Finite time distributed formation method for unmanned surface vessel cluster system

Abstract

The invention provides an unmanned surface vessel cluster system finite time distributed formation method, which not only can ensure that an unmanned surface vessel system reaches an expected formation mode in finite time, but also can ensure that the system speed and the formation error always meet the time-varying constraint requirement in the whole operation period. The method comprises the following steps: establishing kinematics and dynamics models of the three-degree-of-freedom unmanned surface vessel; using a smooth function to approximate saturation constraints of the system, and combining with the fault model to establish a new system dynamic model limited by driver faults and saturation constraints; designing a virtual control law, also known as a kinematics guidance law; designing a parameterized channel rate of the virtual leader; designing a finite time distributed formation controller; and designing an uncertain compensation adaptive law. The method can design a time-varying formation mode and a time-varying constraint function according to the needs of a user, dynamically adjusts the formation form of multiple unmanned surface vessels, and guarantees that the speed and formation tracking errors are not deviated from a specified constraint set all the time.

Description

Technical Field

[0001] The present invention relates to a finite-time formation control method for an unmanned surface vessel system, and in particular to a finite-time distributed formation method for a finite-time unmanned surface vessel cluster system taking into account speed constraints, collaborative formation error constraints and input saturation constraints. Background Art

[0002] In recent years, the formation control problem of multiple unmanned surface vessels (USVs) has attracted extensive attention because it has higher efficiency and performance than a single vessel in completing complex tasks such as environmental monitoring, territorial waters surveillance, and rescue. The development of a distributed formation control strategy based on finite-time stability is of great significance for enhancing the robustness of multiple unmanned surface vessel systems and improving the efficiency of their mission completion.

[0003] In actual operation scenarios, unmanned surface vehicle systems are usually faced with various system constraints due to their performance specifications and requirements, including speed constraints, input or output constraints, and tracking error constraints. If these constraints are ignored, the transient performance of the system may not be satisfied, and may even cause system damage. However, due to the lack of a unified and effective nonlinear control method to process constraint signals, the existing finite-time formation control method for unmanned boat swarm systems (N. Gu, D.Wang, ZH Peng, and L. Liu, “Observer-based finite-time control for distributed path maneuvering of underactuated unmanned surface vehicles with collision avoidance and connectivity preservation,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 8, pp.5105-5115, Aug.2021.) only designs distributed controllers for unconstrained scenarios, which cannot deal with the problem of limited system variables and lacks practical value.

[0004] In addition, the existing control methods that focus on system constraints (BJ Guerreiro, C. Silvestre, R.Cunha, and A. Pascoal, “Trajectory tracking nonlinear model predictivecontrol for autonomous surface craft,” IEEE Trans. Control Syst. Technol.,vol. 22, no. 6, pp. 2160-2175, Nov. 2014.) (ZH Peng, J. Wang, and D. Wang, “Distributed maneuvering of autonomous surface vehicles based on neurodynamic optimization and fuzzy approximation,” IEEE Trans. Control Syst. Technol.,vol. 26, no. 3, pp. 1083-1090, Mar. 2017.) also only consider the control of unmanned surface vehicle systems with a single input constraint or speed constraint, and limit the constraint signal to a constant constraint range and can only achieve asymptotic stability of the system converging in infinite time. However, in actual complex ocean formation tasks, the constraints on system speed, input, etc. are usually changing.

