Real-time reachable domain setting method based on wave interference

Abstract

The invention discloses a real-time reachable domain setting method based on wave interference. The method comprises the following steps: selecting real sea wave interference information based on actual sea conditions; constructing a kinematic equation of the target ship, and adding the real sea wave interference information into the kinematic equation to form an interference ship operation model; discretizing the interference ship operation model so as to determine the state of the interference ship and a discrete motion model with limited control, the discrete motion model comprising a plurality of discrete points; constructing a polyhedron containing all discrete points, and placing external reference points on the polyhedron; carrying out projection calculation on a reachable set boundary point on the constructed polyhedron; and connecting the reachable set boundary points to obtain a real-time reachable set after the ship is added into the wave interference. According to the method, the dynamic reachable domain of the ship can be displayed, and the method has a wide application prospect in a real sea wave interference control reachable range.

Description

Technical Field

[0001] The invention relates to the field of ship control and navigation technology, and in particular to a real-time reachable domain setting method based on wave interference. Background Art

[0002] In the field of modern marine engineering and automatic control, the safety and efficiency of ships have received extensive attention. Especially in complex marine environments, ships are affected by multiple factors such as waves, wind speed, and currents. The uncertainty of these factors poses a huge challenge to the navigation safety of ships. As an important tool for evaluating system safety, the reachable set has achieved remarkable results in the fields of robots, unmanned vehicles, and aircraft control. However, there are relatively few studies specifically targeting the reachable domain of ships under real wave interference, which largely limits the visibility of the reachable domain of ships under interference and the navigation safety of ships in complex marine environments.

[0003] Modeling and simulation of reachable sets are key to understanding and predicting system behavior. With the introduction of reachable set calculation methods in different scenarios, we can have a deeper understanding of the dynamic characteristics and potential risks of the system. By constructing the Lyapunov function, researchers can provide an approximate ellipsoid description for the reachable set of the system, which provides an effective means to evaluate the stability of the system state. Furthermore, some literature regards the reachable set as the zero level set of the viscosity solution of the Hamilton-Jacobi partial differential equation. By solving the equation using the level set method, we can obtain the approximate reachable set of the system within a specific time, which is of great significance for predicting the future state of the system. In the study of linear systems, external and internal ellipsoid estimation methods are used to refine the study of reachable sets. This method provides a practical tool for system analysis by gradually approaching the true reachable boundary. In addition, the reachable set theory of discrete systems is also used to generate reachable sets of continuous systems, which provides theoretical support for dealing with sampling and discretization problems in practical problems.

[0004] Although some progress has been made in the study of reachable areas of satellites and spacecraft, the study of reachable areas of ships under real wave disturbances still faces many challenges. The uncertainty and nonlinear characteristics of waves make it difficult to directly apply traditional reachable set calculation methods. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention discloses a method for setting a real-time reachable domain based on wave interference, which specifically comprises the following steps:

[0006] Select real wave interference information based on actual sea conditions;

[0007] Construct the kinematic equation of the target ship, and add the real wave interference information into the kinematic equation to form the interference ship operation model;

[0008] Discretizing the interfering ship operation model, thereby determining the state of the interfering ship and a discrete motion model with limited control, wherein the discrete motion model includes a plurality of discrete points;

[0009] Construct a polyhedron that contains all discrete points and place external reference points on the polyhedron;

[0010] Perform projection calculation on the constructed polyhedron to determine the boundary points of the reachable set;

[0011] Connect the boundary points of the reachable set to obtain the real-time reachable set after the ship joins the wave disturbance.

[0012] Furthermore, for each reference point in the constructed polyhedron, a projection operation is performed along the direction of the normal vector of the boundary surface to project it into the entire reachable set, thereby finding the boundary point of the reachable set corresponding to the reference point.

[0013] Furthermore, the interfering ship operation model is:

[0014]

[0015] Where u, v, and r represent the longitudinal, lateral, and bow angular velocities, respectively. is the inertia matrix of the ship system, is the hydrodynamic damping coefficient, the matrix τ wave =[τ waveu ,τ wavev ,τ waver ] T Interference from the external environment.

