Tugboat cooperative collision avoidance control method based on finite time convergence control obstacle function

Abstract

The invention discloses a tugboat cooperative collision avoidance control method based on a finite time convergence control obstacle function. The method comprises the following steps: constructing a constraint set for ensuring that an unpowered floating platform is converged to a safe motion area through the constructed finite time convergence collision avoidance control obstacle function; solving the optimal expected speed according to the quadratic programming problem model so as to obtain the expected control force required by the unpowered floating platform; the expected control force is distributed to each tugboat, and the expected pulling force of a towing cable of each tugboat is obtained; the time-varying opposite positions of the tugboats relative to the floating platform are obtained, the virtual expected speed of the tugboats is obtained by combining the expected pulling force, the control force of each tugboat is obtained according to the virtual expected speed, and then control over cooperative collision avoidance of the tugboats is achieved. The problem that a traditional collision avoidance method cannot meet the requirements of real-time performance and accuracy, especially in a complex and dynamically changing environment, the problem of local optimum exists in the ship formation collision avoidance process, and then cooperative collision avoidance control precision is low is solved.

Description

Technical Field

[0001] The present invention relates to the field of safe collision avoidance control of tugboat formations, and in particular to a tugboat collaborative collision avoidance control method based on a finite time convergence control obstacle function. Background Art

[0002] The ocean covers approximately 71% of the Earth's surface and possesses abundant resources. With the continuous development of marine resources and the growing demand for maritime transportation, tugboat formation technology is playing an increasingly important role in modern marine engineering. Tugboat formation technology involves the coordinated operation of multiple tugboats, precisely controlling the course and speed of each vessel to achieve efficient and safe cargo transportation. In practical applications, ships may encounter various obstacles such as other ships, reefs, and icebergs. Therefore, ship collision avoidance control has become a key issue in tugboat formation technology.

[0003] Traditional collision avoidance methods may not meet the requirements of real-time and accuracy, especially in complex and dynamically changing environments. In recent years, the collision avoidance methods for ship formations include artificial potential field method, vector field method, and control obstacle function method. The artificial potential field method adds an abstract artificial gravitational field to the environment, where the target point is the gravitational field and the obstacle is the repulsive field, and guides the tugboat's movement through the combined force of the two. However, the artificial potential field method may have local minimum problems and cannot guarantee that the optimal solution to the problem will be found. The vector field method (VectorFieldMethod) is a control strategy for path planning and collision avoidance. It guides the ship to navigate along a predetermined path while avoiding obstacles by constructing a vector field. However, neither of these two methods is the optimal solution. In the process of ship formation collision avoidance, there is a problem of falling into local optimality, which leads to the problem of low accuracy of collaborative collision avoidance control. Summary of the Invention

[0004] The present invention provides a tugboat cooperative collision avoidance control method based on a finite time convergence control obstacle function to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A tugboat cooperative collision avoidance control method based on a finite time convergence control barrier function comprises:

[0007] S1: Obtain the mathematical model of the unpowered floating platform;

[0008] Mathematical models of tugboats used to tow unpowered floating platforms;

[0009] S2: Based on the mathematical model of the unpowered floating platform and the preset expected path, the virtual expected speed of the unpowered floating platform is obtained;

[0010] S3: The unpowered floating platform and the tugboat are regarded as an integral structure, and a virtual ellipse is set to surround the integral structure to obtain a coordinated navigation motion region;

[0011] The location of the unpowered floating platform is the center point of the virtual ellipse;

[0012] The obstacle is regarded as a circular area body. A finite time convergence collision avoidance control obstacle function is constructed based on the cooperative navigation motion area body and the circular area body. Based on the finite time convergence collision avoidance control obstacle function, a constraint set is constructed to ensure that the unpowered floating platform converges to the safe motion area in a finite time.

[0013] S4: Construct a quadratic programming problem model based on the constraint set and the virtual expected speed;

[0014] The optimal expected speed is obtained by solving a quadratic programming problem model, and the expected control force required for the unpowered floating platform is obtained according to the optimal expected speed;

[0015] The desired control force is distributed to each tugboat through a quadratic programming algorithm to obtain the desired pulling force of the towline of each tugboat;

[0016] S5: Based on the installation position of the towline between the unpowered floating platform and the tugboat, the time-varying relative position of the tugboat relative to the floating platform is obtained;

[0017] According to the time-varying relative position, the tugboat mathematical model and the expected pulling force are combined to obtain the virtual expected speed of the tugboat. The control force of each tugboat is obtained according to the virtual expected speed, thereby realizing the coordinated collision avoidance control of the tugboats.

[0018] Furthermore, the mathematical model of the unpowered floating platform in S1 is expressed as

[0019]

[0020] Where: η0 represents the position vector of the unpowered floating platform in the northeast coordinate system; represents the derivative of the position vector η0; R(ψ0) represents the transformation matrix; v0 represents the velocity vector of the unpowered floating platform in the hull coordinate system; M0 represents the system inertia matrix composed of the rigid body inertia of the unpowered floating platform and the hydrodynamic additional mass; represents the derivative of the velocity vector v0; D0 represents the ship hydrodynamic damping coefficient matrix; g0 represents the unmodeled dynamic term; τ0 represents the environmental force on the unpowered floating platform;

[0021] The mathematical model of the tugboat is expressed as follows:

[0022]

[0023] Where: η i represents the position vector of the i-th tugboat in the northeast coordinate system; Represents the position vector η i The derivative of R(ψ i ) represents the transformation matrix of the i-th tugboat; v i represents the velocity vector of the i-th tugboat in the hull coordinate system; M i represents the system inertia matrix composed of the rigid body inertia and hydrodynamic additional mass of the i-th tugboat; represents the velocity vector v i The derivative of i represents the ship hydrodynamic damping coefficient matrix of the i-th tugboat; g i represents the unmodeled dynamic term of the i-th tugboat; τ i represents the system control force of the i-th tugboat; represents the tension generated by the cable between the i-th tugboat and the unpowered floating platform; represents the environmental force on the i-th tugboat.

