Unmanned underwater vehicle formation transformation and obstacle avoidance control method with time delay

Abstract

The invention discloses an unmanned underwater vehicle formation transformation and obstacle avoidance control method with time delay. The method comprises the following steps: constructing an information exchange topological relation among multiple unmanned underwater vehicles based on an undirected connected graph; motion models of the multiple unmanned underwater vehicles are established, the motion models comprise a leader kinematics model and a follower kinematics model, and the follower kinematics model is a double-integral dynamic model considering time delay and nonlinear factors; based on a leader-follower framework, distributed control input is designed, so that a follower tracks a virtual target position, and tracking control of the multi-unmanned underwater vehicle formation is realized; an obstacle avoidance offset is calculated in combination with specific conditions, and the obstacle avoidance offset is applied to an obstacle avoidance formula to realize the conversion of a dynamic path; and the leader triggers a signal to the follower within a set time, and realizes the transformation of the formation pattern based on a preset target position. According to the method, time delay compensation, uncertainty suppression, formation flexible transformation and smooth obstacle avoidance can be comprehensively solved.

Description

Technical Field

[0001] This invention relates to the technical field of cooperative control of multi-agent systems, and in particular to a time-delayed method for unmanned underwater vehicle formation changing and obstacle avoidance control, which is applicable to achieving formation maintenance, formation changing and dynamic obstacle avoidance of multiple unmanned underwater vehicles in complex marine environments. Background Technology

[0002] With the increasing demands for marine resource development and maritime security, multi-AUV collaborative operation technology is showing broad application prospects in fields such as marine observation, underwater archaeology, subsea pipeline inspection, and military reconnaissance. Compared to a single AUV, multi-AUV swarm systems, through distributed sensor networks and information sharing, can complete more complex underwater operations over a wider range, exhibiting higher operational efficiency and robustness.

[0003] In formation control methods, the leader-follower strategy has become a research hotspot due to its simple structure, high scalability, and low energy consumption. However, existing technologies still face the following technical challenges in practical applications:

[0004] 1. Underwater communication mainly relies on underwater acoustic communication, which suffers from severe time-varying delays (typically ranging from tens of milliseconds to several seconds) and is significantly affected by multipath effects and marine environmental noise. Most existing consensus control protocols assume zero communication delay or only consider fixed delays, making them difficult to adapt to the complex underwater communication environment.

[0005] 2. Unmanned underwater vehicles face uncertainties such as ocean current disturbances and model parameter perturbations during operation. Traditional control methods based on accurate models are difficult to guarantee the robustness of the system.

[0006] 3. Existing research on formation control often considers formation maintenance, formation changes, and obstacle avoidance control separately, lacking a unified framework to coordinate the three. Especially when rapid formation changes are required to pass through narrow waters or avoid large obstacles, ensuring formation stability while achieving safe obstacle avoidance remains a technical challenge.

[0007] 4. Traditional obstacle avoidance strategies based on artificial potential fields are prone to producing local optima, and sudden changes in obstacle avoidance offset may cause drastic changes in vehicle acceleration, affecting control accuracy.

[0008] Therefore, there is an urgent need for a collaborative control method that can comprehensively address time delay compensation, uncertainty suppression, flexible formation transformation, and smooth obstacle avoidance. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for unmanned underwater vehicle formation changing and obstacle avoidance control with time delay.

[0010] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0011] A time-delayed method for unmanned underwater vehicle formation changing and obstacle avoidance control, comprising:

[0012] The information exchange topology among multiple unmanned underwater vehicles is constructed based on an undirected connected graph, which is represented as follows: , where the node set Represents all multi-unmanned underwater vehicles, edge set Represents communication paths, adjacency matrix This indicates the communication strength between multiple unmanned underwater vehicles;

[0013] Establish motion models for multiple unmanned underwater vehicles, including leader kinematics models and follower kinematics models, where the follower kinematics model is a double integral dynamic model that considers time delay and nonlinear factors;

[0014] Based on the leader-follower framework, a distributed control input is designed to enable followers to track the position of virtual targets, thereby achieving tracking control of a multi-unmanned underwater vehicle formation.

