Full-drive unmanned ship safe formation control method based on improved potential function

Abstract

The invention discloses a fully-driven unmanned ship safe formation control method based on an improved potential function, and the method comprises the steps: building a kinematics control law through the built improved potential function used for collision avoidance and communication keeping and the derivative of the improved potential function used for obstacle avoidance based on an updating law of an updating error of a path vector, and achieving the safe formation control of a fully-driven unmanned ship. And control input of the unmanned ship system is obtained, and control over the safe formation of the full-drive unmanned ship is completed. According to the invention, through the improved potential function for collision avoidance and connectivity keeping, the unmanned ship formation can keep collision avoidance and connectivity, the formation pattern is kept as far as possible on the premise of ensuring the safety and connectivity, and the tracking error is reduced, so that the problem that the unmanned ships in the formation are limited by the communication range and signal interference is solved. And meanwhile, through an improved potential function for obstacle avoidance, the obstacle avoidance capability of each ship can be fully considered, so that the unmanned ship formation can avoid static and dynamic obstacles appearing in a track in the sailing process, and potential safety hazards in actual operation are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned ship formation control, and in particular to a safe formation control method for all-drive unmanned ships based on an improved potential function. Background Art

[0002] Unmanned ships, due to their small size, strong concealment, and the ability to carry a variety of advanced communication modules, control modules, and sensor modules, have become an important part of modern marine equipment. In the military field, unmanned ships can be used for sea surface patrols, maritime interception, anti-submarine and anti-missile combat missions. In the civilian field, unmanned ships can be used for applications such as geographic surveying and mapping, environmental monitoring, maritime search and rescue, and resource development. With the rapid development of remote control technology, automatic navigation systems, and artificial intelligence, the autonomy and intelligence level of unmanned ships in performing complex marine tasks have been significantly improved. The development of unmanned ship technology has not only improved the safety and efficiency of marine operations, but also provided new possibilities for marine scientific research. Therefore, unmanned ships have become an important technical tool in the fields of marine scientific research, resource exploration, and rights protection worldwide, providing strong support for building a strong maritime nation.

[0003] Compared with the single-ship operation of unmanned ships, combining multiple unmanned ships to form a collaborative system and completing the target task through mutual communication and cooperation between individuals can show stronger robustness, maneuverability, intelligence, higher operating efficiency and larger operating scale. In practical applications, such as marine resource exploration or environmental monitoring in complex marine environments, unmanned ship groups can work together efficiently, greatly improving operating efficiency and safety. In addition, in military reconnaissance and search and rescue tasks, the effective collaborative operation of unmanned ship groups is also crucial. The formation control problem of unmanned ships belongs to an important research direction in the cooperative control technology of unmanned ships, which has great research value and research significance. The formation control of multiple unmanned ships can significantly improve the efficiency of task execution by optimizing the navigation path, avoiding collisions and maximizing the use of fleet resources. This is particularly important for large-scale marine survey and monitoring tasks.

[0004] At present, the group control strategies of unmanned ship formations include leader-follower method, virtual structure method and graph theory-based formation control schemes. Among them, the distributed formation control method based on graph theory has been deeply studied and applied in the field of unmanned ship formation control;

[0005] The core advantage of this method is that it can effectively form and maintain an orderly collective formation mode through local information exchange between ships. This distributed control method not only simplifies the control structure, but also improves the flexibility and robustness of the formation, enabling the unmanned ship group to better perform tasks in complex and changing marine environments.

[0006] However, although the graph theory-based formation control method has many advantages, its practical application effect and safety still have certain limitations.

[0007] First, in the marine environment, due to the limitations of communication range and signal interference, the unmanned ships in the formation may not always maintain a stable network connection, which will affect the overall coordination of the formation and the reliability of mission execution. For example, communication interruption may lead to the dissolution of the formation or the inability to effectively coordinate between ships, or even collisions between unmanned ships, thus affecting the completion of the mission.

[0008] Second, existing research often fails to fully consider the obstacle avoidance capability of each ship in the control of unmanned ship formations, which may lead to safety hazards in actual operations. For example, in a dense marine traffic environment, the lack of an effective obstacle avoidance strategy may increase the risk of ship collisions. Summary of the invention

[0009] The invention discloses a safe formation control method for all-drive unmanned ships based on an improved potential function to overcome the above technical problems.

[0010] In order to achieve the above object, the technical solution of the present invention is:

[0011] A safe formation control method for all-drive unmanned ships based on an improved potential function comprises the following steps:

[0012] S1: Establish the dynamic model of the unmanned ship in the fully driven unmanned ship safety formation system;

[0013] S2: According to the dynamic model of the unmanned ship, an adaptive fuzzy-based predictor is established to obtain an estimated value of a nonlinear term in the unmanned ship model;

[0014] S3: establishing an improved potential function for collision avoidance and connectivity maintenance and an improved potential function for obstacle avoidance, and obtaining partial derivatives of the improved potential function for collision avoidance and connectivity maintenance and the improved potential function for obstacle avoidance;

[0015] S4: Obtain the tracking error of the unmanned ship formation for the virtual leader, and establish a kinematic control law based on the update law of the update error of the path vector according to the partial derivatives of the improved potential function for collision avoidance and connectivity maintenance and the partial derivatives of the improved potential function for obstacle avoidance;

[0016] S5: According to the kinematic control law and the estimated value of the nonlinear term in the unmanned ship model, the control input of the unmanned ship system is obtained to complete the control of the safe formation of all-drive unmanned ships.

