CN117111465A - A formation control method for surface unmanned boat system - Google Patents

Abstract

The invention discloses a formation control method of the surface unmanned watercraft system, which belongs to the technical field of marine space intelligent unmanned vehicle control. It includes the following steps: S1. Establish a dynamic system model; S2. Combine the formation of the surface unmanned watercraft system with The control problem is converted into a follower's trajectory tracking problem for the virtual leader; S3. Establish a general asymmetric obstacle function that handles error constraints; S4. Use the fuzzy logic system to process the unknown parts of the system and external disturbances; S5. Based on the dynamic system Model, general asymmetric obstacle function and fuzzy logic system, using back-stepping method and combined with fixed-time control theory to design a fixed-time formation control method. According to the method provided by the present invention, the system convergence time does not depend on the selection of the initial state of the system. All signals in the system are bounded. The tracking error of the system always meets the preset constraint conditions during operation, maintaining rapid convergence and at the same time The tracking error of the system is constrained.

Description

A formation control method for surface unmanned boat system

Technical field

The invention relates to a formation control method for a surface unmanned boat system and belongs to the technical field of marine space intelligent unmanned vehicle control.

Background technique

The unmanned surface vehicle (USV for short) is an intelligent unmanned sea vehicle that has the ability to navigate autonomously in the actual ocean environment and can independently complete tasks such as environmental perception and target detection. It plays an important role in the process of ocean exploration and development. role. The unmanned vessel system consists of multiple surface unmanned vehicles. Each surface unmanned vehicle can perform its own sub-tasks in parallel. Through mutual communication and coordination, it can expand the scope of its ability to complete tasks and improve the efficiency of exploration and development work. The formation control of the surface unmanned watercraft system refers to designing an appropriate control strategy to maintain the desired relative position and attitude between multiple surface unmanned watercrafts to maintain the formation and complete the set tasks.

Taking into account the influence of ocean currents, wind and waves and other factors, designing a formation control scheme with fast convergence speed and strong robustness has become a research hotspot. USV is characterized by strong maneuverability and high flexibility, which requires the system to reach stability in a short period of time and puts forward higher requirements on the system's convergence time. Most of the current research on formation control methods mainly focuses on how to improve the tracking accuracy of the system. For multi-USV systems, the output error constraints and convergence time of the system should also be considered to improve the safety and operating efficiency of the system.

The traditional unmanned boat formation control method still has some technical shortcomings, such as (1) the existing unmanned boat formation control strategy rarely considers the problem of unknown environmental interference, and the multi-unmanned boat formation process will inevitably be affected by wind and waves, etc. Interference from the external environment is difficult to be directly measured by sensors; (2) Existing constrained unmanned boat formation control strategies rarely consider solving the problem of asymmetric error constraints; (3) Existing unmanned boat formation control strategies that consider convergence time are less concerned. Most manned and boat formation control strategies make the system stable for a limited time. However, the convergence time of the system depends heavily on the initial state of the system and rarely involves the problem of unmanned boat formation control under fixed time.

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

Contents of the invention

In order to solve the problems existing in the prior art, the present invention provides a formation control method for a surface unmanned vessel system. Aiming at the multi-USV system with output error constraints and time-varying ocean current interference, the designed controller enables the formation task to be achieved. It can be done within a practical fixed time.

The present invention achieves the above objects by adopting the following technical solutions:

A formation control method for a surface unmanned boat system, including the following steps:

S1. Combined with the hydrodynamic characteristics of the surface unmanned vehicle, establish a dynamic system model for the horizontal motion of the surface unmanned vehicle system including a leader and N followers in the X-Y plane;

S2. Introduce a virtual leader and convert the formation control problem of the surface unmanned boat system into a follower's trajectory tracking problem of the virtual leader;

S3. Based on the follower's trajectory tracking error variable for the virtual leader, establish a general asymmetric obstacle function that handles error constraints;

S4. There are uncertain unknown parts and external disturbances in the system model, and the fuzzy logic system is used to process the unknown parts and external disturbances of the system;

S5. Based on the dynamic system model, universal asymmetric obstacle function and fuzzy logic system, use the back-stepping method to integrate steps S3 and S4, and design a fixed-time formation control method based on fixed-time control theory.