[0005] The actual modeled unmanned surface vessel system often has multiple sources of uncertainty, multiple time-varying constraints and complex mission requirements. It even faces a more complex marine environment during the mission implementation, and the risk of failure will increase accordingly. Designing an effective formation control algorithm with strong robustness, strong constraints and fast convergence speed is very important to promote the safe and efficient operation of multiple unmanned surface vessel systems. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention proposes a finite-time distributed formation method for an unmanned surface vessel cluster system considering multiple constraints, and the specific steps are as follows: Step 1: Consider the A network of unmanned surface vessels, including The unmanned surface vessel is modeled using the earth coordinate system and the hull coordinate system, and the following kinematic and dynamic models are obtained: (1), Formula (1) represents Unmanned surface vehicle system, where: It is Position information of an unmanned surface vehicle in the geodetic coordinate system and heading angle The superscript T indicates the transpose of a vector or matrix. Representation vector The derivative with respect to time, is the velocity vector composed of surge, roll and yaw velocity in the ship coordinate system, They represent forward speed, drift speed and yaw angular velocity respectively; is the unknown bounded disturbance vector caused by wind, waves, and surges, They represent unknown bounded disturbances in different speed directions respectively; is the driving force subject to the following fault and saturation constraints, Represent the driving forces in the three speed directions respectively, (2), Formula (2) represents the fault model, where represents the loss efficiency matrix, Represent the loss efficiency factors in different driving force directions, and satisfy , represents an unknown bounded additive fault, saturating the input vector is determined by the saturation function defined below (3), The subscript in the formula , Represents the actual control input in the three speed directions respectively, as well as are two known constant bounds of the saturation function; define , which represents the actual control input vector to be designed; in addition, represents a known nonlinear function, where represents the Coriolis force centripetal matrix and satisfies , and represents a known function matrix, represents the unknown real vector composed of the parameters that cannot be accurately measured in the nonlinear suppression matrix of the system, and the mass matrix is a positive symmetric matrix that satisfies ,matrix represents the transfer matrix and has the following definition ,

[0007] Set the initial state of the unmanned surface vehicle system ,in Represent the function values ​​of the three quantities at the initial moment respectively; set the parameterized path of the virtual leader to , They represent the parameterized trajectories of the forward position, the drift position, and the heading angle, respectively. Represents the set path parameters; sets the desired convergence speed of the parameterized path to , No. The desired formation trajectory of the unmanned surface vessels is , .

[0008] Step 2: Using nonlinear smoothing functions Estimate the saturation function defined in equation (3) : (4), According to Lagrange's mean value theorem, we get the following approximate relationship: (5) , Formula (5) represents the function approximation model, where Represents the approximation error and its absolute value With upper bound ;symbol Representation function For variables The derivative operation satisfies ,in , is the weight coefficient to be selected and satisfies , is a real number to be chosen; in addition, the derivative The function value satisfies ,in is a known positive constant.

[0009] Define a diagonal matrix ,in Respectively represent the nonlinear smooth function in equation (4) The derivative of ; define the total error vector ,in Represent the saturation function estimation errors in the three control force directions respectively; then, combined with the fault model (2), the saturation input vector And the saturation function approximation model (5), the first The unmanned surface vehicle system (1) can be rewritten as follows: (6), Where: Representation Matrix The inverse matrix of Represents the total external uncertainty of the system and is a bounded vector, that is, Norm satisfies ,in Represents the unknown external disturbance bound.

[0010] Step 3: Define the cooperative formation tracking error vectors And virtual error coordinate transformation for (7), Where: Representative The agent and The weights of the adjacency matrix between agents, specifically, Representing an Agent and Agent There is a connection relationship between them, otherwise there is no communication relationship; Represents the connection between the intelligent agent and the virtual leader, If it is equal to 1, it means there is a connection relationship, otherwise it means there is no connection relationship. , Respectively represent and The position information vector of the unmanned surface vehicle, represents the kinematic guidance law to be designed, also called the virtual control law, The matrix in expression (1) The transpose of Step 4: Given the system formation error and speed variable constraints ,

[0011] In the formula Respectively represent the given error variable norm and velocity variable norm The constraint functions are defined as monotonically decreasing functions with the following finite-time properties: (8), Where: , as well as are all given normal numbers, Indicates time, limited time .

[0012] Step 5: Design virtual control law

[0013] (9), Where: , and is the positive control parameter to be designed, is a positive number to be designed, , Respectively The derivative with respect to time, express right For convenience, we use the simplified notation Represents the constraint function term , and control the nonlinear term It is defined as the following piecewise function (10), in is a small positive parameter given in advance, the process coefficient , .

