A method for modeling kinematics and dynamics of an underwater glider considering oil bladder piston

Abstract

The present application relates to a kind of underwater glider kinematics and dynamics modeling method considering oil bladder piston, belong to underwater glider technical field.The inertia matrix of establishing static mass, centroid position, buoyancy, gravity and gravity moment are included;The component of fluid viscous damping force and moment under carrier coordinate system is established;The component of buoyancy under carrier coordinate system is derived;The component of gravity and middle moment under carrier coordinate system is derived;The momentum and momentum moment of each mass are established;The momentum and momentum moment of underwater glider model are established;Finally, according to the underwater glider kinematics and dynamics equation derived above.The present application method divides oil bladder into piston and cavity respectively to carry out kinetic energy analysis, considers the influence of the two parts on underwater glider internal force when modeling, can more real restore the motion process of underwater glider.

Description

Technical Field

[0001] This invention relates to the field of underwater glider technology, and more particularly to a method for kinematic and dynamic modeling of underwater gliders. Background Technology

[0002] After more than 30 years of development, underwater gliders have become a type of long-range, long-endurance, autonomous underwater observation platform that does not require expensive supporting equipment. Underwater gliders are special underwater vehicles that rely on controlled buoyancy for propulsion, and their internal forces are complex. Establishing a dynamic model of an underwater glider is a necessary condition for systematic model-based control and design of this type of vehicle.

[0003] Currently, a commonly used dynamic modeling method is a general approach that constructs momentum and kinetic energy equations. To date, most research on underwater gliders has used this method as the basis for dynamic analysis. The basic idea of ​​this method is to utilize the conversion relationship between kinetic energy and momentum based on Newton's laws. Specifically, by treating buoyancy and attitude control mechanisms as internal sub-modules, the total kinetic energy of the system is obtained by calculating the sub-kinetic energy, added mass, buoyancy, and attitude system of the object separately. Momentum and angular momentum can be obtained by deriving the kinetic energy with respect to linear velocity and angular velocity respectively. Furthermore, their derivatives can also be obtained by calculating external forces and torques.

[0004] However, existing underwater glider models treat the fuel bladder as a single module for kinetic energy analysis. However, the torque generated by the movement of the fuel bladder piston should not be ignored. In other words, the mass distribution of the fuel bladder during operation is not uniform. Summary of the Invention

[0005] The technical problem to be solved by this invention is:

[0006] To overcome the shortcomings of existing technologies, this invention provides a more reasonable and accurate kinematic and dynamic modeling method for underwater gliders, involving force analysis. The oil bladder is divided into a piston and a cavity, and kinetic energy analysis is performed separately to derive the complete force formulas for the underwater glider's internal structure.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A method for kinematic and dynamic modeling of underwater gliders considering oil bladder pistons, characterized by the following steps:

[0009] Step 1: Define the rotation matrix from the carrier coordinate system to the ground coordinate system as follows:

[0010]

[0011] in, For underwater gliders, the yaw angle, pitch angle, and roll angle are given.

[0012] The kinematic representation of an underwater glider is

[0013]

[0014] Where ω=(ω1,ω2,ω3) T Let be the angular velocity of the glider in the carrier coordinate system;

[0015] Step 2: Define the mass distribution of the underwater glider and calculate the static mass inertia matrix, center of mass position, buoyancy, gravity, and gravitational torque; the total mass m of the underwater glider. v Divided into five parts: The mass of the movable slider is m p The position is r p The mass of the cavity is m c The position is r c The piston mass is m d The position is r d The mass of the underwater glider's shell consists of two parts, one of which is uniformly distributed throughout the shell and has a mass of m. h The other parts are grouped into a single mass block m. w The mass is fixed, and the position r w It is determined by the static mass distribution of the glider; the static mass parameter m w and r w It is configured to balance the static torque caused by uneven mass distribution of the underwater glider;

