A method for tracking a master AUV from an AUV based on sliding mode adaptive control

Abstract

The application relates to a method for tracking a main AUV from an AUV based on a sliding mode adaptive control, which decouples the motion of the AUV into horizontal plane motion and longitudinal plane motion, simultaneously considers the influence of non-constant interference and sea current during the motion of the AUV, designs a control law through a sliding mode adaptive control method, and estimates the sea current velocity on line, so as to guide the AUV to the tail of a target AUV to perform distance tracking. Finally, through tracking simulation of linear motion and curve motion of the target AUV respectively, the feasibility of the AUV long-distance guiding and tracking method is verified. Through adaptive control, the influence of parameter error on the stability of the system is eliminated, the sliding mode adaptive control method can estimate the sea current velocity, the system has certain anti-interference ability, and the robustness of the system is also indicated.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology and relates to a method for tracking a master AUV from a slave AUV based on sliding mode adaptive control. Specifically, it relates to a long-range AUV guidance and tracking method based on sliding mode adaptive control (SMAC), which involves decoupling the motion of the UUV and designing control laws using sliding mode adaptive control to guide the AUV to the tail of the target AUV for fixed-distance tracking. Background Technology

[0002] With increasing scarcity of land resources, the ocean, possessing the largest resource reserves on Earth, is receiving growing attention. Autonomous Underwater Vehicles (AUVs), with their inherent advantages such as small size and operational flexibility, have become a crucial means for humankind to explore and utilize the ocean. AUVs can operate without human intervention, carry their own power, and are capable of communication, control, and decision-making to complete designated tasks, leading to their increasingly widespread application in fields such as ocean development and maritime military operations.

[0003] In the civilian sector, typical tasks performed by AUVs include marine environmental monitoring, subsea oil and gas pipeline maintenance, mineral resource sampling, marine biological resource exploration, and marine search and rescue and salvage. In the military sector, typical tasks performed by AUVs include coastline protection, mine detection and countermeasures, underwater target engagement, submarine tracking and containment, and underwater reconnaissance. Among these applications of AUVs, the use of AUVAs for underwater target tracking is an important research direction. AUVA target tracking includes static target tracking, such as submarine cables, pipelines, or fixed paths, as well as dynamic target tracking, such as submarines, surface vessels, underwater vehicles, and marine life. Dynamic target tracking has greater application needs in the military sector, mainly including target tracking and monitoring and dynamic engagement. For example, in submarine warfare, tracking or attacking enemy submarines in ports and during near-shore patrols, once an enemy target is detected, it is followed and its activities are responded to. All of these issues involve the tracking and control of AUVs; therefore, this research has significant practical implications. Summary of the Invention

[0004] Technical problems to be solved

[0005] To overcome the shortcomings of existing technologies, this invention proposes a method for tracking a master AUV from a slave AUV based on sliding mode adaptive control. This method decouples the AUV's motion into horizontal and vertical plane motion. Considering the unpredictable disturbances and ocean currents during AUV motion, a control law is designed using sliding mode adaptive control, and the ocean current velocity is estimated online to guide the AUV to the tail of the target AUV for fixed-distance tracking. Finally, simulations of tracking the target AUV in both linear and curvilinear motions verify the feasibility of this long-range AUV guidance and tracking method.

[0006] Technical solution

[0007] A method for a slave AUV to track a master AUV based on sliding mode adaptive control is characterized by the following steps:

[0008] Step 1: Establish the kinematic and dynamic model of the AUV under the influence of ocean currents, decouple the motion of the AUV into horizontal plane motion and longitudinal plane motion, and obtain the equations of longitudinal plane and horizontal plane motion.

