Multi-unmanned ship aggregation trajectory planning method based on distributed optimization and multi-modal network

Abstract

The invention provides a multi-unmanned ship aggregation trajectory planning method based on distributed optimization and a multi-modal network, and belongs to the technical field of unmanned cluster system collaborative decision. The method comprises the steps that an unmanned ship cluster receives an aggregation instruction through an Ethernet communication protocol, and a preset geographic network communication protocol coverage area serves as an aggregation target area; constructing an undirected graph of the unmanned ship cluster and a corresponding Laplacian communication matrix; taking the distance between the current position and the initial position of each unmanned ship as a cost function; based on the undirected graph of the unmanned ship cluster and the corresponding Laplacian communication matrix, coupling the position constraint of each unmanned ship, and solving the optimal aggregation position of each unmanned ship through a distributed discrete optimization algorithm; and based on the kinematics state model of the unmanned surface vehicle in combination with a quadratic Bezier curve, planning an aggregation trajectory of each unmanned surface vehicle from the current position to the optimal aggregation position. According to the method, the communication efficiency is ensured, and meanwhile, efficient collaborative aggregation of unmanned ship clusters is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of collaborative decision-making of unmanned cluster systems, and in particular to a multi-unmanned boat assembly trajectory planning method based on distributed optimization and multimodal networks. Background Art

[0002] With the development of marine resources and the growing demand for maritime safety, the operational model of unmanned aerial vehicles (UAVs) is shifting from single-platform to multi-vessel collaboration to meet the needs of complex maritime swarming missions. Regional UAV assembly missions require specific UAVs to assemble within a pre-defined sea area to perform targeted operations. The implementation of this mission relies on efficient communication resource allocation and precise signal transmission, while also requiring coordinated decision-making processes within environmental constraints to improve mission execution efficiency.

[0003] Currently, unmanned aerial vehicle communications primarily utilize an IP (Internet Protocol, Ethernet)-based network architecture. However, its static address allocation mechanism struggles to adapt to dynamic topology changes and is prone to positional errors when denied by the Global Navigation Satellite System (GNSS). As the number of unmanned aerial vehicles increases, the throughput of the IP architecture may decline, making it difficult to meet the requirements of large-scale regional coverage missions. For assembly location optimization, traditional centralized algorithms rely on central nodes, posing a single point of failure risk and a heavy communications burden. For trajectory generation, global search algorithms such as A* and Dijkstra can guarantee optimal paths. Sampling-based algorithms (such as RRT and PRM) and deep reinforcement learning methods offer significant adaptability but come at a high computational cost.

[0004] Therefore, existing methods still have shortcomings in terms of communication resource utilization, decision-making capabilities in complex environments, and execution efficiency: the IP modal architecture cannot take into account both dynamic topology and regional coverage requirements; the centralized optimization algorithm has poor adaptability and high communication overhead; the global path planning algorithm has high computational complexity and is difficult to meet real-time requirements, and kinematic constraints require additional processing.

[0005] Therefore, there is an urgent need for a multi-UAV assembly trajectory planning method based on distributed optimization and multimodal networks. Summary of the Invention

[0006] In view of this, the present invention provides a multi-unmanned boat assembly trajectory planning method based on distributed optimization and multimodal network. For the unmanned boat cluster maritime area assembly task, the GN (GeoNetworking) communication protocol is used to realize multi-node information broadcasting in the area through geographic addressing, which can alleviate the network congestion problem; through a distributed optimization algorithm with hybrid constraints and a quadratic Bezier curve-based trajectory planning scheme, the optimal assembly position and assembly trajectory are provided for the unmanned boat cluster.

[0007] To this end, the present invention provides the following technical solutions:

[0008] A multi-unmanned vehicle assembly trajectory planning method based on distributed optimization and multimodal networks includes:

[0009] The unmanned boat swarm receives assembly instructions through the Ethernet communication protocol, and uses the preset geographic network communication protocol coverage area as the assembly target area;

[0010] Construct an undirected graph of the UAV cluster and the corresponding Laplace communication matrix;

[0011] The distance between the current position and the initial position of each unmanned boat is used as the cost function. Based on the undirected graph of the unmanned boat cluster and the corresponding Laplace communication matrix, the position constraints of each unmanned boat are coupled and the optimal assembly position of each unmanned boat is solved through a distributed discrete optimization algorithm.

[0012] Based on the kinematic state model of the unmanned boat and the quadratic Bezier curve, the assembly trajectory of each unmanned boat from its current position to the optimal assembly position is planned.

[0013] Furthermore, it also includes:

[0014] Based on the assembly trajectory, a trajectory tracking control algorithm is used to control each unmanned boat to move from the current position along the assembly trajectory to the optimal assembly position to complete the assembly;

[0015] The assembled unmanned boat cluster performs the target mission in the target area and transmits the mission data to the communication base station through the geographic network communication protocol.

[0016] Furthermore, the undirected graph of the unmanned boat cluster is constructed as follows:

[0017]

[0018] in, represents an undirected graph node set, represents the edge set, Represents the adjacency matrix; and when (i,j)∈Υ then a ij >0;

[0019] The Laplace communication matrix corresponding to the undirected graph is:

[0020]

[0021] in, represents the degree matrix, Represents the adjacency matrix.

[0022] Furthermore, the cost function:

[0023]

[0024] Among them, fi : Reflects that each unmanned boat will take the shortest distance from its current position Entering the area covered by the geographic network communication protocol; is the position state vector of the unmanned boat, Indicates the center coordinates of the geographic network communication protocol coverage area.

[0025] Furthermore, the position constraints of each unmanned boat include:

[0026] The optimal assembly position of the unmanned boats is within the target area;

[0027] A preset safety distance is maintained between the optimal assembly positions of the unmanned boats.

