Multi-unmanned aerial vehicle safety distributed tracking control method for online planning driving

Abstract

The invention discloses a multi-unmanned aerial vehicle safety distributed tracking control method based on online planning driving, and the method comprises the steps: firstly, enabling a leader unmanned aerial vehicle to obtain environment information in real time through a high-precision sensor, generating an optimal flight path for obstacle avoidance based on an Ego-Planner architecture, and dynamically adjusting a path according to the change of an external environment; secondly, designing a state estimator based on online learning for the following unmanned aerial vehicle, and generating an estimation item for high-order information of a leader; and then designing a distributed tracking controller based on feedback control and feedforward control, so that the following unmanned aerial vehicle can accurately track the trajectory of the leader unmanned aerial vehicle, thereby realizing flight crossing in an unknown complex environment. According to the distributed tracking scheme designed by the invention, a feasible thought is provided for efficient cooperation of heterogeneous unmanned aerial vehicle clusters, the cooperation efficiency of the unmanned aerial vehicle clusters can be effectively improved through a leader-following architecture, and military and civilian applications such as national defense military and livelihood economy can be widely supported.

Description

Technical Field

[0001] The present invention belongs to the technical field of cooperative control of unmanned aerial vehicle clusters, and in particular relates to a multi-unmanned aerial vehicle safe distributed tracking control method driven by online planning. Background Art

[0002] In recent years, with the rapid development of UAV technology, multi-UAV collaborative systems have shown excellent application prospects in military reconnaissance, disaster relief, environmental monitoring, resource exploration and other fields. Compared with single UAV systems, multi-UAV systems have stronger collaborative operation capabilities and higher mission flexibility, can efficiently cover a wider area and meet more complex and diverse mission requirements. However, in actual applications, the complexity of the environment continues to increase, especially in complex environments full of unknown obstacles and dynamic changes (such as forests, urban ruins or disaster sites). Multi-UAV systems still face severe challenges in real-time environmental perception, rapid trajectory planning and safe obstacle avoidance. How to achieve real-time planning and efficient and safe distributed tracking of UAV clusters in such complex and dynamic environments has become one of the key technical issues that need to be solved in current research.

[0003] Among traditional path planning methods, grid-map-based A* algorithms and rapidly exploring random trees (RRT) are widely used. These algorithms perform well in structured, static, known environments, but when applied to unstructured, highly dynamic unknown environments, they generally have limitations such as insufficient real-time response capabilities, high computational complexity, and poor robustness. In addition, such methods usually rely on complete prior environmental map information and are difficult to adapt to the needs of unknown environments that change in real time. Therefore, how to achieve real-time autonomous trajectory planning for drone swarms based on limited and dynamically changing environmental information is of great research value.

[0004] For the distributed tracking and control problem of multi-UAV systems, the current mainstream methods include distributed control, event-triggered communication, and graph optimization methods. Among them, the distributed control method realizes the update of online control strategy through the local perception of the UAV itself and the information interaction of neighboring UAVs, effectively reducing the dependence on centralized computing and communication bandwidth; the event-triggered communication strategy aims to reduce redundant data transmission and improve communication efficiency; and the graph optimization method uses sparse topology structure to achieve efficient optimization of global state. However, these methods still have obvious limitations in practical applications: first, if each UAV is equipped with high-performance sensors and computing units, the system cost will increase significantly; second, in an environment with limited or even unstable communication, how to achieve efficient collaboration and information interaction between UAVs is still an unresolved problem; third, the existing distributed tracking methods are not robust enough and adaptable when facing highly dynamic and unknown complex environments, and it is difficult to effectively cope with the rapid changes of obstacles.