[0015] Calculate the obstacle avoidance offset based on the specific situation, and apply the obstacle avoidance offset to the obstacle avoidance formula to realize the transformation of the dynamic path;

[0016] The leader triggers a signal to the followers within a set time, and the formation changes based on the preset target position.

[0017] Furthermore, the motion model of a single unmanned underwater vehicle is a six-degree-of-freedom motion model as follows:

[0018] ;

[0019] in, This represents the spatial position and attitude of an unmanned underwater vehicle in a fixed coordinate system. Represents the dimensions in six directions, where, , , The position is in the three coordinate systems. These are the angles along the three coordinate systems. The spatial position of the unmanned underwater vehicle in a fixed coordinate system The attitude of the unmanned underwater vehicle; Let be the linear velocity and angular velocity of the unmanned underwater vehicle in the moving coordinate system. , ; Let be the linear velocity in the three coordinate systems. Angular velocities in the three coordinate systems; This is the rotation transformation matrix from the moving coordinate system to the fixed coordinate system; The inertia matrix of the system includes the added mass; The Coriolis force matrix includes the added mass; Here is the damping matrix; These are the vectors of gravity, buoyancy, and torque. This represents the thrust and torque vectors.

[0020] Furthermore, the follower kinematic model is represented as:

[0021] ;

[0022] Under normal navigation conditions in undulating ocean currents, neglecting roll velocity, the nonlinear model of the unmanned underwater vehicle is written with five degrees of freedom, where... They represent the first The position and speed of the unmanned underwater vehicle; Let the time delay function be a continuously differentiable nonlinear function with a time delay. Continuously differentiable , ; For the first Distributed control inputs for an unmanned underwater vehicle;

[0023] Nonlinear continuous function Satisfy the following inequalities

[0024] , and All are constant matrices; at the same time, nonlinear functions Define the following vectors and matrices:

[0025]

[0026] ;

[0027] .

[0028] Furthermore, the leader's kinematic model is represented as:

[0029] ;

[0030] in, These represent the position and speed of the underwater vehicle leader.

[0031] Furthermore, the process of designing distributed control inputs is as follows:

[0032] In formation control, the control design objectives for each unmanned underwater vehicle are:

[0033] , ;;

[0034] in ;

[0035] Based on the control design objectives of the formation, design distributed control inputs. :

[0036] ;

[0037] in, , It is used to adjust the intensity of the control input. Representative of followers and Is there a connection between them? Indicates follower Is there a connection with the leader? It refers to the relative positions of the formation; It represents the set of all relationships.

[0038] Furthermore, the obstacle avoidance offset is calculated based on the specific circumstances, including:

[0039] Set a safe distance between the unmanned underwater vehicle and the obstacle. ;

[0040] Real-time calculation of the distance between the unmanned underwater vehicle and obstacles ,like Then calculate the obstacle avoidance offset. :

[0041] ;

[0042] in, The obstacle avoidance benefit coefficient controls the intensity of the obstacle avoidance effect;

[0043] Let be the unit vector pointing to the obstacle. This indicates the current location of the unmanned underwater vehicle. The location of the obstacle. The radius of the obstacle;

[0044] It is a smoothing function. The closer the unmanned underwater vehicle is to the obstacle, the smaller the value becomes, thus making the obstacle avoidance effect stronger.

[0045] Furthermore, the obstacle avoidance formula is as follows:

[0046] .

[0047] Furthermore, the formation change process includes:

[0048] when ≤ ≤ When this happens, proceed with the following steps:

[0049] Calculate the smoothing factor :

[0050] ;

[0051] ;

[0052] and These are the start time and the end time, respectively.

[0053] Formation position update:

[0054] For the A follower, if =1, then:

[0055] ;

[0056] For the first The relative position of the ultimate goal of each follower;

[0057] Obstacle collision avoidance calculation:

[0058] Initialize obstacle avoidance offset:

[0059] ;

[0060] Obstacle avoidance condition judgment: If the first The distance between each follower and the obstacle satisfies:

[0061] ;

[0062] For the first The current position of each follower;

[0063] Then calculate the obstacle avoidance displacement. :

[0064] ;

[0065] The result of the obstacle avoidance formula calculation;

[0066] Obstacle avoidance displacement Superimposed on obstacle avoidance offset This yields the latest obstacle avoidance offset.