[0016] The total mass of the underwater glider is m v =m h +m w +m c +m d +m p =m s +m p The mass of water displaced by the underwater glider is m. e Define net buoyancy as m o =m v -m e The inertia matrix J of the static mass relative to the carrier coordinate system. s The position of the centroid r v Buoyancy B, gravity G, and gravitational torque τ g They are respectively represented as

[0017]

[0018] Among them, J h The mass m of the uniformly distributed shell h The inertia matrix in the carrier coordinate system; k is a unit vector; the operator ∧ is a matrix representation that maps a vector to a vector cross-product operator;

[0019] Step 3: Calculate the fluid viscous damping force and torque, neglecting the fluid viscosity which has little effect on inertial forces and is difficult to calculate. The ideal fluid force is...

[0020]

[0021] Among them, M f Add mass matrix, velocity matrix

[0022] The components of the fluid viscous positional force and torque in the carrier coordinate system are:

[0023] Components of fluid viscous damping force and torque in the carrier coordinate system:

[0024]

[0025] Step 4: Calculate buoyancy; the components of buoyancy in the carrier coordinate system are...

[0026]

[0027] Step 5: Calculate gravity and gravitational torque; components of gravity and gravitational torque in the carrier coordinate system:

[0028]

[0029] Step 6: Calculate m s m p m c m d and m w Momentum and angular momentum; m s m p m c m d and m w The momentum and angular momentum are Q, respectively. s K s Q p K p Q c K c Q d K d Q w and K w , represented as:

[0030]

[0031] Step 7: Calculate the momentum and angular momentum of the underwater glider model. The momentum and angular momentum of the underwater glider model are:

[0032]

[0033] in, Mass matrix M = m h I+M f = diag(m1,m2,m3), rotational inertia matrix J = J h +J f =diag(J1,J2,J3), J f To add rotational inertia;

[0034] Step 8: Derive the kinematic and dynamic equations of the underwater glider. The dynamics of the underwater glider are expressed as follows:

[0035]

[0036] Among them, F ext and Γ ext It includes external forces and torques, ∑f in For the internal forces on each mass block;

[0037] Reversing the relationship in (10), we obtain the derivative of body velocity expressed in terms of body momentum as:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Substituting (10) and (11) into (12), and combining with (3), we obtain the kinematic and dynamic equations of the underwater glider in three-dimensional space as follows:

[0044]

[0045] Control input is

[0046]

[0047] in, F = (Mv + Q) p +Q c +Q d +Q w )×ω+m o gR T k+F ext -u-(u c +ud +u w )

[0048] u is the force acting on the moving mass block m p Control over the upper part, u c u d and u w They respectively represent the action on m c m d and m w The internal force above.

[0049] A further technical solution of the present invention: the ground coordinate system O1-x i y i z i The origin O1 is chosen as a point on the Earth's surface, O1x i and O1y i Located on the horizontal plane, O1z i Parallel to gravity and with downward as positive, i, j, k are unit vectors of o0x0, o0y0, and o0z0, respectively.

[0050] A further technical solution of the present invention: the carrier coordinate system O2-x b y b z b The origin O2 is the center of buoyancy, O2x b Along the longitudinal axis, positive towards the bow, O2y b Located in the wing plane; O2z b The direction pointing towards the vertical wingplate.

[0051] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0052] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0053] The beneficial effects of this invention are as follows:

[0054] This invention provides a more reasonable and accurate kinematic and dynamic modeling method for underwater gliders, involving force analysis. The oil bladder is divided into a piston and a cavity, and kinetic energy analysis is performed separately to derive the complete force formulas within the underwater glider. Specifically, this invention has the following advantages and beneficial effects:

[0055] 1. More reasonable and accurate force analysis. Existing underwater glider modeling methods treat the fuel bladder as a whole for force analysis. However, it is obvious that the mass distribution of the piston and cavity is uneven and should not be analyzed as a whole. This method divides the fuel bladder into piston and cavity for separate kinetic energy analysis, and considers the influence of these two parts on the internal forces of the underwater glider during modeling.

