Wave compensation system modeling and pose control method based on stewart platform

Abstract

The application relates to a wave compensation system modeling and pose control method based on a Stewart platform, which comprises the following steps: step 1, performing dynamic analysis on a shipborne Stewart platform and obtaining a force balance equation; step 2, calculating the action of a gangway mechanism on the upper platform of the Stewart platform; step 3, expanding the force balance equation based on the action of the gangway mechanism on the upper platform of the Stewart platform, and then establishing a dynamic model of the shipborne Stewart platform considering the gangway; and step 4, designing a Stewart platform pose controller based on a backstepping method to control the pose of the Stewart platform. Compared with the prior art, the application has the advantages of improving the precision of wave compensation and improving the pose control precision.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology for nonlinear fully driven systems, and in particular to a wave compensation system modeling and pose control method based on the Stewart platform. Background Technology

[0002] Offshore operations such as wind turbine maintenance and cargo transportation require a stable shipboard platform. However, waves and wind can cause the platform to sway and heave. Wave compensation systems are needed to compensate for these environmental factors and ensure platform stability. Wave compensation systems can be categorized into single-degree-of-freedom (DOF) compensation and multi-DOF compensation, based on the number of degrees of freedom compensated. Single-DOF compensation systems are easier to control but have less effective compensation. A common approach for multi-DOF compensation is to use a high-precision, rigid Stewart platform for six-degree-of-freedom motion compensation. A pontoon mechanism is also mounted on the Stewart platform to handle different operational tasks.

[0003] As the primary mechanism for actively compensating for wave disturbances, the Stewart platform faces challenges beyond its own complex model. The pitch, extension, and rotation of the walkway bridge cause asymmetrical loads on the platform. Furthermore, the ship's motion caused by sea waves further complicates the modeling and precise control of the coupled system between the Stewart platform and the offshore berthing walkway. Existing control methods simply treat this as interference, thus limiting their effectiveness. Therefore, determining the impact of ship motion and walkway bridge operating conditions in the dynamic model is a core issue facing the application of the Stewart platform in wave compensation systems. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a wave compensation system modeling and pose control method based on the Stewart platform.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] This invention provides a method for modeling and pose control of a wave compensation system based on the Stewart platform. The method includes the following steps:

[0007] Step 1: Perform dynamic analysis on the shipborne Stewart platform and obtain the force balance equations;

[0008] Step 2: Calculate the effect of the walkway mechanism on the Stewart upper platform;

[0009] Step 3: Based on the effect of the pontoon mechanism on the Stewart platform, expand the force balance equation and then establish a dynamic model of the shipborne Stewart platform considering the pontoon.

[0010] Step 4: Design a Stewart platform pose controller based on the backstepping method to control the pose of the Stewart platform.

[0011] Preferably, step 1, which involves performing dynamic analysis on the shipborne Stewart platform and obtaining the force balance equations, specifically includes the following steps:

[0012] Step 101: Set up three coordinate systems, namely the inertial coordinate system {O} w}, Fixed in the ship's hull coordinate system {O b} and the platform coordinate system {O} fixed on the Stewart platform. t}, and in the inertial coordinate system {O w Calculate the velocity and angular velocity of the platform's center of mass on Stewart in the inertial coordinate system {O}. w The expressions for the velocity and angular velocity of the center of mass of the Stewart platform under the following conditions are:

[0013]

[0014]

[0015] in, and Let represent the angular velocity and linear velocity of the upper platform in the inertial coordinate system, respectively. and J p =[J pl J pr ] are the angular velocity and linear velocity of the center of mass of the upper platform in the inertial coordinate system {O w} and pose matrix The transformation matrix between them and Representing the platform coordinate system {O t} and ship coordinate system {O b Each and the generalized angular velocity The Jacobian matrix between them, J pl and J pr Representing the platform coordinate system {O t} and ship coordinate system {O b Each and generalized velocity The Jacobian matrix between them, S(·) denotes the spinor, R wb Represents the ship's coordinate system {O b} and inertial coordinate system {O w Rotation matrix between} Represents the platform coordinate system {O t} relative to the ship's coordinate system {O b The pose of} Represents the ship's coordinate system {O b} relative to the inertial coordinate system {O w The pose of}, ψ, θ and All are Euler angles, and x, y, and z are the horizontal, vertical, and ordinate coordinates, representing the position. Platform coordinate system {O t} relative to the ship's coordinate system {O b The position of}, J I =[0 3×3 ,I 3×3 ] is a constant matrix, and Representing the platform coordinate system {O t} relative to the ship's coordinate system {O b The pose q of} t and the ship's coordinate system {O b} relative to the inertial coordinate system {O w The pose q of} b The transformation matrix between each Euler angular velocity and its own angular velocity;