[0016] Furthermore, according to the state constraints, control constraints and motion characteristics of the interfering ship, the state and control-constrained discrete motion model of the interfering ship is obtained as follows:

[0017]

[0018]

[0019] Where k is the time step, Δt is the size of the time step, and u k ,v k ,ψ k ,r k is the value at step k, τ u,k , τ waven,k , τ wavev,k , τ r,k , τ waver,k is the external torque at step k;

[0020] Assume that starting from the initial condition (t0; x0), at t N The reachable set at a certain moment is defined as follows:

[0021]

[0022] t N is the termination time, indicating the final moment when the system reaches the reachable set; t0 is the initial time, indicating the time when the system starts; x0 is the initial state, indicating the state vector of the system at the initial time; y is a state vector in the reachable set; R n is an n-dimensional real number space; It is the control input applied during the process of the ship system passing through control from the initial state to the final state.

[0023] Furthermore, when constructing a polyhedron containing all discrete points and placing external reference points on the polyhedron:

[0024] S41: Assume that the initial conditions of the system (t0, x0) are known. N State variables at a moment The jth component of The minimum and maximum values ​​of are obtained by controlling the limits:

[0025]

[0026] where j∈1,2,…,n.

[0027] S42: The above two function values ​​are respectively recorded as and make:

[0028]

[0029] S43: For discrete system reachable sets Any point in Both Construct a polyhedron from this:

[0030]

[0031] in Apparently

[0032] S44: Assume that the surface of the polyhedron S consists of four faces F1, F2, F3, and F4. For each face F i , a set of reference points distributed on the surface are obtained through different linear combinations of its vertices. Let the surface F i There are p vertices V1,...,V p , then Fi A reference point P on i j It is expressed as:

[0033]

[0034] in Determines the specific position of the reference point on the polyhedron surface, and generates points at any position on the surface by adjusting the weight value. m It is the vertex that defines each face and determines the geometric shape of the polyhedron. i j A reference point on the surface.

[0035] Due to the adoption of the above technical solution, the present invention provides a real-time reachable domain setting method based on wave interference, which has strong real-time response capability and high fidelity by comprehensively considering multiple factors such as wave characteristics and ship characteristics. By combining and analyzing wave characteristics, ship characteristics, and the interaction between the ship and the waves, the reachable domain of the ship can be dynamically displayed, thus having a wide range of application prospects within the interference control range in a real wave environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0037] Figure 1 The present invention is a flow chart of a method for setting a real-time reachable domain based on wave interference.

[0038] Figure 2 This is a simulation diagram of the real-time ocean wave interference effect of the present invention. DETAILED DESCRIPTION

[0039] In order to make the technical solutions and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention:

[0040] like Figure 1 A method for setting a real-time reachable domain based on wave interference is shown, which specifically includes the following steps:

[0041] S1: Select real wave interference information based on actual sea conditions;

[0042] S2: construct the kinematic equation of the target ship, and add the real wave interference information into the kinematic equation to form the interference ship operation model;

[0043] S3: discretizing the interfering ship operation model, thereby determining the state of the interfering ship and a discrete motion model with limited control, wherein the discrete motion model includes a plurality of discrete points;

[0044] S4: construct a polyhedron containing all discrete points and place external reference points on the polyhedron;

[0045] S5: Project and calculate the boundary points of the reachable set on the constructed polyhedron;

[0046] S6: Connect the boundary points of the reachable set to obtain the real-time reachable set after the ship joins the wave interference.

[0047] Further, S1: select the real sea wave interference information according to actual needs, and the sea wave interference formula used is:

[0048]

[0049] Where ρ is the density of seawater, L is the length of the ship, B is the width of the ship, and T m is the ship's draft, ψ α The angle between the wave direction and the ship’s heading is called the encounter angle, s i (t) is the ocean wave function.

[0050]

[0051] Among them A i is the amplitude of the harmonics that make up the waves, ω ei is the encounter frequency, λ i is the wavelength, φ i Defined as a random initial phase in [0,2π).