[0017] Furthermore, the improved potential function for avoiding collision and maintaining connectivity is established as follows:

[0018]

[0019] ρ ij =ρ i -ρ j

[0020] Where: represents the improved potential function for avoiding collision and maintaining connectivity; ρ ij Represents ρ i and ρ j The position difference between i and ρ j They represent the position coordinates of the i-th unmanned ship and the j-th unmanned ship in the earth coordinate system, where ρ i =[x i ,y i ] T , ρ j =[x j ,y j ] T , x j represents the horizontal coordinate of the position of the jth unmanned ship in the earth coordinate system; j represents the ordinate of the position of the jth unmanned ship in the earth coordinate system; j represents the number of the neighboring unmanned ship of the ith unmanned ship; D represents the minimum safe distance between unmanned ships to avoid collision; D m represents the maximum communication distance between unmanned ships to maintain connectivity; ||ρ ij || represents ρ ij The second norm of ;

[0021] The improved potential function for avoiding collision and maintaining connectivity P i The partial derivative of is:

[0022]

[0023] Furthermore, the improved potential function for obstacle avoidance is established as follows:

[0024]

[0025] ρ ik =ρ i -ρ k

[0026] Where: represents the improved potential function for obstacle avoidance; ρ ik Represents ρ i and ρ k The position difference between i represents the position coordinates of the i-th unmanned ship in the earth coordinate system; k represents the index of the obstacle; D orepresents the minimum collision avoidance distance between the unmanned ship and the obstacle; ‖ρ ik ‖ represents ρ ik The second norm of k is the plane coordinate of the obstacle center, ρ k =[x k ,y k ] T represents the position of the kth obstacle in the earth coordinate system;

[0027] The improved potential function for obstacle avoidance P i The partial derivative of is:

[0028]

[0029] Furthermore, the dynamic model of the unmanned ship is established as follows:

[0030]

[0031] Where: α i =[x i ,y i ,ψ i ] T ∈R 3 represents the position and heading of the i-th unmanned ship; x i represents the horizontal coordinate of the position of the unmanned ship in the earth coordinate system; y i represents the vertical coordinate of the position of the unmanned ship in the earth coordinate system; ψ i ∈(-π,π] represents the heading angle of the unmanned ship; [·] T Represents the transpose of the matrix; R 3 represents 3-dimensional Euclidean space; Q i (ψ i ) represents the rotation matrix, Q i (ψ i )∈R 3×3 , R 3×3 represents 3×3 dimensional Euclidean space; Γ i represents the speed of the i-th unmanned ship, where Γ i =[u i ,v i ,r i ] T ∈R 3 ,u i is the turbulence velocity that the unmanned ship experiences while sailing at sea, v i is the sway speed experienced by the unmanned ship during navigation at sea, r i is the yaw speed experienced by the unmanned ship when sailing at sea; and They are αi and Γ i The derivative with respect to time; W i represents the inertia matrix, where E i (Γ i ) represents the Coriolis centripetal matrix, E i (Γ i )=-E i (Γ i ) T ∈R 3 ×3 ; F i (Γ i ) represents the nonlinear damping matrix; h i (Γ i ,α i ) represents the generalized gravity and buoyancy vectors; f i (t) represents the vector of unknown disturbances caused by wind, waves and ocean currents, f i (t) = [f 1i ,f 2i ,f 3i ] T ∈R 3 , f 1i The vector representing the unknown disturbance on the unmanned ship in the longitudinal direction, f 2i The vector representing the unknown disturbance of the unmanned ship in the sway direction, f 3i The vector representing the unknown disturbance of the steering angle of the unmanned ship; θ i represents the control input of the unmanned ship system, θ i =[θ 1i ,θ 2i ,θ 3i ] T ∈R 3 ,θ 1i represents the input of the unmanned ship in the longitudinal direction, θ 2i represents the input of the unmanned ship in the sway direction, θ 3i Represents the input of the steering angle of the unmanned ship;

[0032] in,

[0033]

[0034] The dynamic model of the unmanned ship is rewritten as follows:

[0035]

[0036] In the formula, ε i represents the nonlinear term in the unmanned ship model, ε i =[ε ui ,ε vi,ε ri ] T =W i -1 [-E i (Γ i )Γ i -F i (Γ i )Γ i -h i (Γ i ,α i )+f i (t)],ε i ∈R 3 ; ε ui represents the unknown nonlinear term in the surge direction of the unmanned ship model; ε vi represents the unknown nonlinear term in the sway direction in the unmanned ship model; ε ri Represents the unknown nonlinear term in the steering angle in the unmanned ship model.

[0037] Furthermore, in S2, the formula used to obtain the estimated value of the nonlinear term in the unmanned ship model is as follows:

[0038]

[0039] In the formula, α i represents the position and heading of the i-th unmanned ship; is α i An estimated value of represents the estimated error of the unmanned ship’s position; for The derivative with respect to time; Q i (ψ i ) represents (rotation matrix); represents the gain of the estimator of the position and heading of the unmanned ship, where represents the predictor gain corresponding to the x direction in the position of the unmanned ship, represents the estimator gain corresponding to the y direction in the position of the unmanned ship, represents the estimator gain corresponding to the heading of the unmanned ship; is Γ i The estimated value of express Derivative with respect to time; represents the estimated error of the unmanned ship’s speed; γ i represents a known activation function, where γ i =diag{γ 1i ,γ 2i ,γ 3i}, γ 1iThe data representing the activation function corresponding to the unmanned ship's swaying speed direction, γ 2i The data representing the activation function corresponding to the speed direction of the unmanned ship’s horizontal bar, γ 3i Represents the data of the activation function corresponding to the steering angle of the unmanned ship; H i is the weight matrix, where H i =[H 1i ,H 2i ,H 3i ] T , H 1i The data representing the weight matrix corresponding to the unmanned ship's longitudinal velocity direction, H 2i The data representing the weight matrix corresponding to the speed direction of the unmanned ship, H 3i Data representing the weight matrix corresponding to the steering angle of the unmanned ship; represents the estimated value of H; represents the gain of the unmanned ship speed estimator, where represents the predictor gain corresponding to the speed of the unmanned ship in the longitudinal direction, represents the predictor gain corresponding to the speed of the unmanned ship in the swaying direction, represents the estimator gain corresponding to the steering angle of the unmanned ship; Represents ε i The estimated value of i Represents the function reconstruction error, where ∈ i =[∈ 1i ,∈ 2i ,∈ 3i ] T ,∈ 1i Represents the function reconstruction error corresponding to the longitudinal speed direction in the unmanned ship model, ∈ 2i Represents the function reconstruction error corresponding to the crossbar velocity direction in the unmanned ship model, ∈ 3i Represents the function reconstruction error corresponding to the steering angle in the unmanned ship model; express The derivative with respect to time; P represents the adaptive gain matrix; ξ represents the regularization coefficient.