[0016] Transformation matrix and The expressions are as follows:

[0017]

[0018]

[0019] Step 102: Differentiate the velocity and angular velocity of the platform's center of mass on Stewart to obtain the expressions for acceleration and angular acceleration, respectively:

[0020]

[0021]

[0022] in, and These represent the acceleration and angular acceleration of the upper platform in the inertial coordinate system, respectively.

[0023] Step 103: Obtain the force balance equation based on the kinematic calculation results using the principle of virtual work.

[0024] Preferably, in step 103, the process of obtaining the force balance equation using the principle of virtual work based on the kinematic calculation results specifically involves:

[0025] The inertial force acting on the center of mass of the upper platform is calculated based on the acceleration of the center of mass, and then transformed into the platform coordinate system {O} using the principle of virtual work. t} relative to the ship's coordinate system {O bThe pose q of} t The expression for the transformed inertial force is as follows:

[0026]

[0027] Among them, F I For the inertial force acting on the Stewart platform, m p For Stewart platform quality, I t Let be the rotational inertia matrix of the Stewart platform in the inertial frame;

[0028] The forces acting on the center of mass of the upper platform include inertial force, the equivalent force of the six drive rods, and gravity. These forces are distributed in the platform coordinate system {O}. t} relative to the ship's coordinate system {O b The pose q of} t The equilibrium is reached, and the expression for the force equilibrium equation is obtained as follows:

[0029]

[0030] Among them, F I For the inertial force acting on the Stewart platform, m p Let f be the mass of the platform on Stewart, g be the acceleration due to gravity, and f be the mass of the platform on Stewart. a =(f a1 f a2 f a3 f a4 f a5 f a6 ) T f is the system input. a1 f a2 f a3 f a4 f a5 and f a6 This indicates the driving force required for the six drive levers.

[0031] Preferably, in step 2, in the inertial coordinate system, the action of the bridge mechanism on the Stewart platform includes a force -f1. w and the torque The process of calculating the effect of the bridge mechanism on the Stewart upper platform includes the following steps:

[0032] Step 201: Establish the corresponding coordinate systems {O1}, {O2} and {O3} at the rotation, pitch and extension joints of the walking bridge mechanism according to the Denavit-Hartenberg method;

[0033] Step 202: Use the iterative Newton-Euler method to solve for the acceleration and angular acceleration of the center of mass of each link through forward iteration;

[0034] Step 203: Solve for the force f1 exerted on the link by the Stewart platform through reverse iteration. 1 and the torque

[0035] Step 204: Apply force f1 from the upper platform to the connecting rod. 1 and the torque Transform to inertial coordinate system {O} using a rotation matrix. w In}, the inertial coordinate system {O} can be obtained. w The force f1 exerted by the Stewart upper platform on the connecting rod w and the torque

[0036] Step 205: Obtain the coordinates in the inertial coordinate system {O} w The force exerted by the middle step bridge mechanism on the Stewart upper platform - f1 w and the torque

[0037] Preferably, in step 204, the inertial coordinate system {O} w The force f1 exerted by the Stewart upper platform on the connecting rod w and the torque The expressions are as follows:

[0038]

[0039]

[0040] Where, m brige-f ∈R 3×3 and m brige-n ∈R 3×3 M represents the matrix showing the influence of the force and torque of the step bridge on the acceleration, respectively. brige-f ∈R 3×3 and M brige-n ∈R 3×3 These are the influence matrices of the force and torque on the angular acceleration of the bridge, respectively. brige-f ∈R 3×3 and C brige-n ∈R 3×3 M represents the matrix showing the influence of the force and torque of the bridge on the angular velocity. θ-f ∈R 3×3 and M θ-n ∈R 3×3 These represent the additional terms introduced by the forces and moments acting on the bridge, respectively.