[0052] S2: construct the kinematic equation of the target ship;

[0053] S21: The ship model and kinematic model used are as follows:

[0054]

[0055] where η = [x, y, ψ] T ∈R 3 is the inertial coordinate system O e X e Y e Z e The position state variable of the unmanned boat, (x, y)∈R 3Respectively represent the north and east positions in the inertial coordinate system; ψ∈[-π,π] represents the heading angle of the unmanned boat, that is, the angle between the bow and the north direction. υ=[u,v,r] T ∈R 3 , is the attached coordinate system o b x b y b z b where u, v, and r represent the longitudinal, lateral, and bow angular velocities, respectively.

[0056] R(ψ)∈R 3 is the rotation matrix, which is defined as:

[0057]

[0058] The dynamic equation of the unmanned surface vehicle is as follows:

[0059]

[0060] in is the system inertia matrix; is the Coriolis centripetal force matrix; is the hydrodynamic damping coefficient matrix, τ=[τ u ,0,τ r ] T is the control input of the actuator, where τ u and τ r denote the longitudinal thrust and bow moment respectively; τ w =[τ wu ,τ wv ,τ wr ] T is the external time-varying disturbances such as wind, waves, and currents, c 13 =-c 31 =-m 22 v, c 23 =-c 32 =m 11 u.

[0061] S22: After adding real wave interference, the motion model is organized as follows:

[0062]

[0063] where τ wave =[τ waveu ,τ wavev ,τ waver ] T Interference from the external environment.

[0064] S3: Construct the kinematic equation of the target ship and add real wave interference;

[0065] S31: The discrete linear motion model for determining the state and control constraints of the interfering ship is obtained according to the state constraints, control constraints and motion characteristics of the interfering ship, wherein the interfering ship operation model is discretized as follows:

[0066]

[0067]

[0068] Where k is the time step, Δt is the size of the time step, and u k ,v k ,ψ k ,r k is the value at step k, τ u,k , τ waven,k , τ wavev,k , τ r,k , τ waver,k is the external torque at step k;

[0069] S32: The ship discrete system is the system after the ship interference is discretized. For the discrete system, starting from the initial condition (t0; x0), at t N The reachable set at a time can be defined as follows:

[0070]

[0071] t N is the termination time, indicating the final moment when the system reaches the reachable set; t0 is the initial time, indicating the time when the system starts; x0 is the initial state, indicating the state vector of the system at the initial time; y is a state vector in the reachable set; R n is an n-dimensional real number space; It is the control input applied during the process of the ship system passing through control from the initial state to the final state.

[0072] S4: Based on the reachable set of the discrete system, construct a polyhedron that can contain all discrete points. By analyzing all the reachable points in the discrete system, a polyhedron structure containing all these discrete points is constructed, and reference points are placed at appropriate locations outside the polyhedron.

[0073] S41: Assume that the initial conditions of the system (t0, x0) are known. N State variables at a moment The jth component of The minimum and maximum values ​​of are obtained by controlling the limits:

[0074]

[0075] where j∈1,2,…,n.

[0076] S42: The function values ​​obtained in S41 are recorded as and make:

[0077]

[0078] S43: According to S42, for a discrete system reachable set Any point in Both Construct a polyhedron from this:

[0079]

[0080] in Apparently

[0081] S44: Assume that the surface of the polyhedron S consists of four faces F1, F2, F3, and F4. For each face F i , a set of reference points distributed on the surface can be obtained through different linear combinations of its vertices. Specifically, let the surface F i There are p vertices V1,...,V p , then F i A reference point P on i j It can be expressed as:

[0082]

[0083] in Determines the specific position of the reference point on the polyhedron surface. By adjusting the weight value, points at any position on the surface can be generated. m are the vertices that define each face, which determine the geometry of the polyhedron, P i j A reference point on the surface.

[0084] S5: Perform projection calculation on the constructed polyhedron to determine the boundary points of the reachable set; specifically, for each reference point in the constructed polyhedron, perform a projection operation along the direction of the normal vector of the boundary surface, project it into the entire reachable set, and then find the boundary point of the reachable set corresponding to the reference point.

[0085] Ensure that the reachable boundaries of the system in all directions are effectively described and determined, so that the reachable position of each reference point can be accurately determined, thereby accurately constructing the overall reachable range of the system; provide accurate boundary data.