[0056] 2. The model more closely resembles actual sailing conditions. The model built based on this method can more realistically simulate actual sailing conditions, which is evident in the comparison of simulation and actual sea trial motion data. Figure 5 This is reflected in ( ). Attached Figure Description

[0057] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0058] Figure 1 Coordinate system definition;

[0059] Figure 2 Velocity coordinate system and vehicle coordinate system;

[0060] Figure 3 Mass distribution of an underwater glider;

[0061] Figure 4 Modeling flowchart;

[0062] Figure 5 Comparison of simulation and sea trial motion data: (a) position of movable mass; (b) pitch angle. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0064] This embodiment provides a method for kinematic and dynamic modeling of underwater gliders considering the oil bladder piston, including the following steps:

[0065] Step 1: Define the ground coordinate system, the vehicle coordinate system, and the velocity coordinate system. Ground coordinate system O1-x i y i z i The origin O1 is chosen as a point on the Earth's surface, O1x i and O1y i Located on the horizontal plane, O1z iParallel to gravity and with downward as positive, i, j, k are unit vectors of o0x0, o0y0, and o0z0, respectively. The carrier coordinate system is O2-x. b y b z b The origin O2 is the center of buoyancy, O2x b Along the longitudinal axis, positive towards the bow, O2y b Located in the wing plane; O2z b Pointing in the direction of the vertical airfoil. Both coordinate systems are right-handed Cartesian coordinate systems, such as... Figure 1 As shown. X = (x, y, z) T Let V be the position of the glider in the ground coordinate system, where V = (v1, v2, v3). T Let V be the absolute velocity of the glider in the carrier coordinate system. r =(v r1 ,v r2 ,v r3 ) T Let V be the velocity of the glider relative to the fluid in the carrier coordinate system. c =(v c1 ,v c2 ,v c3 ) T Let ω be the velocity of the water flow relative to the ground coordinate system, where ω = (ω1, ω2, ω3). T Let be the angular velocity of the glider in the carrier coordinate system. Let yaw, pitch, and roll be the angles of rotation. The rotation matrix from the vehicle coordinate system to the ground coordinate system is defined as follows:

[0066]

[0067] The origin of the velocity coordinate system coincides with the origin of the carrier coordinate system. The ox1 axis is in the same direction as the glider's velocity vector. The oz1 axis is located in the glider's longitudinal symmetry plane, perpendicular to the ox1 axis and pointing downwards. The oy1 axis is perpendicular to the x1oz1 plane, and its direction is determined according to the right-hand coordinate system.

[0068] The hydrodynamic forces acting on an underwater glider depend on the velocity and direction of the fluid motion relative to the glider, where the glider's velocity relative to the fluid is V. r V c Let V be the velocity of the water flow relative to the ground coordinate system. When the water flow is stationary relative to the ground coordinate system, V r Equal to the glider's speed V, this invention does not consider water flow motion, i.e., V c =0, then V r =V.

[0069] The relationship between the velocity coordinate system and the carrier coordinate system is represented by the angle of attack α and the sideslip angle β. The angle of attack α is the angle between the projection of the ox1 axis in the velocity coordinate system onto the xoz plane in the carrier coordinate system and the ox axis of the carrier coordinate system. The sideslip angle β is the angle between the ox1 axis in the velocity coordinate system and the xoz plane in the carrier coordinate system, as shown below. Figure 2 As shown. The rotation matrix from the velocity coordinate system to the carrier coordinate system is defined as follows.

[0070]

[0071] Among them, angle of attack Sideslip angle The kinematics of the underwater glider is expressed as

[0072]

[0073] Among them, V r =VR T V c The operator ∧ is a (skew-symmetric) matrix representation that maps a vector R to the vector cross-product operator.

[0074] Step 2: Define the mass distribution of the underwater glider and calculate the inertia matrix, center of mass position, buoyancy, gravity, and gravitational torque for the static mass. For example... Figure 3 As shown, the total mass m of the underwater glider v It can be divided into five parts: the mass of the movable slider is m p The position is r p The mass of the cavity is m c The position is r c The piston mass is m d The position is r d The mass of the underwater glider's shell consists of two parts, one of which is uniformly distributed throughout the shell and has a mass of m. h The other parts are grouped into a single mass block m. w The mass is fixed, and the position r w It is determined by the static mass distribution of the glider. Static mass parameter m w and r w It can be configured to balance the static torque caused by uneven mass distribution in underwater gliders.

