Formation control method of water surface unmanned ship system

Abstract

The application discloses a kind of formation control methods of water unmanned ship system, belong to marine space intelligent unmanned carrier control technical field, it includes the following steps: S1, establish dynamic system model;S2, the formation control problem of water unmanned ship system is converted into follower to virtual leader trajectory tracking problem;S3, establish general asymmetric barrier function of processing error constraint;S4, utilize fuzzy logic system to process unknown part and external disturbance of system;S5, based on dynamic system model, general asymmetric barrier function and fuzzy logic system, utilize backstepping method and combine fixed time control theory design fixed time formation control method.The method provided by the application, system convergence time is not dependent on the selection of system initial state, all signal quantities in system are bounded, and the tracking error of the system always satisfies the preset constraint condition during operation, which maintains fast convergence while constraining the tracking error of the system.

Description

Technical Field

[0001] This invention relates to a formation control method for an unmanned surface vessel system, belonging to the field of marine space intelligent unmanned vehicle control technology. Background Technology

[0002] Unmanned surface vessels (USVs) are intelligent unmanned surface vehicles capable of autonomous navigation and task completion in real-world marine environments, playing a crucial role in ocean exploration and development. A USV system consists of multiple USVs, each capable of executing its own sub-tasks in parallel. Through communication and coordination, they expand their mission capabilities and improve the efficiency of exploration and development. Formation control of a USV system refers to maintaining a desired relative position and attitude among multiple USVs to achieve the designated mission by designing appropriate control strategies.

[0003] Considering the influence of ocean currents, wind, and waves, designing a formation control scheme with fast convergence speed and strong robustness has become a research hotspot. USVs are characterized by high maneuverability and flexibility, requiring the system to reach stability in a short time, which places higher demands on the system's convergence time. Most current research on formation control methods focuses on improving the system's tracking accuracy. However, for multi-USV systems, output error constraints and convergence time should also be considered to improve system safety and operational efficiency.

[0004] Traditional unmanned surface vessel (USV) formation control methods still have some technical shortcomings, such as (1) existing USV formation control strategies rarely consider the problem of unknown environmental interference. During the formation of multiple USVs, they are inevitably affected by external environmental interference such as wind and waves, which are difficult to be directly measured by sensors; (2) existing USV formation control strategies with constraints rarely consider the problem of solving asymmetric error constraints; (3) existing USV formation control strategies that consider convergence time mostly make the system stable for a finite time. However, the convergence time of the system depends heavily on the initial state of the system and rarely involves the USV formation control problem under fixed time.

[0005] It should be noted that the above content falls within the inventor's technical knowledge and does not necessarily constitute prior art. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a formation control method for surface unmanned surface vessel (USV) systems. For multi-USV systems with output error constraints and time-varying ocean current interference, the designed controller enables the formation task to be completed within a fixed time.

[0007] The present invention achieves the above objectives by adopting the following technical solutions:

[0008] A method for formation control of an unmanned surface vessel system includes the following steps:

[0009] S1. Based on the hydrodynamic characteristics of unmanned surface vessels, a dynamic system model is established for the horizontal motion of an unmanned surface vessel system containing one navigator and N followers in the XY plane.

[0010] S2. Introduce a virtual navigator to transform the formation control problem of the unmanned surface vessel system into a trajectory tracking problem of the follower to the virtual navigator;

[0011] S3. Based on the follower's trajectory tracking error variable of the virtual navigator, establish a general asymmetric barrier function to handle error constraints;

[0012] S4. The system model has uncertain unknown parts and external disturbances. Fuzzy logic system is used to process the unknown parts and external disturbances of the system.

[0013] S5. Based on the dynamic system model, the general asymmetric barrier function and the fuzzy logic system, the backstepping method is used to integrate steps S3 and S4, and a fixed-time formation control method is designed in combination with fixed-time control theory.

[0014] In one embodiment of the present invention, in step S1, the dynamic system model established for the i-th follower is as follows:

[0015]

[0016] in, This represents the position and heading angle of the i-th unmanned surface vessel. Indicates η i The first derivative of , where x represents the longitudinal position of the unmanned surface vessel in the geodetic coordinate system, and y represents the lateral position of the unmanned surface vessel in the geodetic coordinate system. υ represents the heading angle of an unmanned surface vessel. i =[u,v,r] T This represents the velocity information of the i-th unmanned surface vessel (USV), where u represents the longitudinal velocity, v represents the yaw velocity, and r represents the angular velocity. This represents the vector consisting of the longitudinal acceleration, sway acceleration, and angular acceleration of the i-th unmanned surface vessel.