[0040] Furthermore, in S4, the tracking error of the unmanned ship formation for the virtual leader is obtained as follows:

[0041]

[0042] α ijd =α id -α jd ∈R 3

[0043] Where: s 1irepresents the tracking error of the unmanned ship for the virtual leader; Q i (ψ i ) represents (rotation matrix); j represents the number of the neighboring unmanned ship of the i-th unmanned ship; I represents the total number of unmanned ships; represents the connection mark between the i-th unmanned ship and the j-th unmanned ship, α j represents the position and heading of the j-th unmanned ship, that is, the position and heading of the neighboring unmanned ship of the i-th unmanned ship; α ijd represents the desired overall formation offset; Indicates the position and heading of the virtual leader; α id represents the expected position and heading of the i-th unmanned ship relative to the virtual leader; α jd represents the expected position and heading of the jth unmanned ship relative to the virtual leader;

[0044] Among them, the position and direction of the virtual leader Get as follows:

[0045]

[0046] Where: Indicates the position and heading of the virtual leader; x 0 (ρ) represents the horizontal coordinate of the virtual leader’s position in the earth coordinates; The vertical coordinate representing the position of the virtual leader in the earth coordinates; represents the heading angle of the virtual leader; represents the path vector, where R represents a 1-dimensional Euclidean space.

[0047] Furthermore, in S4, the kinematic control law is established as follows:

[0048]

[0049] σ i =s 1i +Q i (ψ i ) T s 3i

[0050]

[0051] Where: i c represents the kinematic control law; Y 1i represents the kinematic positive definite diagonal gain matrix, where Y 1i ∈R 3×3 ; σ i represents the sum of the tracking error of the unmanned ship formation and the derivative of the improved potential function; ‖σi ‖ represents σ i The second norm of 1i is a positive constant that helps avoid large virtual control signals in the kinematic control law; represents the sum of the adjacent weights of the i-th unmanned ship, where represents the connectivity between the i-th unmanned ship and the virtual leader; Q i (ψ i ) T Indicates Q i (ψ i ) Represents Γ j The estimated value of Γ j represents the speed of the jth unmanned ship; express right The partial guide, express The derivative with respect to time, is the path vector; Λ represents the path vector The update error of Represents α ijd The derivative with respect to time; s 1i represents the tracking error of the unmanned ship formation for the virtual leader; s 3i represents the sum of the derivatives of the improved potential function; K represents the total number of obstacles; k represents the index of the obstacle.

[0052] Furthermore, in S4, the path vector The update law of the update error is expressed as follows:

[0053]

[0054] In the formula, κ and ω are both positive constants; is the time derivative of Λ.

[0055] Furthermore, in S4, the formula used to obtain the control input of the unmanned ship system is as follows:

[0056]

[0057] Where Y 2i ∈E 3×3 is a dynamic positive definite diagonal gain matrix, o 2i To help avoid the appearance of large positive constants of virtual control signals in the dynamic control law; is the inertia matrix. 2i is the control error of the unmanned ship on the target speed; is Γi c The derivative with respect to time; θ i represents the control input of the unmanned ship system; W i represents the inertia matrix; represents the connectivity mark between the i-th unmanned ship and the j-th unmanned ship; σ i represents the position and heading of the i-th unmanned ship; Represents ε i The estimated value of i Represents the nonlinear term in the unmanned ship model; is Γ i The estimated value of Γ i represents the speed of the i-th unmanned ship.

[0058] Beneficial effects: The invention discloses a method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function. The improved potential function for avoiding collision and maintaining connectivity and the derivative of the improved potential function for avoiding obstacles are established. Based on the update law of the update error of the path vector, a kinematic control law is established to obtain the control input of the unmanned ship system and complete the control of the safe formation of fully-driven unmanned ships. The invention uses an improved potential function for avoiding collision and maintaining connectivity to enable the unmanned ship formation to maintain collision avoidance and connectivity during navigation, that is, to balance between maintaining the formation and meeting the requirements of safety and connectivity. When the formation is maintained and the requirements of safety and connectivity do not conflict, the formation is maintained. When there is a conflict, the formation is maintained as much as possible under the premise of ensuring safety and connectivity, and the tracking error is reduced, thereby solving the problem that the unmanned ships in the formation are limited by the communication range and signal interference. At the same time, through the improved potential function for avoiding obstacles, the obstacle avoidance capability of each ship can be fully considered, so that the unmanned ship formation can avoid static and dynamic obstacles appearing in the trajectory during navigation, and reduce the safety hazards in actual operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] 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 creative labor.