[0009] Step 2: Design a longitudinal plane motion controller based on SMAC, controlling inputs T4 and T5 to make the AUV's depth and pitch angle track a constant reference signal y. d =[y d θ d ] T And to ensure the global stability of the tracking error, define e. y For tracking error;

[0010] The controller is:

[0011] The adaptive law between the system parameters and the ocean current velocity is:

[0012]

[0013]

[0014] Where Γ y F represents the control parameters for adaptive control, and they are constant positive definite symmetric matrices; k and ε are positive definite diagonal matrices. Given a function matrix, and including the velocity v of the AUV relative to the ocean current in the carrier coordinate system. r θ is the pitch angle, C in α is a diagonal positive definite matrix, and f(u,θ) is a function that is only related to the forward velocity u and pitch angle θ in the vehicle coordinate system; This is an estimate of α; Let v be the ocean current speed. f The estimation error. For unknown parameter vector matrix, The result is the estimation of the parameters. The estimation error is the vector matrix of unknown parameters.

[0015] Step 3: Design a horizontal plane motion controller based on SMAC, including yaw angle control and speed control. The control objective of yaw angle control is to make the AUV's heading angle track the target's azimuth angle (ψ→ψ). d Let e ψ =ψ-ψ d For heading angle error; the control objective of speed control is to maintain the distance between the AUV and the target AUV at a set value (r→r). d Let e r =r d -r;

[0016] The yaw angle control law is as follows:

[0017] The speed control law is as follows:

[0018] Adaptive law

[0019] In the yaw angle control law, The physical meaning of the mean parameter is the same as that mentioned above. For a ψ The estimated value; Where c ψ ε ψ The coefficients of the constant term are set; This is the synovial switching function.

[0020] In the speed control law, a r =[mX u mZ w -mx G -X u -X u|u| ] T , For a r The estimated value; w r qq 2 u r |u r |u r ],f(v d ,σ d () represents the projection of the target AUV's velocity magnitude onto the aiming line of the docking AUV; For sliding mode switching function, c r ε r These are the coefficients of the constant term; the physical meanings of the other parameters are the same as above.

[0021] In the adaptive law, Γ r For the designed diagonal positive definite matrix, f r >0 represents the adaptive ocean current parameter in the design; For a r and The estimation error is [missing information], and the physical meanings of the other parameters are the same as those described above.

[0022] The above control system, under the control of the longitudinal plane motion controller, has the following function in the adaptive law: If g > 0, then That is, to ensure the global stability of the system; under the control of the horizontal plane motion controller, when ε r >0, satisfying ε r >|Y r a r -n r |+η, then According to Lyapunov's lemma, the system is guaranteed to converge globally to the equilibrium point e on the sliding surface. r =0, ensuring the global asymptotic stability of the above control system.

[0023] The kinematic and dynamic model of the AUV under the influence of ocean currents is as follows:

[0024] AUV kinematic model:

[0025] AUV dynamics model:

[0026] Where v f Let v be the ocean current velocity, and assume the ocean current is steady and irrotational. r Let η be the velocity of the AUV relative to the ocean current in the carrier coordinate system. η = [η1 η2] T Let be the position coordinates of the AUV in the ground coordinate system, and J(η) be the AUV's kinematic Jacobian matrix. M, C(v) r ), D(v r ) are the inertia matrix, Coriolis force and centripetal force matrix, and damping matrix, respectively; g(η) is the restoring force; and τ is the resultant force on the AUV.

[0027] The motion of the AUV is decoupled into longitudinal plane motion, and the equation of longitudinal plane motion is obtained as follows:

[0028]

[0029] Where m is the mass of the AUV, I xx This is the moment of inertia of the AUV's yaw angle. Add mass to the fluid of the AUV, Y v Y v|v| Nr N r|r| Let be the fluid damping coefficient of the AUV, B be the buoyancy force on the AUV, and G be the gravity force on the AUV. G ,y G ) represents the coordinates of the AUV's center of gravity in the carrier coordinate system.

