0.01，η1＝η2＝1，
Figure BSA0000273886590000083
∈β＝1，cv＝6，cp＝5，c＝1，λi＝1，
Figure BSA0000273886590000086
ro＝60，rd＝100，各无人机相对于虚拟领航者的期望位置分别为：
Figure BSA0000273886590000084
为了简化障碍物的形状，我们假设障碍物为半径为rd＝60m中心在Oβ＝[1000，200，400]Tm的球形物体。同时，设集总干扰为：dsi＝0.12[sin0.5t，sin0.5t，sin0.5t]T，仿真步长为0.1s。In this paper, the initial velocity and position of the virtual navigator are: v L (0) = 50m/s,
Figure BSA0000273886590000082
The flight path is [50t, 200, 400] T m. The maximum speed of the UAV is 60m/s, the maximum acceleration is 10m/s 2 , and the acceleration of gravity g=9.8m/s 2 . The initial state of the UAV is shown in Table 1, and the design parameters of the controller are selected as follows: k=0.01, η 1 =η 2 =1,
Figure BSA0000273886590000083
∈ β = 1, c v = 6, c p = 5, c = 1, λ i = 1,
Figure BSA0000273886590000086
r o =60, r d =100, the expected positions of each UAV relative to the virtual leader are:
Figure BSA0000273886590000084
In order to simplify the shape of the obstacle, we assume that the obstacle is a spherical object with a radius r d =60 m and a center at O β =[1000, 200, 400] T m. At the same time, it is assumed that the aggregate interference is: d si =0.12[sin0.5t, sin0.5t, sin0.5t] T , and the simulation step size is 0.1s.

表格1 无人机初始状态Table 1 Initial state of UAV

Figure BSA0000273886590000085
Figure BSA0000273886590000085

结果表明，本文所提出的避障无人机分布式编队分数阶滑模控制方法能够实现在0～5s内对期望轨迹的快速跟踪，同时在避障完成后能够立刻恢复到期望轨迹。相比于传统的人工势场法，本发明所提出的方法不仅考虑了集总干扰的不利影响，而且能够解决局部极小值问题并实现避障。通过上述仿真结果对比，验证了本发明提出的避障无人机分布式编队分数阶滑模控制方法的有效性和可行性，符合预期。The results show that the fractional-order sliding mode control method of the distributed formation of UAVs for obstacle avoidance proposed in this paper can quickly track the desired trajectory within 0-5s, and at the same time return to the desired trajectory immediately after the obstacle avoidance is completed. Compared with the traditional artificial potential field method, the method proposed by the present invention not only considers the adverse effect of lumped interference, but also can solve the problem of local minimum value and realize obstacle avoidance. Through the comparison of the above simulation results, the validity and feasibility of the fractional-order sliding mode control method for the distributed formation of obstacle-avoiding UAVs proposed by the present invention is verified, which meets expectations.

最后说明，本发明未详细解释该领域技术人员公认常识，以上所述仅为本发明的一个具体实施例，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。Finally, the present invention does not explain in detail the common knowledge recognized by those skilled in the art. The above description is only a specific embodiment of the present invention, and is not intended to limit the present invention. Any modifications made within the spirit and principles of the present invention , equivalent replacements, improvements, etc., should all be included within the protection scope of the present invention.

Claims (3)