[0060] Figure 1 The flowchart of the safe formation control method of all-drive unmanned ships based on the improved potential function of the present invention;

[0061] Figure 2 Schematic diagram of the structure of a safe formation control system of a fully-driven unmanned ship based on an improved potential function in an embodiment of the present invention;

[0062] Figure 3 A simulation trajectory diagram of a fully-driven unmanned ship formation in an embodiment of the present invention;

[0063] Figure 4 A schematic diagram of a following formation error when an unmanned ship formation follows a virtual leader in a time-varying formation in an embodiment of the present invention;

[0064] Figure 5 It is a schematic diagram of the effect of avoiding collision and maintaining connectivity between unmanned ship formations in an embodiment of the present invention. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution 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 described embodiments are 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 creative work are within the scope of protection of the present invention.

[0066] This embodiment introduces a safe formation control method for all-drive unmanned ships based on an improved potential function. Figure 1 As shown, the following steps are included:

[0067] S1: Establish the dynamic model of the unmanned ship in the fully driven unmanned ship safety formation system:

[0068] Specifically, this embodiment considers a fully-driven unmanned ship formation system consisting of I fully-driven unmanned ships, numbered 1, ..., I. The dynamic model of the i-th unmanned ship is described as follows:

[0069]

[0070] Where: α i =[x i ,y i ,ψ i ] T ∈R 3 represents the position and heading of the i-th unmanned ship; x i represents the horizontal coordinate of the position of the unmanned ship in the earth coordinate system; y i represents the vertical coordinate of the position of the unmanned ship in the earth coordinate system; ψ i ∈(-π,π] represents the heading angle of the unmanned ship; [·] T Represents the transpose of the matrix; R 3 represents 3-dimensional Euclidean space; Q i (ψ i ) represents the rotation matrix, Q i (ψ i )∈R3×3 , R 3×3 represents 3×3 dimensional Euclidean space; Γ i represents the speed of the i-th unmanned ship, where Γ i =[u i ,v i ,r i ] T ∈R 3 ,u i is the turbulence velocity that the unmanned ship experiences while sailing at sea, v i is the sway speed experienced by the unmanned ship during navigation at sea, r i is the yaw speed experienced by the unmanned ship when sailing at sea; and They are α i and Γ i The derivative with respect to time; W i represents the inertia matrix, where E i (Γ i ) represents the Coriolis centripetal matrix, E i (Γ i )=-E i (Γ i ) T ∈R 3 ×3 ; F i (Γ i ) represents the nonlinear damping matrix; h i (Γ i ,α i ) represents the generalized gravity and buoyancy vectors; f i (t) represents the vector of unknown disturbances caused by wind, waves and ocean currents, f i (t) = [f 1i ,f 2i ,f 3i ] T ∈R 3 , f 1i The vector representing the unknown disturbance on the unmanned ship in the longitudinal direction, f 2i The vector representing the unknown disturbance of the unmanned ship in the sway direction, f 3i The vector representing the unknown disturbance of the steering angle of the unmanned ship; θ i represents the control input of the unmanned ship system, θ i =[θ 1i ,θ 2i ,θ 3i ] T ∈R 3 ,θ 1i represents the input of the unmanned ship in the longitudinal direction, θ 2irepresents the input of the unmanned ship in the sway direction, θ 3i Represents the input of the steering angle of the unmanned ship;

[0071] in,

[0072]

[0073] For convenience, the dynamic model of the i-th unmanned ship is rewritten as follows:

[0074]

[0075] In the formula, ε i represents the nonlinear term in the unmanned ship model, ε i =[ε ui ,ε vi ,ε ri ] T =W i -1 [-E i (Γ i )Γ i -F i (Γ i )Γ i -h i (Γ i ,α i )+f i (t)],ε i ∈R 3 ; ε ui represents the unknown nonlinear term in the surge direction of the unmanned ship model; ε vi represents the unknown nonlinear term in the sway direction in the unmanned ship model; ε ri represents the unknown nonlinear term in the steering angle in the unmanned ship model;

[0076] S2: According to the dynamic model of the unmanned ship, an adaptive fuzzy-based predictor is established to obtain the estimated value of the nonlinear term in the unmanned ship model

[0077] Specifically, this embodiment adds an adaptive fuzzy-based predictor to estimate the speed of the unmanned ship and the uncertainties in the unmanned ship dynamics model:

[0078] Preferably, in S2, the formula used to obtain the estimated value of the nonlinear term in the unmanned ship model is as follows:

[0079]

[0080] In the formula, α i represents the position and heading of the i-th unmanned ship; is α iAn estimated value of represents the estimated error of the unmanned ship’s position; for The derivative with respect to time; Q i (ψ i ) represents (rotation matrix); represents the gain of the estimator of the position and heading of the unmanned ship, where represents the predictor gain corresponding to the x direction in the position of the unmanned ship, represents the estimator gain corresponding to the y direction in the position of the unmanned ship, represents the estimator gain corresponding to the heading of the unmanned ship; is Γ i The estimated value of express Derivative with respect to time; represents the estimated error of the unmanned ship’s speed; γ i represents a known activation function, where γ i =diag{γ 1i ,γ 2i ,γ 3i}, γ 1i The data representing the activation function corresponding to the unmanned ship's swaying speed direction, γ 2i The data representing the activation function corresponding to the speed direction of the unmanned ship’s horizontal bar, γ 3i Represents the data of the activation function corresponding to the steering angle of the unmanned ship; H i is the weight matrix, where H i =[H 1i ,H 2i ,H 3i ] T , H 1i The data representing the weight matrix corresponding to the unmanned ship's longitudinal velocity direction, H 2i The data representing the weight matrix corresponding to the speed direction of the unmanned ship, H 3i Data representing the weight matrix corresponding to the steering angle of the unmanned ship; represents the estimated value of H; represents the gain of the unmanned ship speed estimator, where represents the predictor gain corresponding to the speed of the unmanned ship in the longitudinal direction, represents the predictor gain corresponding to the speed of the unmanned ship in the swaying direction, represents the estimator gain corresponding to the steering angle of the unmanned ship; Represents ε i The estimated value of i Represents the function reconstruction error, where ∈ i =[∈ 1i ,∈2i ,∈ 3i ] T ,∈ 1i Represents the function reconstruction error corresponding to the longitudinal speed direction in the unmanned ship model, ∈ 2i Represents the function reconstruction error corresponding to the crossbar velocity direction in the unmanned ship model, ∈ 3i Represents the function reconstruction error corresponding to the steering angle in the unmanned ship model; express The derivative with respect to time; P represents the adaptive gain matrix; ξ represents the regularization coefficient;