[0067] The latest obstacle avoidance offset and the first Current position of each follower Add them together to get the first one. The updated position of each follower.

[0068] Compared with existing technologies, the principles and advantages of this technical solution are as follows:

[0069] 1. By explicitly considering time-varying delays and designing corresponding distributed control protocols, underwater communication delays can be effectively compensated, ensuring the stability of the formation in a time-delay environment.

[0070] 2. The nonlinear compensation terms and robust design in the control protocol enable the system to suppress random disturbances in complex marine environments and improve the reliability of formation control.

[0071] 3. The integrated obstacle avoidance mechanism enables the aircraft to avoid obstacles in real time while maintaining formation. The design of safe distance and smooth function avoids trajectory jitter during obstacle avoidance.

[0072] 4. The formation change mechanism triggered by the leader supports the smooth switching of geometric configurations of the formation during task execution (such as changing from a vertical formation to a trapezoidal formation), and the transformation process is stable and controllable.

[0073] 5. The control strategy based on local information exchange reduces the dependence on global communication and improves the scalability and fault tolerance of the system. Attached Figure Description

[0074] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0075] Figure 1 A diagram showing the communication topology of a multi-unmanned underwater vehicle formation;

[0076] Figure 2 This is a schematic diagram illustrating the effects of an unmanned underwater vehicle with collision avoidance and formation changing capabilities.

[0077] Figure 3The graph shows the change of the X-axis position of each unmanned underwater vehicle over time.

[0078] Figure 4 A graph showing the change of the Y-axis position of each unmanned underwater vehicle over time;

[0079] Figure 5 The graph shows the Z-axis position of each unmanned underwater vehicle as a function of time.

[0080] Figure 6 For the angles of various unmanned underwater vehicles Curve graph showing changes over time;

[0081] Figure 7 For the angles of various unmanned underwater vehicles Curve graph showing changes over time;

[0082] Figure 8 Schematic diagrams of formations at different points in time;

[0083] Figure 9 This is a graph showing the change in distance between each unmanned underwater vehicle and an obstacle over time. Detailed Implementation

[0084] The present invention will be further described below with reference to specific embodiments:

[0085] This embodiment describes a time-delay-based unmanned underwater vehicle formation changing and obstacle avoidance control method, including:

[0086] S1. Construct the information exchange topology between multiple unmanned underwater vehicles based on an undirected connected graph, such as... Figure 1 As shown, the undirected connected graph is represented as , where the node set Represents all multi-unmanned underwater vehicles, edge set Represents communication paths, adjacency matrix Represents the communication strength between unmanned underwater vehicles; adjacency matrix Matrix elements Representing the Unmanned underwater vehicle and the first There is information exchange between the unmanned underwater vehicles.

[0087] S2. Establish motion models for multiple unmanned underwater vehicles, including leader kinematics models and follower kinematics models. The motion model for a single unmanned underwater vehicle is a six-degree-of-freedom motion model:

[0088] ;

[0089] in, This represents the spatial position and attitude of an unmanned underwater vehicle in a fixed coordinate system. Represents the dimensions in six directions, where, , , The position is in the three coordinate systems. These are the angles along the three coordinate systems. The spatial position of the unmanned underwater vehicle in a fixed coordinate system The attitude of the unmanned underwater vehicle; Let be the linear velocity and angular velocity of the unmanned underwater vehicle in the moving coordinate system. , ; Let be the linear velocity in the three coordinate systems. Angular velocities in the three coordinate systems; This is the rotation transformation matrix from the moving coordinate system to the fixed coordinate system; The inertia matrix of the system includes the added mass; The Coriolis force matrix includes the added mass; Here is the damping matrix; These are the vectors of gravity, buoyancy, and torque. This represents the thrust and torque vectors.

