Obstacle avoidance unmanned aerial vehicle distributed formation fractional order sliding mode control method

Abstract

The application discloses an obstacle avoidance unmanned aerial vehicle distributed formation fractional order sliding mode control method based on an artificial potential field method and a cerebellar model neural network, which is used for unmanned aerial vehicle formation obstacle avoidance control and processing of influences of external interference and internal parameter uncertainty. The cerebellar model neural network is introduced to approximately estimate and compensate adverse influences of lumped interference, and an adaptive fractional order sliding mode controller is designed based on the artificial potential field method. The application realizes stability and good obstacle avoidance performance of a closed loop tracking control system of the unmanned aerial vehicle formation, and simulation examples prove that the method has certain effectiveness and good performance.

Description

Technical Field

[0001] This invention relates to the field of aviation unmanned aerial vehicle (UAV) control, and specifically to a problem of distributed formation fractional sliding mode control of obstacle avoidance UAVs considering the effects of lumped interference. Background Technology

[0002] In recent years, with the increasing maturity of unmanned aerial vehicles (UAVs), single UAVs have gradually become insufficient to meet the needs of some complex tasks, prompting researchers to study the cooperative control of multi-UAV swarms. Compared to single UAVs, UAV swarms offer significant advantages in military and civilian fields such as loading and transportation, wildfire monitoring, disaster relief, battlefield reconnaissance, and strike operations. However, due to the influence of complex factors such as external interference, obstacles, and uncertainties in internal parameters, the cooperative control of UAV swarms has become more complex and challenging. Therefore, the problem of rapid tracking control and obstacle avoidance of UAV swarms under conditions of external interference, internal parameter uncertainties, and obstacles has attracted widespread attention from scholars.

[0003] To address the obstacle avoidance problem in drone formation, numerous scholars both domestically and internationally have proposed various algorithms. Patent CN112180954A invented a drone obstacle avoidance method based on an artificial potential field. Its main contribution is the introduction of an additional lateral obstacle avoidance control force, thus solving the adverse effects of local minima on drone obstacle avoidance. However, this method cannot ensure that the drone immediately returns to the desired position after avoiding obstacles. Patent CN111290429A invented a drone formation and obstacle avoidance control method based on a consensus algorithm and an artificial potential field. By introducing auxiliary traction acceleration information perpendicular to the obstacle's movement direction, the influence of local minima can be eliminated. However, during obstacle avoidance, the position tracking error and velocity tracking error of drones based on this method fluctuate significantly, affecting the stability of the formation. Furthermore, neither of the above two methods considers the impact of lumped disturbances (external disturbances and internal parameter uncertainties) on the formation control system.

[0004] Numerous scholars have conducted extensive research on the impact of external disturbances and parameter uncertainties on the control performance of nonlinear systems. Research results show that neural networks can effectively estimate and compensate for these factors. Furthermore, an improved artificial potential field method can solve local minima and achieve cooperative obstacle avoidance in formation. In addition, a designed fractional-order sliding mode controller ensures the stability and global robustness of the closed-loop formation control system and addresses the problem that traditional obstacle avoidance algorithms cannot immediately return to the desired position after avoiding obstacles. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the present invention proposes a distributed formation fractional sliding mode control method for obstacle avoidance UAVs, which mainly consists of the following steps:

[0006] Step 1: Establish the dynamic model of the i-th UAV as shown below:

[0007]

[0008] Where i is the number of the drone in the formation, i = 1, ..., n, and n is the number of drones in the formation, V i ,ψ i , These represent the airspeed, pitch angle, and yaw angle of the UAV, respectively. i y i and z i Let m be the three-dimensional coordinates of the UAV. i Where g is the fuselage mass, g is the acceleration due to gravity, and the system control input is... θ i T represents the roll angle. i It is engine thrust, u xi u yi u zi These are the control inputs for the X, Y, and Z axes, respectively, n i It is the dynamic load factor, D i It is resistance;

[0009] Step 2: Transform the UAV dynamics model from Step 1 into a state-space equation. The nonlinear model considering lumped disturbances can be described as follows:

[0010]

[0011] Where, p i =[x i ,y i ,z i ] T For position vectors, Let d be the velocity vector. si For lumped interference, G and R i It can be obtained from the following formula:

[0012] G = [0 0 -g] T

[0013]

[0014] Step 3: Utilize a cerebellum model neural network to achieve online estimation of lumped disturbances. The specific process is as follows:

[0015] The structure of the cerebellar model neural network includes an input space, an associative memory space, a receptive domain space, a weighted memory space, and an output space.