[0005] In addition, in recent years, researchers have also proposed methods that combine artificial potential fields with heuristic sub-goal points, as well as trajectory planning methods based on reinforcement learning. Although the artificial potential field method is simple and easy to implement, it is prone to falling into local optimal solutions; while the reinforcement learning method has limited policy generalization ability in unknown environments, and its real-time performance and learning efficiency are difficult to meet actual needs. To sum up, the current field of multi-UAV cooperative obstacle avoidance and distributed tracking control still faces the following key pain points:

[0006] 1) Equipping all UAVs with high-performance sensors and powerful computing devices is costly and has low economic feasibility;

[0007] 2) In complex and communication-constrained environments, there are serious obstacles to efficient cooperation and real-time information sharing among UAVs;

[0008] 3) The adaptability and robustness of existing methods to dynamically changing environments are insufficient, and it is difficult to quickly and effectively respond to the real-time changes and complex scenarios of obstacles. Summary of the Invention

[0009] Aiming at the technical problem in the existing multi-UAV cooperative system that it is difficult to equip each UAV with high-performance sensors and high-computing-capability devices due to cost and power consumption limitations, the present invention proposes a distributed tracking control method based on Ego-Planner autonomous dynamic planning and a fusion feedback-feedforward structure. This method enables a small number of high-cost leader UAVs to work in cooperation with a large number of low-cost follower UAVs, effectively reducing the overall system cost and significantly improving the real-time performance and robustness in complex dynamic environments, and realizing safe distributed trajectory tracking control of multi-UAVs.

[0010] The object of the present invention is achieved through the following technical solutions: An online planning-driven multi-UAV safe distributed tracking control method, comprising the following steps:

[0011] S1. Establish a multi-UAV cluster system, clarify the network communication topology structure of the multi-UAV cluster, and define the task objectives of distributed safe tracking control; there are the following sub-steps:

[0012] S11. Define the number and three-dimensional sizes of the leader UAVs and follower UAVs;

[0013] S12. Describe the networked UAV system using a graph, model it through an undirected graph G=(V, E), where each vertex represents a UAV, the vertex set V={1, 2,..., n}, and n represents the number of UAVs; the edge set represents the communication link between UAVs; use the adjacency matrix A=[a ij ∈R n×n to represent the connection relationship, a ij= 1 indicates that there is a direct communication link between UAV i and UAV j, otherwise a ij = 0; The network structure is further characterized by the Laplacian matrix L = D - A, where the degree matrix D = diag(d1, d2,..., d n ), and To distinguish the interaction between the leader UAV and the follower UAVs, a diagonal matrix B = diag(b1, b2,..., b n ) is defined. When the i-th follower UAV receives the state information from the leader UAV, b i > 0, otherwise b i = 0;

[0014] S13. Randomly set a scenario with a large number of obstacles, and determine the initial position and the end position of the leader;

[0015] S14. Define the task objective of distributed safe tracking control as enabling the UAV swarm to achieve the task objective of distributed safe tracking control under the defined network communication topology;

[0016] S2. Autonomously plan the trajectory for the leader UAV based on Ego - Planner:

[0017] First, establish the trajectory optimization problem for the leader UAV, expressed as:

[0018] J Opt = λ s J s + λ o J o + λ d J d

[0019] where J s 、J o 、J d are the cost functions for trajectory smoothness, obstacle avoidance, and dynamic performance, and λ s 、λ o 、λ d are the weight factors of the cost functions for trajectory smoothness, obstacle avoidance, and dynamic performance respectively;

[0020] Then, use the L - BFGS optimization algorithm to solve the optimization problem, obtain the discrete trajectory control points, and generate the dynamic reference trajectory of the leader UAV;

[0021] S3. Generate a state estimator for the follower UAVs based on online learning; The follower UAVs generate the feed - forward control terms by estimating the high - order trajectory information obtained in real - time through the neural network;

[0022] S4. Design a distributed tracking controller based on a feedback-feedforward structure: Take the difference between the state of the follower UAV and the state of the leader UAV as the feedback term, and use the high-order information estimated by online learning as the feedforward control term to design the tracking controller for the follower UAV.