[0024] Furthermore, the S2 specifically includes the following steps:

[0025] S21: Based on a preset expected path, obtain a position error and a velocity error of the unpowered floating platform according to a mathematical model of the unpowered floating platform;

[0026] And the position error E 10 and speed error E 20 The expression is

[0027]

[0028] Where: η d represents the desired position vector of the unpowered floating platform; η0 represents the actual position vector of the unpowered floating platform; represents the virtual desired speed of the unpowered floating platform; ν0 represents the actual speed vector of the unpowered floating platform;

[0029] Combined with the mathematical model of the unpowered floating platform, the position error E is obtained 10 and speed error E 20 The error derivative of , and the expression of the error derivative is

[0030]

[0031] Where: d0 represents the total interference and uncertainty term of the unpowered floating platform;

[0032] S22: Obtain the virtual expected speed of the unpowered floating platform according to the error derivative based on the backstepping method;

[0033] And the expression of virtual desired speed is

[0034]

[0035] Where: K 10 represents the design constant; represents the derivative of the desired trajectory; T represents the transpose.

[0036] Furthermore, the S3 specifically includes the following steps:

[0037] S31: The unpowered floating platform and the tugboat are considered as a whole, and a virtual ellipse is set to enclose them to obtain the coordinated navigation motion area;

[0038] And the two fixed points of the virtual ellipse are denoted as F1 and F2 and and And define the virtual ellipse constraint condition satisfied by any point P on the ellipse boundary line as |PF1|+|PF2|=2a, where a represents a constant and a>0;

[0039] At the same time, the location of the unpowered floating platform is taken as the center point of the virtual ellipse;

[0040] S32: The obstacle is considered as a circular area, and the center of the circular area is denoted as η b , the radius of the circular area is recorded as R b At the same time, any point on the circular area is recorded as

[0041] Based on the virtual ellipse constraint, the minimum safe distance between the unpowered floating platform and the tugboat is obtained according to the location of the unpowered floating platform and the obstacles. The system of equations, and

[0042] The expression of the equation group is

[0043]

[0044] Where: Indicates the position coordinates of the fixed point F1; Indicates the position coordinates of fixed point F2; Indicates the position coordinate of the unpowered floating platform; y p ,x p Represents the position coordinates of point P; Indicates the location coordinates of the obstacle;

[0045] By solving the equations to obtain the position coordinates of point P to obtain |Pη0|, and then obtain the minimum safety distance

[0046] S33: According to the minimum safety distance Construct a finite time convergent collision avoidance control obstacle function;

[0047] And the finite time convergence collision avoidance control obstacle function h 0b The expression of (η0) is

[0048]

[0049] Where: η b represents the position of the obstacle and b=1,……,N0; N0 represents the number of obstacles;

[0050] And according to the finite time convergence collision avoidance control obstacle function h 0b (η0), the safe movement area of ​​the unpowered floating platform and the tugboat formation is defined as

[0051]

[0052] S34: Based on the finite time convergence collision avoidance control obstacle function, a constraint set is constructed to ensure that the unpowered floating platform converges to the safe motion area in a finite time;

[0053] And the constraint set The expression is

[0054]

[0055] Where: Indicates h 0b The derivative of (η0); h 0b Indicates h 0b is the abbreviated form of (η0); ζ0, ρ represent design parameters and ζ0>0, 0<ρ<1; T0 represents the upper bound of the time for convergence to the safe motion region.

[0056] Furthermore, the S4 specifically includes the following steps:

[0057] S41: Construct a quadratic programming problem model based on the constraint set and the virtual desired speed;

[0058] And the expression of the quadratic programming problem model is

[0059]

[0060] Where: represents the optimal expected speed; Represents the objective function of the quadratic programming problem model;

[0061] S42: Solve and obtain the optimal expected speed through the quadratic programming problem model And according to the optimal expected speed, the speed error of the unpowered floating platform is updated to

[0062]

[0063] and obtaining a desired control force required for the unpowered floating platform based on the updated speed error of the unpowered floating platform;

[0064] And the expression of expected control force is

[0065]

[0066] Where: τ0 represents the desired control force required for the unpowered floating platform; K 20 represents a positive design constant; Represents the estimated value of d0 based on the radial basis function neural network;

[0067] S43: Construct the cost function and constraints of the quadratic programming algorithm, which is expressed as

[0068] Cost function: minJ = T T ΩT+s T Qs

[0069] Constraints:

[0070]

[0071] Where: represent the minimum and maximum horizontal tensions of the towline respectively; T represents the desired horizontal tension of the towline of the tugboat and represents the expected horizontal tension of the i-th towline, i.e., the expected pulling force; Ω, Q represents the weight matrix; N represents the number of tugboats; θ i It refers to the angle between the i-th streamer and the heading of the unpowered floating platform in the northeast coordinate system; B0,s represents the intermediate parameter;

[0072] The desired control force is distributed to each tugboat through the quadratic programming algorithm to obtain the expected tension of the towline of each tugboat.