[0017] Let the transformation matrix between the body coordinate system and the geodetic coordinate system of the i-th unmanned surface vessel be represented as:

[0018]

[0019] M i ∈R 3×3 The inertial matrix of the i-th unmanned surface vessel is denoted as: M i =diag{m u m v m r},in m represents the mass of the unmanned surface vessel. It is the added mass of the unmanned surface vessel, I z The moment of inertia representing the rotation of an unmanned surface vessel;

[0020] C i ∈R 3×3 The Coriolis force matrix of the i-th unmanned surface vessel is represented as:

[0021]

[0022] D i ∈R 3×3 The damping force matrix of the i-th unmanned surface vessel is represented as: D i =diag{d u d v d r}, where d u =-(X) u +X u|u |u|), d v =-(Y v +Y v|v |v|), d r =-(N) r +N r|r |r|);X u X u|u| Y v N r and X u|u| Y v|v| N r|r| Linear and quadratic damping coefficients, respectively;

[0023] τ wi ∈R 3 τ represents the external ocean current disturbance experienced by the i-th unmanned surface vessel. i ∈R 3 This represents the input control force of the i-th unmanned surface vessel;

[0024] Define x 1i =η i ,x 2i =υ i Therefore, the dynamic model of the unmanned surface vessel can be represented as:

[0025]

[0026] in, x 1i x 2i The first derivative,

[0027] In one embodiment of the present invention, step S2 includes:

[0028] S2.1 Before the mission begins, based on the desired formation required for the formation mission, set one real navigator and several virtual navigators, and set the relative distance and angle between each virtual navigator and the real navigator. During the operation of the unmanned surface vessel system, the relative distance and angle between the virtual navigator and the real navigator remain unchanged, forming a fixed formation.

[0029] S2.2 The formation control problem of the surface unmanned surface vessel system, which determines the distance and angle between the followers and the real navigator, is transformed into the trajectory tracking problem of each follower to the corresponding virtual navigator.

[0030] In step S2.1, the distance and angle between the virtual navigator and the real navigator are as follows:

[0031]

[0032] Where, x vl Indicates the vertical position of the virtual navigator, y vl Indicates the lateral movement position of the virtual navigator. The heading angle of the virtual navigator, x l Indicates the vertical position of the true navigator, y l Indicates the lateral direction and position of the true navigator. The heading angle represents the actual navigator. These represent the horizontal and vertical distances between the virtual navigator and the real navigator, respectively. This indicates the trajectory information of the virtual navigator.

[0033] In one embodiment of the present invention, the general asymmetric barrier function established in step S3 is:

[0034]

[0035] Where, β i It is an intermediate variable for establishing the general error constraint function, Ξ L Ξ H It is the error constraint boundary vector, Ξ L It is by Ξ Lj The vector formed, Ξ H It is Ξ Hj The vector formed, ΞL =[Ξ L1 ,Ξ L2 ,Ξ L3 ] T Ξ H =[Ξ H1 ,Ξ H2 ,Ξ H3 ] T .

[0036] Specifically, step S3 includes:

[0037] S3.1 Define the follower's trajectory tracking error variable for the virtual navigator as:

[0038]

[0039] Z 1i Z 2i x represents the trajectory tracking error and velocity tracking error of the follower and virtual navigator, respectively. 1i x represents the trajectory of the follower. 1d Let x represent the expected trajectory of the follower. 2i α represents the speed of the follower. 1i It is a virtual control law of followers;

[0040] S3.2, Constrain the trajectory tracking error of the follower;

[0041] Throughout the motion control process, in order to meet the trajectory tracking accuracy requirements of the follower towards the virtual navigator, it is necessary to constrain the trajectory tracking error of the follower. The constraint conditions are set as follows:

[0042] -Ξ Lj <Z 1ij <Ξ Hj j = 1, 2, 3;

[0043] Among them, Z 1ij Ξ represents the tracking error between the follower and the virtual navigator in the longitudinal, sway, and heading directions. Lj and Ξ Hj Denotes the corresponding constraint boundary equation, Ξ Lj >0,Ξ Hj >0 represents a continuously differentiable, n-order time-varying constraint equation, Ξ Lj and Ξ Hj They can be unequal, which means the constraints are asymmetric;

[0044] S3.3 Establish a general asymmetric obstacle function to handle the asymmetric error constraint problem in the formation operation of multiple surface unmanned surface vessels.