[0030] The motion of the AUV is decoupled into horizontal surface motion, resulting in the equation of horizontal surface motion;

[0031]

[0032] In the formula, m is the mass of the AUV, and I yy Let x be the moment of inertia of the pitch angle. G z G Let be the coordinates of the AUV's center of gravity in the carrier coordinate system. Add mass to the fluid of the AUV, X u X u|u| Z w Z w|w| M q M q|q| x is the fluid damping coefficient. B Thrust τ in the direction x =T1,z B Thrust τ in the direction z =T2+T3, Yaw torque τ ψ =T2L2-T3L3.

[0033] Beneficial effects

[0034] This invention proposes a method for tracking a master AUV from a slave AUV based on sliding mode adaptive control. The method decouples the AUV's motion into horizontal and vertical plane motion. Considering the unpredictable disturbances and ocean currents during AUV motion, a control law is designed using sliding mode adaptive control, and the ocean current velocity is estimated online to guide the AUV to the tail of the target AUV for fixed-distance tracking. Finally, simulations of tracking the target AUV in both linear and curvilinear motions verify the feasibility of this long-range AUV guidance and tracking method.

[0035] The AUV long-range guidance and control method proposed in this invention has the following advantages compared with existing guidance technologies:

[0036] (1) Eliminate the influence of parameter errors on system stability through adaptive control.

[0037] (2) The sliding mode adaptive control method can estimate the ocean current velocity, giving the system a certain anti-interference ability and demonstrating the robustness of the system. Attached Figure Description

[0038] Figure 1 AUV Depth and Pitch Angle Control Framework Diagram

[0039] Figure 2 AUV yaw angle control frame

[0040] Figure 3 AUV forward speed control framework diagram

[0041] Figure 4 Simulation results of longitudinal plane control

[0042] Figure 5 : Thrust variation of the two vertical thrusters

[0043] Figure 6 Estimated results of water flow velocity

[0044] Figure 7 AUV horizontal plane tracking path

[0045] Figure 8 Horizontal tracking error and control input

[0046] Figure 9 : Estimation error of ocean current velocity

[0047] Figure 10 AUV horizontal plane circular tracking path

[0048] Figure 11 Horizontal tracking error and control input

[0049] Figure 12 : Estimation error of ocean current velocity

[0050] Figure 13 Schematic diagram of thrust direction of each thruster Detailed Implementation

[0051] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0052] This invention proposes a long-range guidance and tracking method for AUVs based on sliding mode adaptive control.

[0053] The implementation steps are as follows:

[0054] S1: Establish a kinematic and dynamic model of the AUV under the influence of ocean currents, and decouple the six degrees of freedom motion of the AUV into horizontal plane motion and longitudinal plane motion, simplifying it into equations of longitudinal plane and horizontal plane motion.

[0055] S2: Design a sliding mode adaptive controller based on SMAC (Self-Motion Controller), considering the influence of ocean currents and the parameter uncertainties in the modeling equations. Based on these characteristics, design a sliding mode adaptive controller and appropriately modify the adaptive law. The control objective of the AUV in the longitudinal plane is to design control inputs T4 and T5 to ensure that the AUV's depth and pitch angle track a constant reference signal y under unknown model parameters. d =[y d θ d ] T This ensures the global stability of the tracking error. The control flowchart is as follows: Figure 1 As shown.

[0056] S3: Design a horizontal plane motion controller based on SMAC, since the yaw equation of the AUV is related to x B The coupling effect of the motion equations in the direction is not strong, therefore the horizontal plane motion can be further decoupled into yaw angle control and speed control. The control objective of yaw angle control is to make the AUV's heading angle track the target's azimuth angle (ψ→ψ). d The speed control objective is to maintain the distance between the AUV and the target AUV at a set value (r→r0). The control flowcharts are as follows: Figure 2 , 3 As shown. Detailed implementation method:

[0058] S1: Establish a kinematic and dynamic model of the AUV under the influence of ocean currents, and decouple the six degrees of freedom motion of the AUV into horizontal plane motion and longitudinal plane motion, simplifying it into equations of longitudinal plane and horizontal plane motion.