[0081] Specifically, in this embodiment, H 1i , H 2i , H 3i , γ 1i , γ 2i , γ 3i ,∈ 1i ,∈ 2i ,∈ 3i ,P,ξ, All are normal numbers.

[0082] S3: establishing an improved potential function for collision avoidance and connectivity maintenance and an improved potential function for obstacle avoidance, and obtaining partial derivatives of the improved potential function for collision avoidance and connectivity maintenance and the improved potential function for obstacle avoidance;

[0083] Specifically, in this embodiment, an improved potential function for avoiding collision and maintaining connectivity in the following form is established to avoid mutual collision and maintain connectivity between the unmanned ships in the unmanned ship formation.

[0084] Preferably, the improved potential function for avoiding collision and maintaining connectivity is established as follows:

[0085]

[0086] ρ ij =ρ i -ρ j

[0087] Where: represents the improved potential function for avoiding collision and maintaining connectivity; ρ ij Represents ρ i and ρ j The position difference between i and ρ j They represent the position coordinates of the i-th unmanned ship and the j-th unmanned ship in the earth coordinate system, where ρ i =[x i ,y i ] T , ρ j =[xj ,y j ] T , x j represents the horizontal coordinate of the position of the jth unmanned ship in the earth coordinate system; y j represents the ordinate of the position of the jth unmanned ship in the earth coordinate system; j represents the number of the neighboring unmanned ship of the ith unmanned ship; D represents the minimum safe distance between unmanned ships to avoid collision; D m represents the maximum communication distance between unmanned ships to maintain connectivity; ||ρ ij || represents ρ ij The second norm of ;

[0088] The improved potential function for avoiding collision and maintaining connectivity P i The partial derivative of is:

[0089]

[0090] Preferably, the improved potential function for obstacle avoidance is established as follows: wherein the improved potential function for obstacle avoidance is used to avoid static and dynamic obstacles:

[0091]

[0092] ρ ik =ρ i -ρ k

[0093] Where: represents the improved potential function for obstacle avoidance; ρ ik Represents ρ i and ρ k The position difference between i represents the position coordinates of the i-th unmanned ship in the earth coordinate system; k represents the index of the obstacle; D o represents the minimum collision avoidance distance between the unmanned ship and the obstacle; ‖ρ ik ‖ represents ρ ik The second norm of k is the plane coordinate of the obstacle center, ρ k =[x k ,y k ] T represents the position of the kth obstacle in the earth coordinate system. In this embodiment, the obstacle is modeled as a closed circle.

[0094] The improved potential function for obstacle avoidance P i The partial derivative of is:

[0095]

[0096] Specifically, in this embodiment, the obstacle is modeled as a closed circle.

[0097] S4: Obtain the tracking error s of the unmanned ship formation for the virtual leader 1i , and according to the derivative of the improved potential function, based on the path vector The update law of the update error is used to establish the kinematic control law Γ i c ;

[0098] Preferably, in S4, the tracking error s of the unmanned ship formation for the virtual leader is 1i Get as follows:

[0099]

[0100] α ijd =α id -α jd ∈R 3

[0101] Where: s 1i represents the tracking error of the unmanned ship for the virtual leader; Q i (ψ i ) represents (rotation matrix); j represents the number of the neighboring unmanned ship of the i-th unmanned ship; I represents the total number of unmanned ships; represents the connectivity mark between the ith unmanned ship and the jth unmanned ship, that is, the connectivity mark between the ith unmanned ship and its neighbor unmanned ship. If the ith unmanned ship can obtain the path information (position and heading information) from the jth unmanned ship, then otherwise, α j represents the position and heading of the j-th unmanned ship, that is, the position and heading of the neighboring unmanned ship of the i-th unmanned ship; α ijd represents the desired overall formation offset; Indicates the position and heading of the virtual leader; α id represents the expected position and heading of the i-th unmanned ship relative to the virtual leader; α jd represents the expected position and heading of the jth unmanned ship relative to the virtual leader;

[0102] Among them, the position and direction of the virtual leader Get as follows:

[0103] The fleet of unmanned vessels follows a virtual leader that moves along a path parameterized by:

[0104]

[0105] Where: Indicates the position and heading of the virtual leader; x 0 (ρ) represents the horizontal coordinate of the virtual leader’s position in the earth coordinates; The vertical coordinate representing the position of the virtual leader in the earth coordinates; represents the heading angle of the virtual leader; represents the path vector, where R represents a 1-dimensional Euclidean space; in this embodiment, it is assumed that is bounded.