1. A distributed formation fractional order sliding mode control method of an obstacle avoidance unmanned aerial vehicle based on an artificial potential field method and a cerebellum model neural network comprises the following steps:
step 1, establishing an ith unmanned aerial vehicle dynamics model:
Figure FSA0000273886580000011
wherein i is the number of the unmanned aerial vehicles in the formation, i =1, \ 8230, n, n is the number of the unmanned aerial vehicles in the formation, V i ，ψ i ，
Figure FSA0000273886580000012
Respectively representing the airspeed, pitch angle, course angle, x of the unmanned aerial vehicle i ，y i And z i Three-dimensional coordinates for unmanned aerial vehicles, m i Is the fuselage mass, g is the gravitational acceleration, and the control inputs to the system are
Figure FSA0000273886580000013
θ i Showing the roll angle, T i Is hairThrust of motive machine u xi ，u yi ，u zi Control inputs in the X-axis, Y-axis, Z-axis directions, n i Is the dynamic load coefficient, D i Is a resistance force;
step 2, converting the unmanned aerial vehicle dynamic model in the step 1 into a state space equation, and simultaneously considering modeling of lumped interference:
definition of p i ＝[x i ，y i ，z i ] T And
Figure FSA0000273886580000014
for the position vector and velocity vector of the ith drone, respectively, the nonlinear dynamical model considering lumped interference can be expressed as:
Figure FSA0000273886580000015
wherein d is si For lumped interference, G and R i Obtained by the following formula:
G＝[0 0 -g] T
Figure FSA0000273886580000016
and 3, estimating the lumped interference by using the cerebellum model neural network according to the step 2, wherein the specific steps are as follows:
the relation between the input and the output of the cerebellum model neural network is as follows:
Figure FSA0000273886580000017
wherein y is the output vector, I is the input vector, W is the connection weight vector of the receiving domain, phi is the multi-dimensional receiving domain basis function vector,
Figure FSA0000273886580000018
and σ are each a Gaussian functionA value and a variance;
cerebellum model neural network on-line approximation lumped interference d si The expression of (c) is:
Figure FSA0000273886580000019
where ε is the approximation error, W * ，φ * ，
Figure FSA00002738865800000110
σ * Are respectively W, phi,
Figure FSA00002738865800000111
optimum parameter vector of sigma, W *T Is W * Transpose of (d) si * Is d si The optimal vector of (2);
the cerebellum model neural network estimation error can be expressed as:
Figure FSA00002738865800000112
wherein,
Figure FSA0000273886580000021
are respectively W, phi, d si An estimated value of (d);
and (3) converting the nonlinear function into a partial linear form by using a Taylor expansion linearization technique, namely:
Figure FSA0000273886580000022
wherein,
Figure FSA0000273886580000023
and
Figure FSA0000273886580000024
are respectively as
Figure FSA0000273886580000025
And σ, H is a higher order term, and has:
Figure FSA0000273886580000026
Figure FSA0000273886580000027
and is
Figure FSA0000273886580000028
And
Figure FSA0000273886580000029
is defined as:
Figure FSA00002738865800000210
Figure FSA00002738865800000211
according to the formula:
Figure FSA00002738865800000212
wherein the uncertainty term
Figure FSA00002738865800000213
Representing an approximation error term and assuming that the approximation error term is bounded, namely | | | delta | is less than or equal to delta, delta is a normal number, and | | | delta | is an Euclidean norm of delta;
the cerebellum model neural network self-adaptation law is obtained by a Lyapunov stability analysis method as follows:
Figure FSA00002738865800000214
Figure FSA00002738865800000215
Figure FSA00002738865800000216
wherein λ is max Is a matrix
Figure FSA00002738865800000217
L is the laplacian matrix, a is the adjacency matrix of the leader,
Figure FSA00002738865800000218
is the product of Crohn's disease, I 3 Is a 3 x 3 identity matrix, s is a fractional order global integral sliding mode as designed herein,
Figure FSA00002738865800000219
η σ ，ζ 1 ，ζ 2 and ζ 3 Are all normal numbers, W 0 ，
Figure FSA00002738865800000220
σ 0 Are each W * ，
Figure FSA00002738865800000221
σ * The initial estimate of (a);
step 4, designing a self-adaptive fractional order sliding mode controller based on an artificial potential field method according to the step 2;
and 5, verifying the stability of the unmanned aerial vehicle formation closed-loop control system.
2. The obstacle avoidance unmanned aerial vehicle distributed formation fractional order sliding mode control method according to claim 1, characterized in that the step 4 of designing an adaptive fractional order sliding mode controller based on an artificial potential field method comprises the following steps:
an adaptive fractional order sliding mode controller designed based on an artificial potential field method is composed of a track tracking controller and a collaborative obstacle avoidance controller, namely:
u＝u α +u β
wherein u is an adaptive fractional order sliding mode controller α For trajectory tracking controllers u β A cooperative obstacle avoidance controller;
(1) Trajectory tracking controller design
Position tracking error vector e of ith unmanned aerial vehicle i (t) and velocity tracking error vector
Figure FSA0000273886580000031
Comprises the following steps:
Figure FSA0000273886580000032
wherein p is i (t) and
Figure FSA0000273886580000033
respectively actual position vector and expected position vector of the unmanned plane, v i (t) and
Figure FSA0000273886580000034
respectively an actual speed vector and an expected speed vector of the unmanned aerial vehicle, and t is time;
distributed coupled position tracking error of unmanned aerial vehicle formation
Figure FSA0000273886580000035
Can be described as:
Figure FSA0000273886580000036
wherein λ i Elements of the adjacency matrix Λ, a, being the leader ij To follow up a neighbor matrix
Figure FSA0000273886580000037