[0016] The details are as follows:

[0017] (1) Input space: For input I = [I1, I2, ..., I q ] T ∈R q I is a continuous input space with q dimensions;

[0018] (2) Associative memory space: Several different elements are piled up into a block, and each block is subjected to a receptive domain basis function. Here, the Gaussian function is used as the basis function, which can be expressed as:

[0019]

[0020] in, For the j-th input I j The Gaussian function corresponding to the k-th block, and σ jk These are the mean and variance of the corresponding Gaussian function, respectively, and M is the number of blocks;

[0021] (3) Receiving domain space: In this space, the multidimensional receiving domain basis functions are defined as:

[0022]

[0023] Where L represents the Lth receiver domain basis function, and N is the number of receiver domain basis functions. A multidimensional receiver domain basis function is represented by a vector as follows:

[0024]

[0025] in, And σ can be represented by the following vectors:

[0026]

[0027] (4) Weight memory space: The N components of the weight memory space for each position in the receptive domain space to a specific adjustable value can be represented as:

[0028] W = [w1, ..., w L ,…,w N ] T

[0029] Among them, w L This represents the connection weight of the Lth receiver domain basis function;

[0030] (5) Output Space: The output of the entire cerebellum model neural network can be represented as:

[0031]

[0032] The output of the cerebellar model neural network can be represented by a vector as follows:

[0033]

[0034] Cerebellar model neural network online approximation of lumped perturbation d si The expression is:

[0035]

[0036] Where ε is the approximation error, W *T and φ * Let W and φ be the optimal parameter vectors, respectively. and σ * They are respectively The optimal parameter vector of σ, d si * is d si The optimal vector;

[0037] The estimation error of the cerebellar model neural network can be expressed as:

[0038]

[0039] in, and These are the estimated values ​​of W and φ, respectively;

[0040] To achieve a good estimate of lumped disturbances, a Taylor expansion linearization technique is used to transform the nonlinear function into a partially linear form, i.e.:

[0041]

[0042] in, and They are respectively And the estimated values ​​of σ, where H is a higher-order term, and we have:

[0043]

[0044] and and Defined as:

[0045]

[0046] Based on the above formula, we get:

[0047]

[0048] Among them, the uncertain terms Let ||Δ|| represent the approximation error term, and assume that it is bounded, i.e., ||Δ||≤δ, where δ is a positive constant and ||Δ|| is the Euclidean norm of Δ.

[0049] Using Lyapunov stability analysis, the adaptive law of the cerebellar model neural network is derived as follows:

[0050]

[0051] Where, λ ma For matrix The largest eigenvalue, L is the Laplace matrix, and Λ is the adjacency matrix of the leader. Let I3 be the Kronecker product, I3 be the 3×3 identity matrix, and s be the fractional-order global integral sliding mode designed in this paper. η σ ζ1, ζ2, and ζ3 are all positive constants, W0, σ0 represents W * , σ * The initial estimate;

[0052] Step 4: Design an adaptive fractional sliding mode controller based on the artificial potential field method;

[0053] First, it needs to be explained that the implementation of the control system of this invention requires the UAV formation to meet the designed formation configuration during flight. Therefore, the desired position of the i-th UAV should satisfy:

[0054]

[0055] in Indicates the virtual leader's position. This indicates the desired position of each drone relative to the virtual leader;

[0056] Graph theory is an important component of formation flying, and this invention employs undirected graphs. in Describes the set of nodes in graph G. Represents an edge set. Let represent the adjacency matrix; in an undirected graph, we can obtain: and a ij =a ji When the i-th drone can receive information from the j-th drone, (j,i)∈ε, and a ij =1, otherwise, a ij =0; Definition Let be a degree matrix, where Therefore, the Laplacian matrix is A communication topology with one leader and 0 or n followers can be represented as follows: in Represents the node set; the adjacency matrix of the leader is Λ=diag{λ1,…,λ n If the i-th follower can receive information from the leader, then λ i >0, otherwise, λ i =0;

[0057] An adaptive fractional sliding mode controller u based on the artificial potential field method consists of two parts: a trajectory tracking controller and a cooperative obstacle avoidance controller.