[0041] Preferably, in step 3, the dynamic model of the shipborne Stewart platform considering the walkway bridge is as follows:

[0042]

[0043] in, Represents the platform coordinate system {O t} relative to the ship's coordinate system {O b The pose of} Represents the ship's coordinate system {O b} relative to the inertial coordinate system {O w The pose of}, ψ, θ and All are Euler angles, J∈R 6×6 Let f represent the motion Jacobian matrix of the Stewart platform. a =(f a1 f a2 f a3 f a4 f a5 f a6 ) T f is the system input. a1 f a2 f a3 f a4 f a5 and f a6 M represents the driving force required for the six drive levers. t C represents the equivalent inertia matrix in the task space. t Let G be a first-order matrix representing the task space. t M represents the gravity term. b Let C represent the second-order influence matrix of ship motion. b M represents the first-order influence matrix of ship motion. θ This represents the additional matrix introduced by the bridging action.

[0044] Preferably, in step 4, the process of designing the Stewart platform pose control algorithm based on the backstepping method specifically includes:

[0045] Step 401: Using the pose q of the Stewart upper platform relative to the lower platform t Let O be the controlled variable, and define the platform coordinate system as {O}. t} relative to the ship's coordinate system {O b The desired pose of} is q td And calculate its first derivative. and second derivative

[0046] Step 402: Design a control algorithm using the backstepping method to obtain the pose controller.

[0047] Preferably, in step 401, the first derivative... and second derivative The calculation expressions are as follows:

[0048]

[0049]

[0050] in, and Let R be the rotation matrix. wb The first and second derivatives;

[0051] Preferably, the rotation matrix R wb The expressions for the first and second derivatives are as follows:

[0052]

[0053]

[0054] Preferably, in step 402, the expression for the pose controller is:

[0055]

[0056] Where k1 and k2 are both positive controller parameters,

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1. This invention considers the dynamic influence of ship motion on the Stewart platform, incorporates the ship's motion into the system's dynamic model, and uses the relative pose between the upper and lower Stewart platforms as the controlled variable. It provides an algorithm to calculate the expected value of the relative pose between the upper and lower Stewart platforms based on the ship's motion, effectively compensating for the swaying and heave of the upper Stewart platform caused by sea waves, thereby effectively improving the accuracy of wave compensation.

[0059] 2. This invention incorporates the function of the step bridge mechanism into the Stewart platform dynamics model, which solves the error caused by load asymmetry due to changes in the step bridge's working conditions and improves the accuracy of posture control. Attached Figure Description

[0060] Figure 1 This is a flowchart of the method of the present invention.

[0061] Figure 2 This is a schematic diagram of the coordinate system for dynamic analysis of the shipborne Stewart platform of the present invention.

[0062] Figure 3 This is a schematic diagram of the joint space coordinate system of the walkway mechanism of the present invention. Detailed Implementation

[0063] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0064] like Figure 1 As shown, this invention provides a method for modeling and pose control of a wave compensation system based on the Stewart platform. The method includes the following steps:

[0065] Step 1: Perform dynamic analysis on the shipborne Stewart platform and obtain the force balance equations;

[0066] Step 2: Calculate the effect of the pontoon mechanism on the Stewart platform. In the inertial coordinate system, the effect of the pontoon mechanism on the Stewart platform includes the force -f1. w and the torque

[0067] Step 3: Introduce the effect of the pontoon bridge mechanism on the Stewart platform to expand the force balance equation of the Stewart platform and establish a dynamic model of the shipborne Stewart platform considering the pontoon bridge.

[0068] Step 4: Design a pose control algorithm for the Stewart platform based on the backstepping method to control the pose of the Stewart platform.