[0086] S6: Figure 2As shown in the figure, based on the boundary points of the reachable set, the reachable set of the ship under the condition of wave interference is obtained; specifically, by modeling the interference characteristics of the waves in the current environment, combining the dynamic characteristics and control capabilities of the ship, the boundary of the reachable set of the ship under interference conditions is determined.

[0087] S61: Use the convex hull of all boundary points to approximate the reachable set of the system, and finally obtain the reachable set:

[0088]

[0089] From t0 to t f All control inputs between. Represents starting from the initial state x0 at the initial time t0, at the terminal time t f Q is a set of constraints in the state space, usually representing the range or limit of reachable states.

[0090] The method disclosed in the present invention has strong real-time response capability and high fidelity by comprehensively considering multiple factors such as wave characteristics and ship characteristics. By combining and analyzing wave characteristics, ship characteristics, and the interaction between the ship and the waves, the reachable domain of the ship can be dynamically displayed, thus having a wide range of application prospects within the interference control range in a real wave environment.

[0091] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A real-time reachable domain setting method based on wave interference, characterized in that include: Select real wave interference information based on actual sea conditions; Construct the kinematic equation of the target ship, and add the real wave interference information into the kinematic equation to form the interference ship operation model; Discretizing the interfering ship operation model, thereby determining the state of the interfering ship and a discrete motion model with limited control, wherein the discrete motion model includes a plurality of discrete points; Construct a polyhedron that contains all discrete points and place external reference points on the polyhedron; Perform projection calculation on the constructed polyhedron to determine the boundary points of the reachable set; Connect the boundary points of the reachable set to obtain the real-time reachable set after the ship joins the wave disturbance.

2. The method for setting a real-time reachable domain based on wave interference according to claim 1, characterized in that: For each reference point in the constructed polyhedron, a projection operation is performed along the direction of the normal vector of the boundary surface to project it into the entire reachable set, thereby finding the boundary point of the reachable set corresponding to the reference point.

3. The method for setting a real-time reachable domain based on wave interference according to claim 1, characterized in that: The interfering ship operation model is: Where u, v, and r represent the longitudinal, lateral, and bow angular velocities, respectively. is the inertia matrix of the ship system, is the hydrodynamic damping coefficient, the matrix τ wave =[τ waveu ,τ wavev ,τ waver ] T Interference from the external environment.

4. The method for setting a real-time reachable domain based on wave interference according to claim 1, characterized in that: According to the state constraints, control constraints and motion characteristics of the interfering ship, the state and control-constrained discrete motion model of the interfering ship is obtained as follows: Where k is the time step, Δt is the size of the time step, and u k ,v k ,ψ k ,r k is the value at step k, τ u,k , τ waven,k , τ wavev,k , τ r,k , τ waver,k is the external torque at step k; Assume that starting from the initial condition (t0; x0), at t N The reachable set at a certain moment is defined as follows: t N is the termination time, indicating the final moment when the system reaches the reachable set; t0 is the initial time, indicating the time when the system starts; x0 is the initial state, indicating the state vector of the system at the initial time; y is a state vector in the reachable set; R n is an n-dimensional real number space; It is the control input applied during the process of the ship system passing through control from the initial state to the final state.

5. The method for setting a real-time reachable domain based on wave interference according to claim 1, characterized in that: When constructing a polyhedron that contains all discrete points and placing external reference points on the polyhedron: S41: Assume that the initial conditions of the system (t0, x0) are known. N State variables at a moment The jth component of The minimum and maximum values ​​of are obtained by controlling the limits: where j∈1,2,…,n. S42: The above two function values ​​are respectively recorded as and make: S43: For discrete system reachable sets Any point in Both Construct a polyhedron from this: in Apparently S44: Assume that the surface of the polyhedron S consists of four faces F1, F2, F3, and F4. For each face F i , a set of reference points distributed on the surface are obtained through different linear combinations of its vertices. Let the surface F i There are p vertices V1,...,V p , then F i A reference point P on i j It is expressed as: in Determines the specific position of the reference point on the polyhedron surface, and generates points at any position on the surface by adjusting the weight value. m It is the vertex that defines each face and determines the geometric shape of the polyhedron. i j A reference point on the surface.

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