[0014] Step 6: Definition , yes The derivative with respect to time, represents the desired reference channel, and uses the filtered gradient method to design the channel rate of the virtual leader (11), In the formula and is the positive parameter to be designed; Step 7: Design a nonlinear tracking differential observer to estimate the virtual control law of formula (9) The time derivative of (12), Where: express The estimate, represent The estimate, express The time derivative of represents the positive real parameter to be selected; in addition, for any vector

[0015] And the given positive constant , define mathematical operators ,in Representation vector The weight, express The symbol function of express The absolute value of Step 8: Design of finite-time control input vector for an unmanned surface vehicle system (13), Where: and is the positive control parameter to be designed; for convenience, the simplified notation is used Represents the constraint function term , Represents unknown parameters The estimated signal, Represents the unknown external disturbance boundary The estimated signal, nonlinear control function Satisfies the following definitions: ,

[0016] in is a small positive parameter given in advance, the process coefficient , In addition, the hyperbolic tangent diagonal function matrix The definition is as follows:

[0017] In the formula is the nonlinear crossover function vector Multiply the unit vector on the left , as well as The amount obtained, are three positive real numbers to be selected; Step 9: Design an adaptive update law to compensate for system uncertainty: (14), (15), Where: are all normal numbers to be designed.

[0018] In a specific embodiment of the present invention, in step 2, .

[0019] The finite-time distributed formation control scheme proposed in the present invention can not only ensure that multiple agents can achieve the desired formation mode in a limited time, but also ensure that the speed and coordination error vector are always within the specified constraint set under the conditions of internal and external multi-source uncertainty, driver failure and multiple constraints. Compared with the prior art, the advantages of the present invention are: (1) For the case where multiple unmanned surface vehicle systems have multiple constraint variables and multiple sources of internal and external uncertainties, step 4 establishes a monotone decreasing function with finite time performance as the constraint upper bound, which is more in line with the actual application requirements, but it is difficult to design a finite time controller. Steps 5 and 8 process the time-varying constraints by designing a virtual control law with a tangent barrier function and control input, which can realize the design of finite time distributed controllers under the conditions of multiple time-varying constraint requirements and multiple uncertain couplings.

[0020] (2) The present invention introduces a smooth function as an approximation of the saturation function in the control design, and reduces the dynamic order of the system while dealing with the saturation constraint. In addition, the present invention avoids solving the derivative of the virtual control law with the help of a nonlinear differential tracker, thereby avoiding the computational complexity explosion problem of the traditional backstepping method. Therefore, the controller designed by the present invention not only has the advantages of low complexity, strong robustness, and fast convergence speed, but most importantly, it can ensure that the speed and formation errors do not deviate from the specified constraint set during the entire operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Shows the schematic diagram of the overall control process; Figure 2 A two-dimensional plan view showing the motion trajectories of multiple unmanned surface vessels; Figure 3 A running trajectory graph showing the speed variable norm; Figure 4 A running trajectory curve graph showing the formation error norm; Figure 5 A motion trajectory graph showing the adaptive law norm; Figure 6 The operating trajectory curve of the system control input norm is shown. DETAILED DESCRIPTION

[0022] The present invention provides a finite-time distributed formation method for an unmanned surface vessel cluster system based on finite-time stability, which can ensure that the speed and formation errors do not deviate from the specified time-varying constraint set under internal and external multi-source uncertainties, and form the desired formation mode in a finite time. The technical ideas of the method are as follows: first, the hyperbolic tangent function is used to design the Lyapunov function to ensure the time-varying constraint requirements of the system; second, a nonlinear continuous smooth function is introduced to approximate the system input saturation, and the saturation error, system external disturbance and additive fault are used as the total external uncertainty factors of the system; then, the virtual control law and the actual control input are iteratively designed with the help of an adaptive compensation strategy, and a nonlinear differential tracker is introduced to avoid solving the derivative of the virtual control law, thereby reducing the complexity of the design algorithm, and finally an effective finite-time formation control scheme is formed to achieve the desired system performance.