[0058] u = u α +u β

[0059] Where u is an adaptive fractional-order sliding mode controller, u α For trajectory tracking controller, u β For collaborative obstacle avoidance controllers;

[0060] (1) Track tracking controller design

[0061] The position tracking error vector of the i-th UAV is e i (t) and velocity tracking error vector for:

[0062]

[0063] Where p i (t) and These are the actual position vector and the expected position vector of the UAV, respectively. i (t) and These are the actual velocity vector and the expected velocity vector of the UAV, respectively, where t is time.

[0064] Distributed Coupled Position Tracking Error of UAV Formation It can be described as:

[0065]

[0066] Where λ i For each element of the leader's adjacency matrix Λ, a ij Adjacency matrix The element, e j (t) represents the position tracking error vector of the j-th UAV, where j is the UAV number, j = 1, ..., n;

[0067] The above formula can be rewritten as:

[0068]

[0069] Among them, l ii and l ijAll are elements of the Laplace matrix L;

[0070] Therefore, the distributed coupled position tracking error vector is:

[0071]

[0072] in,

[0073] The distributed coupled velocity tracking error vector is obtained from the above equation. for:

[0074]

[0075] Distributed coupled velocity tracking error vector Design a fractional-order global integral sliding mode:

[0076]

[0077] Where s is the fractional-order global integral sliding mode, and D -α Represents the distributed coupled velocity tracking error vector The fractional integral, where α∈(0,1) is the fractional order and c is a positive constant, h(t) can be expressed as:

[0078]

[0079] Here, k is a positive constant. h(0) is the initial value of h(t). It is the initial distributed coupled velocity tracking error vector. It is the fractional integral value at t=0;

[0080] Differentiating with respect to s, we get:

[0081]

[0082] To effectively reduce chattering in sliding mode control and improve the convergence rate of tracking error, the following convergence law is used in this paper:

[0083]

[0084] Where η1, η2, All are design parameters and are positive constants; tanh(·) is the hyperbolic tangent function.

[0085] Based on the above, the trajectory tracking controller is designed as follows:

[0086]

[0087] in, The lumped interference estimated by the neural network of the cerebellar model;

[0088] (2) Collaborative obstacle avoidance controller design

[0089] Unlike traditional artificial potential field methods, the controller proposed in this paper designs a virtual agent β on the surface of the obstacle and ensures that the speed of the UAVs in the formation is consistent with the speed of the virtual agent β. Furthermore, a repulsive force function is designed between the UAVs and the virtual agent β, and an obstacle avoidance prediction mechanism and concavity / convexity functions are introduced into the controller.

[0090] Assume the obstacle is a circle with radius r. o The center of the ball is O β Since the object is a sphere, the state information of the virtual agent β can be derived from the following formula:

[0091] p i,β =τp i +(I-τ)O β ,v i,β =τPv i

[0092] Where, p i,β v i,β Let be the position and velocity of the virtual agent β corresponding to the i-th drone, respectively. I3 is a 3×3 identity matrix, and ||·|| is the Euclidean norm;

[0093] During formation flying, the i-th UAV not only shares the detected obstacle information but also receives obstacle information from neighboring UAVs. By comparing the received obstacle information, a pair of obstacle information is selected, with the specific selection principles as follows:

[0094] 1) When multiple pairs of obstacle information have different velocity values, the maximum velocity value max(||v) is used. i,β Use ||) to select the corresponding obstacle information;

[0095] 2) When multiple pairs of obstacle information have the same velocity value, the minimum distance value min(||p) is used. i -p i,β Use ||) to select the corresponding obstacle information;

[0096] 3) If neither of the above two conditions is met, then a pair of obstacle information is randomly selected;

[0097] Therefore, the cooperative obstacle avoidance controller is designed as follows:

[0098]