[0090] Specifically, the follower kinematic model is a double-integral dynamic model that considers time delay and nonlinear factors: ;

[0091] Under normal navigation conditions in undulating ocean currents, neglecting roll velocity, the nonlinear model of the unmanned underwater vehicle is written with five degrees of freedom, where... They represent the first The position and speed of the unmanned underwater vehicle; Let the time delay function be a continuously differentiable nonlinear function with a time delay. Continuously differentiable , ; For the first Distributed control inputs for an unmanned underwater vehicle;

[0092] Nonlinear continuous function Satisfy the following inequalities

[0093] , and All are constant matrices; at the same time, nonlinear functions Define the following vectors and matrices:

[0094]

[0095] ;

[0096] .

[0097] Specifically, the leader's kinematic model is represented as:

[0098] ;

[0099] in, These represent the position and speed of the underwater vehicle leader.

[0100] S3. Based on the leader-follower framework, a distributed control input is designed to enable followers to track the virtual target position and realize the tracking control of multiple unmanned underwater vehicle formations.

[0101] The process of designing distributed control inputs is as follows:

[0102] In formation control, the control design objectives for each unmanned underwater vehicle are:

[0103] , ;

[0104] in ;

[0105] Based on the control design objectives of the formation, design distributed control inputs. :

[0106] ;

[0107] in, , It is used to adjust the intensity of the control input. Representative of followers and Is there a connection between them? Indicates follower Is there a connection with the leader? It refers to the relative positions of the formation; It represents the set of all relationships.

[0108] S4. Calculate the obstacle avoidance offset based on the specific situation, and apply the obstacle avoidance offset to the obstacle avoidance formula to realize the transformation of the dynamic path;

[0109] In this step, the obstacle avoidance offset is calculated based on the specific circumstances, including:

[0110] Set a safe distance between the unmanned underwater vehicle and the obstacle. ;

[0111] Real-time calculation of the distance between the unmanned underwater vehicle and obstacles ,like Then calculate the obstacle avoidance offset. :

[0112] ;

[0113] in, The obstacle avoidance benefit coefficient controls the intensity of the obstacle avoidance effect;

[0114] Let be the unit vector pointing to the obstacle. This indicates the current location of the unmanned underwater vehicle. The location of the obstacle. The radius of the obstacle;

[0115] It is a smoothing function. The closer the unmanned underwater vehicle is to the obstacle, the smaller the value becomes, thus making the obstacle avoidance effect stronger.

[0116] The obstacle avoidance formula is as follows:

[0117] .

[0118] In the above,

[0119] distance Calculation: By calculating the distance between the unmanned underwater vehicle (UUV) and the obstacle, it is determined whether obstacle avoidance is necessary. The smaller the distance, the closer the UUV is to the obstacle.

[0120] Unit vector The unit vector pointing from the position of the unmanned underwater vehicle to the position of the obstacle is used to determine the direction of obstacle avoidance.

[0121] Obstacle avoidance gain coefficient This coefficient is used to adjust the intensity of obstacle avoidance. If the distance is too close, the obstacle avoidance offset will become larger, propelling the unmanned underwater vehicle away from the obstacle.

[0122] Smoothing function By introducing a smoothing function To avoid sudden changes in obstacle avoidance operations that could cause severe shaking of the unmanned underwater vehicle's trajectory.

[0123] Motion Update: Finally, the calculated obstacle avoidance offset is combined with the motion commands of the unmanned underwater vehicle to update the speed and position of the unmanned underwater vehicle, so that the vehicle maintains a safe distance during movement.

[0124] S5. The leader triggers a signal to the followers within a set time, and the formation changes based on the preset target position.

[0125] The process of formation changes includes:

[0126] when ≤ ≤ When this happens, proceed with the following steps:

[0127] Calculate the smoothing factor :

[0128] ;

[0129] ;

[0130] and These are the start time and the end time, respectively.

[0131] Formation position update:

[0132] For the A follower, if =1, then:

[0133] ;

[0134] For the first The relative position of the ultimate goal of each follower;

[0135] Obstacle collision avoidance calculation:

[0136] Initialize obstacle avoidance offset:

[0137] ;

[0138] Obstacle avoidance condition judgment: If the first The distance between each follower and the obstacle satisfies:

[0139] ;

[0140] For the first The current position of each follower;

[0141] Then calculate the obstacle avoidance displacement. :

[0142] ;

[0143] The result of the obstacle avoidance formula calculation;

[0144] Obstacle avoidance displacement Superimposed on obstacle avoidance offset This yields the latest obstacle avoidance offset.