[0023] The specific steps of the method of the present invention are as follows: Step 1: Consider the A network of unmanned surface vessels, including The unmanned surface vessel is modeled using the earth coordinate system and the hull coordinate system, and the following kinematic and dynamic models are obtained: (1), Formula (1) represents Unmanned surface vehicle system, where: It is Position information of an unmanned surface vehicle in the geodetic coordinate system and heading angle The superscript T indicates the transpose of a vector or matrix. Representation vector The derivative with respect to time, is the velocity vector composed of surge, roll and yaw velocity in the ship coordinate system, They represent forward speed, drift speed and yaw angular velocity respectively; is the unknown bounded disturbance vector caused by wind, waves, and surges, They represent unknown bounded disturbances in different speed directions respectively; is the driving force subject to the following fault and saturation constraints, Represent the driving forces in the three speed directions respectively, (2), Formula (2) represents the fault model, where represents the loss efficiency matrix, Represent the loss efficiency factors in different driving force directions, and satisfy , represents an unknown bounded additive fault, saturating the input vector is determined by the saturation function defined below (3), The subscript in the formula , Represents the actual control input in the three speed directions respectively, as well as are two known constant bounds of the saturation function; define , which represents the actual control input vector to be designed; in addition, represents a known nonlinear function, where represents the Coriolis force centripetal matrix and satisfies , and represents a known function matrix, represents the unknown real vector composed of the parameters that cannot be accurately measured in the nonlinear suppression matrix of the system, and the mass matrix is a positive symmetric matrix that satisfies ,matrix represents the transfer matrix and has the following definition ,

[0024] Set the initial state of the unmanned surface vehicle system ,in Represent the function values ​​of the three quantities at the initial moment respectively; set the parameterized path of the virtual leader to , They represent the parameterized trajectories of the forward position, the drift position, and the heading angle, respectively. Represents the set path parameters; sets the desired convergence speed of the parameterized path to , No. The expected formation trajectory of the unmanned surface vessels is , .

[0025] Step 2: Using nonlinear smoothing functions Estimate the saturation function defined in equation (3) : (4), According to Lagrange's mean value theorem, we get the following approximate relationship: (5) , Formula (5) represents the function approximation model, where Represents the approximation error and its absolute value With upper bound ;symbol Representation function For variables The derivative operation satisfies ,in , is the weight coefficient to be selected and satisfies , is a real number to be chosen; in addition, the derivative The function value satisfies ,in is a known positive constant.

[0026] Define a diagonal matrix ,in Respectively represent the nonlinear smooth function in equation (4) The derivative of ; define the total error vector ,in Represent the saturation function estimation errors in the three control force directions respectively; then, combined with the fault model (2), the saturation input vector And the saturation function approximation model (5), the first The unmanned surface vehicle system (1) can be rewritten as follows: (6), Where: Representation Matrix The inverse matrix of Represents the total external uncertainty of the system and is a bounded vector, that is, Norm satisfies ,in Represents the unknown external disturbance bound.

[0027] Step 3: Define the cooperative formation tracking error vectors And virtual error coordinate transformation for (7), Where: Representative The agent and The weights of the adjacency matrix between agents, specifically, Representing an Agent and Agent There is a connection relationship between them, otherwise there is no communication relationship; Represents the connection between the intelligent agent and the virtual leader, If it is equal to 1, it means there is a connection relationship, otherwise it means there is no connection relationship. , Respectively represent and The position information vector of the unmanned surface vehicle, represents the kinematic guidance law to be designed, also called the virtual control law, The matrix in expression (1) The transpose of Step 4: Given the system formation error and speed variable constraints ,

[0028] In the formula Respectively represent the given error variable norm and velocity variable norm The constraint functions are defined as monotonically decreasing functions with the following finite-time properties: (8), Where: , as well as are all given normal numbers, Indicates time, limited time .

[0029] Step 5: Design virtual control law

[0030] (9), Where: , and is the positive control parameter to be designed, is a positive number to be designed, , Respectively The derivative with respect to time, express right For convenience, we use the simplified notation Represents the constraint function term , and control the nonlinear term It is defined as the following piecewise function (10), in is a small positive parameter given in advance, the process coefficient , .

[0032] Step 6: Definition , yes The derivative with respect to time, represents the desired reference channel, and uses the filtered gradient method to design the channel rate of the virtual leader (11), In the formula and is a positive parameter to be designed.

[0033] Step 7: Design a nonlinear tracking differential observer to estimate the virtual control law of formula (9) The time derivative of (12), Where: express The estimate, represent The estimate, express The time derivative of represents the positive real parameter to be selected; in addition, for any vector

[0034] And the given positive constant , define mathematical operators ,in Representation vector The weight, express The symbol function of express The absolute value of Step 8: Design of finite-time control input vector for an unmanned surface vehicle system (13), Where: and is the positive control parameter to be designed; for convenience, the simplified notation is used Represents the constraint function term , Represents unknown parameters The estimated signal, Represents the unknown external disturbance boundary The estimated signal, nonlinear control function Satisfies the following definitions: ,

[0035] in is a small positive parameter given in advance, the process coefficient , In addition, the hyperbolic tangent diagonal function matrix The definition is as follows:

[0036] In the formula is the nonlinear crossover function vector Multiply the unit vector on the left , as well as The amount obtained, are three positive real numbers to be selected; Step 9: Design an adaptive update law to compensate for system uncertainty: (14), (15), Where: are all normal numbers to be designed. Specific embodiments According to the specific implementation steps of the technical solution of the present invention, an embodiment is given as follows.