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

in, Represents the position and heading angle of the i-th surface unmanned vehicle,/> represents the first derivative of eta _i , x represents the longitudinal position of the surface unmanned vehicle in the geodetic coordinate system, y represents the swaying direction position of the surface unmanned vehicle in the geodetic coordinate system,/> represents the heading angle of the surface unmanned vehicle, υ _i = [u, v, r] ^T represents the speed information of the i-th surface unmanned vehicle, u represents the longitudinal speed of the surface unmanned vehicle, v represents the lateral direction of the surface unmanned vehicle Swing speed, r represents the steering angular speed of the unmanned watercraft on the water surface, Represents the vector composed of the longitudinal acceleration, sway acceleration, and steering angular acceleration of the i-th surface unmanned vehicle;

Representing the transformation matrix between the body coordinate system and the geodetic coordinate system of the i-th surface unmanned vehicle, it is expressed as:

M _i ∈R ^3×3 represents the inertia matrix of the i-th surface unmanned vehicle, expressed as: M _i =diag{m _u m _v m _r }, where m represents the mass of the surface unmanned vehicle,/> is the additional mass of the surface unmanned vehicle, and I _z represents the moment of inertia of the surface unmanned vehicle;

C _i ∈R ^3×3 represents the Coriolis force matrix of the i-th surface unmanned vehicle, expressed as:

D _i ∈R ^3×3 represents the damping force matrix of the i-th surface unmanned vehicle, expressed 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;

τ _wi ∈R ³ represents the external ocean current interference suffered by the i-th unmanned surface vessel, and τ _i ∈R ³ represents the input control force of the i-th unmanned surface vessel;

Define x _1i = η _i , x _2i = υ _i , then the dynamic model of the surface unmanned vehicle is expressed as:

in, are the first derivatives of x _1i and x _2i respectively,

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

S2.1. Before the mission starts, set a real leader and several virtual leaders according to the desired formation required by the formation task, and set the relative distance and angle between each virtual leader and the real leader. During the operation of the surface unmanned watercraft system, the relative distance and angle between the virtual pilot and the real pilot remain unchanged, forming a fixed formation;

S2.2. Convert the formation control problem of the surface unmanned boat system to determine the distance and angle between the follower and the real leader into the trajectory tracking problem of each follower to the corresponding virtual leader.

Among them, in step S2.1, the distance and angle of the virtual pilot relative to the real pilot are as follows:

Among them, x _vl represents the longitudinal position of the virtual leader, y _vl represents the lateral position of the virtual leader, represents the heading angle of the virtual pilot, x _l represents the longitudinal position of the real pilot, y _l represents the swaying direction position of the real pilot,/> Represents the heading angle of the real pilot,/> Represents the horizontal distance and vertical distance between the virtual leader and the real leader respectively,/> Indicates the trajectory information of the virtual leader.

In one embodiment of the present invention, the universal asymmetric barrier function established in step S3 is:

Among them, β _i is the intermediate variable to establish the general error constraint function, Ξ _L and Ξ _H are the error constraint boundary vectors, Ξ _L is the vector composed of Ξ _Lj , Ξ _H is the vector composed of Ξ _Hj , Ξ _L = [Ξ _L1 , Ξ _L2 , Ξ _L3 ] ^T , Ξ _H = [Ξ _H1 , Ξ _H2 , Ξ _H3 ] ^T .