[0106] Preferably, the kinematic control law Γ i c Set up as follows:

[0107]

[0108] σ i =s 1i +Q i (ψ i ) T S 3i

[0109]

[0110] Where: i c represents the kinematic control law; Y 1i represents the kinematic positive definite diagonal gain matrix, where Y 1i ∈R 3×3 ; σ i represents the sum of the tracking error of the unmanned ship formation and the derivative of the improved potential function; ‖σ i ‖ represents σ i The second norm of 1i is a positive constant that helps avoid large virtual control signals in the kinematic control law; represents the sum of the adjacent weights of the i-th unmanned ship, where represents the connectivity identifier between the ith unmanned ship and the virtual leader. If the ith unmanned ship can obtain the path information from the virtual leader, then otherwise, Q i (ψ i ) T Indicates Q i (ψ i ) Represents Γ j The estimated value of Γ j represents the speed of the jth unmanned ship; express right The partial guide, express The derivative with respect to time, is the path vector; Λ represents the path vector The update error of Represents α ijd The derivative with respect to time; s 1i represents the tracking error of the unmanned ship formation for the virtual leader; s 3i represents the sum of the derivatives of the improved potential function; K represents the total number of obstacles; k represents the index of the obstacle;

[0111] Preferably, the path vector The update law of the update error is expressed as follows:

[0112] Specifically, for the path vector It can be updated smoothly. In this embodiment, the filter is used to design the update error Λ as:

[0113]

[0114] In the formula, κ and ω are both positive constants; is the time derivative of Λ;

[0115] S5: According to the kinematic control law Γ i c , obtain the control input θ of the unmanned ship system i , in order to complete the control of the safe formation of all-drive unmanned ships.

[0116] Specifically, this embodiment uses the backstepping method to design the control input θ i for:

[0117]

[0118] Where Y 2i ∈R 3×3 is a dynamic positive definite diagonal gain matrix, o 2i To help avoid the appearance of large positive constants of virtual control signals in the dynamic control law; is the inertia matrix. 2i is the control error of the unmanned ship on the target speed; is Γ i c The derivative with respect to time.

[0119] A method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function in this embodiment is to establish a kinematic control law based on the update law of the update error of the path vector through the improved potential function for collision avoidance and connectivity and the derivative of the improved potential function for obstacle avoidance, obtain the control input of the unmanned ship system, and complete the control of the safe formation of fully-driven unmanned ships. The present invention uses an improved potential function for collision avoidance and connectivity to enable the unmanned ship formation to maintain collision avoidance and connectivity during navigation, that is, to balance between maintaining the formation and meeting the requirements of safety and connectivity. When the formation is maintained and the requirements of safety and connectivity do not conflict, the formation is maintained. When there is a conflict, the formation is maintained as much as possible under the premise of ensuring safety and connectivity, and the tracking error is reduced, thereby solving the problem that the unmanned ships in the formation are limited by the communication range and signal interference. At the same time, through the improved potential function for obstacle avoidance, compared with the existing formation control method based on graph theory, the obstacle avoidance capability of each ship can be fully considered, so that the unmanned ship formation avoids static and dynamic obstacles appearing in the trajectory during navigation, and reduces the safety hazards in actual operation.

[0120] In summary, this embodiment can be applied to the safe formation control of unmanned ships. Through the fuzzy predictor, the improved potential function and the tracking differentiator, the dynamic control law is designed by the backstepping method, which can realize the formation control of unmanned ships under the premise of ensuring safety and connectivity, so that the unmanned ship formation can maintain the formation and track the parameterized virtual leader in a sea area with dynamic obstacles and static obstacles, avoid static and dynamic obstacles in the path during the tracking process, and avoid collisions between unmanned ships and maintain connectivity.

[0121] A specific embodiment of the present invention is as follows:

[0122] In the embodiment, a multi-unmanned ship formation cluster system consisting of five fully-driven unmanned ships is taken as an example. Figure 2 As shown, the scheme described in this embodiment is further described. Figure 2 The paper shows five unmanned ships following a virtual leader in a time-varying formation along a parameterized path, avoiding dynamic and static obstacles in the area during the process. The virtual leader is set to follow a path with parameters The initial positions and directions of the five unmanned ships are: 1 =[-13,193,2*π / 3] T Γ 1 =[0,0,0] T ; α 2 =[-7,198,3*π / 4] T Γ 2 =[0,0,0] T ; α3 =[-5,202,3*π / 4] T Γ 3 =[0,0,0] T ; α 4 =[2,206,0] T Γ 4 =[0,0,0] T ; α 5 =[8,210,7*π / 6] T Γ 5 =[0,0,0] T The expected formation position and direction of each unmanned ship for the virtual leader is: α 1d =[0,0,0] T ; α 2d =[-a,-a,0] T ; α 3d =[a,-a,0] T ; α 4d =[-2a,2a,0] T ; α 5d =[2a,-2a,0] T , where a = 2.76-0.003(t-210) T ,200 <t<210;a=2.76,t> 210. The predictor gain of the fuzzy predictor is The initial value of H is H = [0.1, 0.3, 0.5] T P = 100; ξ = 0.02. In the control law, Y 1i =diag[0.2,0.2,0.2]; Y 2i =diag[129,169,13.8]; 1i =1; 2i =1;κ=10;ω=10.

[0123] The parameter of the improved potential function is chosen as D m =15; D = 1. The simulation time is set to 1200 seconds, and the obstacle is modeled as a closed disk. The position and radius of the obstacle, as well as the minimum collision avoidance distance D between the unmanned ship and the obstacle are o The information is as follows:

[0124]

[0125] The tracking effect of the unmanned ship formation on the virtual leader is as follows Figure 3 As shown, it can be seen that after avoiding the obstacles, the tracking error of the formation approaches zero. Figure 4 and Figure 5The improved potential function is demonstrated to have an effect on collision avoidance and connectivity maintenance of the unmanned ship formation, so that the distance between adjacent unmanned ships is kept within a range where there will be no collision and connectivity is maintained. Figure 4 The figure shows the tracking effect of each unmanned ship in the unmanned ship formation on the virtual leader. As can be seen from the figure, the unmanned ship formation will sacrifice the tracking performance as little as possible to complete the obstacle avoidance task. After completing the obstacle avoidance task, the tracking error of the unmanned ship formation will approach zero. Figure 5 It can be seen that under the action of the improved potential function, each ship in the unmanned ship formation can avoid collisions with each other and maintain connectivity within a distance, thereby avoiding problems such as mutual collisions and network connection interruptions.