[0045] In one embodiment of the present invention, in step S4, the unknown equations of the system are defined:

[0046]

[0047] Using fuzzy logic systems to approximate the estimation of unknown equations, we have:

[0048] Where · represents the Hadama product, W 1i W 2i S represents the ideal fuzzy weight matrix. 1i S 2i Let ζ be the membership function vector. 1i This represents the approximation error vector. It integrates external disturbances. It is the derivative of the virtual control law. Let ζ represent a small positive number. 2i This indicates the approximation error.

[0049] In one embodiment of the present invention, the specific process of step S5 is as follows:

[0050] The virtual control law is designed as follows:

[0051]

[0052]

[0053] ψ = [ψ1, ψ2, ψ3] T For ease of representation, △ is used. j1 ,△ j2 ,ψ j j = 1, 2, 3 as △ 11 ,△ 21 ,△ 31 ,△ 12 ,△ 22 ,△ 32 The general variable form of ψ1,ψ2,ψ3;

[0054]

[0055]

[0056] The virtual adaptive law is designed as follows:

[0057] Represents χ 1i The estimated value, χ 1i For the introduced unknown positive parameter, χ 1i=||W 1i || 2 ;

[0058] Among them, K 11 and K 12 To control the gain, K represents an intermediate variable. 11 K 12 a1 represents the control gain, and ε1 is a positive number; a1, c1, ε1 and γ1 are positive numbers to be designed, and |||| denotes the L2 norm;

[0059] The design of the true control law is as follows:

[0060]

[0061]

[0062] The design law of true adaptiveness is:

[0063] Represents χ 2i The estimated value, χ 2i For the introduced unknown positive parameter, χ 2i =||W 2i || 2 ;

[0064] in, c², ε², and γ² are small positive numbers, and K... 21 and K 22 To control the gain.

[0065] The beneficial effects of this application include, but are not limited to:

[0066] The formation control method for unmanned surface vessels (USVs) provided by this invention introduces a virtual navigator formation strategy based on the desired formation and establishes constraint equations based on the tracking error limit of the USVs. On the basis of fixed-time control theory, a fuzzy logic system is used to approximate the unknown terms of the system and wave disturbances. At the same time, an asymmetric obstacle equation is used to constrain the output error of the system, thereby improving the system's safety. Finally, an adaptive fuzzy fixed-time formation control algorithm is proposed based on the backstepping method, which enables the multi-USV system to converge to the desired formation configuration within a fixed time and complete the formation task.

[0067] The formation control method for unmanned surface vessel (USV) systems provided by this invention introduces a general constraint equation to handle the asymmetric constraint problem in the formation process of multiple USV systems. This constraint equation can also be used in symmetric and unconstrained cases. The system convergence time does not depend on the selection of the initial state of the system, all semaphores in the system are bounded, and the tracking error of the system always meets the preset constraint conditions during operation. While maintaining fast convergence, the tracking error of the system is constrained, thereby improving the system's safety.

[0068] The purpose of introducing a virtual navigator in this invention is to provide followers with the desired position information during the formation process. If the followers can track the corresponding virtual navigator within a limited time, they can form the desired formation with the real navigator, thereby achieving the purpose of formation. Attached Figure Description

[0069] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0070] Figure 1 This is a control logic block diagram of the present invention;

[0071] Figure 2 This is a flowchart of the method of the present invention;

[0072] Figure 3 This is a diagram illustrating the formation tracking effect.

[0073] Figure 4 for Figure 3 Color illustrations;

[0074] Figure 5 The tracking error effect diagram for USV0;

[0075] Figure 6 for Figure 5 Color illustrations;

[0076] Figure 7 The tracking error effect diagram of USV1;

[0077] Figure 8 for Figure 7 Color illustrations;

[0078] Figure 9 For control input of USV0;

[0079] Figure 10 For control input of USV1;

[0080] Figure 11 The oscillation error constraint performance of USV0;

[0081] Figure 12 This represents the sway error constraint performance of USV0;

[0082] Figure 13 This represents the roll angle error constraint performance of USV0; Detailed Implementation

[0083] The present invention will be further illustrated below with reference to specific embodiments. It should be noted that many specific details are set forth in the following description to provide a thorough understanding of the invention; however, the invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0084] In this embodiment, a system consisting of three identical USVs was selected to verify the effectiveness of the proposed control algorithm. Each USV can obtain its own state information through its own onboard outdoor positioning devices (such as GPS), speed measuring devices (such as Doppler velocimeters), and other sensors. Different individuals can exchange information via radio. The desired control objective is that the three USVs can form a triangular formation and maintain it within a finite time.