Specifically, step S3 includes:

S3.1. Define the trajectory tracking error variable of the follower to the virtual leader as:

Among them, Z _1i and Z _2i represent the trajectory tracking error and speed tracking error of the follower and the virtual leader respectively, x _1i represents the follower's trajectory, x _1d represents the follower's expected trajectory, x _2i represents the follower's speed, α _1i is the virtual control law of the follower;

S3.2. Constrain the follower’s trajectory tracking error;

During the entire motion control process, in order to meet the accuracy requirements of the follower's trajectory tracking of the virtual leader, it is necessary to constrain the follower's trajectory tracking error. The constraint conditions are set as follows:

-Ξ _Lj <Z _1ij <Ξ _Hj ,j＝1,2,3;

Among them, Z _1ij represents the tracking error of the follower and the virtual leader in the longitudinal direction, sway direction, and heading angle, Ξ _Lj and Ξ _Hj represent the corresponding constraint boundary equations, Ξ _Lj >0, Ξ _Hj >0 are continuous n-order possible For micro time-varying constraint equations, Ξ _Lj and Ξ _Hj can be unequal, which means that the constraints are asymmetric;

S3.3. Establish a general asymmetric obstacle function to deal with the asymmetric error constraint problem during multi-surface unmanned boat formation operations.

In one embodiment of the present invention, in step S4, the unknown equation of the system is defined:

Using fuzzy logic system to approximate unknown equations, there are:

Among them, · represents the Hadamard product, W _1i and W _2i represent the ideal fuzzy weight matrix, S _1i and S _2i are the membership function vectors, ζ _1i represents the approximation error vector, is the integrated external disturbance,/> is the derivative of the virtual control law,/> represents a small positive number, and ζ _2i represents the approximation error.

In one embodiment of the present invention, the specific process of step S5 is:

The designed virtual control law is:

ψ=[ψ ₁ , ψ ₂ , ψ ₃ ] ^T , for convenience of expression, △ _j1 , △ _j2 , ψ _j , j＝1,2,3 are used as △ ₁₁ , △ ₂₁ , △ ₃₁ , △ ₁₂ , △ ₂₂ , △ ₃₂ , ψ ₁ , ψ ₂ , ψ ₃ general variable form;

The designed virtual adaptive law is:

Represents the estimated value of χ _1i , χ _1i is the unknown positive parameter introduced, χ _1i =||W _1i || ² ;

Among them, K ₁₁ and K ₁₂ are control gains, Represents intermediate variables, K ₁₁ , K ₁₂ , a ₁ represents control gain, ε ₁ is a positive number; a ₁ ,/> c ₁ , ε ₁ and γ ₁ are positive numbers to be designed, |||| represents the second norm;

Design the real control law as:

Design the real adaptive law as:

Represents the estimated value of χ _2i , χ _2i is the unknown positive parameter introduced, χ _2i =||W _2i || ² ;

in, c ₂ , ε ₂ and γ ₂ are small positive numbers, K ₂₁ and K ₂₂ are control gains.

The beneficial effects of this application include but are not limited to:

The formation control method of the surface unmanned vehicle system provided by the present invention introduces a virtual leader formation strategy according to the desired formation, and establishes a constraint equation according to the tracking error limit of the USV; based on the fixed time control theory, the fuzzy logic system is used to control the system The unknown items and wave disturbances are approximated, and the asymmetric obstacle equation is used to constrain the output error of the system to improve the safety of the system. Finally, an adaptive fuzzy fixed-time formation control algorithm is proposed based on the back-stepping method to realize the multi-USV system at a fixed time. Converge to the desired formation configuration and complete the formation mission.

The formation control method of the surface unmanned vehicle system provided by the present invention introduces a universal constraint equation to deal with the asymmetric constraint problem in the formation process of multiple USV systems. The constraint equation can also be used in symmetric constraint and unconstrained situations. The system convergence time does not depend on the selection of the system's initial state. All signals in the system are bounded. The system's tracking error always meets the preset constraints during operation. It maintains rapid convergence while constraining the system's tracking error. , which improves the security of the system.

The purpose of introducing a virtual leader in this invention is to provide followers with expected position information in the formation process. If the follower tracks the corresponding virtual leader within a limited time, it can form the desired formation with the real leader, thereby achieving formation. the goal of.