[0023] The beneficial effects of the present invention are as follows: The present invention proposes a method for obstacle avoidance and distributed tracking of networked UAVs based on EGO-Planner autonomous dynamic planning and a distributed learning control strategy integrating feedforward-feedback, which solves the problems of high cost, high communication burden, and insufficient adaptability in the prior art. Specifically, a small number of high-cost leader UAVs equipped with high-performance sensors and computing devices are used. Through real-time environmental perception and path planning, they generate efficient and safe dynamic reference trajectories. A large number of low-cost follower UAVs then use visual sensors and online learning neural networks to estimate and obtain the high-order trajectory information of the leader UAV in real time to achieve accurate real-time trajectory tracking, effectively reducing the overall perception, computing cost, and risk of the UAV system. The improvements of the present invention are reflected in the following two aspects:

[0024] 1) The present invention proposes an online UAV distributed tracking framework for complex unknown environments. Through a small number of leader UAVs equipped with high-precision sensors, combined with EGO-Planner, environmental perception and real-time trajectory optimization are realized, providing efficient and safe dynamic reference trajectories for a large number of low-cost follower UAVs, significantly improving the adaptability and robustness of the UAV cluster in dynamic complex scenarios, and reducing the overall perception and computing cost of the system.

[0025] 2) The present invention designs a distributed tracking control method integrating feedforward-feedback. The follower UAV only uses position information and uses an online learning neural network to estimate the high-order trajectory information of the leader UAV in real time to achieve accurate distributed trajectory tracking and dynamic obstacle avoidance, effectively reducing the real-time communication requirements between UAVs, and significantly improving the cooperation efficiency and safety of the UAV swarm in communication-limited and complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flowchart of an online planning-driven multi-UAV safe distributed tracking control method of the present invention;

[0027] Figure 2 is a multi-UAV cluster safety obstacle-crossing diagram of the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0028] The technical solution of the present invention will be further described below with reference to the drawings.

[0029] As Figure 1As shown in the figure, an online planning-driven multi-UAV safe distributed tracking control method of the present invention includes the following steps:

[0030] S1. Establish a multi-UAV cluster system, clarify the safe cooperative tracking problem, clarify the network communication topology structure of the multi-UAV cluster, and define the task objectives of distributed safe tracking control to ensure that multiple UAVs can cooperate in real time in an unknown complex environment and safely cross the obstacle area; the following sub-steps are included:

[0031] S11. Define the number and three-dimensional dimensions of the leader UAV and the follower UAVs. In this embodiment, the number of UAVs is defined as n = 5, including 1 leader UAV and 4 follower UAVs; define the three-dimensional dimension of each UAV as

[0032] 0.47m × 0.47m × 0.11m;

[0033] S12. Describe the networked UAV system using a graph, model it through an undirected graph G = (V, E), where each vertex represents a UAV, the vertex set V = {1, 2,..., n}, and n represents the number of UAVs; the edge set represents the communication link between UAVs; use the adjacency matrix A = [a ij ∈ R n×n to represent the connection relationship between the follower UAVs. When a ij = 1, it means there is a direct communication link between UAV i and UAV j, otherwise a ij = 0; further characterize the network structure through the Laplacian matrix L = D - A, where the degree matrix D = diag(d1, d2,..., d n ), and To distinguish the interaction between the leader UAV and the follower UAVs, define the diagonal matrix B = diag(b1, b2,..., b n ). When the i-th follower UAV receives the state information from the leader UAV, b i > 0, otherwise b i = 0;

[0034] For the four follower UAVs without high-value sensors in this embodiment, the adjacency matrix A is defined as:

[0035]

[0036] The Laplacian matrix L is defined as:

[0037]

[0038] The degree matrix D is defined as:

[0039]

[0040] B is defined as: B = diag([1.4, 1.2, 0, 0]).

[0041] S13. Randomly set up a scenario with a large number of obstacles, and determine the initial position and end position of the leader; for the four follower drones, maintain a formation offset of [0.4, 0.8, 1.2, 1.6] on the Z-axis, so that the drone swarm maintains a formation in space to pass through the dense area. The initial scenario randomly generates 11 static obstacle areas with a radius of 0.3 m and a height of 5 m and 7 static obstacle areas with a radius of 0.5 m and a height of 3 m as the environmental constraints during the trajectory optimization process, as Figure 2 shown. Set the spatial step size of the simulation to [-20, 20], and the simulation time range to [0, 50] seconds.

[0042] S14. Define the task objective of distributed safe tracking control as enabling the drone swarm to achieve the task objective of distributed safe tracking control under the defined network communication topology.

[0043] S2. Based on Ego-Planner, autonomously plan the trajectory for the leader drone; establish the trajectory optimization problem for the leader drone, where the optimization objectives include trajectory smoothness, obstacle avoidance constraints, and dynamic feasibility constraints, and further establish the optimization function. Use the L-BFGS optimization algorithm to solve the established optimization problem, and the solution result is discrete trajectory control points.