[0038] Step 1: Establish the unmanned surface vehicle system model as shown in formula (1). Select a directed network consisting of a virtual leader and five unmanned surface vehicles, and its communication topology adjacency matrix is ​​defined as follows: , , and the remaining matrix elements are all 0. Set the initial position state of the five unmanned surface vehicle systems They are , , , and , defining the parameterized path of the virtual leader as , and the desired formation pattern , given the input saturation function parameters are , .

[0039] Step 2: Substitute the driver fault model (2) and the approximate model of the saturation function (4) into model (1) to obtain model (6).

[0040] Step 3: Define the collaborative formation error in equation (7): and virtual control error .

[0041] Step 4: Select the time-varying constraint function in the form of equation (8), and the parameters in the constraint function are defined as and , .

[0042] Step 5: Design a virtual control law in the form of equation (9). The parameters of the virtual controller are selected as .

[0043] Step 6: Design the virtual leader channel rate as shown in equation (11) , some parameters of the controller are selected as , the desired virtual leader rate is chosen as .

[0044] Step 7: Design a nonlinear tracking differential observer as shown in Equation (12). Some parameters of the observer are selected as , .

[0045] Step 8: Design the finite-time control input vector in the form of equation (13). Some parameters of the controller are selected as .

[0046] Step 9: Design the adaptive law of equations (14) and (15). The adaptive law parameters are chosen as , .

[0047] Figure 2 The two-dimensional plane diagram formed by the motion trajectory of the unmanned surface vehicle system is displayed, indicating that the desired time-varying formation pattern has been formed. Figure 3 and Figure 4 are the running trajectories of the velocity norm and formation error norm respectively. Figure 3 and Figure 4 It can be seen that during the entire operation, the speed and formation errors never deviate from the given set of time-varying constraints. In addition, the formation error eventually converges to a small neighborhood of the origin, which means that the proposed control algorithm can meet the constraints of the system. Figure 5 It shows that the parameter adaptation law and the external uncertainty adaptation law of the proposed method are both bounded. Figure 6 It can be seen that the saturation input and the driver fault input are bounded and their value range is relatively small, that is, the proposed control method allows the system to be subject to both driver fault and saturation constraints. Under the internal and external multi-source uncertainties and multiple time-varying constraints, the system's time-varying formation performance can be achieved while meeting the constraint requirements and maximizing the controller performance.