Description of drawings

The drawings described here are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application. In the attached picture:

Figure 1 is a control logic block diagram of the present invention;

Figure 2 is a flow chart of the method of the present invention;

Figure 3 shows the formation tracking rendering;

Figure 4 is a color image of Figure 3;

Figure 5 is the tracking error effect diagram of USV0;

Figure 6 is a color image of Figure 5;

Figure 7 is the tracking error rendering of USV1;

Figure 8 is a color image of Figure 7;

Figure 9 shows the control input of USV0;

Figure 10 shows the control input of USV1;

Figure 11 shows the surge error constraint performance of USV0;

Figure 12 shows the sway error constraint performance of USV0;

Figure 13 shows the roll angle error constraint performance of USV0;

Detailed ways

The present invention will be further described below in conjunction with specific embodiments. It should be noted that many specific details are set forth in the following description in order to fully understand the present invention. However, the present invention can also be implemented in other ways different from those described here. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

In the embodiment, a system composed of three identical USVs is selected to verify the effectiveness of the proposed control algorithm. Each USV can obtain its own status information through its own outdoor positioning equipment (such as GPS), speed measuring device (such as Doppler speedometer) and other sensors. Different individuals can exchange information through radio. The expected control goal is Three USVs can form and maintain a triangular formation within a limited time.

In order to more clearly present the technical means included in the controller designed in the present invention, the specific technical principles are shown in Figure 1. According to the design process in Figure 2, the design work of the formation controller is completed.

The model parameters of the three USVs are:

The initial state of the virtual pilot USV is set to η _l = [0,0,0]. There is a corresponding relationship between the expected trajectory and the expected speed. The expected speed is set to: υ _l = [1,0.5,0.1], simulation Time is: t∈[0,65]. The initial states of the two follower USVs are set to eta ₀ =[-2.5,-2.5,0.2], eta ₁ =[-2.5,2.5,-0.1]. The desired configuration composed of two virtual leaders and a real leader is:

The assumptions for external time-varying ocean currents and wave interference are as follows:

In order to deal with the external interference and unknown items of the system, a fuzzy logic system containing 7 fuzzy rules is selected to approximate it. The membership function is designed as follows:

S _ij (Z _i )=exp[-0.5(Z _i +4-j)],i=1,2.j=1,...,7.

Where Z ₁ =[β _i ·ψ,α _1i ] ^T ∈R ⁶ ,

In order to deal with the tracking error constraint problem, the error constraint equation is as follows:

Ξ _Lj =0.5+9exp(-0.3t)j=1,2,3;

Ξ _Hj =0.3+8exp(-0.4t)j=1,2,3;

In order to realize the fixed time formation of unmanned boats, the designed formation controller parameters are set as:

K ₁₁ =K ₂₁ =15, K ₁₂ =K ₂₂ =5, a ₁ =a ₂ =1, γ ₁ =γ ₂ =10, c ₁ =c ₂ =0.01, ε ₁ =ε ₂ =0.1, ε ₁ =ε ₂ =0.1,/>

Figures 3 and 4 show the formation effect of three USVs. It can be seen that the control method designed in the present invention can realize the triangular formation configuration of the multi-USV system within a limited time.

The position and speed tracking errors of the two follower USVs are shown in Figure 5- and Figure 8 respectively. It can be seen that under different initial states, the two follower USVs can achieve accurate tracking of the virtual leader in a short time. And the tracking error can converge to a small neighborhood near the origin.

It can be seen from Figures 9 and 10 that the control input signal designed by the present invention is bounded and smooth and meets the actual physical constraints of the USV.

Considering the similarity of the USVs of the two followers, USV0 is chosen as an example to show the constraints of the system tracking error. Figures 11 to 13 show the error constraint performance of USV0. 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 capabilities.

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

The above specific embodiments cannot be used to limit the scope of the present invention. For those skilled in the art, any substitutions, improvements or transformations made to the embodiments of the present invention fall within the scope of the present invention.

Everything that is not described in detail in the present invention is a well-known technology for those skilled in the art.