[0028] Furthermore, the distributed discrete optimization algorithm is used to solve the optimal assembly position of each unmanned boat, including:

[0029] Taking the sum of the cost functions of each unmanned boat as the target and coupling the position constraints of each unmanned boat, a distributed optimization model is constructed:

[0030]

[0031] Where q is the compact form of the position vector, S i and S are constant constraint vectors and their compact forms, and is the upper bound of the roll and pitch constraints, and is the lower bound of the roll and pitch constraints, is the center coordinate in the equation, b i is the lumped vector of boundary constraints;

[0032] Design of a discrete distributed optimization protocol for a swarm system of unmanned watercraft with hybrid constraints:

[0033]

[0034] in, and is the spanned form of the constant constraint vector; θ is a constant; q i (k+1) is the position vector q i The update law of η i (k+1) is an auxiliary variable The update law of , which is used to handle inequality constraints; and Auxiliary variables for handling inequality constraints.

[0035] Furthermore, the kinematic state model of the unmanned boat includes:

[0036]

[0037] Among them, x i ,y i is the position coordinate in the earth coordinate system, ψ i represents the heading angle in the Earth coordinate system, ζ iu represents the rolling linear velocity, ζ iv represents the pitching linear velocity, ζ ir Indicates the heading angular velocity.

[0038] Furthermore, the kinematic state model of the unmanned boat is combined with a quadratic Bezier curve to plan the assembly trajectory of each unmanned boat from the current position to the optimal assembly position, including:

[0039] Determine the second-order Bezier curve;

[0040] The control point is determined by the current position of the unmanned boat, the straight-line distance between the current position of the unmanned boat and the optimal assembly position, the initial linear speed direction, and the adjustment coefficient;

[0041] The first derivative of the second-order Bezier curve is used to determine the initial velocity of the unmanned boat.

[0042] When the initial speed of the unmanned boat is less than or equal to the preset speed threshold, the unmanned boat's current position is used as the starting point, and the unmanned boat's optimal assembly position is used as the end point. The unmanned boat assembly trajectory is determined by combining the second-order Bezier curve with the control point and the unmanned boat's initial speed.

[0043] When the initial speed of the unmanned boat is greater than a preset speed threshold, the adjustment coefficient is adjusted, and the control point and the initial speed are updated; based on the second-order Bezier curve combined with the updated control point and the updated initial speed of the unmanned boat, the assembly trajectory of the unmanned boat is determined.

[0044] Furthermore, the second-order Bezier curve:

[0045] B i (t) = (1-t) 2 G 0i +2(1-t)tG 1i +t 2 G 2i ,

[0046] in, The current position of the unmanned boat is the initial point of the assembly trajectory, G 1i represents the control point, represents the optimal assembly position, which serves as the end point of the assembly trajectory.

[0047] Furthermore, the control point position is determined based on the current position of the unmanned boat, the straight-line distance between the current position of the unmanned boat and the optimal assembly position, the adjustment coefficient, and the linear speed direction, including:

[0048]

[0049] Among them, G 1i represents the control point, Indicates the straight-line distance between the current position of the unmanned boat and the optimal assembly position, represents the initial linear velocity direction vector, τ∈[0,τ max ] represents the adjustment coefficient, τ max =ζ m / 2D.

[0050] Advantages and positive effects of the present invention:

[0051] The present invention adopts a multimodal network architecture that integrates IP and GN, which can adapt to the dynamic topology changes of the unmanned boat cluster and cover the communication needs within the specified sea area, significantly improving the utilization rate of communication resources; at the same time, by designing a discrete-time distributed optimization algorithm, the unmanned boat can independently decide the optimal assembly position based on local information, avoiding the single point failure and communication burden of the centralized algorithm, thereby enhancing the mission adaptability and scalability; at the same time, the trajectory generated by the second-order Bezier curve is combined with the position, speed and heading angle of the unmanned boat to ensure smooth trajectory and efficient calculation, reducing the additional processing required for sharp turns and dynamic adjustments, and providing a reliable reference for trajectory tracking control.

[0052] Combining the above technologies, the present invention achieves efficient collaborative assembly of unmanned boat clusters while ensuring communication efficiency, and is both real-time and practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0054] Figure 1 Schematic diagram of a regional assembly mission scenario for a swarm of unmanned boats in a multimodal network environment according to an embodiment of the present invention;

[0055] Figure 2 Schematic diagram of the communication architecture of an unmanned boat in a multimodal network environment according to an embodiment of the present invention;

[0056] Figure 3 Schematic diagram of trajectory planning of a swarm of unmanned boats based on Bezier curves in an embodiment of the present invention;

[0057] Figure 4 This is a topology diagram of communication between unmanned boat clusters in an embodiment of the present invention;

[0058] Figure 5 The three-dimensional optimal assembly decision result and decision iteration curve of the unmanned boat cluster in an embodiment of the present invention;

[0059] Figure 6 is a cost function curve in an embodiment of the present invention;

[0060] Figure 7 is the auxiliary variable η in the embodiment of the present invention i (k) Iteration curve;

[0061] Figure 8 The three-dimensional assembly trajectory of the unmanned boat based on Bezier curve planning in an embodiment of the present invention;

[0062] Figure 9 The two-dimensional assembly trajectory of the unmanned boat based on Bezier curve planning in an embodiment of the present invention;

[0063] Figure 10 This is a flow chart of the unmanned boat regional assembly method based on distributed optimization and multimodal network in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0065] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0066] The present invention provides a method for regional assembly trajectory planning of multiple unmanned boats based on distributed optimization and multimodal networks, which is applicable to unmanned boat cluster systems at sea and aims to improve the efficiency and speed of unmanned boats in collaboratively executing maritime tasks. Aiming at the problem of determining the optimal assembly position of an unmanned boat cluster and generating an assembly trajectory in regional assembly tasks; first, in an IP-GN multimodal network environment, a hybrid constraint distributed optimization algorithm for the unmanned boat cluster is determined, and the assembly position is flexibly determined according to the initial position; and GN technology is used to achieve efficient information transmission in a designated sea area, significantly improving the utilization rate of communication resources; secondly, a method for generating the assembly trajectory of an unmanned boat is proposed based on the Bezier curve, which simplifies the planning process and takes into account the kinematic feasibility. The present invention provides a feasible solution for regional assembly tasks of unmanned boat clusters, thereby achieving efficient collaborative assembly and rapid trajectory planning of unmanned boat clusters.