[0073] Furthermore, the S5 specifically includes the following steps:

[0074] S51: constructing a mathematical model of the towline according to the expected tension of the towline of each tugboat, and solving the expected horizontal length of the towline according to the mathematical model of the towline;

[0075] And the mathematical model of the tow cable is expressed as

[0076]

[0077] Where: represents the horizontal tension of the towline on the i-th tugboat; L R represents the nominal length of the streamer; σ represents the density of the streamer; E and A represent the Young's modulus and cross-sectional area of ​​the streamer respectively; D H The horizontal length of the streamer is the expected horizontal length of the streamer obtained by the mathematical model of the streamer.

[0078] S52: Acquire the real-time position of the unpowered floating platform, and based on the installation position of the towline between the unpowered floating platform and the tugboat, acquire the time-varying relative position of the tugboat relative to the floating platform;

[0079] And the formula for obtaining the time-varying relative position is

[0080]

[0081] Where: represents the time-varying relative position of the i-th tugboat relative to the floating platform; represents the connection position between the unpowered floating platform and the i-th towline; represents the intermediate parameter; ψ0 represents the bow angle of the unpowered floating platform; p0 represents the design constant;

[0082] S53: Obtain the position error E of the i-th tugboat according to the time-varying relative position 1i and velocity error E 2i , whose expression is

[0083]

[0084] Where: a ij Represents the adjacency matrix of the decision variables of the i-th tugboat and the j-th tugboat, that is, if the i-th tugboat can obtain the information of the j-th tugboat, then a ij =1, otherwise 0; a i0 represents the adjacency matrix of the decision variables between the i-th tugboat and the unpowered floating platform, that is, if the i-th tugboat can obtain the state information of the unpowered floating platform, then a i0 =1, otherwise 0; represents the virtual expected speed of the i-th tugboat to be solved;

[0085] S54: Based on the position error and speed error of the i-th tugboat, and combined with the tugboat mathematical model and the expected pulling force, the position error and speed error derivatives of the i-th tugboat are obtained, and their expressions are:

[0086]

[0087] Where: a id ,B i , di Indicates the intermediate parameter; φ i represents the angle between the i-th towline and the X-axis of the tugboat in the hull coordinate system; Indicates E 1i ,E 2i The first derivative of

[0088] S55: Obtaining a virtual desired speed of the i-th tugboat according to the position error and speed error derivative of the i-th tugboat based on the backstepping method;

[0089] And the expression of the virtual expected speed of the i-th tugboat is

[0090]

[0091] Where: K 1i represents the design constant; denote the derivatives of the time-varying relative positions of the i-th and j-th tugboats respectively;

[0092] At the same time, the optimal virtual expected speed v of the i-th tugboat is obtained based on the quadratic programming method. i * , and according to the optimal virtual expected speed v i * The speed error E of the i-th tugboat 2i Updated to

[0093]

[0094] And based on the updated speed error E of the i-th tugboat 2i , obtain the expected control force required for the i-th tugboat; and the expression of the expected control force required for the i-th tugboat is

[0095]

[0096] Where: τ i represents the desired control force required for the i-th tugboat; K 2i represents a positive design constant; Represents the radial basis function neural network based on d i Estimated values ​​for network estimation;

[0097] And the control of tugboats' coordinated collision avoidance is achieved based on the expected control force required by the i-th tugboat.

[0098] Beneficial effects: The present invention provides a tugboat collaborative collision avoidance control method based on a finite-time convergent control obstacle function, constructs a finite-time convergent collision avoidance control obstacle function, and the finite-time convergent collision avoidance control obstacle function constructed by the present invention not only ensures the safety of the system, but also ensures that the system state reaches a safe area within a finite time; and constructs a constraint set based on the finite-time convergent collision avoidance control obstacle function to ensure that the unpowered floating platform converges to a safe motion area within a finite time; and solves and obtains the optimal expected speed by constructing a quadratic programming problem model, and obtains the expected control force required for the unpowered floating platform based on the optimal expected speed, and then distributes the expected control force to each tugboat to obtain the expected tension of the towline of each tugboat; by obtaining the time-varying relative position of the tugboat relative to the floating platform, and combining the expected tension to obtain the virtual expected speed of the tugboat, and obtaining the control force of each tugboat based on the virtual expected speed, thereby realizing the control of the tugboat collaborative collision avoidance, thereby greatly improving the efficiency and control accuracy of the towing system composed of the tugboat and the unpowered floating platform in achieving collaborative motion while maintaining collision avoidance. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to 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 any creative labor.

[0100] Figure 1 Flowchart of the tugboat cooperative collision avoidance control method based on the finite time convergence control barrier function of the present invention;

[0101] Figure 2 This is a flowchart of obtaining the desired control force required for the unpowered floating platform in this embodiment;

[0102] Figure 3 This is a technical roadmap for realizing coordinated collision avoidance control of tugboats in this embodiment. DETAILED DESCRIPTION

[0103] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0104] This embodiment provides a tugboat cooperative collision avoidance control method based on a finite time convergence control barrier function, such as Figures 1 to 3 As shown, the specific steps include:

[0105] S1: Obtain the mathematical model of the unpowered floating platform;

[0106] Mathematical models of tugboats used to tow unpowered floating platforms;

[0107] Specifically, in this embodiment, under the condition of environmental interference, the position and heading information of the tugboat and the unpowered floating platform are collected by the sensor system, and the dynamic and kinematic models, i.e., mathematical models, of the motion of the tugboat and the unpowered floating platform can be obtained by using this position and heading information and the parameters of the tugboat system itself.