[0099] in, Represents a cooperative obstacle avoidance controller, ∈ β c p c v All are positive numbers, p γ,β and v γ,β The position and velocity of the virtual agent β are selected based on the above principles, k β This is an obstacle avoidance prediction mechanism that determines whether the drone needs to avoid obstacles when it detects them. ρ(z) is a continuous, smooth, concave-convex function that can change the degree of influence of the repulsive force on the drone. β And ρ(z) can be obtained from the following formula:

[0100]

[0101] Where, r i r is the radius of the drone. d r is the detection radius of the UAV. o O is the radius of the obstacle. β d is the center of the obstacle. io d represents the distance between the drone and the obstacle. io =||p i -O β ||, Determines the maximum range of the repulsive force field affecting the drone.

[0102] Step 5: Verify the stability of the drone formation closed-loop control system.

[0103] Based on the aforementioned adaptive fractional sliding mode controller, it is necessary to prove the stability of the formation closed-loop control system under the influence of lumped disturbances.

[0104] Define the Lyapunov function V:

[0105]

[0106] Differentiating with respect to V, we get:

[0107]

[0108]

[0109] After equivalent transformation, it is not difficult to conclude that:

[0110]

[0111] The above formula can be described as:

[0112]

[0113] Where χ and b are positive constants, they can be obtained from the following formula:

[0114]

[0115] Based on the above formula, we can obtain:

[0116]

[0117] From the above equation, we can conclude that, according to the Lyapunov stability condition, all error signals are bounded, therefore the above closed-loop control system is asymptotically stable.

[0118] Compared with existing technologies, the beneficial effects of the present invention are reflected in the following aspects:

[0119] (1) The obstacle avoidance UAV distributed formation fractional sliding mode control method based on artificial potential field method and cerebellum model neural network proposed in this invention has the advantages of fast tracking speed and high control accuracy, and ensures that the formation can quickly recover to the desired position after obstacle avoidance.

[0120] (2) The distributed formation fractional sliding mode control method for obstacle avoidance UAVs based on artificial potential field method and cerebellum model neural network proposed in this invention takes into account the adverse effects of lumped disturbance;

[0121] (3) The distributed formation fractional sliding mode control method for obstacle avoidance UAV based on artificial potential field method and cerebellum model neural network proposed in this invention can solve the local minima problem and successfully achieve formation obstacle avoidance. Attached Figure Description

[0122] To better demonstrate the advantages of the method designed in this invention, a traditional artificial potential field method for obstacle avoidance was compared with the obstacle avoidance UAV distributed formation fractional sliding mode control method designed in this invention. The results show that the method proposed in this invention has better tracking and obstacle avoidance performance.

[0123] Figure 1 This is a diagram of the UAV formation communication topology of the present invention;

[0124] Figure 2 A comparison diagram of three-dimensional trajectory simulation;

[0125] Figure 3 A simulation comparison chart of x-axis position tracking error;

[0126] Figure 4 A simulation comparison chart of the position tracking error along the y-axis;

[0127] Figure 5 The simulation comparison chart shows the position tracking error along the z-axis. Detailed Implementation

[0128] The present invention will be further explained in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0129] To enable those skilled in the art to better understand the implementation of this invention, please refer to [link / reference needed]. Figure 1-5 This invention utilizes Matlab 2017a software to simulate UAV formation tracking control and obstacle avoidance to verify its reliability. This paper presents simulation results of a formation consisting of a virtual leader and four identical UAVs. The Laplace matrix L of the UAV formation communication topology is:

[0130]

[0131] In this paper, the initial velocity and position of the virtual navigator are: v L (0) = 50 m / s, The flight path is [50t, 200, 400]. T The drone's maximum speed is 60 m / s, and its maximum acceleration is 10 m / s². 2 The acceleration due to gravity is g = 9.8 m / s². 2 The initial state of the UAV is shown in Table 1. The design parameters of the controller are selected as follows: k = 0.01, η1 = η2 = 1. ∈ β =1,c v =6,c p =5, c=1, λ i =1, r o =60, r d =100, and the expected positions of each drone relative to the virtual navigator are as follows: To simplify the shape of the obstacle, we assume that the obstacle has a radius of r. d =60m center at O β =[1000,200,400] T A spherical object of size m. Meanwhile, let the lumped interference be: d si =0.12[sin0.5t,sin0.5t,sin0.5t] T The simulation step size is 0.1s.