[0067] The multimodal architecture of the method of the present invention includes:

[0068] The unmanned boat cluster consists of N unmanned boats. The unmanned boat cluster receives assembly instructions through the Ethernet communication protocol and uses the preset geographic network communication protocol coverage area as the assembly target area.

[0069] like Figure 1 As shown, under the IP-GN multimodal network architecture, the ground station sends data to the target area ( Figure 1 The system sends assembly commands within a large circular area. Neighboring unmanned vehicles receive "forward / stay" commands via IP. The unmanned vehicle that executes the "forward" command illuminates its indicator light and proceeds to the area covered by the geographic network communication protocol. Once within the coverage area, the unmanned vehicle transmits mission data back using the GN protocol. The ground station only needs to receive GN data to obtain mission information, eliminating the need to process IP data outside the area. This architecture enables flexible positioning and on-demand addressing, significantly improving network resource utilization. The regional assembly mission can be modeled as a distributed optimization and trajectory planning problem to determine the optimal assembly location and trajectory for each vehicle.

[0070] like Figure 2 As shown in Figure 1, the multimodal network environment consists of a core domain and two application network modes—IP mode and GN mode. Furthermore, corresponding application services and dedicated terminals are deployed within the access network. The multimodal backbone network consists of two core network elements (routing devices) and an interdomain controller.

[0071] The unmanned boat assembly process of the method of the present invention includes:

[0072] Step 1: Construct an undirected graph of the UAV cluster and the corresponding Laplace communication matrix;

[0073] Step 1.1: Use graph theory to describe the internal communication of the UAV cluster. The undirected graph of the UAV cluster includes: the node set, edge set and adjacency matrix of the UAV cluster;

[0074] The undirected graph containing N unmanned boats is represented as:

[0075] Among them, the node set Edge Set and the adjacency matrix (If (i,j)∈Υ then a ij >0). There is a path between any pair of nodes, is a connected graph.

[0076] Step 1.2, corresponding Laplace communication matrix;

[0077] First, define the degree matrix as:

[0078]

[0079] in, Represents node v i degree;

[0080] Determine the graph Corresponding Laplace communication matrix:

[0081] satisfy And when i≠j, l is satisfied ij =-a ij .

[0082] In this embodiment, the communication topology between N unmanned boats is as follows: is connected and undirected.

[0083] The neighbor set of the i-th unmanned boat is defined as Assemble for the unmanned boat.

[0084] The symmetric positive definite matrix Q can be uniquely decomposed into Q = H T H, where is a lower triangular matrix with strictly positive diagonal elements. Assume is an orthogonal matrix, where definition

[0085] Step 2: The distance between the current position and the initial position of each UAV is used as the cost function. Based on the undirected graph of the UAV cluster and the corresponding Laplace communication matrix, the position constraints of each UAV are coupled and the optimal assembly position of each UAV is solved through a distributed discrete optimization algorithm.

[0086] Step 2.1: Use the distance between the current position and the initial position of each unmanned boat as the cost function; and determine the feasible position constraints of the unmanned boat based on the coverage area of ​​the geographic network communication protocol and the safety distance limit of the unmanned boat;

[0087] The coverage area of ​​the geographic network communication protocol is defined as a circular area with a radius of l1>0 The safety distance of each unmanned boat is defined as a circle with a radius of l2>0 (l1>l2).

[0088] Therefore, the feasible position constraint of the i-th unmanned boat can be expressed as:

[0089]

[0090] in, is the position state vector of the unmanned boat, Represents the center coordinate of Φ1. The constraints l1-l2 ensure that the i-th unmanned boat can fully converge to the coverage area of ​​the geographic network communication protocol.

[0091] Each unmanned boat has an independent cost function:

[0092]

[0093] Among them, f i : It reflects that each unmanned boat will move from its initial position to the nearest Entering the GN area. Equality constraints It is used to depict the distribution position of unmanned boats before entering the GN area, ensuring that they are evenly distributed around the center of the geographic network communication protocol coverage area.

[0094] Therefore, the position constraint of the i-th unmanned boat is expressed as:

[0095]

[0096] make

[0097] and

[0098] Then set the vector:

[0099] S i =[1,-1] T , and

[0100] Combined with feasibility constraints:

[0101] Taking the sum of the cost functions of each unmanned boat as the target and coupling the position constraints of each unmanned boat, a distributed optimization model is constructed:

[0102]

[0103] In order to ensure the solvability of the constrained optimization problem, it is assumed that there is Make and Established;

[0104] in and Assume that the cost function f i (q i ) is convex, and for i = 1, 2, ..., N, the gradient is global σ Lipschitz.

[0105] Step 2.2, design a discrete distributed optimization protocol with hybrid constraints for the unmanned boat swarm system;

[0106] Distributed optimization algorithm for the i-th unmanned boat in step k+1:

[0107]

[0108] in, and q i (k+1) is the position vector q i The update law of η converges to the optimal solution through iterative calculation. i Auxiliary variables defined in (k+1) Used to handle inequality constraints.

[0109] Step 2.3: Optimality and convergence analysis.

[0110] Analyze the relationship between the equilibrium point and the optimal solution. The Lagrangian function of the convex optimization problem is defined as follows:

[0111]

[0112] in, and is the Lagrange multiplier.

[0113] If and only if there exists a Lagrange multiplier η * and Make Satisfies the Karush–Kuhn–Tucker conditions:

[0114]

[0115] Sq* -b≤0 4N ,η * ≥0 4N ,η *T (Sq * -b)=0,

[0116]

[0117] but It is the optimal solution of the distributed optimization model.