[0126] 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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 safe formation control method for all-drive unmanned ships based on improved potential function, characterized in that: The steps include: S1: Establish the dynamic model of the unmanned ship in the fully driven unmanned ship safety formation system; S2: According to the dynamic model of the unmanned ship, an adaptive fuzzy-based predictor is established to obtain an estimated value of a nonlinear term in the unmanned ship model; S3: establishing an improved potential function for collision avoidance and connectivity maintenance and an improved potential function for obstacle avoidance, and obtaining partial derivatives of the improved potential function for collision avoidance and connectivity maintenance and the improved potential function for obstacle avoidance; S4: Obtain the tracking error of the unmanned ship formation for the virtual leader, and establish a kinematic control law based on the update law of the update error of the path vector according to the partial derivatives of the improved potential function for collision avoidance and connectivity maintenance and the partial derivatives of the improved potential function for obstacle avoidance; S5: According to the kinematic control law and the estimated value of the nonlinear term in the unmanned ship model, the control input of the unmanned ship system is obtained to complete the control of the safe formation of all-drive unmanned ships.

2. The method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function according to claim 1, characterized in that: The improved potential function for avoiding collision and maintaining connectivity is established as follows: r ij =ρ i -r j Where: represents the improved potential function for avoiding collision and maintaining connectivity; ρ ij Represents ρ i and ρ j The position difference between i and ρ j They represent the position coordinates of the i-th unmanned ship and the j-th unmanned ship in the earth coordinate system, where ρ i =[x i ,y i ] T , ρ j =[x j ,y j ] T , x j represents the horizontal coordinate of the position of the jth unmanned ship in the earth coordinate system; y j represents the ordinate of the position of the jth unmanned ship in the earth coordinate system; j represents the number of the neighboring unmanned ship of the ith unmanned ship; D represents the minimum safe distance between unmanned ships to avoid collision; D m represents the maximum communication distance between unmanned ships to maintain connectivity; ||ρ ij || represents ρ ij The second norm of ; The improved potential function for avoiding collision and maintaining connectivity P i The partial derivative of is:

3. The method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function according to claim 1, characterized in that: The improved potential function for obstacle avoidance is established as follows: r ik =ρ i -r k Where: represents the improved potential function for obstacle avoidance; ρ ik Represents ρ i and ρ k The position difference between i represents the position coordinates of the i-th unmanned ship in the earth coordinate system; k represents the index of the obstacle; D o represents the minimum collision avoidance distance between the unmanned ship and the obstacle; ‖ρ ik ‖ represents ρ ik The second norm of k is the plane coordinate of the obstacle center, ρ k =[x k ,y k ] T represents the position of the kth obstacle in the earth coordinate system; The improved potential function for obstacle avoidance P i The partial derivative of is:

4. The method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function according to claim 1, characterized in that: The dynamic model of the unmanned ship is established as follows: Where: α i =[x i ,y i ,ψ i ] t ∈R 3 represents the position and heading of the i-th unmanned ship; x i The horizontal coordinate of the position of the unmanned ship in the earth coordinate system; y i represents the vertical coordinate of the position of the unmanned ship in the earth coordinate system; ψ i ∈(-π,π] represents the heading angle of the unmanned ship; [·] T Represents the transpose of the matrix; R 3 represents 3-dimensional Euclidean space; Q i (ψ i ) represents the rotation matrix, Q i (ψ i )∈R 3×3 , R 3 ×3 represents 3×3 dimensional Euclidean space; Γ i represents the speed of the i-th unmanned ship, where Γ i =[u i ,v i ,r i ] T ∈R 3 ,u i is the turbulence velocity that the unmanned ship experiences while sailing at sea, v i is the sway speed experienced by the unmanned ship during navigation at sea, r i is the yaw speed experienced by the unmanned ship when sailing at sea; and They are α i and Γ i The derivative with respect to time; W i represents the inertia matrix, where E i (Γ i ) represents the Coriolis centripetal matrix, E i (Γ i )=-E i (Γ i ) T ∈R 3×3 ; F i (Γ i ) represents the nonlinear damping matrix; h i (Γ i ,α i ) represents the generalized gravity and buoyancy vectors; f i (t) represents the vector of unknown disturbances caused by wind, waves and ocean currents, f i (t) = [f 1i ,f 2i ,f 3i ] T ∈R 3 , f 1i The vector representing the unknown disturbance on the unmanned ship in the longitudinal direction, f 2i The vector representing the unknown disturbance of the unmanned ship in the sway direction, f 3i The vector representing the unknown disturbance of the steering angle of the unmanned ship; θ i represents the control input of the unmanned ship system, θ i =[θ 1i ,θ 2i ,θ 3i ] T ∈R 3 ,θ 1i represents the input of the unmanned ship in the longitudinal direction, θ 2i represents the input of the unmanned ship in the sway direction, θ 3i Represents the input of the steering angle of the unmanned ship; in, The dynamic model of the unmanned ship is rewritten as follows: In the formula, ε i represents the nonlinear term in the unmanned ship model, ε i =[ε ui ,ε vi ,ε ri ] T =W i -1 [-E i (Γ i )Γ i -F i (Γ i )Γ i -h i (Γ i ,α i )+f i (t)],ε i ∈R 3 ; ε ui represents the unknown nonlinear term in the surge direction of the unmanned ship model; ε vi represents the unknown nonlinear term in the sway direction in the unmanned ship model; ε ri Represents the unknown nonlinear term in the steering angle in the unmanned ship model.