[0145] The latest obstacle avoidance offset and the first Current position of each follower Add them together to get the first one. The updated position of each follower.

[0146] The feasibility of the method described in this invention is demonstrated through specific experiments below:

[0147] Define the initial variable as AUVi=

[0148] The initial state of the formation leader unmanned vehicle is as follows:

[0149] AUVL = [50; 0; 0; -0.17; 0; 0.8; 0; 0; 0; 0];

[0150] The initial states of each follower UAV in the formation are as follows:

[0151] AUV1 = [25.2; 48; -6.8; 0.13; 0.8; 0.1; 0; 0; 0; 0];

[0152] AUV2 = [54.5; 35; -6.5; 0.1; 1.8; 0.1; 0; 0; 0; 0];

[0153] AUV3 = [24.2; 50; -7.3; 0; 1.6; -0.3; 0; 0; 0; 0];

[0154] AUV4 = [43.5; 27.8; -5.5; 0.02; 2.7; 0.25; 0; 0; 0; 0];

[0155] AUV5 = [19; 22.5; -7; 0.12; 0.35; 0.5; 0; 0; 0; 0];

[0156] The initial relative positional deviation of the formation is defined as:

[0157] =[20 * cos(2 * π * (i - 1) / 5);20 * sin(2 * π * (i - 1) / 5);0;0;0];

[0158] Define the final target relative position of the formation transformation trapezoidal formation:

[0159] = [15; 10; 0; 0; 0];

[0160] = [-15; 10; 0; 0; 0];

[0161] = [-20; -10; 0; 0; 0];

[0162] = [0; -10; 0; 0; 0];

[0163] = [20; -10; 0; 0; 0];

[0164] The position and radius of obstacle 1: obstacles1 = [-20;-50;-73]; obstacles_radius1 =12;

[0165] The position and radius of obstacle 2: obstacles2 = [2;65;-25 ]; obstacles_radius2 = 8;

[0166] safe distance = 4; Obstacle avoidance bonus coefficient = 20.0;

[0167] Parameter design of the control protocol: =0.2, =1;

[0168] Parameter design of the nonlinear factor matrix: .

[0169] This invention focuses on the formation control problem of multiple unmanned underwater vehicles (AUVs) and proposes a control protocol for scenarios with environmental interference. The movement trajectory of the follower AUVs is guided by their behavior, and the follower AUVs can communicate with each other. Sufficient conditions are derived through algebraic graph theory and matrix theory. Finally, simulation experiments verify the effectiveness of the proposed formation control method. Figures 3 to 7 It can be seen that followers can reliably track the leader's trajectory. Figure 8 The shapes of the formation changes were shown. Figure 9 It can be seen that the formation is able to maintain a safe distance from obstacles and avoid collisions.

[0170] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any changes made in accordance with the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for formation changing and obstacle avoidance control of unmanned underwater vehicles with time delay, characterized in that, include: The information exchange topology among multiple unmanned underwater vehicles is constructed based on an undirected connected graph, which is represented as follows: , where the node set Represents all multi-unmanned underwater vehicles, edge set Represents communication paths, adjacency matrix This indicates the communication strength between the various unmanned underwater vehicles; Establish motion models for multiple unmanned underwater vehicles, including leader kinematics models and follower kinematics models, where the follower kinematics model is a double integral dynamic model that considers time delay and nonlinear factors; Based on the leader-follower framework, a distributed control input is designed to enable followers to track the position of virtual targets, thereby achieving tracking control of a multi-unmanned underwater vehicle formation. Calculate the obstacle avoidance offset based on the specific situation, and apply the obstacle avoidance offset to the obstacle avoidance formula to realize the transformation of the dynamic path; The leader triggers a signal to the followers within a set time, and the formation changes based on the preset target position.