[0044] First, establish the trajectory optimization problem for the leader drone, expressed as:

[0045] J Opt = λ s J s + λ o J o + λ d J d

[0046] where J s 、J o 、J d are the cost functions for trajectory smoothness, obstacle avoidance, and dynamic performance, and λ s 、λ o 、λ d are the weight factors of the cost functions for trajectory smoothness, obstacle avoidance, and dynamic performance respectively;

[0047] Then, use the L-BFGS optimization algorithm to solve the optimization problem to obtain discrete trajectory control points and generate the dynamic reference trajectory of the leader drone;

[0048] Step S2 specifically includes the following sub-steps:

[0049] S21. Define the control points Q of the B-spline curve i , and initialize the positions of the control points. Since the backend optimization of the present invention is also based on the optimized control points, for multiple discrete control points, uniform B-splines are used to generate a smooth and continuous curve, and an initial trajectory route is generated.

[0050] S22. Define the trajectory smoothness constraint, and construct the trajectory smoothness cost function J by weighted consideration of the acceleration and the change rate of the higher-order derivative (such as jerk) of the trajectory s to ensure that the planned trajectory is geometrically smooth enough, which is convenient for the leader UAV to have a continuous and stable power output during control, and avoid sudden changes and high-frequency control inputs. The online trajectory planning algorithm achieves a smooth effect by directly penalizing the magnitudes of the velocity and acceleration. Due to the convex hull property of the B-spline, the present invention only needs to penalize the control points. Therefore, the trajectory smoothness cost function can be expressed in the following form:

[0051]

[0052] where represents the trajectory smoothness cost function, N C represents the total number of control points of the B-spline curve, A i represents the acceleration vector of the i-th curve segment, J i represents the acceleration change rate (Jerk) vector of the i-th curve segment, and ‖‖2 represents the 2-norm.

[0053] S23. Set the obstacle avoidance constraint. The leader UAV uses its own environmental perception sensor to obtain the obstacle position O in real time i ; define the safety distance threshold d safe . In this embodiment, d safe = 0.5 m. When the distance between the planned trajectory and the obstacle is less than the safety threshold, by increasing the weight factor λ o of the cost function J o , the trajectory is guided away from the obstacle. By reasonably setting the safety distance, while reducing the redundant computational overhead, it can ensure that the leader UAV can pass safely and quickly in a complex environment.

[0054] The cost function J o is expressed as:

[0055]

[0056] where the obstacle position d i = (Q i - p i ) T v, d i represents the projection distance from the control point to the obstacle, and p irepresents the anchor point on the obstacle surface, and v represents the anchor point p i to the trajectory control point Q i is the unit normal vector; the function ReLU(x) = max(0, x), that is, if the distance is less than d safe penalty is imposed, and the closer the distance, the heavier the penalty.

[0057] When the projected distance d between any control point and the obstacle i is less than the set safety distance d safe the system will dynamically adjust the control point configuration and re-iterate the trajectory optimization process to achieve the reconstruction of the obstacle avoidance trajectory.

[0058] S24. Define the dynamic feasibility constraint, comprehensively considering the dynamic model of the UAV and the kinematic performance constraints, including speed, acceleration, and Jerk. By setting the dynamic performance cost function J d and its weight factor λ d to ensure the dynamic feasibility of the planned trajectory. By setting the magnitude of the weight factor to drive the behavior strategy of the UAV in complex or simple environments, enabling it to pass safely or quickly, making this method more universal for different environments.