[0118] Consider step 2.2 and based on the known premise Available Therefore, if the initial state satisfy Then the equality constraint This will always hold true in the position state update law in step 2.2.

[0119] First, assume that (q * ,η * ) is the equilibrium point of step 2.3, which means that there is Make

[0120]

[0121] Solving the first equation of the equilibrium point yields satisfy in Make Right now:

[0122]

[0123] In addition, further At the same time, according to (·) + From the definition of , we can deduce that the second equation of the equilibrium point is equivalent to the complementary relaxation condition. In summary, the above formula satisfies all the conditions of Karush–Kuhn–Tucker, indicating that q * is the optimal solution of the step-distributed optimization model.

[0124] On the contrary, suppose q * is the optimal solution of the step-distributed optimization model. Therefore, there exists a Lagrange multiplier η that satisfies the Karush–Kuhn–Tucker condition * and , which satisfies the equilibrium condition and η * =(η * +Sq * -b) + Condition. The first Karush–Kuhn–Tucker condition is left-multiplied Available

[0125]

[0126] This is equivalent to the first equilibrium condition. Therefore, (q * ,η * ) is the equilibrium point of a distributed discrete-time system.

[0127] In summary, if there is η * and So that (q * ,η * ) is the equilibrium point of the distributed discrete-time system, then q * is the optimal solution of the step-distributed optimization model.

[0128] Lyapunov stability theory is used to prove that the state of a distributed discrete-time system can converge to the optimal solution. The following Lyapunov function is selected:

[0129] V(q(k),η(k))=V1(q(k))+θV2(η(k)),

[0130] in, V2(η(k))=||η(k)-η * || 2 , And Q=H T H. Then the difference of V(q(k),η(k)) can be expressed as:

[0131] V(q(k+1),η(k+1))-V(q(k),η(k))

[0132] =V1(q(k+1))-V1(q(k))+θ[V2(η(k+1))-V2(η(k))]

[0133] Consider (η * +Sq * -b) + ≥0 and the variational inequality (η-η * ) T (-Sq * +b)≥0, we can get [(η * +Sq * -b) + -η * ] T (Sq * -b)≤0.

[0134] Using the convexity of the cost function f(q(k)) and the above inequality, V1(q(k+1))-V1(q(k)) can be further expressed as:

[0135]

[0136] Consider η(k+1)=[η(k)+Sq(k+1)-b] + We can get:

[0137] [η(k+1)-η(k)-Sq(k+1)+b] T [η(k+1)-η * ]≤0.

[0138] Therefore, V2(η(k+1))-V2(η(k)) can be written as:

[0139] V2(n(k+1))-V2(n(k))≤-||n(k+1)-n(k)|| 2 +2[Sq(k+1)-b] T [η(k+1)-η * ]

[0140] according to The Lipschitz condition of , we can get:

[0141]

[0142] Finally, the differential form of V(q(k),η(k)) can be further expressed as:

[0143]

[0144] in, Therefore, if the parameter θ satisfies It can be obtained that V(q(k+1),η(k+1))-V(q(k),η(k))≤0. According to LaSalle invariant set theory, q(k) will converge to the set . If V(q(k+1),η(k+1))-V(q(k),η(k))=0, the differential form of V(q(k),η(k)) shows that q(k) satisfies the Karush–Kuhn–Tucker condition. Therefore, q(k) is the optimal solution to the convex optimization problem in the step-distributed optimization model. This completes the proof of the convergence of the state of the unmanned vehicle swarm, demonstrating that the system state can asymptotically converge to the optimal assembly position.

[0145] Step 3: Based on the kinematic state model of the UAV and the quadratic Bezier curve, plan the assembly trajectory of each UAV from its current position to the optimal assembly position;

[0146] Step 3.1: According to the mathematical definition of Bezier curve, the initial point q of each unmanned boat is given 0i and end point By properly selecting the trajectory control points, a smooth and controllable assembly trajectory that is consistent with the driving speed and easy to change can be generated.

[0147] No. The horizontal kinematic model of an unmanned boat is established as follows:

[0148]

[0149] Among them, x i ,y i ,ψ i is the position state and heading angle in the earth coordinate system, ζ iu and ζ iv is the rolling and pitching linear velocity, ζ ir is the heading angular velocity.

[0150] Step 3.2: Based on the horizontal kinematic model of the unmanned boat, the second-order Bezier curve trajectory planning diagram based on the kinematic state is shown in the attached figure. Figure 3 shown.

[0151] First, define the expression of the second-order Bezier curve:

[0152] B i (t) = (1-t) 2 G 0i +2(1-t)tG 1i +t 2 G 2i ,

[0153] in G 1i and are the initial point, control point and optimal assembly position respectively. Secondly, calculate the initial point G 0i and control point G 1i The straight-line distance between Next, let is the maximum linear velocity of the i-th unmanned boat, where ζ ium and ζ ivm denote the maximum rolling and pitching linear velocities respectively. Therefore, the maximum adjustment coefficient τ can be derived as τ max =ζ m / 2D, the value range of τ satisfies τ∈[0,τ max ]. Furthermore, based on the known heading angle ψ i , the initial linear velocity direction vector can be expressed as Then, control point G 1i The position is offset by a specified distance along the yaw direction, and the calculation formula is:

[0154] On this basis, the initial velocity ζ0 can be obtained by solving the first-order derivative of the second-order Bezier curve, and its expression is: Finally, if the initial velocity ζ0 exceeds the maximum velocity ζ iu , the adjustment coefficient τ should continue to be adjusted as follows: After completing this step, the control point G will be updated 1i and initial velocity ζ0, and then generate the assembly trajectory B based on the Bezier curve that meets the requirements of the first step i (t).