[0059] S1-1: The kinematic model of the AUV under the influence of ocean currents is established as follows:

[0060]

[0061] Establish an AUV dynamic model under the influence of ocean currents.

[0062]

[0063] Where v f Let v be the ocean current velocity, and assume the ocean current is steady and irrotational. r Let η be the velocity of the AUV relative to the ocean current in the carrier coordinate system. η = [η1 η2] T Let be the position coordinates of the AUV in the ground coordinate system, and J(η) be the AUV's kinematic Jacobian matrix. M, C(v) r ), D(v r ) are the inertia matrix, Coriolis force and centripetal force matrix, and damping matrix, respectively; g(η) is the restoring force; and τ is the resultant force on the AUV.

[0064] To facilitate guidance and control, the motion of the AUV is decoupled into two parts: horizontal plane motion and longitudinal plane motion. The coupling effect between them is ignored, and it is assumed that roll is stable under the restoring moment of gravity. The specific models of the longitudinal and horizontal planes are shown in steps 1-2 and 1-3.

[0065] S1-2. Establish a longitudinal plane motion model of an AUV with a vertical thruster.

[0066] 1-2-1, Establish the longitudinal motion equation of the AUV

[0067] The motion model of an AUV in the vertical plane can be described by forward velocity u, longitudinal velocity v, and pitch angular velocity r. With the center of buoyancy as the origin of the carrier's coordinate system, it is assumed that roll can remain stable under the restoring torque of buoyancy, i.e., the roll motion parameters... Since the x, z, ψ, q values ​​are zero, the horizontal motion parameters {x, z, ψ, q} are also zero. Therefore, the longitudinal motion equation is as follows.

[0068]

[0069] Where m is the mass of the AUV, I xx This is the moment of inertia of the AUV's yaw angle. Add mass to the fluid of the AUV, Y v Y v|v| N r N r|r| Let be the fluid damping coefficient of the AUV, B be the buoyancy force on the AUV, and G be the gravity force on the AUV. G ,y G ) represents the coordinates of the AUV's center of gravity in the vehicle coordinate system, and θ is the pitch angle of the following vehicle. τ y , τ θ The force used to control y and θ.

[0070] S1-2-2: Considering the influence of steady ocean currents on the longitudinal motion of AUVs, equation (3) is rewritten in the following vector form.

[0071]

[0072] Where, y = [y θ] T For system status output, v r =[v r r] T The input to the kinematic equations is also the velocity of the AUV relative to the ocean current, v. f =[v fy 0] T Let n be the ocean current velocity in the ground coordinate system. yThe dynamic disturbances experienced by the AUV during underwater movement are described below, with the specific contents of each parameter matrix as follows:

[0073]

[0074] L2, L3, L4, and L5 are the straight-line distances from the corresponding thrusters to the geometric center of the AUV.

[0075] S1-2-3: In the actual tracking process, in order to ensure the detection range and accuracy of the sensor, both the AUV and the target AUV try to adjust their pitch angles as much as possible during the movement to keep them stable near 0°. Based on this assumption: θ∈(-π / 12,π / 12), that is, θ changes within a small range (-15°,+15°) around 0°. At this time, cosθ≈1 can be approximated, so the AUV motion equation, equation (5), can be rewritten as

[0076]

[0077] S1-3. Establish a horizontal motion model of an AUV with a vertical thruster.

[0078] S1-3-1: Establishing the equations of motion for the AUV on the horizontal plane

[0079] The motion of an AUV on the horizontal plane can be described by its forward velocity u, lateral velocity w, and directional angular velocity q. Its motion parameters on the horizontal plane are {x, z, ψ, q}. Ignoring the effects of roll parameters and other degrees of freedom on the horizontal plane motion, and considering the influence of steady ocean currents on the AUV's horizontal plane motion, with the center of buoyancy as the origin of the carrier's coordinate system, we can obtain the AUV's equations of motion on the horizontal plane.