[0108] And the mathematical model of the unpowered floating platform is expressed as

[0109]

[0110] Where: η0 represents the position vector of the unpowered floating platform in the northeast coordinate system; represents the derivative of the position vector η0; R(ψ0) represents the transformation matrix; v0 represents the velocity vector of the unpowered floating platform in the hull coordinate system; M0 represents the system inertia matrix composed of the rigid body inertia of the unpowered floating platform and the hydrodynamic additional mass; represents the derivative of the velocity vector v0; D0 represents the ship hydrodynamic damping coefficient matrix; g0 represents the unmodeled dynamic term; τ0 represents the environmental force on the unpowered floating platform, where for the unpowered floating platform, its system control force τ0 is the pulling force exerted on it by the tugboat formation;

[0111] The mathematical model of the tugboat is expressed as follows:

[0112]

[0113] Where: η i represents the position vector of the i-th tugboat in the northeast coordinate system; Represents the position vector η i The derivative of R(ψ i ) represents the transformation matrix of the i-th tugboat; v i represents the velocity vector of the i-th tugboat in the hull coordinate system; M i represents the system inertia matrix composed of the rigid body inertia and hydrodynamic additional mass of the i-th tugboat; represents the velocity vector v i The derivative of i represents the ship hydrodynamic damping coefficient matrix of the i-th tugboat; g i represents the unmodeled dynamic term of the i-th tugboat; τ i represents the system control force of the i-th tugboat; represents the tension generated by the cable between the i-th tugboat and the unpowered floating platform; represents the environmental force on the i-th tugboat;

[0114] S2: Based on the mathematical model of the unpowered floating platform and the preset expected path, a virtual expected speed of the unpowered floating platform is obtained; in order to ensure that the unpowered floating platform completes the path tracking goal, the virtual expected speed of the unpowered floating platform is designed by using the backstepping method through the motion mathematical model of the unpowered floating platform; specifically, the following steps are included:

[0115] S21: Based on a preset expected path, obtain a position error and a velocity error of the unpowered floating platform according to a mathematical model of the unpowered floating platform;

[0116] And the position error E 10 and speed error E 20 The expression is

[0117]

[0118] Where: η d represents the desired position vector of the unpowered floating platform; η0 represents the actual position vector of the unpowered floating platform; represents the virtual desired speed of the unpowered floating platform; ν0 represents the actual speed vector of the unpowered floating platform;

[0119] Combined with the mathematical model of the unpowered floating platform, the position error E is obtained 10 and speed error E 20 The error derivative of , and the expression of the error derivative is

[0120]

[0121] Where: d0 represents the total interference and uncertainty term of the unpowered floating platform;

[0122] S22: Obtain the virtual expected speed of the unpowered floating platform according to the error derivative based on the backstepping method;

[0123] And the expression of virtual desired speed is

[0124]

[0125] Where: K 10 represents the design constant; represents the derivative of the desired trajectory; T represents the transpose.

[0126] This embodiment, based on the designed virtual desired speed of the unpowered floating platform, designs a finite-time convergent control barrier function to ensure that the system consisting of the tugboat and the platform can safely avoid collisions. Unlike traditional formations, the tugboat and the platform are connected by a towline, so collision avoidance should be considered as a whole. The system consisting of the tugboat and the unpowered floating platform is considered as a whole, surrounded by an ellipse. The obstacle avoidance design is combined with information such as the location of the obstacle to obtain a finite-time convergent collision control barrier function (FTCBF) for the tugboat system. The designed quadratic programming problem is then solved to keep the floating platform and tugboat within the safe zone, thereby achieving collision avoidance. The specific implementation process is as follows:

[0127] S3: The unpowered floating platform and the tugboat are regarded as an integral structure, and a virtual ellipse is set to surround the integral structure to obtain a coordinated navigation motion region;

[0128] The location of the unpowered floating platform is the center point of the virtual ellipse;

[0129] The obstacle is regarded as a circular area body. A finite time convergence collision avoidance control obstacle function is constructed based on the cooperative navigation motion area body and the circular area body. Based on the finite time convergence collision avoidance control obstacle function, a constraint set is constructed to ensure that the unpowered floating platform converges to the safe motion area in a finite time.

[0130] The specific steps include:

[0131] S31: The unpowered floating platform and the tugboat are considered as a whole, and a virtual ellipse is set to enclose them to obtain the coordinated navigation motion area;

[0132] And the two fixed points of the virtual ellipse are denoted as F1 and F2 and and And define the virtual ellipse constraint condition satisfied by any point P on the ellipse boundary line as |PF1|+|PF2|=2a, where a represents a constant and a>0;

[0133] At the same time, the location of the unpowered floating platform is set as the center point of a virtual ellipse. Within this virtual ellipse, both the tugboat and the unpowered floating platform are contained within the ellipse. The center point of the ellipse is the location coordinate of the unpowered floating platform, and the tugboats are scattered around the floating platform to study it as a whole.