[0132] Table 1 Initial State of the UAV

[0133]

[0134] The results show that the proposed obstacle-avoidance UAV distributed formation fractional-order sliding mode control method can achieve rapid tracking of the desired trajectory within 0–5 seconds, and can immediately recover to the desired trajectory after obstacle avoidance. Compared with the traditional artificial potential field method, the method proposed in this invention not only considers the adverse effects of lumped disturbances, but also solves the local minima problem and achieves obstacle avoidance. The simulation results verify the effectiveness and feasibility of the proposed obstacle-avoidance UAV distributed formation fractional-order sliding mode control method, meeting expectations.

[0135] Finally, it should be noted that this 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 this invention and is not intended to limit this invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A fractional-order sliding mode control method for distributed formation of obstacle-avoiding UAVs based on an improved artificial potential field method and a cerebellum model neural network, comprising the following steps: Step 1: Establish the dynamic model of the i-th UAV: Where i is the number of the drone in the formation, i = 1, ..., n, and n is the number of drones in the formation, V i , ψ i , These represent the airspeed, pitch angle, and yaw angle of the UAV, respectively. i y i and z i Let m be the three-dimensional coordinates of the UAV. i Where g is the fuselage mass, g is the acceleration due to gravity, and the system control input is... θ i T represents the roll angle. i It is engine thrust, u xi u yi u zi These are the control inputs for the X, Y, and Z axes, respectively, n i It is the dynamic load factor, D i It is resistance; Step 2: Transform the UAV dynamics model from Step 1 into state-space equations, while also considering the modeling of lumped disturbances: Define p i =[x i ,y i ,z i ] T and Let be the position vector and velocity vector of the i-th UAV, respectively. Then, the nonlinear dynamic model considering lumped disturbances can be expressed as: Where d si For lumped interference, G i and R i Obtained from the following formula: G i =[0 0-g] T Step 3: Based on Step 2, use the cerebellum model neural network to estimate the lumped interference, as follows: The relationship between the input and output of the cerebellar model neural network is as follows: Where y is the output vector, I is the input vector, W is the connection weight vector of the receiving domain, and φ is the basis function vector of the multidimensional receiving domain. σ and σ' are the mean and variance of the Gaussian function, respectively; Cerebellar model neural network online approximation of lumped perturbation d si The expression is: Where ε is the approximation error, W * φ * , σ * W and φ are respectively. The optimal parameter vector of σ, W *T For W * transpose, d si * For d si The optimal vector; The estimation error of the cerebellar model neural network can be expressed as: in, W, φ, and d are respectively. si The estimated value; The Taylor expansion linearization technique is used to transform the nonlinear function into a partially linear form, namely: in, and They are respectively And the estimated values ​​of σ, where H is a higher-order term, and we have: and and Defined as: Based on the above formula, we get: Among them, the uncertain terms Let ||Δ|| denote the approximation error term, and assume that it is bounded, i.e., ||Δ||≤δ, where δ is a positive constant and ||Δ|| is the Euclidean norm of Δ. Using Lyapunov stability analysis, the adaptive law of the cerebellar model neural network is derived as follows: Where, λ max For matrix The largest eigenvalue, L is the Laplace matrix, and Λ is the adjacency matrix of the leader. Let I3 be the Kronecker product, I3 be the 3×3 identity matrix, and s be the fractional global integral sliding mode. η σ ζ1, ζ2, and ζ3 are all positive constants, W0, σ0 represents W * , σ * The initial estimate; Step 4: Based on Step 2, an adaptive fractional sliding mode controller is designed using the improved artificial potential field method. An adaptive fractional sliding mode controller based on an improved artificial potential field method consists of two parts: a trajectory tracking controller and a cooperative obstacle avoidance controller. in=in α +in β Where u is the adaptive fractional-order sliding mode controller for the entire formation, u α For the trajectory tracking controller of the entire formation, u β It serves as a collaborative obstacle avoidance controller for the entire formation; (1) Track tracking controller design The position tracking error vector of the i-th UAV is e i (t) and velocity tracking error vector for: Where p i (t) and These are the actual position vector and the expected position vector of the