[0085] To more clearly illustrate the technical means incorporated into the controller designed in this invention, the specific technical principles are as follows: Figure 1 As shown. According to Figure 2 The design process was followed to complete the design of the formation controller.

[0086] The model parameters for the three USVs are:

[0087]

[0088] Set the initial state of the virtual navigator USV to η. l = [0,0,0], the desired trajectory and the desired velocity are related, and the desired velocity is set as: υ l = [1, 0.5, 0.1], simulation time: t∈[0, 65]. The initial states of the two follower USVs are set as η0 = [-2.5, -2.5, 0.2] and η1 = [-2.5, 2.5, -0.1]. The desired configuration consisting of the two virtual navigators and the real navigator is:

[0089] The following assumptions are made regarding external time-varying ocean currents and wave disturbances:

[0090]

[0091] To handle external interference and unknowns in the system, a fuzzy logic system containing seven fuzzy rules is selected for approximation. The membership function is designed as follows:

[0092] Sij (Z i )=exp[-0.5(Z i +4-j)],i=1,2.j=1,...,7.

[0093] Where Z1=[β i ·ψ,α 1i ] T ∈R 6 ,

[0094] To address the tracking error constraint problem, the error constraint equation is as follows:

[0095] Ξ Lj =0.5+9exp(-0.3t)j=1,2,3;

[0096] Ξ Hj =0.3+8exp(-0.4t)j=1,2,3;

[0097] To achieve fixed-time formation of unmanned surface vessels, the parameters of the designed formation controller are set as follows:

[0098] K 11 =K 21 =15, K 12 =K 22 =5, a1=a2=1, γ1=γ2=10, c1=c2=0.01, ε1=ε2=0.1, ε1=ε2=0.1,

[0099] Figure 3 and Figure 4 The diagram shows the formation effect of three USVs, demonstrating that the control method designed in this invention can achieve a triangular formation configuration for multiple USV systems within a finite time.

[0100] The position and velocity tracking errors of the two follower USVs are as follows: Figure 5 -and Figure 8 As shown, under different initial states, the two follower USVs can achieve accurate tracking of the virtual navigator in a short time, and the tracking error can converge to a small neighborhood near the origin.

[0101] from Figure 9 and Figure 10 It can be seen that the control input signal designed in this invention is bounded and smooth, satisfying the actual physical constraints of the USV.

[0102] Considering the similarity between the two followers USV, USV0 is chosen as an example to demonstrate the constraints on the system tracking error. Figures 11-13The error constraint performance of USV0 is shown, and it can be found that the position tracking error of the follower USV always meets the specified constraint conditions, which means that the designed controller has good transient stability response capability.

[0103] The two-dimensional plane described in the above implementation examples can be any plane in three-dimensional space, and is also applicable to the formation control of other multi-agent systems.

[0104] The above specific embodiments should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, any alternative improvements or modifications made to the embodiments of the present invention shall fall within the scope of protection of the present invention.

[0105] Any aspects of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A formation control method for an unmanned surface vessel system, characterized in that, Includes the following steps: S1. Based on the hydrodynamic characteristics of unmanned surface vessels, a dynamic system model is established for the horizontal motion of an unmanned surface vessel system containing one navigator and N followers in the XY plane. S2. Introduce a virtual navigator to transform the formation control problem of the unmanned surface vessel system into a trajectory tracking problem of the follower to the virtual navigator; S3. Based on the follower's trajectory tracking error variable of the virtual navigator, a general asymmetric barrier function for handling error constraints is established as follows: ； in, , These are intermediate variables used to establish the general error constraint function. , It is the error constraint boundary vector. and This represents the corresponding constraint boundary equation. , It is by The vector formed yes The vector formed , , This indicates the tracking error between the follower and the virtual navigator. S4. The system model contains uncertain unknowns and external disturbances. Fuzzy logic is used to handle these unknowns and disturbances. The specific process is as follows: Define the unknown equations of the system: ， ； Using fuzzy logic systems to approximate the estimation of unknown equations, we have: , ; in, Indicates the expected trajectory of the followers. This indicates the speed tracking error between the follower and the virtual navigator. Represents the Hadama product. , Represents the ideal fuzzy weight matrix. , For membership function vectors, This represents the approximation error vector. ; It integrates external disturbances. It is the virtual control law of the followers. It is the derivative of the virtual control law. Represents a small positive number. Indicates the approximation error; For ease of representation, we use As The general variable form; ， ， ； in, This indicates the tracking error of the follower and the virtual navigator in the longitudinal direction, sway direction, and heading angle. S5. Based on the dynamic system model, the general asymmetric barrier function, and the fuzzy logic system, steps S3 and S4 are integrated using the backstepping method, and a fixed-time formation control method is designed in conjunction with fixed-time control theory. The specific process is as follows: The virtual control law is designed as follows: ， ； in, Let represent the transformation matrix between the body coordinate system and the geodetic coordinate system of the i-th unmanned surface vessel. ; The virtual adaptive law is designed as follows: , express The estimated value, For the introduced unknown positive parameters, ; in, and To control the gain, Indicates intermediate variables. , , Indicates control gain. It is a positive number; and For positive numbers to be designed, Represents the L2 norm; The design of the true control law is as follows: ， ； in, , Let the Coriolis force matrix of the i-th unmanned surface vessel be represented. Let the damping force matrix of the i-th unmanned surface vessel be represented. Indicates the speed of the followers. , This represents the vector consisting of the longitudinal acceleration, sway acceleration, and angular acceleration of the i-th unmanned surface vessel. The design law of true adaptiveness is: , express The estimated value, For the introduced unknown positive parameters, ; in, and Small positive number, and To control the gain.