Claims

1. A finite-time distributed formation method for an unmanned surface vessel swarm system, characterized in that: The specific steps are as follows: Step 1: Consider the A network of unmanned surface vessels, including The unmanned surface vessel is modeled using the earth coordinate system and the hull coordinate system, and the following kinematic and dynamic models are obtained: （1）， Formula (1) represents Unmanned surface vehicle system, where: It is Position information of an unmanned surface vehicle in the geodetic coordinate system and heading angle The superscript T indicates the transpose of a vector or matrix. Representation vector The derivative with respect to time, is the velocity vector composed of surge, roll and yaw velocity in the ship coordinate system, They represent forward speed, drift speed and yaw angular velocity respectively; is the unknown bounded disturbance vector caused by wind, waves, and surges, They represent unknown bounded disturbances in different speed directions respectively; is the driving force subject to the following fault and saturation constraints, Represent the driving forces in the three speed directions respectively, （2）， Formula (2) represents the fault model, where represents the loss efficiency matrix, Represent the loss efficiency factors in different driving force directions, and satisfy , represents an unknown bounded additive fault, saturating the input vector is determined by the saturation function defined below （3）， The subscript in the formula , Represents the actual control input in the three speed directions respectively, as well as are two known constant bounds of the saturation function; define , which represents the actual control input vector to be designed; in addition, represents a known nonlinear function, where represents the Coriolis force centripetal matrix and satisfies , and represents a known function matrix, represents the unknown real vector composed of the parameters that cannot be accurately measured in the nonlinear suppression matrix of the system, and the mass matrix is a positive symmetric matrix that satisfies ,matrix represents the transfer matrix and has the following definition ， Set the initial state of the unmanned surface vehicle system ,in Respectively represent the function values ​​of the three quantities at the initial moment; The parameterized path to set the virtual leader is , They represent the parameterized trajectories of the forward position, the drift position, and the heading angle, respectively. Represents the set path parameters; sets the desired convergence speed of the parameterized path to , No. The expected formation trajectory of the unmanned surface vessels is , ; Step 2: Using nonlinear smoothing functions Estimate the saturation function defined in equation (3) : （4）， According to Lagrange's mean value theorem, we get the following approximate relationship: （5） ， Formula (5) represents the function approximation model, where Represents the approximation error and its absolute value With upper bound ;symbol Representation function For variables The derivative operation satisfies , in , is the weight coefficient to be selected and satisfies , is a real number to be chosen; in addition, the derivative The function value satisfies ,in is a known positive constant; Define a diagonal matrix ,in Respectively represent the nonlinear smooth function in equation (4) The derivative of ; define the total error vector ,in Represent the saturation function estimation errors in the three control force directions respectively; then, combined with the fault model (2), the saturation input vector And the saturation function approximation model (5), the first The unmanned surface vehicle system (1) can be rewritten as follows: （6）， Where: Representation Matrix The inverse matrix of Represents the total external uncertainty of the system and is a bounded vector, that is, Norm satisfies ,in represents the unknown external disturbance bound; Step 3: Define the cooperative formation tracking error vectors And virtual error coordinate transformation for （7）， Where: Representative The agent and The weights of the adjacency matrix between agents, specifically, Representing an Agent and Agent There is a connection relationship between them, otherwise there is no communication relationship; Represents the connection between the intelligent agent and the virtual leader, If it is equal to 1, it means there is a connection relationship, otherwise it means there is no connection relationship. , Respectively represent and The position information vector of the unmanned surface vehicle, represents the kinematic guidance law to be designed, also called the virtual control law, The matrix in expression (1) The transpose of Step 4: Given the system formation error and speed variable constraints ， In the formula Respectively represent the given error variable norm and velocity variable norm The constraint functions are defined as monotonically decreasing functions with the following finite-time properties: （8）， Where: , as well as are all given normal numbers, Indicates time, limited time ; Step 5: Design virtual control law （9）， Where: , and is the positive control parameter to be designed, is a positive number to be designed, , Respectively The derivative with respect to time, express right For convenience, we use the simplified notation Represents the constraint function term , and control the nonlinear term It is defined as the following piecewise function （10）， in is a small positive parameter given in advance, the process coefficient , ； Step 6: Definition , yes The derivative with respect to time, represents the desired reference channel, and uses the filtered gradient method to design the channel rate of the virtual leader （11）， In the formula and is the positive parameter to be designed; Step 7: Design a nonlinear tracking differential observer to estimate the virtual control law of formula (9) The time derivative of （12）， Where: express The estimate, represent The estimate, express The time derivative of represents the positive real parameter to be selected; in addition, for any vector ; And the given positive constant , define mathematical operators ,in Representation vector The weight, express The symbol function of express The absolute value of Step 8: Design of finite-time control input vector for an unmanned surface vehicle system （13）， Where: and is the positive control parameter to be designed; For convenience, simplified notation is used Represents the constraint function term , Represents unknown parameters The estimated signal, Represents the unknown external disturbance boundary The estimated signal, nonlinear control function Satisfies the following definitions: ， in is a small positive parameter given in advance, the process coefficient , ; In addition, the hyperbolic tangent diagonal function matrix The definition is as follows: In the formula is the nonlinear crossover function vector Multiply the unit vector on the left , as well as The amount obtained, are three positive real numbers to be selected; Step 9: Design an adaptive update law to compensate for system uncertainty: （14）， （15）， Where: are all normal numbers to be designed.

2. The finite-time distributed formation method for the unmanned surface vessel swarm system according to claim 1, characterized in that: In step 2, .

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