[0069] Step 1, the process of performing dynamic analysis on the shipborne Stewart platform and obtaining the force balance equations, specifically includes the following steps:

[0070] like Figure 2 As shown, three coordinate systems are first defined: the inertial coordinate system {O} w}, The ship's coordinate system fixed on the ship (i.e., the Stewart platform) {O b} and the platform coordinate system {O} fixed on the Stewart platform. t};

[0071] In the inertial coordinate system {O w The angular velocity and linear velocity can be obtained from the analysis of the velocity and angular velocity of the center of mass of the platform on Stewart.

[0072]

[0073]

[0074] in, and Let represent the angular velocity and linear velocity of the upper platform in the inertial coordinate system, respectively. and J p =[J pl J pr ] are the angular velocity and linear velocity of the center of mass of the upper platform in the inertial coordinate system {O w}and The transformation matrix between them and Representing the platform coordinate system {O t} and ship coordinate system {O b Each and the generalized angular velocity The Jacobian matrix between them, J pl and J pr Representing the platform coordinate system {O t} and ship coordinate system {O b Each and generalized velocity The Jacobian matrix between them, S(·) denotes the spinor, R wb Represents the ship's coordinate system {O b} and inertial coordinate system {O w The rotation matrix between}, R bt Represents the platform coordinate system {O t} and the ship's coordinate system {O b Rotation matrix between} Represents the platform coordinate system {O t} relative to the ship's coordinate system {O b The pose of} Represents the ship's coordinate system {O b} relative to the inertial coordinate system {O w The pose of}, ψ, θ and All are Euler angles. Platform coordinate system {O t} relative to the ship's coordinate system {O b The position of}, J I =[0 3×3 ,I 3×3 ] is a constant matrix, and Representing the platform coordinate system {O t} relative to the ship's coordinate system {O b The pose q of} t and the ship's coordinate system {O b} relative to the inertial coordinate system {O w The pose q of} b The transformation matrix between each Euler angular velocity and its own angular velocity, the transformation matrix and The expressions are as follows:

[0075]

[0076]

[0077] Differentiating the angular velocity and velocity of the upper platform's center of mass with respect to time yields the angular acceleration of the upper platform's center of mass. and acceleration The expression is:

[0078]

[0079]

[0080] The inertial force acting on the center of mass of the upper platform is calculated based on the acceleration of the center of mass, and then transformed into the platform coordinate system {O} using the principle of virtual work. t} relative to the ship's coordinate system {O b The pose q of} t The expression for the transformed inertial force is as follows:

[0081]

[0082] Among them, F I For the inertial force acting on the Stewart platform, m p For Stewart platform quality;

[0083] The forces acting on the center of mass of the upper platform include inertial force, the equivalent force of the six drive rods, and gravity. These forces are distributed in the platform coordinate system {O}. t} relative to the ship's coordinate system {O b The pose q of} t Based on the equilibrium, the expression for the force balance equation can be obtained as follows:

[0084]

[0085] Among them, F I For the inertial force acting on the Stewart platform, m p Let f be the mass of the platform on Stewart, g be the acceleration due to gravity, and f be the mass of the platform on Stewart. a =(f a1 f a2 f a3 f a4 f a5 f a6 ) T This is the system input, representing the driving force required for the six drive levers.

[0086] In step 2, the process of calculating the effect of the step bridge mechanism on the Stewart upper platform is as follows:

[0087] like Figure 3 As shown, coordinate systems {O1}, {O2} and {O3} are established in the joint space of the walkway mechanism according to the Denavit–Hartenberg method. {O1}, {O2} and {O3} represent the coordinate systems of the rotation, pitch and extension joints of the walkway, respectively.