[0080]

[0081] In the formula, m is the mass of the AUV, and I yy Let x be the moment of inertia of the pitch angle. G z G Let be the coordinates of the AUV's center of gravity in the carrier coordinate system. Add mass to the fluid of the AUV, X u X u|u| Z w Z w|w| M q M q|q| x is the fluid damping coefficient. B Thrust τ in the direction x =T1,z B Thrust τ in the direction z =T2+T3, Yaw torque τ ψ =T2L2-T3L3,u rw represents the forward velocity under ocean current interference. r v is the lateral velocity under ocean current interference. xf With v zf The components of the ocean current velocity on the x and z axes.

[0082] S1-3-2: Decouple the horizontal motion of the AUV into yaw motion and x-axis motion. B Movement in a certain direction.

[0083] Because the yaw equation of an AUV is related to x B The coupling effect of the motion equations in the direction is not strong, therefore the horizontal plane motion can be further decoupled into yaw angle control and speed control. The control objective of yaw angle control is to make the AUV's heading angle track the target's azimuth angle (ψ→ψ). d The control objective of speed control is to maintain the distance between the AUV and the target AUV at a set value (r→r0).

[0084] (1) The pitch angle motion model is as follows

[0085]

[0086] Rewritten in vector form as:

[0087]

[0088] in, a3=mz G a4 = mx G a5 = -M q a6 = -M q|q| n ψ External environmental interference. Let a be the cause. ψ =[a1 a2 a3 a4 a5 a6] T and set For a ψ The estimated value, the parameter estimation error is remember τ ψ The force used to control ψ.

[0089] (2) The forward motion model of the AUV is

[0090]

[0091] Rewritten in vector form as:

[0092]

[0093] in, a3 = -mx G a4 = -X u a5 = -Xu|u| , where n x This is to account for dynamic modeling errors and external disturbances. Let a be the modeling error. r =[a1 a2 a3 a4 a5] T ,set up For a r The estimated value, parameter estimation error τ x The force output by the thruster is the force in the x-direction.

[0094] S2: Design a longitudinal plane motion controller based on SMAC

[0095] S2-1: Based on the AUV depth and pitch angle control framework, design the required sliding surface. The process is as follows:

[0096] Define the system's output vector as y = [y θ] T Its target tracking state curve is y d =[y d θ d ] T Then the tracking error can be defined as

[0097] e y =yy d (12)

[0098] Taking its derivative, we get

[0099]

[0100] The designed sliding mode function must guarantee the existence of the sliding surface and ensure global stability of the system on the sliding surface. The designed sliding mode switching function is as follows:

[0101]

[0102] Where C is the control parameter, which is a diagonal positive definite matrix.

[0103] S2-2: Design a control law to ensure that the system state can reach the sliding surface from any state, and to ensure that the system state does not leave the sliding surface after entering the sliding mode.

[0104] Differentiating equation (14) for the sliding mode switching function, we get

[0105]

[0106] Where, let f CDG =f C (v r ,r)+f D (v r ,r)+f G (θ).

[0107] Since the system matrix M > 0 and is symmetric and positive definite, in order to derive the system's control input, a second Lyapunov function is designed here as follows:

[0108]

[0109] Taking the derivative, we get

[0110]

[0111] Among them, design Then there is

[0112] Due to ocean current parameter v f Unknown, defined here Let be an estimate of the ocean current velocity, and define the estimation error of the ocean current velocity. Simultaneously define Let be an estimate of α, then we have

[0113] Therefore, the control input of the system can be designed as follows:

[0114]

[0115] Among them, -ks y -εsgns y The term is an exponential reaching law chosen to ensure that the system can reach the sliding surface quickly enough in any state and has minimal chattering, where k and ε are positive definite diagonal matrices, i.e., k = diag(k i ),k i >0, ε=diag(ε i ),ε i >0.

[0116] The above control input design assumes that all system parameters are known. To ensure good parameter estimation performance when parameters are unknown, it is assumed that the system's dynamic model (3-77) has a linear parameterized form, i.e.