2. The formation control method for an unmanned surface vessel system according to claim 1, characterized in that, In step S1, the dynamic system model established for the i-th follower is as follows: ； in, This represents the position and heading angle of the i-th unmanned surface vessel. It represents the input control force of the i-th unmanned surface vessel. express The first derivative, This indicates the longitudinal position of the unmanned surface vessel in the geodetic coordinate system. This represents the lateral sway position of the unmanned surface vessel in the geodetic coordinate system. Indicates the heading angle of the unmanned surface vessel. This represents the speed information of the i-th unmanned surface vessel. This indicates the longitudinal velocity of the unmanned surface vessel. Represents the sway speed of the unmanned surface vessel. This indicates the turning angular velocity of the unmanned surface vessel. Let the transformation matrix between the body coordinate system and the geodetic coordinate system of the i-th unmanned surface vessel be represented as: ， ； , represented as: ,in , , , Represents the quality of unmanned surface vessels. It is the added mass of the unmanned surface vessel. The moment of inertia representing the rotation of an unmanned surface vessel; Represented as: ； Represented as: ,in , , ; , , , and , , Linear and quadratic damping coefficients, respectively; definition Therefore, the dynamic model of the unmanned surface vessel can be represented as: ； in, Indicates the trajectory of the followers. , They are respectively , The first derivative, , , This represents the external ocean current interference experienced by the i-th unmanned surface vessel.

3. The formation control method for an unmanned surface vessel system according to claim 1, characterized in that, Step S2 includes: S2.1 Before the mission begins, based on the desired formation required for the formation mission, set one real navigator and several virtual navigators, and set the relative distance and angle between each virtual navigator and the real navigator. During the operation of the unmanned surface vessel system, the relative distance and angle between the virtual navigator and the real navigator remain unchanged, forming a fixed formation. S2.2 The formation control problem of the surface unmanned surface vessel system, which determines the distance and angle between the followers and the real navigator, is transformed into the trajectory tracking problem of each follower to the corresponding virtual navigator.

4. The formation control method for the unmanned surface vessel system according to claim 3, characterized in that, In step S2.1, the distance and angle of the virtual navigator relative to the real navigator are as follows: ； in, Indicates the vertical position of the virtual navigator. Indicates the lateral movement position of the virtual navigator. Indicates the heading angle of the virtual navigator. Indicates the vertical position of the true navigator. Indicates the lateral direction and position of the true navigator. The heading angle represents the actual navigator. These represent the horizontal and vertical distances between the virtual navigator and the real navigator, respectively. This indicates the trajectory information of the virtual navigator.

5. The formation control method for an unmanned surface vessel system according to claim 1, characterized in that, Step S3 includes: S3.1 Define the follower's trajectory tracking error variable for the virtual navigator as: ； S3.2, Constrain the trajectory tracking error of the follower; Throughout the motion control process, in order to meet the trajectory tracking accuracy requirements of the follower towards the virtual navigator, it is necessary to constrain the trajectory tracking error of the follower. The constraint conditions are set as follows: ； For continuous Time-varying constraint equations that are differentiable in order. and They can be unequal, which means the constraints are asymmetric; S3.3 Establish a general asymmetric obstacle function to handle the asymmetric error constraint problem in the formation operation of multiple surface unmanned surface vessels.

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