[0155] So far, in a multimodal network environment, a discrete distributed optimization algorithm with position constraints has been successfully used to determine the optimal assembly position of each unmanned boat, and the assembly trajectory of the unmanned boat cluster has been generated based on the Bezier curve, completing the regional assembly task of the unmanned boat system.

[0156] Application Examples

[0157] Based on the above method, for the unmanned boat swarm maritime regional assembly task, a discrete time distributed optimization algorithm with constraints and trajectory planning scheme are used to provide the optimal assembly position and assembly trajectory for the unmanned boat swarm. For the optimal assembly problem, a discrete time distributed optimization protocol q with position constraints is designed in a multimodal network environment based on IP and GN. i (k+1) and η i (k+1), generate the optimal assembly position q * , so that the unmanned boat can go to the designated sea area and use the GN mode to transmit mission information. For the assembly trajectory planning problem, the speed of each unmanned boat is used to calculate the speed of each unmanned boat. m ,ζ0 and heading angle ψ i State, using the second-order Bezier curve to generate the initial connection position G 0i and the optimal assembly position G 2i The smooth trajectory B(t) can provide a reliable reference for trajectory tracking control. The present invention provides a feasible solution for the unmanned boat cluster regional assembly task, which specifically includes the following steps:

[0158] S1. Define the node set, edge set and adjacency matrix of the unmanned boat cluster, construct an undirected graph of the unmanned boat cluster; and determine the Laplace communication matrix of the undirected graph of the unmanned boat cluster.

[0159] In this embodiment, there are 6 unmanned boats in the unmanned boat cluster, that is, N=6; graph theory is introduced to describe the node set, edge set and adjacency matrix inside the unmanned boat;

[0160] Combine Figure 4 As shown, define an undirected graph containing 6 unmanned boats Includes: Node Set Edge Set and the adjacency matrix (If (i,j)∈Υ then a ij >0). In this embodiment, there is a path between any pair of nodes. is a connected graph.

[0161] The degree matrix is ​​defined as:

[0162]

[0163] in, Represents node v i degree.

[0164] Definition Graph The Laplace communication matrix is:

[0165] satisfy And when i≠j, l is satisfied ij =-a ij .

[0166] In this embodiment, the communication topology between the six unmanned boats It is connected and undirected, and the neighbor set of the i-th unmanned boat is defined as Assemble for the unmanned boat.

[0167] Determine the Laplace communication matrix of the undirected graph of the unmanned watercraft swarm for:

[0168]

[0169] in, is an orthogonal matrix, is the Laplace communication matrix The positive eigenvalue of λ6=5. The symmetric positive definite matrix Q can be uniquely decomposed into Q=H T H, where Q can be expressed as

[0170]

[0171] and is a lower triangular matrix with strictly positive diagonal elements. Definition

[0172] S2. Design a communication architecture based on a multimodal network environment; establish a total cost function; determine a discrete distributed optimization protocol with hybrid constraints; analyze the relationship between the optimal assembly position and the equilibrium point, and use Lyapunov stability theory to prove that all unmanned boats can eventually converge to the optimal assembly position.

[0173] S2.1: Construction of regional assembly mission scenarios based on multimodal network environment.

[0174] Combine Figure 1 As shown in the figure, six unmanned boats will work together to perform the maritime area assembly mission. In order to improve the utilization of communication resources, under the multi-modal network architecture that integrates IP and GN communication modes, the ground station transmits the assembly command to the set GN collection area through the GN protocol, as shown in the figure. Figure 1 As shown in the large circle in the middle, adjacent UAVs receive "forward" or "stay" commands via IP. The UAV executing the "forward" command will illuminate its indicator light, while the others remain off. The "forward" UAV will proceed to the designated GN area to carry out its mission. Once within the GN area, the "forward" UAV can transmit mission results back to the ground station using the GN protocol. The ground station only needs to receive GN protocol data to obtain mission execution information, without having to process IP protocol data outside the GN area. This multimodal network architecture enables flexible positioning and on-demand addressing of UAVs, significantly improving network resource utilization for maritime unmanned system assembly missions.

[0175] Therefore, the regional assembly task can be modeled as a distributed optimization decision-making and trajectory planning problem to determine the optimal assembly location and motion trajectory of each unmanned boat.

[0176] like Figure 2 As shown in the figure, the multimodal network environment consists of a core domain and two application network modes—IP mode and GN mode. In addition, corresponding application services and dedicated terminals are deployed within the access network. The multimodal backbone network consists of two core network elements (routing devices) and an interdomain controller. The network elements are interconnected with a link bandwidth of 100 gigabits per second (Gbps). The IP and GN access networks, respectively, consist of two multimodal network elements, an intradomain controller, fixed terminals, and unmanned boat terminals. The link bandwidth between the access network and the core domain is 10 Gbps, and the bandwidth between wired nodes within the access network is configured to 100 megabits per second (Mbps).

[0177] S2.2. Establish the cost function and location constraints for the regional assembly task.

[0178] Determine the feasible location constraints of the unmanned boat by combining the coverage area of ​​the geographic network communication protocol and the safety distance of the unmanned boat;

[0179] In this embodiment, the coverage area of ​​the geographic network communication protocol is a circular area with a radius of l1=30m. The safe distance of each unmanned boat is a circle with a radius of l2=4m.

[0180] The feasible position constraint of the i-th unmanned boat is expressed as:

[0181]

[0182] in, is the position state vector of the unmanned boat, The constraint l1-l2=26 ensures that the i-th unmanned boat can completely converge to the coverage area of ​​the geographic network communication protocol.

[0183] Determine the independent cost function for each drone:

[0184]

[0185] Among them, f i : It reflects that each unmanned boat will move from its initial position to the nearest Enter the GN area;

[0186] In this embodiment, the initial assembly position is set to γ 21 =[-31,0] T , γ 22 =[-26,27] T , γ 23 =[14,14] T , γ 24 =[34,17] T , γ 25 =[22,-24] T And γ 26 =[-19,-28] T .