2. The method for time-delayed formation changing and obstacle avoidance control of unmanned underwater vehicles according to claim 1, characterized in that, The motion model of a single unmanned underwater vehicle is a six-degree-of-freedom motion model: ； in, This represents the spatial position and attitude of an unmanned underwater vehicle in a fixed coordinate system. Represents the dimensions in six directions, where, , , The position is in the three coordinate systems. These are the angles along the three coordinate systems. The spatial position of the unmanned underwater vehicle in a fixed coordinate system The attitude of the unmanned underwater vehicle; Let be the linear velocity and angular velocity of the unmanned underwater vehicle in the moving coordinate system. , ; Let be the linear velocity in the three coordinate systems. Angular velocities in the three coordinate systems; This is the rotation transformation matrix from the moving coordinate system to the fixed coordinate system; The inertia matrix of the system includes the added mass; The Coriolis force matrix includes the added mass; Here is the damping matrix; These are the vectors of gravity, buoyancy, and torque. This represents the thrust and torque vectors.

3. The method for time-delayed formation changing and obstacle avoidance control of unmanned underwater vehicles according to claim 2, characterized in that, The follower kinematic model is represented as follows: ； Under normal navigation conditions in undulating ocean currents, neglecting roll velocity, the nonlinear model of the unmanned underwater vehicle is written with five degrees of freedom, where... They represent the first The position and speed of the unmanned underwater vehicle; Let the time delay function be a continuously differentiable nonlinear function with a time delay. Continuously differentiable , ; For the first Distributed control inputs for an unmanned underwater vehicle; Nonlinear continuous function Satisfy the following inequalities , and All are constant matrices; Meanwhile, nonlinear functions Define the following vectors and matrices: ； 。 4. The method for time-delayed formation changing and obstacle avoidance control of unmanned underwater vehicles according to claim 3, characterized in that, The kinematic model of the leader is represented as follows: ； in, These represent the position and speed of the underwater vehicle leader.

5. The method for time-delayed formation changing and obstacle avoidance control of unmanned underwater vehicles according to claim 4, characterized in that, The process of designing distributed control inputs is as follows: In formation control, the control design objectives for each unmanned underwater vehicle are: ； in ; Based on the control design objectives of the formation, design distributed control inputs. : ； in, , It is used to adjust the intensity of the control input. Representative of followers and Is there a connection between them? Indicates follower Is there a connection with the leader? It refers to the relative positions of the formation; It represents the set of all relationships.

6. A method for time-delayed formation changing and obstacle avoidance control of unmanned underwater vehicles according to claim 5, characterized in that, The obstacle avoidance offset is calculated based on the specific circumstances, including: Set a safe distance between the unmanned underwater vehicle and the obstacle. ; Real-time calculation of the distance between the unmanned underwater vehicle and obstacles ,like Then calculate the obstacle avoidance offset. : ； in, The obstacle avoidance benefit coefficient controls the intensity of the obstacle avoidance effect; Let be the unit vector pointing to the obstacle. This indicates the current location of the unmanned underwater vehicle. The location of the obstacle. The radius of the obstacle; It is a smoothing function. The closer the unmanned underwater vehicle is to the obstacle, the smaller the value becomes, thus making the obstacle avoidance effect stronger.

7. A method for time-delayed formation changing and obstacle avoidance control of unmanned underwater vehicles according to claim 6, characterized in that, The obstacle avoidance formula is as follows: 。 8. A method for time-delayed formation changing and obstacle avoidance control of unmanned underwater vehicles according to claim 7, characterized in that, The process of formation changes includes: when ≤ ≤ When this happens, proceed with the following steps: Calculate the smoothing factor : ； ； and These are the start time and the end time, respectively. Formation position update: For the A follower, if =1, then: ； For the first The relative position of the ultimate goal of each follower; Obstacle collision avoidance calculation: Initialize obstacle avoidance offset: ； Obstacle avoidance condition judgment: If the first The distance between each follower and the obstacle satisfies: ; For the first The current position of each follower; Then calculate the obstacle avoidance displacement. : ； The result of the obstacle avoidance formula calculation; Obstacle avoidance displacement Superimposed on obstacle avoidance offset This yields the latest obstacle avoidance offset. The latest obstacle avoidance offset and the first Current position of each follower Add them together to get the first one. The updated position of each follower.

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