[0075] The total mass of the underwater glider is m v =m h +m w +m c +m d +m p =m s +m p The mass of water displaced by the underwater glider is m. e Define net buoyancy as mo =m v -m e Assume the shape of the underwater glider is relative to the longitudinal plane O2x. b z b and horizontal plane O2x b y b Symmetrical, completely wet exterior, both positional and damping forces conform to the linear assumption. The inertia matrix J of the static mass relative to the carrier coordinate system. s The position of the centroid r v Buoyancy B, gravity G, and gravitational torque τ g They are respectively represented as

[0076]

[0077] Among them, J h The mass m of the uniformly distributed shell h The inertia matrix in the carrier coordinate system.

[0078] Step 3: Calculate the fluid viscous damping force and torque. Ignoring fluid viscosity, which has a small impact on inertial forces and is difficult to calculate, the ideal fluid forces are:

[0079]

[0080] Among them, M f Add mass matrix, velocity matrix

[0081] The components of the fluid viscous positional force and torque in the carrier coordinate system are:

[0082] Components of fluid viscous damping force and torque in the carrier coordinate system:

[0083]

[0084] Step 4: Calculate buoyancy. The components of buoyancy in the carrier coordinate system are:

[0085]

[0086] Step 5: Calculate gravity and gravitational moment. Components of gravity and gravitational moment in the carrier coordinate system:

[0087]

[0088] Step 6: Calculate m s m p m c m d and m w The momentum and angular momentum. ms m p m c m d and m w The momentum and angular momentum are Q, respectively. s K s Q p K p Q c K c Q d K d Q w and K w They can be written

[0089]

[0090] Step 7: Calculate the momentum and angular momentum of the underwater glider model. The momentum and angular momentum of the underwater glider model are:

[0091]

[0092] in, Mass matrix M = m h I+M f = diag(m1,m2,m3), rotational inertia matrix J = J h +J f =diag(J1,J2,J3), J f To add rotational inertia.

[0093] Step 8: Derive the kinematic and dynamic equations of the underwater glider. The dynamics of the underwater glider are expressed as follows:

[0094]

[0095] Among them, F ext and Γ ext It includes external forces and torques, encompassing hydrodynamic forces and moments. ∑f in Let be the internal forces on each mass block.

[0096] Reversing the relationship in (10), we obtain the derivative of body velocity expressed in terms of body momentum as:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] Substituting (10) and (11) into (12), and combining with (3), we obtain the kinematic and dynamic equations of the underwater glider in three-dimensional space as follows:

[0103]

[0104] Control input is

[0105]

[0106] in, F = (Mv + Q) p +Q c +Q d +Q w )×ω+m o gR T k+F ext -u-(u c +u d +u w )

[0107] u is the force acting on the moving mass block m p Control over the upper part, u c u d and u w They respectively represent the action on m c m d and m w The internal force above.

[0108] Figure 4 The modeling flowchart is shown. Figure 5 The simulation results and sea trial results with and without considering the piston are presented. In the simulation, the steady-state position of the moving mass during descent / ascent is symmetrical with respect to point 0. In the sea trial, the steady-state position of the moving mass during ascent is farther from point 0, indicating that assembly errors generated a bow-diving torque. When the oil bladder volume decreases, the piston moves towards the stern, and vice versa. To compensate for the torque generated by the piston position change, the steady-state position of the slider during descent / ascent in the simulation considering the piston is closer to the bow / stern. The comparison shows that the simulation results considering the piston are closer to the sea trial results.