UAV, respectively. i (t) and These are the actual velocity vector and the expected velocity vector of the UAV, respectively, where t is time. Distributed Coupled Position Tracking Error of UAV Formation It can be described as: Where λ i For each element of the leader's adjacency matrix Λ, a ij For the adjacency matrix of followers The element, e j (t) represents the position tracking error vector of the j-th UAV, where j is the UAV number, j = 1, ..., n; The above formula can be rewritten as: Among them, l ii and l ij All are elements of the Laplace matrix L; Therefore, the distributed coupled position tracking error vector can be described as: in, The distributed coupled velocity tracking error vector is obtained from the above equation. for: Distributed coupled velocity tracking error vector Design a fractional-order global integral sliding mode: Where s is the fractional-order global integral sliding mode, and D -α Represents the distributed coupled speed tracking error vector Fractional integrals, The derivative is α∈(0,1) represents the fractional order, c is a positive constant, and h(t) can be expressed as: Here, k is a positive constant. h(0) is the initial value of h(t). It is the initial distributed coupled velocity tracking error vector. It is the fractional integral value at t=0; To effectively reduce chattering in sliding mode control and improve the convergence rate of tracking error, the following convergence law is used: Where η1, η2, All are positive constants, and tanh(·) is the hyperbolic tangent function; The trajectory tracking controller is designed as follows: (2) Collaborative obstacle avoidance controller design Collaborative obstacle avoidance involves designing a virtual agent β on the surface of the obstacle and ensuring that the speed of the drones in the formation is consistent with the speed of the virtual agent β. In addition, a repulsive force function is designed between the drones and the virtual agent β, and an obstacle avoidance prediction mechanism and concave-convex functions are introduced into the controller. Assume the obstacle is a circle with radius r. o The center of the ball is O β Since the object is a sphere, the state information of the virtual agent β can be derived from the following formula: p i,β =τp i +(I3-τ)O β ,v i,β =τPv i Where, p i,β v i,β Let be the position and velocity of the virtual agent β corresponding to the i-th drone, respectively. I3 is a 3×3 identity matrix, and ||·|| is the Euclidean norm; During 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 principle is as follows: 1) When multiple pairs of obstacle information have different velocity values, the maximum velocity value max(||v) is used. i,β Use ||) to select the corresponding obstacle information; 2) When multiple pairs of obstacle information have the same velocity value, the minimum distance value min(||p) is used. i -p i,β Use ||) to select the corresponding obstacle information; 3) If neither of the above two conditions is met, then randomly select a pair of obstacle information; Therefore, the cooperative obstacle avoidance controller is designed as follows: Where i is the drone's number, Represents a cooperative obstacle avoidance controller, ∈ β c p c v All are positive numbers, p γ,β and v γ,β The position and velocity of the virtual agent β are selected based on the above principles, k β This is an obstacle avoidance prediction mechanism that determines whether the drone needs to avoid obstacles when it detects them. ρ(z) is a continuous, smooth, concave-convex function that can change the degree of influence of the repulsive force on the drone. β And ρ(z) can be obtained from the following equation: Where, r i r is the radius of the drone. d r is the detection radius of the UAV. o O is the radius of the obstacle. β d is the center of the obstacle. io d represents the distance between the drone and the obstacle. io =||p i -O β ||, Determines the maximum range of the repulsive force field affecting the drone. Step 5: Verify the stability of the drone formation closed-loop control system.

2. The obstacle avoidance UAV distributed formation fractional-order sliding mode control method according to claim 1, characterized in that, The process of verifying the stability of the UAV formation closed-loop control system in step 5 is as follows: Define the Lyapunov function V as: Differentiating with respect to V, we get: After equivalent transformation, it is not difficult to conclude that: The above formula can be described as: Where χ and b are positive constants, they can be obtained from the following formula: The above inequality equation can be rewritten as: From the above equation, we can conclude that, according to the Lyapunov stability condition, all error signals are bounded, therefore the above closed-loop control system is asymptotically stable.

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