[0134] S32: The obstacle is considered as a circular area, and the center of the circular area is denoted as η b , the radius of the circular area is recorded as R b At the same time, any point on the circular area is recorded as

[0135] Based on the virtual ellipse constraint, the minimum safe distance between the unpowered floating platform and the tugboat is obtained according to the location of the unpowered floating platform and the obstacles. The system of equations, and

[0136] The expression of the equation group is

[0137]

[0138] Where: Indicates the position coordinates of the fixed point F1; Indicates the position coordinates of fixed point F2; Indicates the position coordinate of the unpowered floating platform; y p ,x p Represents the position coordinates of point P; Indicates the location coordinates of the obstacle;

[0139] By solving the equations to obtain the position coordinates of point P to obtain |Pη0|, and then obtain the minimum safety distance |Pη0| is the position η0 of the unpowered floating platform and the position η of the obstacle b The distance from the intersection point P of the connecting line and the ellipse to η0;

[0140] S33: To avoid collision between the unpowered floating platform and the tugboat and the obstacle, the ellipse is prevented from colliding with the obstacle, and then the minimum safety distance is set. Construct a finite time convergent collision avoidance control obstacle function;

[0141] And the finite time convergence collision avoidance control obstacle function h 0b The expression of (η0) is

[0142]

[0143] Where: η b represents the position of the obstacle and b=1,……,N0; N0 represents the number of obstacles;

[0144] And according to the finite time convergence collision avoidance control obstacle function h 0b (η0), the safe movement area of ​​the unpowered floating platform and the tugboat formation is defined as

[0145]

[0146] S34: In order to ensure that the unpowered floating platform can enter the safe area within a limited time, a constraint set is constructed based on the finite time convergence collision avoidance control obstacle function to ensure that the unpowered floating platform converges to the safe movement area within a limited time;

[0147] And the constraint set S 0b The expression of (ν0) is

[0148]

[0149] Where: Indicates h 0b The derivative of (η0); h 0b Indicates h 0b The abbreviation of (η0); ζ0, ρ represent design parameters and ζ0>0, 0<ρ<1; T0 represents the upper bound of the time to converge to the safe motion region;

[0150] S4: Construct a quadratic programming problem model based on the constraint set and the virtual expected speed;

[0151] The optimal expected speed is obtained by solving a quadratic programming problem model. Based on the optimal expected speed, the expected control force required for the unpowered floating platform is obtained. The expected control force is distributed to each tugboat through a quadratic programming algorithm to obtain the expected pulling force of each tugboat's towline.

[0152] The specific steps include:

[0153] S41: Construct a quadratic programming problem model based on the constraint set and the virtual desired speed;

[0154] And the expression of the quadratic programming problem model is

[0155]

[0156] Where: represents the optimal expected speed; Represents the objective function of the quadratic programming problem model;

[0157] S42: Solve and obtain the optimal expected speed through the quadratic programming problem model And according to the optimal expected speed, the speed error of the unpowered floating platform is updated to

[0158]

[0159] and obtaining a desired control force required for the unpowered floating platform based on the updated speed error of the unpowered floating platform;

[0160] And the expression of expected control force is

[0161]

[0162] Where: τ0 represents the desired control force required for the unpowered floating platform; K 20 represents a positive design constant; Represents the estimated value of d0 based on the radial basis function neural network, which includes:

[0163] Since d0 is unknown, a radial basis function neural network is used to estimate it, and its expression is: in represents the weight matrix, m represents the number of neurons; h0(δ0) represents the Gaussian basis function and μ0=[μ 0,1 μ 0,2 μ 0,3 ],μ 0,1 μ 0,2 μ 0,3 represents the design constant; in this embodiment, τ0 is the resultant force of the tugboat formation. Through the quadratic programming algorithm, τ0 can be distributed to each tugboat, and then the expected pulling force of the unpowered floating platform on each tugboat can be obtained;

[0164] S43: Construct the cost function and constraints of the quadratic programming algorithm, which is expressed as

[0165] Cost function: minJ = T T ΩT+s T Qs

[0166] Constraints:

[0167]

[0168] Where: represent the minimum and maximum horizontal tensions of the towline respectively; T represents the desired horizontal tension of the towline of the tugboat and represents the expected horizontal tension of the i-th towline, i.e., the expected pulling force; Ω, Q represents the weight matrix; N represents the number of tugboats; θ i It refers to the angle between the i-th streamer and the heading of the unpowered floating platform in the northeast coordinate system; B0,s represents the intermediate parameter; (l xi ,l yi ) represents the position of the towing point where the i-th towline is fixed on the unpowered floating platform;

[0169] The desired control force is distributed to each tugboat through a quadratic programming algorithm to obtain the desired pulling force of the towline of each tugboat;

[0170] S5: Based on the installation position of the towline between the unpowered floating platform and the tugboat, the time-varying relative position of the tugboat relative to the floating platform is obtained. Based on the time-varying relative position, the tugboat mathematical model and the expected pulling force are combined to obtain the virtual expected speed of the tugboat. Based on the virtual expected speed, the control force of each tugboat is obtained, thereby realizing the coordinated collision avoidance control of the tugboats.

[0171] The specific steps include:

[0172] S51: constructing a mathematical model of the towline according to the expected tension of the towline of each tugboat, and solving the expected horizontal length of the towline according to the mathematical model of the towline;

[0173] And the mathematical model of the tow cable is expressed as

[0174]

[0175] Where: represents the horizontal tension of the towline on the i-th tugboat; L R represents the nominal length of the streamer; σ represents the density of the streamer; E and A represent the Young's modulus and cross-sectional area of ​​the streamer respectively; D H The horizontal length of the streamer is the expected horizontal length of the streamer obtained by the mathematical model of the streamer. T H represents the design parameters;

[0176] S52: Acquire the real-time position of the unpowered floating platform, and based on the installation position of the towline between the unpowered floating platform and the tugboat, acquire the time-varying relative position of the tugboat relative to the floating platform;