[0088] The acceleration of the center of mass of each link in the three joint spaces is calculated by forward iteration using the iterative Newton-Euler method. and angular acceleration In the joint space representation, if we treat the platform on Stewart as joint -0 in the first step of the forward iteration, we can set:

[0089]

[0090] in, To provide the inertial frame acceleration for the Stewart platform, For the inertial frame angular acceleration of the Stewart platform, The angular velocity of the inertial frame on the Stewart platform;

[0091] The force f1 exerted on the connecting rod by the upper platform was calculated through reverse iteration. 1 and the torque Considering that the wave compensation mechanism will be subjected to forces at the end of the walkway under certain specific operational tasks, such as offshore wind turbine maintenance, and to prevent damage to the mechanical mechanism, this force should be relatively small within a safe range. Therefore, the first step of the reverse iteration is set as follows:

[0092]

[0093] in, The force acting on the end of the pedestrian bridge. This represents the torque acting on the end of the walkway bridge;

[0094] The connecting rod is subjected to a force f1 from the upper platform. 1 and the torque Transform to inertial coordinate system {O} using a rotation matrix. w In}, the inertial coordinate system {O} can be obtained. w The force f1 exerted by the Stewart upper platform on the connecting rod w and the torque The expression is:

[0095]

[0096]

[0097] Where, m brige-f ∈R 3×3 and m brige-n ∈R 3×3 M represents the matrix showing the influence of the force and torque of the step bridge on the acceleration, respectively. brige-f ∈R 3×3 and M brige-n ∈R 3×3 These are the influence matrices of the force and torque on the angular acceleration of the bridge, respectively. brige-f ∈R 3×3 and C brige-n ∈R 3×3 M represents the matrix showing the influence of the force and torque of the bridge on the angular velocity. θ-f ∈R 3×3 and M θ-n ∈R 3×3 These represent the additional terms introduced by the force and torque of the step bridge, respectively. All of these matrices can be determined by the iterative Newton-Euler method.

[0098] In the inertial coordinate system {O w In the context of the bridge mechanism, the action of the bridge mechanism on the Stewart platform includes the force -f1. w and the torque

[0099] In step 3, the process of establishing the dynamic model of the shipborne Stewart platform considering the walkway bridge is as follows:

[0100] The force balance equations in step 1 are expanded. The forces acting on the center of mass of the upper platform include inertial force, the equivalent force of the six-drive rod, and gravity. Considering the effect of the step bridge mechanism, the forces are determined based on the pose q of the upper platform relative to the lower platform on Stewart. t The following can be obtained from the lower equilibrium:

[0101]

[0102] Substituting the various physical quantities, we can obtain the expression for the dynamic model of the shipborne Stewart platform considering the walkway bridge as follows:

[0103]

[0104] Where, J∈R 6×6 Let f represent the motion Jacobian matrix of the Stewart platform. a =(f a1 f a2 f a3 f a4 f a5 fa6 ) T f is the system input. a1 f a2 f a3 f a4 f a5 and f a6 M represents the driving force required for the six drive levers. t C represents the equivalent inertia matrix in the task space. t Let G be a first-order matrix representing the task space. t M represents the gravity term. b Let C represent the second-order influence matrix of ship motion. b M represents the first-order influence matrix of ship motion. θ This represents the additional matrix introduced by the bridging action.

[0105] In step 4, the process of designing the Stewart platform pose control algorithm (Stewart platform pose controller) based on the backstepping method is as follows:

[0106] Choose the pose q of the Stewart upper platform relative to the lower platform. t As the controlled variable, the design of the Stewart platform pose controller is divided into two parts: pose expectation calculation and control algorithm design.

[0107] The specific process for calculating the expected pose value is as follows:

[0108] The wave compensation system dynamic model derived in step 3 is based on the platform coordinate system {O} t} relative to the ship's coordinate system {O b The pose q of} t As the controlled variable, the wave compensation system directly controls the platform coordinate system {O}. t} relative to the inertial coordinate system {O w The pose of the} remains constant. Therefore, it is necessary to use the ship's coordinate system {O} as observed in real time. b} relative to the inertial coordinate system {O w The pose q of} b and its first derivative and second derivative Computation platform coordinate system {O t} relative to the ship's coordinate system {O b The expected pose q td and its first derivative and second derivative

[0109] The desired pose can be obtained based on the rotation of the spatial coordinate system and vector relationships. The expressions for the elements in the array are as follows:

[0110] θ td =arcsin(-R) wb (3,1))

[0111]

[0112]

[0113]

[0114] Among them, R wb (i,j) represents the ship's coordinate system {O b} and inertial coordinate system {O w The elements in the i-th row and j-th column of the rotation matrix between};

[0115] Desired pose q td It can also be expressed as:

[0116] q td =T(q) b )

[0117] Where T(·) represents the coordinate system {O} of the ship's hull. b} relative to the inertial coordinate system {O w The pose q of} b Solve for the platform coordinate system {O t} relative to the ship's coordinate system {O b The expected pose q td The function.