[0117]

[0118] in, For unknown parameter vector matrix, Given a function matrix, This is an estimate of α.

[0119] Therefore, a new control input expression can be obtained.

[0120]

[0121] in, The parameter estimation results are given, and the parameter estimation error is defined as follows:

[0122] S2-3: Obtaining the adaptive law for parameters and the adaptive law for ocean current velocity

[0123] Design a third Lyapunov function.

[0124]

[0125] Among them, Γ y F represents the control parameters for adaptive control, and is a constant positive definite symmetric matrix.

[0126] Differentiating it, we have

[0127]

[0128] Therefore, the adaptive law of system parameters and ocean current velocity can be obtained as follows:

[0129]

[0130] Finally, after eliminating the influence of ocean currents and parameter estimation errors, the derivative of the third Lyapunov function is obtained.

[0131]

[0132] Since C is a diagonal positive definite matrix, when ks y +εsgns y The term is large enough to eliminate dynamic error interference n y Sometimes, Therefore, the overall stability of the system can be guaranteed.

[0133] S2-4: To obtain a better adaptive effect, the adaptive law is modified as follows:

[0134]

[0135] Among them, functions are defined.

[0136]

[0137] In the function g(e0), as long as g > 0 is sufficiently large, we have This ensures the overall stability of the system.

[0138] S3: Design a horizontal plane motion controller based on SMAC

[0139] S3-1: Design of a SMAC-based yaw angle motion controller

[0140] (1) Based on the AUV yaw angle motion control framework, the required sliding surface is designed as follows:

[0141] Pitch tracking error is

[0142] e ψ =ψ-ψ d (27)

[0143] Design the sliding mode switching function as follows:

[0144]

[0145] Among them, c ψ For control parameters, c ψ >0 can guarantee the sliding surface It exists and is globally stable.

[0146] (2): Design a control law to ensure that the system state can reach the sliding surface from any state, and to ensure that the system state does not leave the sliding surface after entering the sliding mode.

[0147] Define Lyapunov functions

[0148]

[0149] Γ ψ The control parameters are for adaptive control, and are constant positive definite symmetric matrices.

[0150] Differentiating the Lyapunov function, we get

[0151]

[0152] Where a ψ =[a1 a2 a3 a4 a5 a6] T , a3=mz G a4 = mx G a5 = -M q a6 = -M q|q| n ψ External environmental interference. For a ψ Compared with the estimated value The error. And to simplify writing, let...

[0153] Therefore, the control law can be taken as follows:

[0154]

[0155] k ψ With ε ψ The selected control coefficient.

[0156] (3): Add the adaptive law of parameters as follows

[0157]

[0158] Substituting it into equation (30), we get

[0159]

[0160] At this point, as long as ε ψ Satisfying ε ψ -|n ψ |>η>0, then there is It can be seen that after introducing adaptive control, the control input is smaller than that of simple sliding mode control. It effectively reduces the performance loss due to the control input, and the control effect can be manifested as a reduction in system chattering.

[0161] S3-2: Design of a Forward Velocity Controller Based on SMAC

[0162] (1) Based on the AUV forward velocity control framework, the required sliding surface is designed as follows:

[0163] The position input error of the controller is

[0164] e r =r d -r (34)

[0165] Considering the influence of ocean currents, the distance r between the AUV and the target AUV, and the relationship between their speeds are as follows:

[0166]

[0167] Among them, v d Let σ be the velocity of the target AUV. d The lead angle of the target AUV's velocity vector, u r v is the velocity of the AUV relative to the water flow. f This represents the projection of the water flow velocity onto the AUV's aiming line.

[0168] v f =v fx cosψ-v fz sinψ.

[0169] Differentiating equation (34), we get

[0170]

[0171] Due to the water flow velocity v f The unknown, design the sliding mode switching function as follows:

[0172]

[0173] Among them, c r >0 is a control parameter. This is an estimate of the derivative of the position tracking error. Let $\frac{ ...