Claims (8)

1. The formation control method of the unmanned surface vehicle system is characterized by comprising the following steps of:

s1, combining the hydrodynamic characteristics of a water surface unmanned ship, and establishing a dynamic system model aiming at the horizontal movement of a water surface unmanned ship system comprising a navigator and N followers on an X-Y plane;

s2, introducing a virtual navigator, and converting a formation control problem of the unmanned surface vehicle system into a track tracking problem of a follower on the virtual navigator;

s3, based on the track tracking error variable of the follower to the virtual pilot, establishing a general asymmetric barrier function for processing error constraint;

s4, processing the unknown part and external disturbance of the system by using a fuzzy logic system, wherein the unknown part and the external disturbance of the system model are uncertain;

s5, integrating the step S3 and the step S4 by using a back-stepping method based on a dynamic system model, a general asymmetric barrier function and a fuzzy logic system, and designing a fixed time formation control method by combining a fixed time control theory.

2. The method for controlling the formation of the surface unmanned ship system according to claim 1, wherein in step S1, the dynamic system model established for the i-th follower is:

wherein,representing the position and heading angle of the ith surface unmanned ship,/->Representing eta _i First order of (2)Derivative, x represents the longitudinal position of the surface unmanned aerial vehicle in the geodetic coordinate system, y represents the transverse direction position of the surface unmanned aerial vehicle in the geodetic coordinate system, < >>Indicating course angle, v of unmanned surface vehicle _i ＝[u,v,r] ^T The speed information of the ith surface unmanned ship is represented, u represents the longitudinal speed of the surface unmanned ship, v represents the swaying speed of the surface unmanned ship, r represents the steering angular speed of the surface unmanned ship, and>a vector representing the longitudinal acceleration, the transverse oscillation acceleration and the steering angular acceleration of the ith unmanned surface vehicle;

the conversion matrix of the satellite coordinate system and the geodetic coordinate system of the ith surface unmanned ship is expressed as:

M _i ∈R ^3×3 the inertial matrix representing the ith surface unmanned ship is expressed as: m is M _i ＝diag{m _u m _v m _r }, whereinm represents the mass of the unmanned surface vessel, +.>Is the additional mass of the unmanned surface vessel, I _z Representing the rotational inertia of the unmanned surface vehicle;

C _i ∈R ^3×3 the coriolis force matrix representing the ith surface unmanned boat is expressed as:

D _i ∈R ^3×3 the damping force matrix representing the ith surface unmanned ship is expressed as: d (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;

τ _wi ∈R ³ represents the external ocean current interference, tau, suffered by the ith surface unmanned ship _i ∈R ³ Is the input control force of the ith unmanned surface vehicle;

definition x _1i ＝η _i ,x _2i ＝υ _i Then the dynamic model of the surface unmanned boat is expressed as:

wherein,respectively x _1i ，x _2i First derivative of>

3. The formation control method of the surface unmanned ship system according to claim 1, wherein step S2 comprises:

s2.1, before a task starts, setting a real navigator and a plurality of virtual navigators according to an expected formation required by a formation task, setting the relative distance and angle between each virtual navigator and the real navigator, and keeping the relative distance and angle between the virtual navigator and the real navigator unchanged in the operation process of the unmanned surface vessel system to form a fixed formation;

s2.2, converting the formation control problem of the unmanned surface vehicle system for determining the distance and the angle between the follower and the real navigator into the track tracking problem of each follower on the corresponding virtual navigator.

4. A method of controlling a surface unmanned ship system according to claim 3, wherein in step S2.1, the distance and angle of the virtual pilot with respect to the real pilot are as follows:

wherein x is _vl Representing the longitudinal position of the virtual pilot, y _vl Represents the yaw direction position of the virtual pilot,representing the course angle, x of a virtual pilot _l Representing the longitudinal position of a real pilot, y _l Represents the position of the real pilot in the direction of the yaw, < >>Indicating the heading angle of the real pilot +.>Respectively representing the horizontal distance and the longitudinal distance between the virtual pilot and the real pilot, +.>Track information representing a virtual pilot.