[0177] In order to obtain the desired position information of the tugboat, this embodiment introduces the time-varying relative position And the formula for obtaining the time-varying relative position is

[0178]

[0179] Where: represents the time-varying relative position of the i-th tugboat relative to the floating platform; represents the connection position between the unpowered floating platform and the i-th towline; represents the intermediate parameter; ψ0 represents the bow angle of the unpowered floating platform; p0 represents the design constant;

[0180] S53: Obtain the position error E of the i-th tugboat according to the time-varying relative position 1i and velocity error E 2i , whose expression is

[0181]

[0182] Where: a ij Represents the adjacency matrix of the decision variables of the i-th tugboat and the j-th tugboat, that is, if the i-th tugboat can obtain the information of the j-th tugboat, then a ij =1, otherwise 0; a i0 represents the adjacency matrix of the decision variables between the i-th tugboat and the unpowered floating platform, that is, if the i-th tugboat can obtain the state information of the unpowered floating platform, then ai0 =1, otherwise 0; represents the virtual expected speed of the i-th tugboat to be solved;

[0183] S54: Based on the position error and speed error of the i-th tugboat, and combined with the tugboat mathematical model and the expected pulling force, the position error and speed error derivatives of the i-th tugboat are obtained, and their expressions are:

[0184]

[0185] Where: a id ,B i , d i Indicates the intermediate parameter; φ i represents the angle between the i-th towline and the X-axis of the tugboat in the hull coordinate system; Indicates E 1i ,E 2i The first derivative of

[0186] S55: Obtaining a virtual desired speed of the i-th tugboat according to the position error and speed error derivative of the i-th tugboat based on the backstepping method;

[0187] And the expression of the virtual expected speed of the i-th tugboat is

[0188]

[0189] Where: K 1i represents the design constant; denote the derivatives of the time-varying relative positions of the i-th and j-th tugboats respectively;

[0190] At the same time, the optimal virtual expected speed v of the i-th tugboat is obtained based on the quadratic programming method. i * , and according to the optimal virtual expected speed v i * The speed error E of the i-th tugboat 2i Updated to

[0191]

[0192] And based on the updated speed error E of the i-th tugboat 2i , obtain the expected control force required for the i-th tugboat; and the expression of the expected control force required for the i-th tugboat is

[0193]

[0194] Where: τ i represents the desired control force required for the i-th tugboat; K 2i represents a positive design constant; Represents the radial basis function neural network based on d i The estimated value of the network estimation is performed; wherein the design principle of obtaining the desired control force required for the i-th tugboat in this embodiment is the same as that of obtaining the desired control force required for the unpowered floating platform, which will not be described in detail here;

[0195] And the control of tugboats' coordinated collision avoidance is achieved based on the expected control force required by the i-th tugboat.

[0196] This embodiment uses the current position of the unpowered floating platform and the installation position of the towline on the platform and tugboat as a basis to determine the time-varying relative position of the tugboat relative to the floating platform. This is used to determine the tugboat's virtual desired velocity. Combining the desired control force with the tugboat's mathematical model of motion, the control input force for each tugboat is determined, ultimately enabling the tugboat and unpowered floating platform to coordinate motion while maintaining collision avoidance across the entire system. The finite-time convergent collision avoidance control obstacle function in this embodiment demonstrates superior control performance compared to the artificial potential field method and the traditional control obstacle function method, as analyzed below:

[0197] Artificial potential field methods introduce an abstract artificial gravitational field into the environment, where the target point represents the gravitational field and the obstacles represent the repulsive fields. The combined force of these two forces guides the tugboat's motion. However, these methods can be prone to local minima and cannot guarantee an optimal solution. The control barrier function (CBF) is a constraint-based control method designed to ensure that the system state always remains within the safe region. CBF defines a barrier function that is positive within the safe region, zero on the safety boundary, and negative within the danger region. A control law is then designed to ensure that the derivative of the barrier function remains nonnegative, preventing the system from entering the danger region and thus ensuring system safety. CBF methods offer strict safety guarantees and can handle nonconvex and time-varying constraints, making them applicable to more complex environments. The finite-time convergent collision avoidance control barrier function (FTCBF) is a special type of control barrier function that not only guarantees system safety but also ensures that the system state reaches the safe region within a finite time. Compared with the traditional control barrier function, FTCBF ensures that the derivative of the barrier function remains negative under all possible control inputs through the control law, thereby forcing the system state to converge to the safe region within a finite time. In summary, the beneficial effects of the method described in this embodiment are as follows: by constructing a finite-time convergent collision avoidance control obstacle function, not only the safety of the system is guaranteed, but also the system state is ensured to reach a safe area within a finite time; and based on the finite-time convergent collision avoidance control obstacle function, a constraint set is constructed to ensure that the unpowered floating platform converges to a safe motion area within a finite time; and by constructing a quadratic programming problem model to solve and obtain the optimal expected speed, and based on the optimal expected speed, the expected control force required for the unpowered floating platform is obtained, and then the expected control force is distributed to each tugboat to obtain the expected tension of each tugboat's towline; by obtaining the time-varying relative position of the tugboat relative to the floating platform and combining the expected tension to obtain the virtual expected speed of the tugboat, and based on the virtual expected speed, the control force of each tugboat is obtained, thereby realizing the control of the coordinated collision avoidance of the tugboats, thereby greatly improving the efficiency and control accuracy of the towing system composed of the tugboat and the unpowered floating platform in achieving coordinated motion while maintaining collision avoidance.