[0187] Each unmanned boat is evenly distributed around the center of the geographic network communication protocol coverage area, and the equality constraint is Describe the distribution of unmanned boats before they enter the coverage area of ​​the geographic network communication protocol.

[0188] Express the feasible position constraint as a linear inequality constraint:

[0189] q ix ≤-1+[(30-4) 2 -(q iy -1) 2 ] 1 / 2

[0190] q iy ≤1+[(30-4) 2 -(q ix +1) 2 ] 1 / 2

[0191] make

[0192] and

[0193] Then set the vector:

[0194] S i =[1,-1] T , and

[0195] Finally, combined with the feasible constraints Based on the cost function and the assembly constraints of the unmanned boats, a distributed optimization model is constructed to solve the problem of selecting the optimal assembly location of the unmanned boat system:

[0196]

[0197] In order to ensure the solvability of the constrained optimization problem, the distributed optimization model is transformed:

[0198] Assume existence Make and Established, of which and

[0199] Furthermore, assuming that the cost function f i (q i ) is convex, and for i=1,2,…,6, the gradient is a global σ-Lipschitz, where σ=1.

[0200] S2.3. Design a discrete distributed optimization protocol with hybrid constraints for the i-th unmanned boat in step k+1:

[0201]

[0202] in, The gain is set to θ = 0.05. i (k+1) is the position vector q i The update law of η converges to the optimal solution through iterative calculation. i Auxiliary variables defined in (k+1) Used to handle inequality constraints. The initial value of the discrete system is set to [q 01 ;η 01 ]=[γ 21 ;04],[q 02 ;η 02 ]=[γ 22 ;04],[q 03 ;η 03 ]=[γ 23 ;04],[q 04 ;η04 ]=[γ 24 ;04],[q 05 ;η 05 ]=[γ 25 ;04] and [q 06 ;η 06 ]=[γ 26 ;04]. The maximum number of iterations is set to 400.

[0203] S2.4. Optimality and convergence analysis.

[0204] (1) Analyze the relationship between the equilibrium point and the optimal solution. The Lagrangian function of the convex optimization problem in the distributed optimization model is determined as follows:

[0205]

[0206] in, and is the Lagrange multiplier. The objective function and inequality constraints in convex optimization problems are both convex functions; the equality constraints are affine.

[0207] The optimal solution is determined by the KKT (Karush–Kuhn–Tucker) condition; specifically, if and only if there exists a Lagrange multiplier η * and Make Requirements:

[0208]

[0209] Sq * -b≤0 24 ,η * ≥0 24 ,η *T (Sq * -b)=0,

[0210]

[0211] but It is the optimal solution to the convex optimization problem in the distributed optimization model.

[0212] The specific proof process is as follows:

[0213] Based on known premises We can get:

[0214]

[0215] Therefore, if the initial state satisfy Then the equality constraint This will always hold true in the position state update law in S2.3. The initial value satisfies

[0216] First, assume that (q * ,η * ) is the equilibrium point of S2.3, which means that there is So that,

[0217]

[0218] Solving the above equation, we can get satisfy in Make It can be deduced that:

[0219]

[0220] according to(·) + From the definition of , we can deduce that the second equation for the equilibrium point is equivalent to the complementary relaxation condition in S2.4.

[0221] Further available

[0222] In summary, the above formula satisfies all the conditions of Karush–Kuhn–Tucker, indicating that q * It is the optimal solution of the distributed optimization model.

[0223] On the contrary, suppose q * is the optimal solution of the distributed optimization model. Therefore, there exists a Lagrange multiplier η that satisfies the Karush–Kuhn–Tucker condition * and It satisfies the equilibrium condition and η * =(η * +Sq * -b) + condition.

[0224] The first Karush–Kuhn–Tucker conditional left multiplication Available

[0225]

[0226] This is equivalent to the first equilibrium condition. Therefore (q * ,η * ) is the equilibrium point of the distributed discrete-time system. In summary, if there exists η * and So that (q * ,η *) is the equilibrium point of the distributed discrete-time system, then q * This is the optimal solution of the distributed optimization model. This concludes the theoretical proof that the equilibrium point is the optimal solution.

[0227] Lyapunov stability theory is used to prove that the state of a distributed discrete-time system can converge to the optimal solution.

[0228] In this embodiment, the Lyapunov function:

[0229] V(q(k),η(k))=V1(q(k))+θV2(η(k)),

[0230] Where θ = 0.05, , V2(η(k))=||η(k)-η * || 2 , Q=H T H.

[0231] The difference of V(q(k),η(k)) can be expressed as:

[0232] V(q(k+1),η(k+1))-V(q(k),η(k))

[0233] =V1(q(k+1))-V1(q(k))+θ[V2(η(k+1))-V2(η(k))]

[0234] Consider (η * +Sq * -b) + ≥0 and the variational inequality (η-η * ) T (-Sq * +b)≥0, we can get [(η * +Sq * -b) + -η * ] T (Sq * -b)≤0.

[0235] Using the convexity of the cost function f(q(k)), V1(q(k+1))-V1(q(k)) can be further expressed as:

[0236]

[0237] Consider η(k+1)=[η(k)+Sq(k+1)-b] + We can get:

[0238] [η(k+1)-η(k)-Sq(k+1)+b] T [η(k+1)-η* ]≤0.

[0239] Therefore, V2(η(k+1))-V2(η(k)) can be written as:

[0240] V2(n(k+1))-V2(n(k))≤-||n(k+1)-n(k)|| 2 +2[Sq(k+1)-b] T [η(k+1)-η * ]

[0241] according to The Lipschitz condition of , we can get:

[0242]

[0243] Finally, the differential form of V(q(k),η(k)) can be further expressed as:

[0244]

[0245] in, Therefore, if the parameter θ satisfies It can be obtained that V(q(k+1),η(k+1))-V(q(k),η(k))≤0. According to LaSalle invariant set theory, q(k) will converge to the set The maximum invariant subset of . If V(q(k+1),η(k+1))-V(q(k),η(k))=0, then the difference form of V(q(k),η(k)) shows that q(k) satisfies the Karush–Kuhn–Tucker condition. Therefore, q(k) is the optimal solution to the convex optimization problem in step 2.2.