[0059] Adopt the strategy that the higher-order quantities of the speed, acceleration, and Jerk terms of the UAV dynamics cannot be greater than the limit values. Here, Jerk is the derivative of acceleration with respect to time and is regarded as the rate of change of acceleration. Similarly, due to the characteristics of the B-spline curve, it is only necessary to check at the control points. Therefore, the dynamic feasibility constraint can be expressed as:

[0060]

[0061] where ω v represents the weight parameter of speed, ω a represents the weight parameter of acceleration, ω j represents the weight parameter of Jerk, V i represents the speed vector of the i-th curve segment; F(C) (C = V i , A i or J i ) is a piecewise penalty function, specifically:

[0062]

[0063] where c r represents a certain one-dimensional component of speed / acceleration / Jerk. The coefficients a1, b1, c1, a2, b2, c2 can be obtained by satisfying the second-order continuity condition; c m is the maximum value of the dynamic soft constraint threshold, within which the trajectory is penalty-free; c jThe dynamic hard constraint threshold will incur severe penalties if exceeded. λ is the slope parameter used to control the smoothness of the penalty near the threshold. Here, the value of ∈ is much less than 1 to ensure that the final result meets the constraints because the cost function is a compromise of all weighted terms.

[0064] S25. Finally, construct the optimization function for the leader UAV, integrate the above constraints, and form the specific optimization objective function as follows:

[0065] J Opt = λ s J s + λ o J o + λ d J d

[0066] where λ s , λ o , λ d are the weight factors for trajectory smoothness, obstacle avoidance, and dynamic feasibility respectively; J s , J o , J d are the specific cost functions under their respective constraints, and are further solved by the subsequent L - BFGS.

[0067] S26. Use the L - BFGS optimization algorithm to iteratively optimize the objective function proposed above, and update the control point positions in real time until the collision - free and dynamic - limit constraints are satisfied. Feed the distances between the control point positions calculated during the optimization process and the obstacles, as well as the trajectory smoothness information, back to the subsequent trajectory generation process in real time to enhance the robustness and safety of the trajectory planning.

[0068] The optimization objective function changes continuously with the addition of new obstacles, which requires the solver to be able to restart and solve quickly. And the objective function is mainly composed of quadratic terms, and the Hessian information can accelerate the convergence speed. However, obtaining the exact Hessian consumes a large amount of computer resources. Therefore, this invention uses quasi - Newton methods to approximately calculate the Hessian matrix from the gradient information. After comparing the Barzilai - Borwein method, the truncated Newton method, and the L - BFGS method, it is found that the L - BFGS method performs the best, balancing the restart cost and the accuracy of the inverse Hessian estimation.

[0069] The L - BFGS algorithm approximates the Hessian matrix through the evaluation of the previous objective function, which not only maintains a high convergence speed but also avoids the large computational cost of directly calculating the inverse Hessian matrix. Specifically, for an unconstrained optimization problem Its update step is an approximate Newton step:

[0070]

[0071] where α k is the step size, represents the gradient, y k and y k+1 are the k-th update results respectively; H k is the approximate Hessian matrix, and its update formula is:

[0072]

[0073] where

[0074] In this process, H k is not explicitly calculated. The algorithm efficiently performs two-loop regression updates by right-multiplying the gradient and recursively unfolds m steps. The Barzilai-Borwein step size weight is used as the initial approximate Hessian matrix for the L-BFGS update and is defined as:

[0075] or

[0076] A monotonic line search that satisfies the strong Wolfe conditions is adopted to ensure the convergence of the algorithm.

[0077] S27. Based on the adjusted trajectory, calculate the interpolation point p i of the new control point Q ij and the corresponding repulsive direction vector Further determine the minimum distance d ij between the control point and the obstacle, dynamically adjust the position of the control point according to the safety distance threshold, and use the gradient information to guide the control point away from the obstacle; find all the control points on the trajectory, find all the control points inside the obstacle, and the control points adjacent to the control point located inside the obstacle. It is necessary to use the traditional A* algorithm to search for a feasible path between the two points starting from and ending at these two adjacent control points that are not inside the obstacle.

[0078] S28. In each optimization iteration, by real-time monitoring the position Q i of the control point, detect whether there is a collision risk between the trajectory and the obstacle, generate a collision-free guidance path through the path search algorithm. If it is detected that the position of the control point may cause a collision, adjust the positions of these control points, and recalculate the trajectory using the collision-free guidance path provided by the path search algorithm;

[0079] As defined in S23, d = (Q - p)T v, take the safety distance d safe = 0.5 m, and take the vector v as the unit vector in the direction from point Q to point p, that is In the actual planning process, by receiving the data from the on-board sensors of the leader UAV (including odometer, camera pose, and depth map data), the geometric information of the obstacle (anchor point p) is obtained, and then the distance d is calculated based on the control point position and the anchor point p. If it is determined that the distance between two adjacent control points is less than the safety distance, a cost term of magnitude (d - d safe ) 2 in the direction of v will be applied to deviate the trajectory from the obstacle.