[0118] The dynamic positioning system is used to make the ship's coordinate system {O} b Relative inertial coordinate system {O w The position coordinates of} [x b y b z b If the first derivative remains unchanged, then... and second derivative The calculation expression is:

[0119]

[0120]

[0121] Based on the properties of the rotation matrix and the relationship between Euler angles and the rotational speed, the rotation matrix R can be solved. wb First and second derivatives:

[0122]

[0123]

[0124] in, and The rotation matrix R is respectively wb The first and second derivatives;

[0125] The specific process of control algorithm design is as follows:

[0126] Designing control algorithms using the backstepping method:

[0127] Define the error; the expressions for the error are as follows:

[0128] z1 = q t -q td

[0129]

[0130] Where z1 is the pose error, z2 is the first derivative error of the pose, and k1 is a positive controller parameter;

[0131] The Lyapunov function corresponding to the error is obtained. The expression of the Lyapunov function is:

[0132]

[0133] Where V is a Lyapunov function;

[0134] The control algorithm (pose controller) is obtained, and its expression is:

[0135]

[0136] Where k1 and k2 are both positive controller parameters,

[0137] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for modeling and pose control of a wave compensation system based on the Stewart platform, characterized in that, The method includes the following steps: Step 1: Perform dynamic analysis on the shipborne Stewart platform and obtain the force balance equations; Step 2: Calculate the effect of the walkway mechanism on the Stewart upper platform; Step 3: Based on the force balance equations of the effect of the walkway mechanism on the Stewart platform, a dynamic model of the shipborne Stewart platform considering the walkway is established. Step 4: Design a Stewart platform pose controller based on the backstepping method to control the pose of the Stewart platform; In step 3, the dynamic model of the shipborne Stewart platform considering the walkway bridge is as follows: in, Represents the platform coordinate system Relative to the ship's coordinate system The position, Representing the ship's coordinate system Relative to the inertial coordinate system The position, , and All are Euler angles. This represents the motion Jacobian matrix of the Stewart platform. For system input, , , , , and This indicates the driving force required for the six drive links. This represents the equivalent inertia matrix in the task space. Represents a first-order matrix in the task space. Represents the gravity term. This represents the second-order influence matrix of ship motion. This represents the first-order influence matrix of ship motion. This represents the additional matrix introduced by the bridge's action; In step 4, the process of designing the Stewart platform pose control algorithm based on the backstepping method is as follows: Step 401: Pose the Stewart upper platform relative to the lower platform. As the controlled variable, a platform coordinate system is established. Relative to the ship's coordinate system The desired pose is And calculate its first derivative. and second derivative ; Step 402: Design a control algorithm using the backstepping method to obtain the pose controller; In step 402, the expression for the pose controller is: in, and All are positive controller parameters. .