5. The formation control method of a surface unmanned ship system according to claim 1, wherein the general asymmetric barrier function established in step S3 is:

wherein beta is _i Is an intermediate variable for establishing a general error constraint function _L 、Ξ _H Is an error constraint boundary vector, xi _L Is prepared from xi _Lj Vectors of composition, xi _H Is xi _Hj Vectors of composition, xi _L ＝[Ξ _L1 ,Ξ _L2 ,Ξ _L3 ] ^T ，Ξ _H ＝[Ξ _H1 ,Ξ _H2 ,Ξ _H3 ] ^T 。

6. The formation control method of the surface unmanned ship system according to claim 5, wherein step S3 comprises:

s3.1, defining a track tracking error variable of a follower to a virtual navigator as follows:

wherein Z is _1i 、Z _2i Respectively representing the track tracking error and the speed tracking error of the follower and the virtual navigator, and x _1i Representing the track of the follower, x _1d Representing the expected trajectory of the follower, x _2i Representing the speed of the follower, alpha _1i Is a virtual control law of the follower;

s3.2, restraining a track tracking error of the follower;

in the whole motion control process, in order to meet the track tracking precision requirement of the follower on the virtual navigator, the track tracking error of the follower needs to be restrained, and the restraint conditions are set as follows:

-Ξ _Lj <Z _1ij <Ξ _Hj ,j＝1,2,3；

wherein Z is _1ij Representing tracking errors of longitudinal direction, transverse direction and course angle of follower and virtual pilot, and the xi _Lj And xi _Hj Representing the corresponding constraint boundary equation, xi _Lj >0,Ξ _Hj >0 is a continuous n-order differentiable time-varying constraint equation _Lj And xi _Hj May not be equal, meaning that the constraint is asymmetric;

s3.3, establishing a general asymmetric barrier function to solve the problem of asymmetric error constraint in the formation operation process of the multi-water surface unmanned ship.

7. The method for controlling the formation of the surface unmanned ship system according to claim 6, wherein in step S4, an unknown equation of the system is defined:

approximate estimation of unknown equation by fuzzy logic system includes:

wherein, represents Hadamard product, W _1i 、W _2i Represents an ideal fuzzy weight matrix, S _1i 、S _2i Zeta is the membership function vector _1i Representing the approximation error vector, is an integrated external disturbance, ++>Is the derivative of the virtual control law,/>Represents a small positive number, ζ _2i Representing the approximation error.

8. The formation control method of the surface unmanned ship system according to claim 7, wherein the specific process of step S5 is as follows:

the virtual control law is designed as follows:

ψ＝[ψ ₁ ,ψ ₂ ,ψ ₃ ] ^T for convenience of presentation, we adopt _j1 ,△ _j2 ,ψ _j J=1, 2,3 as delta ₁₁ ,△ ₂₁ ,△ ₃₁ ,△ ₁₂ ,△ ₂₂ ,△ ₃₂ ,ψ ₁ ,ψ ₂ ,ψ ₃ Is a common variable form of (a);

the virtual self-adaptive law is designed as follows:

representing χ _1i Is χ _1i For the introduced unknown positive parameters χ _1i ＝||W _1i || ² ；

Wherein K is ₁₁ And K ₁₂ In order to control the gain of the gain control,representing intermediate variables, K ₁₁ ，K ₁₂ ，a ₁ Indicating the control gain, epsilon ₁ Is a positive number; a, a ₁ ，/>c ₁ ,ε ₁ And gamma ₁ Is a positive number to be designed and is a number, I represent a second norm;

the design of the real control law is as follows:

the real self-adaptive law is designed as follows:

representing χ _2i Is χ _2i For the introduced unknown positive parameters χ _2i ＝||W _2i || ² ；

Wherein,c ₂ ,ε ₂ and gamma ₂ Is a small positive number, K ₂₁ And K ₂₂ To control the gain.