[0080] S3. Generate a state estimator for the follower UAV based on online learning; the follower UAV adopts an online learning method to fit the unknown function through a neural network, estimate the dynamic model and high-order trajectory information of the leader, and obtain the feedforward control term; it includes the following sub-steps:

[0081] S31. Define the dynamic models of the leader UAV and the follower UAV;

[0082] Taking the dynamic reference trajectory obtained in step S2 as the state of the leader UAV, establish the dynamic model of the leader UAV, expressed as:

[0083]

[0084] where, x0(t) represents the state of the leader UAV, is the first derivative of x0(t), and f(x0, t) is an unknown smooth function;

[0085] The follower UAV adopts a second-order dynamic model, and the state space model of each UAV is expressed as:

[0086]

[0087] where, x i1 (t) is the position state, x i2 (t) is the velocity state, u i (t) is the control input, and y i (t) is the system output; the leader UAV only provides position information reference to the follower UAV. The follower UAV uses a neural network to estimate the model uncertainty of the leader UAV, generate a feedforward signal and a reference signal for tracking, and complete distributed tracking through a distributed tracking controller, achieving precise control only relying on position data and effectively reducing communication resource consumption.

[0088] S32. Design a tracking control law based on the feedforward-feedback control strategy. Specifically, the follower UAV generates a feedforward control term by following the high-order trajectory information obtained through real-time estimation by the neural network. Meanwhile, calculate the feedback control term in real time to dynamically correct the real-time deviation of the follower UAV's trajectory, ensuring that the follower UAV can continuously and accurately track the leader UAV's trajectory.

[0089] The follower UAV uses the neural network online learning method to estimate the model uncertainties and external disturbances existing in the leader UAV's trajectory planning process in real time. Specifically, let the function g(ξ):R p →R be a smooth function, and it is restricted within the set ; then, there exists a group of linearly parameterized basis function vectors φ(ξ) = [φ1(ξ), φ2(ξ), …, φ r (ξ)] T and an optimal parameter vector Θ * ∈R r , such that the function g(ξ) can be approximately expressed as:

[0090] g(ξ) = Θ *T φ(ξ) + ∈(ξ)

[0091] where ∈(ξ) represents the approximation error, bounded by a certain positive constant δ within the set S * ; is the unknown nonlinear dynamic term in the system (including model uncertainties and external disturbances), which is used as the feedforward control term to compensate for the unknown dynamics in advance and improve the tracking accuracy and disturbance rejection performance; ∈(ξ) is the model perturbation term.

[0092] For any i ∈ {1, 2, …, r}, the basis function is designed in the form of a Gaussian kernel function:

[0093]

[0094] where μ i represents the center of the kernel function, and σ i represents the corresponding kernel function width;

[0095] The optimal parameter vector Θ * is defined as the vector that minimizes the supremum of the approximation error estimate on the set S , that is:

[0096]

[0097] Combine the basis function vector φ(ξ) through the optimal parameter vector Θ * to approximate the coefficient vector of g(ξ).

[0098] S4. Design a distributed tracking controller based on a feedback-feedforward structure: Use the difference between the state of the follower UAV and the state of the leader UAV as the feedback term, and use the high-order information estimated by online learning as the feedforward control term to design the tracking controller for the follower UAV to achieve precise trajectory tracking. The specific implementation method is as follows:

[0099] S41. Define the form of the distributed tracking controller for the follower UAV that integrates the above feedforward and feedback control mechanisms as follows:

[0100]

[0101] where, x i1 is the position state of the i-th follower UAV, x i2 is the velocity state of the i-th follower UAV, k ∈ and k p represent the controller gains, k ∈ is the position formation control term, k p is the velocity-based control term, η i represents the first derivative of the position state of the follower UAV; ∈ 1i is the weighted combined signal of the position errors between the follower UAVs and between the follower UAVs and the leader UAV; rec(α) is the reciprocal function, when α ≠ 0, rec(α)·α = 1, and when α = 0, rec(α) = 0. l iy is the element in the i-th row and j-th column of the matrix L. represents the supremum of the approximate error estimate obtained by the i follower UAVs.