[0198] 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 above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above 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 tugboat cooperative collision avoidance control method based on a finite time convergence control barrier function, characterized in that: The specific steps include: S1: Obtain the mathematical model of the unpowered floating platform; Mathematical models of tugboats used to tow unpowered floating platforms; S2: Based on the mathematical model of the unpowered floating platform and the preset expected path, the virtual expected speed of the unpowered floating platform is obtained; S3: The unpowered floating platform and the tugboat are regarded as an integral structure, and a virtual ellipse is set to surround the integral structure to obtain a coordinated navigation motion area, with the location of the unpowered floating platform being the center point of the virtual ellipse; The obstacle is regarded as a circular area body. A finite time convergence collision avoidance control obstacle function is constructed based on the cooperative navigation motion area body and the circular area body. Based on the finite time convergence collision avoidance control obstacle function, a constraint set is constructed to ensure that the unpowered floating platform converges to the safe motion area in a finite time. S4: Construct a quadratic programming problem model based on the constraint set and the virtual expected speed; The optimal expected speed is obtained by solving a quadratic programming problem model, and the expected control force required for the unpowered floating platform is obtained according to the optimal expected speed; The desired control force is distributed to each tugboat through a quadratic programming algorithm to obtain the desired pulling force of the towline of each tugboat; S5: Based on the installation position of the towline between the unpowered floating platform and the tugboat, the time-varying relative position of the tugboat relative to the floating platform is obtained; According to the time-varying relative position, the tugboat mathematical model and the expected pulling force are combined to obtain the virtual expected speed of the tugboat. The control force of each tugboat is obtained according to the virtual expected speed, thereby realizing the coordinated collision avoidance control of the tugboats.

2. The tugboat cooperative collision avoidance control method based on finite time convergence control barrier function according to claim 1 is characterized in that: The mathematical model of the unpowered floating platform in S1 is expressed as follows: Where: η0 represents the position vector of the unpowered floating platform in the northeast coordinate system; represents the derivative of the position vector η0; R(ψ0) represents the transformation matrix; v0 represents the velocity vector of the unpowered floating platform in the hull coordinate system; M0 represents the system inertia matrix composed of the rigid body inertia of the unpowered floating platform and the hydrodynamic additional mass; represents the derivative of the velocity vector v0; D0 represents the ship hydrodynamic damping coefficient matrix; g0 represents the unmodeled dynamic term; τ0 represents the environmental force on the unpowered floating platform; The mathematical model of the tugboat is expressed as follows: Where: η i represents the position vector of the i-th tugboat in the northeast coordinate system; Represents the position vector η i The derivative of R(ψ i ) represents the transformation matrix of the i-th tugboat; ν i represents the velocity vector of the i-th tugboat in the hull coordinate system; M i represents the system inertia matrix composed of the rigid body inertia and hydrodynamic additional mass of the i-th tugboat; represents the velocity vector ν i The derivative of i represents the ship hydrodynamic damping coefficient matrix of the i-th tugboat; g i represents the unmodeled dynamic term of the i-th tugboat; τ i represents the system control force of the i-th tugboat; represents the tension generated by the cable between the i-th tugboat and the unpowered floating platform; represents the environmental force on the i-th tugboat.

3. The tugboat cooperative collision avoidance control method based on finite time convergence control barrier function according to claim 2 is characterized in that: The S2 specifically includes the following steps: S21: Based on a preset expected path, obtain a position error and a velocity error of the unpowered floating platform according to a mathematical model of the unpowered floating platform; And the position error E 10 and speed error E 20 The expression is Where: η d represents the desired position vector of the unpowered floating platform; η0 represents the actual position vector of the unpowered floating platform; θ0 represents the virtual desired velocity of the unpowered floating platform; ν0 represents the actual velocity vector of the unpowered floating platform; Combined with the mathematical model of the unpowered floating platform, the position error E is obtained 10 and speed error E 20 The error derivative of , and the expression of the error derivative is Where: d0 represents the total interference and uncertainty term of the unpowered floating platform; S22: Obtain the virtual expected speed of the unpowered floating platform according to the error derivative based on the backstepping method; And the expression of virtual desired speed is Where: K 10 represents the design constant; η d represents the derivative of the desired trajectory; T represents the transpose.

4. The tugboat cooperative collision avoidance control method based on finite time convergence control barrier function according to claim 3 is characterized in that: The S3 specifically includes the following steps: S31: The unpowered floating platform and the tugboat are considered as a whole, and a virtual ellipse is set to enclose them to obtain the coordinated navigation motion area; And the two fixed points of the virtual ellipse are denoted as F1 and F2 and and And define the virtual ellipse constraint condition satisfied by any point P on the ellipse boundary line as |PF1|+|PF2|=2a, where a represents a constant and a>0; At the same time, the location of the unpowered floating platform is taken as the center point of the virtual ellipse; S32: The obstacle is considered as a circular area, and the center of the circular area is denoted as η b , the radius of the circular area is recorded as R b At the same time, any point on the circular area is recorded as Based on the virtual ellipse constraint, the minimum safe distance between the unpowered floating platform and the tugboat is obtained according to the location of the unpowered floating platform and the obstacles. The system of equations, and The expression of the equation group is Where: Indicates the position coordinates of the fixed point F1; Indicates the position coordinates of fixed point F2; Indicates the position coordinate of the unpowered floating platform; y p ,x p Represents the position coordinates of point P; Indicates the location coordinates of the obstacle; By solving the equations to obtain the position coordinates of point P to obtain |Pη0|, and then obtain the minimum safety distance S33: According to the minimum safety distance Construct a finite time convergent collision avoidance control obstacle function; And the finite time convergence collision avoidance control obstacle function h 0b The expression of (η0) is Where: η b represents the position of the obstacle and b=1,……,N0; N0 represents the number of obstacles; And according to the finite time convergence collision avoidance control obstacle function h 0b (η0), the safe movement area of ​​the unpowered floating platform and the tugboat formation is defined as S34: Based on the finite time convergence collision avoidance control obstacle function, a constraint set is constructed to ensure that the unpowered floating platform converges to the safe motion area in a finite time; And the constraint set The expression is Where: Indicates h 0b The derivative of (η0); h 0b Indicates h 0b is the abbreviated form of (η0); ζ0, ρ represent design parameters and ζ0>0, 0<ρ<1; T0 represents the upper bound of the time to converge to the safe motion region.