[0174] Taking the derivative of the sliding mode switching function (37), we can obtain

[0175]

[0176] Where, f(v) d ,σ d The velocity of the target AUV is projected onto the AUV's line of sight, and its magnitude can be expressed as f(v). d ,σ d ) = v d sinσ d =v dx cosψ+v dy sinψ.

[0177] To ensure the existence and global stability of the sliding surface, we define the first Lyapunov function.

[0178]

[0179] Differentiating it, we have

[0180]

[0181] (2): Design a control law to ensure that the system state can reach the sliding surface from any state, and to ensure that the system state does not leave the sliding surface after entering the sliding mode.

[0182] Define the second Lyapunov function

[0183]

[0184] Differentiating it, we have

[0185]

[0186] Among them, it is defined w r qq 2 u r |u r |u r ].

[0187] When designing the control law, an exponential reaching law is chosen, where k r , ε r The selected control parameters.

[0188]

[0189] Since the parameters and ocean current velocity are unknown, select control input.

[0190]

[0191] S2-3: Obtaining the adaptive law for parameters and the adaptive law for ocean current velocity

[0192] Design a third Lyapunov function.

[0193]

[0194] Among them, Γ r For the designed diagonal positive definite matrix, f r >0 represents the designed adaptive ocean current parameter, which can be obtained by differentiating with respect to V3.

[0195]

[0196] Therefore, the parameter error term in the above equation can be eliminated by designing an adaptive law, thus obtaining the adaptive law.

[0197]

[0198] Here, only ε r >0 is large enough to satisfy ε r >|Y r a r -n r |+η, then According to Lyapunov's lemma, the system can be guaranteed to converge globally to the equilibrium point e on the sliding surface. r =0, which further ensures the global asymptotic stability of the above control system.

[0199] To verify the effectiveness of the above guidance method, the following embodiments are also provided in this invention.

[0200] In the MATLAB verification, it is assumed that the forward velocity u of the AUV is... r =3m / s, the maximum thrust output of each thruster is 20N, and the maximum thrust change rate is 20N / s.

[0201] Example 1

[0202] Example 1 verifies the control effect of the depth and pitch angle sliding mode adaptive controller designed in step S2. In the simulation, it is assumed that the distance between the two vertical thrusters and the geometric center is L4 = L5 = 0.40m.

[0203] Let the ocean current velocity in the kinematic model be...

[0204] v f =[0.3 0] T (48)

[0205] The initial state of the AUV is y = [-2 1.2] T The target state is y d =[-10 0] T The simulation time was set to 80 seconds, the sampling period to 0.1 seconds, and the disturbance torque to be...

[0206]

[0207] Where U(-1,+1) represents a uniform distribution between (-1,+1).

[0208] The selected control parameters and adaptive parameters are as follows:

[0209] C=I2, k=20I2, ε=0.01I2, Γ y =10I2, F=diag(5,0), g=1

[0210] Therefore, the final simulation results can be obtained as follows: Figures 4 to 6 As shown

[0211] Figure 4 The curves showing the changes in pitch angle and depth during the control process are presented. As can be seen from Figure (a), in the initial state of the simulation, the AUV is in a large pitch angle state. After about 8 seconds of adjustment, the pitch angle eventually stabilizes at around 0°. As can be seen from Figure (b), due to the AUV's certain forward velocity and large pitch angle, the AUV's depth initially rises a short distance from -2m within about 0s to 1s, but after about 8 seconds of adjustment, the AUV's depth eventually stabilizes at the desired depth.