[0102] Perform the following coordinate transformation:

[0103] p 1i = x i1 - x0,

[0104]

[0105] where, p 1i represents the relative position error between the follower UAV and the leader UAV, p 2i represents the difference between the velocity of the follower UAV and the velocity of the leader UAV estimated by the neural network; x0 represents the position state of the leader UAV;

[0106] where represents the neural network estimate of the leader velocity, φ γ (x i1 , t) represents the column vector of basis functions used to estimate the high-order state of the leader, and the basis function uses a Gaussian kernel function, represents the time derivative of the neural network estimation parameter of, is the optimal parameter vector estimated by the neural network for the i-th follower UAV.

[0107] From this, it can be deduced that:

[0108]

[0109] where η i represents the first derivative of the position state of the follower UAV (i.e., velocity);

[0110] Therefore, it can be obtained that:

[0111]

[0112] Define indicating writing the elements in p 2i as a column vector, where n is the number of its elements; 1 n represents a column vector with all elements being 1; represents the leader velocity term of the neural network: e γi represents the neural network estimation error of the i-th follower UAV: It should be noted that E1 = (L + B)P1.

[0113] The variables P1 and P2 can be expressed as:

[0114] P1 = X - X0,

[0115]

[0116] The following compact model can be obtained:

[0117]

[0118] where Δ represents the robust compensation term vector, and refers to all the stacked column vectors; Therefore, the adaptation law for the multi-UAV distributed tracking control algorithm based on neural network and leader online trajectory planning in complex scenarios is defined as:

[0119]

[0120] where k f is the filtering gain, and k δ is the adaptation gain coefficient for error boundary estimation.

[0121] S42. By reasonably constructing the Lyapunov function, it can be proved that the system error of the controller converges to zero, that is, the system reaches a stable state.

[0122] For the adaptive law of the multi - UAV distributed tracking control algorithm based on neural network and leader online trajectory planning in complex scenarios that has been proposed, consider the following candidate form of the Lyapunov function:

[0123]

[0124] where \(k\) f represents the neural network parameter update gain, and \(k\) δ represents the error upper - bound estimation gain, and \(\hat{\epsilon}_i\) represents the estimated error upper - bound of the \(i\) - th follower UAV. Taking the derivative of the above Lyapunov function gives:

[0125]

[0126] where \(k\in\mathbb{R}^+\) represents the positive gain related to the weighted position error term. According to the definition of the adaptive law, the choice of the first - term adaptive law makes:

[0127]

[0128] The choice of the second - term adaptive law makes:

[0129]

[0130] where \(e\) γi represents the actual value of the neural network approximation error. Next, let According to the composite - function differential chain rule, we obtain the following relationship:

[0131]

[0132] where \(\xi\) i \(\in[\min(x\) i1 ,x_0),\max(x\) i1 ,x_0)]\). According to the conditions of Theorem 1 mentioned above the matrix \(\Xi\) is a positive - definite matrix.

[0133] Therefore, the derivative of the Lyapunov function is obtained as follows:

[0134]

[0135] Therefore, \(V_1\) is non - increasing before \(P_1\equiv P_2\equiv0\), which means \(P_1(\infty)\to0\), that is holds for all \(i\in\mathcal{I}\).

[0136] Through simulation experiments, it is verified that the leader UAV can quickly cross the obstacle area, the follower UAVs can quickly and safely follow without collision, and the tracking error tends to 0, and the data verifies the robustness and accuracy of the algorithm.

[0137] In this embodiment, the number of leader drones for an online planning-driven multi-UAV safe distributed tracking control method is set to 1, and the number of follower drones is set to 4. The three-dimensional size of the UAVs is 0.47 m × 0.47 m × 0.11 m. A random complex scenario is set up, and the map is globally unknown. Through the online planning of the leader, the follower drones can safely follow through the complex scenario, enabling the UAV swarm to pass through the scenario in a safe manner to verify the algorithm.