5. The tugboat cooperative collision avoidance control method based on finite time convergence control barrier function according to claim 4 is characterized in that: The S4 specifically includes the following steps: S41: Construct a quadratic programming problem model based on the constraint set and the virtual desired speed; And the expression of the quadratic programming problem model is Where: represents the optimal expected speed; Represents the objective function of the quadratic programming problem model; S42: Solve and obtain the optimal expected speed through the quadratic programming problem model And according to the optimal expected speed, the speed error of the unpowered floating platform is updated to and obtaining a desired control force required for the unpowered floating platform based on the updated speed error of the unpowered floating platform; And the expression of expected control force is Where: τ0 represents the desired control force required for the unpowered floating platform; K 20 represents a positive design constant; Represents the estimated value of d0 based on the radial basis function neural network; S43: Construct the cost function and constraints of the quadratic programming algorithm, which is expressed as Cost function: minJ = T T ΩT+s T Qs Constraints: Where: represent the minimum and maximum horizontal tensions of the towline respectively; T represents the desired horizontal tension of the towline of the tugboat and represents the expected horizontal tension of the i-th towline, i.e., the expected pulling force; Ω, Q represents the weight matrix; N represents the number of tugboats; θ i It refers to the angle between the i-th streamer and the heading of the unpowered floating platform in the northeast coordinate system; B0,s represents the intermediate parameter; The desired control force is distributed to each tugboat through the quadratic programming algorithm to obtain the expected tension of the towline of each tugboat.

6. The tugboat cooperative collision avoidance control method based on finite time convergence control barrier function according to claim 5 is characterized in that: The S5 specifically includes the following steps: S51: constructing a mathematical model of the towline according to the expected tension of the towline of each tugboat, and solving the expected horizontal length of the towline according to the mathematical model of the towline; And the mathematical model of the tow cable is expressed as Where: represents the horizontal tension of the towline on the i-th tugboat; L R represents the nominal length of the streamer; σ represents the density of the streamer; E and A represent the Young's modulus and cross-sectional area of ​​the streamer respectively; D H The horizontal length of the streamer is the expected horizontal length of the streamer obtained by the mathematical model of the streamer. T H represents the design parameters; S52: Acquire the real-time position of the unpowered floating platform, and based on the installation position of the towline between the unpowered floating platform and the tugboat, acquire the time-varying relative position of the tugboat relative to the floating platform; And the formula for obtaining the time-varying relative position is Where: represents the time-varying relative position of the i-th tugboat relative to the floating platform; represents the connection position between the unpowered floating platform and the i-th towline; represents the intermediate parameter; ψ0 represents the bow angle of the unpowered floating platform; p0 represents the design constant; S53: Obtain the position error E of the i-th tugboat according to the time-varying relative position 1i and velocity error E 2i , whose expression is Where: a ij Represents the adjacency matrix of the decision variables of the i-th tugboat and the j-th tugboat, that is, if the i-th tugboat can obtain the information of the j-th tugboat, then a ij =1, otherwise 0; a i0 represents the adjacency matrix of the decision variables between the i-th tugboat and the unpowered floating platform, that is, if the i-th tugboat can obtain the state information of the unpowered floating platform, then a i0 =1, otherwise 0; represents the virtual expected speed of the i-th tugboat to be solved; S54: Based on the position error and speed error of the i-th tugboat, and combined with the tugboat mathematical model and the expected pulling force, the position error and speed error derivatives of the i-th tugboat are obtained, and their expressions are: Where: a id ,B i , d i Indicates the intermediate parameter; φ i represents the angle between the i-th towline and the X-axis of the tugboat in the hull coordinate system; Indicates E 1i ,E 2i The first derivative of S55: Obtaining a virtual desired speed of the i-th tugboat according to the position error and speed error derivative of the i-th tugboat based on the backstepping method; And the expression of the virtual expected speed of the i-th tugboat is Where: K 1i represents the design constant; denote the derivatives of the time-varying relative positions of the i-th and j-th tugboats respectively; At the same time, the optimal virtual expected speed v of the i-th tugboat is obtained based on the quadratic programming method. i * , and according to the optimal virtual expected speed v i * The speed error E of the i-th tugboat 2i Updated to And based on the updated speed error E of the i-th tugboat 2i , obtain the expected control force required for the i-th tugboat; and the expression of the expected control force required for the i-th tugboat is Where: τ i represents the desired control force required for the i-th tugboat; K 2i represents a positive design constant; Represents the radial basis function neural network based on d i Estimated values ​​for network estimation; And the control of tugboats' coordinated collision avoidance is achieved based on the expected control force required by the i-th tugboat.

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