[0246] According to the definition of V(q(k+1),η(k+1))-V(q(k),η(k))≤0 and V(q(k+1),η(k+1)), we can get V(q(k),η(k))≤V(q0,η0), where η0 is the initial state. Therefore, the state variables q(k),η(k) are bounded. Therefore, there exists an increasing subsequence and limiting points and to ensure and in is the optimal solution to the mixed constraint optimization problem in the distributed optimization model. Therefore, The Karush–Kuhn–Tucker conditions apply. So for any initial point q(k) is the optimal solution to the convex optimization problem in the distributed optimization model. So far, the proof of the convergence of the state of the unmanned boat cluster has been completed, proving that the system state q(k) can asymptotically converge to the optimal assembly position q * .

[0247] S3. Establish a kinematic model of the unmanned boat; design a trajectory planning method based on the second-order Bezier curve.

[0248] Given the initial point q of each unmanned boat 0i and end point By properly selecting the trajectory control points, a smooth and controllable assembly trajectory that is consistent with the driving speed and easy to change can be generated.

[0249] S3.1. According to the mathematical definition of Bezier curve, Horizontal kinematic model of an unmanned boat:

[0250]

[0251] Among them, x i ,y i ,ψ i is the position state and heading angle in the earth coordinate system, ζ iu and ζ iv is the lateral and longitudinal sway velocity, ζ ir is the heading angular velocity.

[0252] S3.2. The mathematical expression of the Bezier curve B(t) is:

[0253]

[0254] Where t∈[0,1] is the normalized curve interpolation parameter. G l represents the control point, l is the number of the control point. c (c = l-1) represents the order of the curve, and For higher-order Bezier curves, the local shape of the curve can be modified by adjusting the control points individually. However, due to the high computational complexity of higher-order Bezier curves, this embodiment uses second-order Bezier curves to plan the assembly trajectory of the UAV cluster based on known heading angle and velocity information, thereby reducing the complexity of trajectory design.

[0255] According to the horizontal kinematic model of the unmanned boat, the second-order Bezier curve trajectory planning diagram based on the kinematic state is as follows: Figure 3 shown.

[0256] The optimal assembly position and initial position can be known from S2; the optimal assembly position: G 21 =[-26.9,0.8] T , G 22=[-17.9,20.7] T , G 23 =[11.4,14.7] T , G 24 =[22.7,11.7] T , G 25 =[15.7,-18.9] T , G 26 =[-10.9,-23] T .

[0257] Step 1: Determine the expression of the second-order Bezier curve:

[0258] B i (t) = (1-t) 2 G 0i +2(1-t)tG 1i +t 2 G 2i ,

[0259] in, G 1i and are the initial point, control point and optimal assembly position respectively.

[0260] Step 2: Calculate the initial point G 0i and the optimal assembly position G 2i The straight-line distance between:

[0261]

[0262] Step 3: Calculate the adjustment coefficient based on the maximum linear speed of the unmanned boat.

[0263] set up is the maximum linear velocity of the i-th unmanned boat, where ζ ium and ζ ivm denote the maximum rolling and pitching linear velocities respectively. Therefore, the maximum adjustment coefficient τ can be derived as τ max =ζ m / 2D, the value range of τ satisfies τ∈[0,τ max ].

[0264] Step 4: Calculate the speed direction based on the heading angle, based on the known heading angle ψ i , the initial linear velocity direction vector can be expressed as

[0265] Step 5: Obtain the control point through the initial linear velocity direction vector, the straight-line distance between the initial point and the optimal assembly position, the adjustment coefficient, and the starting point. 1i The position is offset by a specified distance along the yaw direction, and the calculation formula is:

[0266] The generated control points are G 11 =[0.32,-27,0.87] T , G 12 =[0.17,-17.93,20.72] T , G 13 =[0.61,11.45,14.55] T , G 14 =[1,22.68,11.74] T , G 15 =[0.77,15.65,-18.96] T , G 16 =[0.13,-10.89,-23.07] T .

[0267] Step 6: Calculate the initial velocity. The initial velocity ζ0 can be obtained by solving the first-order derivative of the second-order Bezier curve, and its expression is

[0268] Step 7: Adjust and recalculate parameters. If the initial speed ζ0 exceeds the maximum speed ζ iu , the adjustment coefficient τ should continue to be adjusted as follows: After completing this step, the control point G will be updated 1i and initial velocity ζ0, and then generate the assembly trajectory B based on the Bezier curve that meets the requirements of the first step i (t).

[0269] Using the assembly trajectory B designed based on Bezier curve i (t), high-precision trajectory tracking is achieved through backstepping control, model predictive control, linear matrix inequality and integral PID control algorithms.

[0270] In summary, in a multimodal network environment, the multi-unmanned boat system based on discrete distributed optimization protocol and trajectory planning method can effectively complete the maritime area assembly task. Figure 5-9 As shown in the figure, each unmanned boat can determine the optimal assembly position and generate the corresponding assembly trajectory. The optimal assembly position and decision iteration process of the six unmanned boats are shown in the attached figure. Figure 5 As shown; attached Figure 6 Show that the cost function f(q) and f i (q i ) all converge to the minimum value; Figure 7 Auxiliary variables with fast convergence characteristics are demonstrated The iterative trajectory of Figure 8 The three-dimensional assembly trajectory and control point distribution based on Bezier curve planning are presented; Figure 9 A two-dimensional trajectory projection is given, which clearly shows the complete motion trajectory of each unmanned boat from the initial position to the optimal assembly position.