5. The method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function according to claim 1, characterized in that: In S2, the formula used to obtain the estimated value of the nonlinear term in the unmanned ship model is as follows: In the formula, α i represents the position and heading of the i-th unmanned ship; is α i An estimated value of represents the estimated error of the unmanned ship’s position; for The derivative with respect to time; Q i (ψ i ) represents (rotation matrix); represents the gain of the estimator of the position and heading of the unmanned ship, where represents the predictor gain corresponding to the x direction in the position of the unmanned ship, represents the estimator gain corresponding to the y direction in the position of the unmanned ship, represents the estimator gain corresponding to the heading of the unmanned ship; is Γ i The estimated value of express Derivative with respect to time; represents the estimated error of the unmanned ship’s speed; γ i represents a known activation function, where γ i =diag{γ 1i ,γ 2i ,γ 3i }, γ 1i The data representing the activation function corresponding to the unmanned ship's swaying speed direction, γ 2i The data representing the activation function corresponding to the speed direction of the unmanned ship’s horizontal bar, γ 3i Represents the data of the activation function corresponding to the steering angle of the unmanned ship; H i is the weight matrix, where H i =[H 1i ,H 2i ,H 3i ] T , H 1i The data of the weight matrix corresponding to the unmanned ship's longitudinal speed direction, H 2i The data representing the weight matrix corresponding to the speed direction of the unmanned ship, H 3i Data representing the weight matrix corresponding to the steering angle of the unmanned ship; represents the estimated value of H; represents the gain of the unmanned ship speed estimator, where represents the predictor gain corresponding to the speed of the unmanned ship in the longitudinal direction, represents the predictor gain corresponding to the speed of the unmanned ship in the swaying direction, represents the estimator gain corresponding to the steering angle of the unmanned ship; Represents ε i The estimated value of i Represents the function reconstruction error, where ∈ i =[∈ 1i ,∈ 2i ,∈ 3i ] T ,∈ 1i Represents the function reconstruction error corresponding to the longitudinal speed direction in the unmanned ship model, ∈ 2i Represents the function reconstruction error corresponding to the crossbar velocity direction in the unmanned ship model, ∈ 3i Represents the function reconstruction error corresponding to the steering angle in the unmanned ship model; express The derivative with respect to time; P represents the adaptive gain matrix; ξ represents the regularization coefficient.

6. The method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function according to claim 1, characterized in that: In S4, the tracking error of the unmanned ship formation for the virtual leader is obtained as follows: α ijd ＝α id -α jd ∈R 3 Where: s 1i represents the tracking error of the unmanned ship for the virtual leader; Q i (ψ i ) represents (rotation matrix); j represents the number of the neighboring unmanned ship of the i-th unmanned ship; I represents the total number of unmanned ships; represents the connection mark between the i-th unmanned ship and the j-th unmanned ship, α j represents the position and heading of the j-th unmanned ship, that is, the position and heading of the neighboring unmanned ship of the i-th unmanned ship; α ijd represents the desired overall formation offset; Indicates the position and heading of the virtual leader; α id represents the expected position and heading of the i-th unmanned ship relative to the virtual leader; α jd represents the expected position and heading of the jth unmanned ship relative to the virtual leader; Among them, the position and direction of the virtual leader Get as follows: Where: represents the position and heading of the virtual leader; x0(ρ) represents the horizontal coordinate of the position of the virtual leader in the earth coordinates; The vertical coordinate representing the position of the virtual leader in the earth coordinates; represents the heading angle of the virtual leader; represents the path vector, where R represents a 1-dimensional Euclidean space.

7. The method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function according to claim 1, characterized in that: In S4, the kinematic control law is established as follows: Where: F i c represents the kinematic control law; Y 1i represents the kinematic positive definite diagonal gain matrix, where Y 1i ∈R 3×3 ; σ i represents the sum of the tracking error of the unmanned ship formation and the derivative of the improved potential function; ‖σ i ‖ represents σ i The second norm of 1i is a positive constant that helps avoid large virtual control signals in the kinematic control law; represents the sum of the adjacent weights of the i-th unmanned ship, where represents the connectivity between the i-th unmanned ship and the virtual leader; Q i (ψ i ) T Indicates Q i (ψ i ) Represents Γ j The estimated value of Γ j represents the speed of the jth unmanned ship; express right The partial guide, express The derivative with respect to time, is the path vector; Λ represents the path vector The update error of Represents α ijd The derivative with respect to time; s 1i represents the tracking error of the unmanned ship formation for the virtual leader; s 3i represents the sum of the derivatives of the improved potential function; K represents the total number of obstacles; k represents the index of the obstacle.

8. The method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function according to claim 7, characterized in that: In S4, the path vector The update law of the update error is expressed as follows: In the formula, κ and ω are both positive constants; is the time derivative of Λ.

9. The method for controlling a safe formation of fully-driven unmanned ships based on an improved potential function according to claim 1, characterized in that: In S4, the formula used to obtain the control input of the unmanned ship system is as follows: Where Y 2i ∈R 3×3 is a dynamic positive definite diagonal gain matrix, o 2i To help avoid the appearance of a large positive constant of the virtual control signal in the dynamic control law; W i T =W i ∈R 3×3 is the inertia matrix, s 2i is the control error of the unmanned ship on the target speed; is Γ i c Derivative with respect to time; θ i represents the control input of the unmanned ship system; W i represents the inertia matrix; represents the connectivity mark between the i-th unmanned ship and the j-th unmanned ship; σ i represents the position and heading of the i-th unmanned ship; Represents ε i The estimated value of i Represents the nonlinear term in the unmanned ship model; is Γ i The estimated value of Γ i represents the speed of the i-th unmanned ship.

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