2. The wave compensation system modeling and pose control method based on the Stewart platform according to claim 1, characterized in that, Step 1, which involves performing dynamic analysis on the shipborne Stewart platform and obtaining the force balance equations, specifically includes the following steps: Step 101: Set up three coordinate systems, namely the inertial coordinate system. Fixed in the ship's hull coordinate system and the platform coordinate system fixed on the Stewart platform. and in the inertial coordinate system Calculate the velocity and angular velocity of the platform's center of mass on Stewart in the inertial coordinate system. The expressions for the velocity and angular velocity of the center of mass of the upper platform on the Stewart platform are as follows: in, and Let represent the angular velocity and linear velocity of the upper platform in the inertial coordinate system, respectively. and The angular velocity and linear velocity of the center of mass of the upper platform in the inertial coordinate system are respectively... With pose matrix The transformation matrix between them and Representing the platform coordinate system and hull coordinate system Each and generalized angular velocity Jacobi matrix between and Representing the platform coordinate system and hull coordinate system Each and generalized speed Jacobi matrix between To express the search for spinors, Representing the ship's coordinate system With inertial coordinate system Rotation matrix between Represents the platform coordinate system Relative to the ship's coordinate system The position, Representing the ship's coordinate system Relative to the inertial coordinate system The position, , and All are Euler angles. , and The horizontal, vertical, and ordinates represent position. Platform coordinate system Relative to the ship's coordinate system Location, It is a constant matrix. and Representing the platform coordinate system Relative to the ship's coordinate system position and hull coordinate system Relative to the inertial coordinate system position The transformation matrix between each Euler angular velocity and its own angular velocity; Transformation matrix and The expressions are as follows: ； Step 102: Differentiate the velocity and angular velocity of the platform's center of mass on Stewart to obtain the expressions for acceleration and angular acceleration, respectively: in, and These represent the acceleration and angular acceleration of the upper platform in the inertial coordinate system, respectively. Step 103: Obtain the force balance equation based on the kinematic calculation results using the principle of virtual work.

3. The wave compensation system modeling and pose control method based on the Stewart platform according to claim 2, characterized in that, In step 103, the process of obtaining the force balance equation using the principle of virtual work based on the kinematic calculation results is as follows: The inertial force acting on the center of mass of the upper platform is calculated based on the acceleration of the center of mass, and then transformed into the platform coordinate system using the principle of virtual work. Relative to the ship's coordinate system position The expression for the transformed inertial force is as follows: in, The inertial force acting on the Stewart platform. For Stewart platform quality, Let be the rotational inertia matrix of the Stewart platform in the inertial frame; The forces acting on the center of mass of the upper platform include inertial force, the equivalent force of the six drive rods, and gravity. These forces are distributed in the platform coordinate system. Relative to the ship's coordinate system position The equilibrium is reached, and the expression for the force equilibrium equation is obtained as follows: in, The inertial force acting on the Stewart platform. For Stewart platform quality, It is the acceleration due to gravity. For system input, , , , , and This indicates the driving force required for the six drive levers.

4. The wave compensation system modeling and pose control method based on the Stewart platform according to claim 3, characterized in that, In step 2, in the inertial coordinate system, the action of the bridge mechanism on the Stewart platform includes the application of force. and the torque The process of calculating the effect of the bridge mechanism on the Stewart platform includes the following steps: Step 201: Establish corresponding coordinate systems at the rotation, pitch, and extension joints of the walking bridge mechanism according to the Denavit-Hartenberg method. , and ; Step 202: Use the iterative Newton-Euler method to solve for the acceleration and angular acceleration of the center of mass of each link through forward iteration; Step 203: Solve for the force exerted on the link by the Stewart platform through reverse iteration. and the torque ; Step 204: Apply the force from the upper platform to the connecting rod. and the torque Transform to inertial coordinate system using rotation matrix. In the meantime, the inertial coordinate system can be obtained. The force exerted by the Stewart upper platform on the connecting rod and the torque ; Step 205: Obtain the coordinates in the inertial coordinate system Force exerted by the middle step bridge mechanism on the Stewart upper platform and the torque .

5. The wave compensation system modeling and pose control method based on the Stewart platform according to claim 4, characterized in that, In step 204, the inertial coordinate system The force exerted by the Stewart upper platform on the connecting rod and the torque The expressions are as follows: in, and These represent the matrix showing the influence of the force and torque of the step bridge on the acceleration, respectively. and These are the influence matrices of the forces and torques acting on the bridge on the angular acceleration, respectively. and These represent the matrix representing the influence of the force and torque of the bridge on the angular velocity, respectively. and These represent the additional terms introduced by the forces and moments of the bridge, respectively.

6. The wave compensation system modeling and pose control method based on the Stewart platform according to claim 1, characterized in that, In step 401, the first derivative and second derivative The calculation expressions are as follows: in, and Rotation matrix The first and second derivatives.

7. The wave compensation system modeling and pose control method based on the Stewart platform according to claim 6, characterized in that, The rotation matrix The expressions for the first and second derivatives are as follows: 。

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