[0271] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-unmanned boat assembly trajectory planning method based on distributed optimization and multimodal network, characterized in that: include: The unmanned boat swarm receives assembly instructions through the Ethernet communication protocol, and uses the preset geographic network communication protocol coverage area as the assembly target area; Construct an undirected graph of the UAV cluster and the corresponding Laplace communication matrix; The distance between the current position and the initial position of each unmanned boat is used as the cost function. Based on the undirected graph of the unmanned boat cluster and the corresponding Laplace communication matrix, the position constraints of each unmanned boat are coupled and the optimal assembly position of each unmanned boat is solved through a distributed discrete optimization algorithm. Based on the kinematic state model of the unmanned boat and the quadratic Bezier curve, the assembly trajectory of each unmanned boat from its current position to the optimal assembly position is planned.

2. The method for planning the assembly trajectory of multiple unmanned boats based on distributed optimization and multimodal networks according to claim 1, characterized in that: Also includes: Based on the assembly trajectory, a trajectory tracking control algorithm is used to control each unmanned boat to move from the current position along the assembly trajectory to the optimal assembly position to complete the assembly; The assembled unmanned boat cluster performs the target mission in the target area and transmits the mission data to the communication base station through the geographic network communication protocol.

3. The method for planning the assembly trajectory of multiple unmanned boats based on distributed optimization and multimodal networks according to claim 1 is characterized in that: The undirected graph for constructing the unmanned boat cluster is: in, represents an undirected graph node set, represents the edge set, Represents the adjacency matrix; and when (i,j)∈Υ then a ij >0; The Laplace communication matrix corresponding to the undirected graph is: in, represents the degree matrix, Represents the adjacency matrix.

4. The method for planning the assembly trajectory of multiple unmanned boats based on distributed optimization and multimodal networks according to claim 1, characterized in that: The cost function: in, Reflects that each unmanned boat will take the shortest distance from its current position Entering the area covered by the geographic network communication protocol; is the position state vector of the unmanned boat, Indicates the center coordinates of the geographic network communication protocol coverage area.

5. The method for planning the assembly trajectory of multiple unmanned boats based on distributed optimization and multimodal networks according to claim 1 is characterized in that: The position constraints of each unmanned boat include: The optimal assembly position of the unmanned boats is within the target area; A preset safety distance is maintained between the optimal assembly positions of the unmanned boats.

6. The method for planning the assembly trajectory of multiple unmanned boats based on distributed optimization and multimodal networks according to claim 1, characterized in that: The distributed discrete optimization algorithm is used to solve the optimal assembly position of each unmanned boat, including: Taking the sum of the cost functions of each unmanned boat as the target and coupling the position constraints of each unmanned boat, a distributed optimization model is constructed: Where q is the compact form of the position vector, S i and S are constant constraint vectors and their compact forms, and is the upper bound of the roll and pitch constraints; and is the lower bound of the roll and pitch constraints; is the center coordinate in the equation, b i is the lumped vector of boundary constraints; Design of a discrete distributed optimization protocol for a swarm system of unmanned watercraft with hybrid constraints: in, and is the spanned form of the constant constraint vector; θ is a constant; q i (k+1) is the position vector q i The update law of η i (k+1) is an auxiliary variable The update law of , which is used to handle inequality constraints; and Auxiliary variables for handling inequality constraints.

7. The method for planning the assembly trajectory of multiple unmanned boats based on distributed optimization and multimodal networks according to claim 1, characterized in that: The kinematic state model of the unmanned boat includes: Among them, x i ,y i is the position coordinate in the earth coordinate system, ψ i represents the heading angle in the Earth coordinate system, ζ iu represents the rolling linear velocity, ζ iv represents the pitching linear velocity, ζ ir Indicates the heading angular velocity.

8. The method for planning the assembly trajectory of multiple unmanned boats based on distributed optimization and multimodal networks according to claim 1 is characterized in that: The kinematic state model of the unmanned boat is combined with a quadratic Bezier curve to plan the assembly trajectory of each unmanned boat from the current position to the optimal assembly position, including: Determine the second-order Bezier curve; The control point is determined by the current position of the unmanned boat, the straight-line distance between the current position of the unmanned boat and the optimal assembly position, the initial linear speed direction, and the adjustment coefficient; The first derivative of the second-order Bezier curve is used to determine the initial velocity of the unmanned boat. When the initial speed of the unmanned boat is less than or equal to the preset speed threshold, the unmanned boat's current position is used as the starting point, and the unmanned boat's optimal assembly position is used as the end point. The unmanned boat assembly trajectory is determined by combining the second-order Bezier curve with the control point and the unmanned boat's initial speed. When the initial speed of the unmanned boat is greater than a preset speed threshold, the adjustment coefficient is adjusted, and the control point and the initial speed are updated; based on the second-order Bezier curve combined with the updated control point and the updated initial speed of the unmanned boat, the assembly trajectory of the unmanned boat is determined.

9. The method for planning the assembly trajectory of multiple unmanned boats based on distributed optimization and multimodal networks according to claim 8, characterized in that: The second-order Bezier curve: B i (t)=(1-t) 2 G 0i +2(1-t)tG 1i +t 2 G 2i , in, The current position of the unmanned boat is the initial point of the assembly trajectory, G 1i represents the control point, represents the optimal assembly position, which serves as the end point of the assembly trajectory.

10. The method for multi-unmanned boat assembly trajectory planning based on distributed optimization and multimodal network according to claim 8, characterized in that: The control point position is determined based on the current position of the unmanned boat, the straight-line distance between the current position of the unmanned boat and the optimal assembly position, the adjustment coefficient, and the linear speed direction, including: Among them, G 1i represents the control point, Indicates the straight-line distance between the current position of the unmanned boat and the optimal assembly position, represents the initial linear velocity direction vector, τ∈[0,τ max ] represents the adjustment coefficient, τ max =ζ m / 2D.

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