Element of (e) j (t) is a position tracking error vector of a jth unmanned aerial vehicle, j is the number of the unmanned aerial vehicle, and j =1, \ 8230;, n;
the above formula can be rewritten as:
Figure FSA0000273886580000038
wherein l ii And l ij Are all elements of the laplace matrix L;
thus, the distributed coupled position tracking error vector may be described as:
Figure FSA0000273886580000039
wherein,
Figure FSA00002738865800000310
distributed coupled velocity tracking error vector from above
Figure FSA00002738865800000311
Comprises the following steps:
Figure FSA00002738865800000312
error vector for distributed coupled velocity tracking
Figure FSA00002738865800000313
Designing a fractional order global integral sliding mode:
Figure FSA00002738865800000314
wherein s is a fractional order global integral sliding mode, D -α Representing distributed coupled velocity tracking error vectors
Figure FSA00002738865800000315
Is given by a fractional integral of (a), α ∈ (0, 1) is the fractional order, c is a positive number, and h (t) can be expressed as:
Figure FSA00002738865800000316
where k is a normal number, where k is,
Figure FSA00002738865800000317
h (0) is the initial value of h (t),
Figure FSA00002738865800000318
is the initial distributed coupling velocity tracking error vector,
Figure FSA00002738865800000319
is a fractional order integral value at time t =0;
in order to effectively reduce the buffeting problem in sliding mode control and improve the rate of tracking error convergence, the approach law used herein is as follows:
Figure FSA00002738865800000320
wherein eta 1 ，η 2 ，
Figure FSA00002738865800000321
Are all normal numbers, and tanh (·) is a hyperbolic tangent function;
according to the above, the trajectory tracking controller is designed to:
Figure FSA0000273886580000041
wherein,
Figure FSA0000273886580000042
lumped interference estimated for a cerebellar model neural network;
(2) Design of cooperative obstacle avoidance controller
Different from the traditional artificial potential field method, the controller provided by the invention designs a virtual intelligent body beta on the surface of the barrier, keeps the speed of the unmanned aerial vehicle in formation consistent with that of the virtual intelligent body beta, designs a repulsion function between the unmanned aerial vehicle and the virtual intelligent body beta, and introduces an obstacle avoidance prediction mechanism and a concave-convex function into the controller;
assume that the obstacle has a radius r o The center of the sphere is O β The state information of the virtual agent β can therefore be derived from the following equation:
p i，β ＝τp i +(I 3 -τ)O β ，v i，β ＝τPv i
wherein p is i，β ，v i，β Respectively the position and the speed of the virtual agent beta corresponding to the ith unmanned aerial vehicle,
Figure FSA0000273886580000043
Figure FSA0000273886580000044
I 3 is a 3 × 3 identity matrix, and | | · | | is an euclidean norm;
in formation flight, the ith unmanned aerial vehicle not only needs to share detected obstacle information, but also receives obstacle information from adjacent unmanned aerial vehicles, and a pair of obstacle information is selected by comparing the obtained obstacle information, wherein the specific selection principle is as follows:
1) When the speed values of a plurality of pairs of obstacle information are different, according to the maximum speed value max (| | v) i，β | |) to select corresponding obstacle information;
2) When the speed values of a plurality of pairs of obstacle information are the same, according to the minimum distance value min (| | p) i -p i，β | |) to select corresponding obstacle information;
3) If the two conditions are not met, randomly selecting a pair of obstacle information;
therefore, the cooperative obstacle avoidance controller is designed as follows:
Figure FSA0000273886580000045
wherein i is the number of the unmanned aerial vehicle,
Figure FSA0000273886580000046
a cooperative obstacle avoidance controller is shown,
Figure FSA00002738865800000411
c p ，c v are all normal numbers, p γ，β And v γ，β Is the position and velocity, k, of the virtual agent beta selected according to the above principles β For an obstacle avoidance prediction mechanism, which determines whether the unmanned aerial vehicle needs to avoid an obstacle when detecting an obstacle, ρ (z) is a continuous smooth concave-convex function which can change the influence degree of repulsion on the unmanned aerial vehicle, k β And ρ (z) can be obtained by the following formula:
Figure FSA0000273886580000047
Figure FSA0000273886580000048
wherein r is i Radius of unmanned plane, r d Radius of detection for unmanned aerial vehicle, r o Radius of obstacle, O β Is the center of the obstacle, d io Is the distance between the drone and the obstacle, d io ＝||p i -O β ||，
Figure FSA0000273886580000049
Determining the maximum range of the unmanned aerial vehicle influenced by the repulsive force field,
Figure FSA00002738865800000410
3. the obstacle avoidance unmanned aerial vehicle distributed formation fractional order sliding mode control method according to claim 1, wherein the process of verifying the stability of the unmanned aerial vehicle formation closed-loop control system in step 5 is as follows:
defining the Lyapunov function V as:
Figure FSA0000273886580000051
deriving V as:
Figure FSA0000273886580000052
after equivalent transformation, it is easy to obtain:
Figure FSA0000273886580000053
Figure FSA0000273886580000054
the above formula can be described as:
Figure FSA0000273886580000055
wherein χ and b are normal, and can be obtained by the following formula:
Figure FSA0000273886580000056
Figure FSA0000273886580000057
the above inequality equation can be rewritten as:
Figure FSA0000273886580000058
the following is obtained from the above equation: according to the Lyapunov stability condition, all error signals are bounded, and therefore the closed loop control system is asymptotically stable.
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