[0109] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for kinematic and dynamic modeling of an underwater glider considering an oil bladder piston, characterized in that... The steps are as follows: Step 1: Define the rotation matrix from the carrier coordinate system to the ground coordinate system as follows: in, For underwater gliders, the yaw angle, pitch angle, and roll angle are given. The kinematic representation of an underwater glider is Where ω=(ω1,ω2,ω3) T Let be the angular velocity of the glider in the carrier coordinate system; Step 2: Define the mass distribution of the underwater glider and calculate the static mass inertia matrix, center of mass position, buoyancy, gravity, and gravitational torque; the total mass m of the underwater glider. v Divided into five parts: The mass of the movable slider is m p The position is r p The mass of the cavity is m c The position is r c The piston mass is m d The position is r d The mass of the underwater glider's shell consists of two parts, one of which is uniformly distributed throughout the shell and has a mass of m. h The other parts are grouped into a single mass block m. w The mass is fixed, and the position r w It is determined by the static mass distribution of the glider; the static mass parameter m w and r w It is configured to balance the static torque caused by uneven mass distribution of the underwater glider; The total mass of the underwater glider is m v =m h +m w +m c +m d +m p =m s +m p The mass of water displaced by the underwater glider is m. e Define net buoyancy as m o =m v -m e The inertia matrix J of the static mass relative to the carrier coordinate system. s The position of the centroid r v Buoyancy B, gravity G, and gravitational torque τ g They are respectively represented as Among them, J h The mass m of the uniformly distributed shell h The inertia matrix in the carrier coordinate system; k is a unit vector; the operator ∧ is a matrix representation that maps a vector to a vector cross-product operator; Step 3: Calculate the fluid viscous damping force and torque, neglecting the fluid viscosity which has little effect on inertial forces and is difficult to calculate. The ideal fluid force is... Among them, M f Add mass matrix, velocity matrix The components of the fluid viscous positional force and torque in the carrier coordinate system are: Components of fluid viscous damping force and torque in the carrier coordinate system: Step 4: Calculate buoyancy; the components of buoyancy in the carrier coordinate system are... Step 5: Calculate gravity and gravitational torque; components of gravity and gravitational torque in the carrier coordinate system: Step 6: Calculate m s m p m c m d and m w Momentum and angular momentum; m s m p m c m d and m w The momentum and angular momentum are Q, respectively. s K s Q p K p Q c K c Q d K d Q w and K w , is represented as: Step 7: Calculate the momentum and angular momentum of the underwater glider model. The momentum and angular momentum of the underwater glider model are: in, Mass matrix M = m h I+M f = diag(m1,m2,m3), rotational inertia matrix J = J h +J f =diag(J1,J2,J3), J f To add rotational inertia; Step 8: Derive the kinematic and dynamic equations of the underwater glider. The dynamics of the underwater glider are expressed as follows: Among them, F ext and Γ ext It includes external forces and torques, ∑f in For the internal forces on each mass block; Reversing the relationship in (10), we obtain the derivative of body velocity expressed in terms of body momentum as: Substituting (10) and (11) into (12), and combining with (3), we obtain the kinematic and dynamic equations of the underwater glider in three-dimensional space as follows: Control input is wherein, F=(Mv+Q p +Q c +Q d +Q w )×ω+m o gR T k+F ext -u-(u c +u d +u w ) u is the force acting on the moving mass block m p Control over the upper part, u c u d and u w They respectively represent the action on m c m d and m w The internal force above.

2. The kinematics and dynamics modeling method for underwater gliders considering the oil bladder piston according to claim 1, characterized in that: The ground coordinate system O1-x i y i z i The origin O1 is chosen as a point on the Earth's surface, O1x i and O1y i Located on the horizontal plane, O1z i Parallel to gravity and with downward as positive, i, j, k are unit vectors of o0x0, o0y0, and o0z0, respectively.

3. The kinematics and dynamics modeling method for underwater gliders considering the oil bladder piston according to claim 1, characterized in that: The carrier coordinate system O2-x b y b z b The origin O2 is the center of buoyancy, O2x b Along the longitudinal axis, positive towards the bow, O2y b Located in the wing plane; O2z b The direction pointing towards the vertical wingplate.

4. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

5. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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