[0138] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. An online planning-driven multi-UAV safe distributed tracking control method, characterized in that It includes the following steps: S1. Establish a multi-UAV cluster system, clarify the network communication topology of the multi-UAV cluster, and define the task objectives of distributed secure tracking control; there are the following sub-steps: S11. Define the number and three-dimensional sizes of the leader UAV and the follower UAVs; S12. Describe the networked UAV system using a graph, modeled by an undirected graph G=(V, E). Each vertex represents a UAV, and the vertex set V = {1, 2,..., n}, where n represents the number of UAVs; the edge set represents the communication link between UAVs; use the adjacency matrix A = [a ij ∈ R n×n to represent the connection relationship between follower UAVs. a ij = 1 indicates that there is a direct communication link between UAV i and UAV j, otherwise a ij = 0; the Laplacian matrix L = D - A, where the degree matrix D = diag(d1, d2,..., d n ), and To distinguish the interaction between the leader UAV and the follower UAVs, define the diagonal matrix B = diag(b1, b2,..., b n ). When the i-th follower UAV receives the state information from the leader UAV, b i > 0, otherwise b i = 0; S13. Randomly set a scenario with a large number of obstacles, and determine the initial position and end position of the leader; S14. Define the task objective of distributed secure tracking control as enabling the UAV cluster to achieve the task objective of distributed secure tracking control under the defined network communication topology; S2. Autonomously plan a trajectory for the leader UAV based on Ego-Planner: First, establish a leader UAV trajectory optimization problem, expressed as: J Opt = λ s J s + λ o J o + λ d J d Among them, J s , J o , J d are the cost functions for trajectory smoothness, obstacle avoidance, and dynamic performance, and λ s , λ o , λ d are the weight factors of the cost functions for trajectory smoothness, obstacle avoidance, and dynamic performance, respectively; Then, use the L-BFGS optimization algorithm to solve the optimization problem, obtain discrete trajectory control points, and generate a dynamic reference trajectory for the leader UAV; S3. Generate a state estimator for the follower UAVs based on online learning; the follower UAVs generate a feedforward control term by estimating the high-order trajectory information obtained in real time through a neural network; S4. Design a distributed tracking controller based on a feedback-feedforward structure: use the difference between the state of the follower UAV and the state of the leader UAV as the feedback term, and use the high-order information estimated by online learning as the feedforward control term to design the tracking controller for the follower UAVs.

2. An online planning-driven multi-UAV safe distributed tracking control method according to claim 1, characterized in that The step S3 includes the following sub-steps: S31. Define the dynamic models of the leader UAV and the follower UAVs; Take the dynamic reference trajectory obtained in step S2 as the state of the leader UAV, and establish the dynamic model of the leader UAV, expressed as: where \(x_0(t)\) represents the state of the leader UAV, \(\dot{x}_0(t)\) is the first derivative of \(x_0(t)\), and \(f(x_0,t)\) is an unknown smooth function; The follower UAVs adopt a second-order dynamic model, and the state space model of each UAV is expressed as: where x i1 (t) is the position state, x i2 (t) is the velocity state, u i (t) is the control input, y i (t) is the system output; S32. Design a tracking control law based on a feedforward-feedback control strategy. The follower UAVs use the neural network online learning method to estimate the model uncertainties and external disturbances existing in the leader UAV trajectory planning process in real time, and use them as the feedforward control term.

3. An online planning-driven multi-UAV safe distributed tracking control method according to claim 1, characterized in that, The specific implementation method of the step S4 is: define the form of the distributed tracking controller as follows: where, x i1 is the position state of the i-th follower UAV, x i2 is the velocity state of the i-th follower UAV, k ∈ and k p represent the controller gains, k ∈ is the position formation control term, k p is the velocity-based control term; η i represents the first derivative of the position state of the follower UAV; rec(α) is the reciprocal function; l iy is the element in the i-th row and j-th column of the matrix L; p 2i represents the difference between the velocity of the follower UAV and the velocity of the leader UAV estimated by the neural network; x0 represents the position state of the leader UAV, φ γ (x i1 , t) represents the column vector of basis functions; represents the neural network parameter estimation vector learned by the i-th follower UAV, represents the supremum of the approximate error estimation obtained by the i-th follower UAV.

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