[0212] Figure 5 The diagram illustrates the changes in the output thrust values ​​of the two vertical thrusters during the adjustment and control process. Due to the initial large error, the thrust output is rapidly increased to its maximum value of 20N to minimize it as quickly as possible. At this point, the sliding surface switching function s(t) is large, and the exponential term (i.e., the -ks term) in the sliding surface approach term designed in the control law plays a major role, enabling the system state to quickly reach the sliding surface. Subsequently, the thrust value gradually decreases between 4s and 8s, indicating that the system state has approached the sliding surface. The effect of the exponential term gradually decreases, while the effect of the -εsgn(s) term increases. The curve after 10s shows that the system slides stably on the sliding surface and eventually converges to the equilibrium point. The irregular chattering on the curve indicates the thrust output made by the system to resist external disturbances, demonstrating the system's robustness.

[0213] Figure 6The results of the AUV's estimation of ocean current velocity are shown. During the initial 0-5 seconds, due to large errors, the adaptive term was masked, and the prior estimation results were used directly. After 5 seconds, the system gradually stabilized, and the adaptive law of the ocean current began to take effect. After about 10 seconds of adjustment, the estimated ocean current velocity gradually approached the actual value and stabilized near it, indicating the good estimation results of the adaptive law.

[0214] It is evident that the designed sliding mode adaptive control law has good pitch and depth control effects, the steady-state error can converge to zero, and it has a certain anti-interference capability.

[0215] Example 2

[0216] The distance between the two lateral thrusters and the geometric center is L2 = L3 = 0.55m.

[0217] Let the ocean current velocity on the horizontal surface in the kinematic model be...

[0218] v f =[0.3 0.2 0] T (50)

[0219] The AUV's initial coordinates are (60,0), the initial yaw angle is 0 rad, the simulation time is set to 80 s, and the sampling period is 0.1 s.

[0220] The disturbance torque is

[0221]

[0222] The selected control parameters and adaptive parameters are as follows:

[0223]

[0224] 1. Tracking effect of target in uniform linear motion

[0225] Given the initial position coordinates of the target (0, 60), its equation of motion is:

[0226]

[0227] The simulation results of horizontal plane guidance and tracking are as follows Figures 7 to 9 As shown.

[0228] Figures 7 to 9 The simulation results of tracking a uniform linear motion target using an improved sliding mode adaptive control algorithm are presented. The simulation time is 100 seconds. From Figure 7 and Figure 8It can be seen that from 0 to 35 seconds, under the action of the control law, the docking AUV starts from the initial coordinate point and gradually corrects its velocity and attitude angle, thus tracking the target AUV very well. After 35 seconds, the docking AUV performs stable, fixed-distance tracking behind the target AUV, and under the influence of external forces and ocean currents, its position tracking error and yaw angle tracking error converge to zero, demonstrating that the designed controller has strong stable control capabilities.

[0229] from Figure 9 As can be seen in (b), the estimation error of the ocean current velocity by the docking AUV stabilized near zero after 50s. This indicates that the continuous excitation of the tracking error signal caused the estimation error of the ocean current velocity to converge to zero, which also reflects the good estimation effect of the modified adaptive law.

[0230] 2. Tracking effect of the target performing a maneuvering turn.

[0231] Given the initial position coordinates of the target (30, 40), its equation of motion is:

[0232]

[0233] The final guidance simulation results are as follows Figures 10 to 12 As shown.

[0234] Figures 10 to 12 The simulation results of guiding and tracking an AUV target during circular motion are presented. The simulation time is 100 seconds. From Figures 10 to 12 It can be seen that within 0-25 seconds after the start of the simulation, under the action of the control law, the docking AUV starts from the initial coordinate point and gradually corrects its velocity and attitude angle, thus tracking the target AUV very well. After 25 seconds, the docking AUV performs stable, fixed-distance tracking behind the target AUV, and under the influence of external force interference and ocean currents, its position tracking error and yaw angle tracking error both converge to zero. Figure 11 The continuous jitter of the control input after 20 seconds of simulation in (c) indicates that the controller is overcoming the "chatter" caused by external interference, which is consistent with the theory.

[0235] from Figure 12 (b) It can also be seen that the estimation error of the ocean current velocity by the docking AUV stabilized near zero after 40 seconds, but compared to Figure 8 The estimation results in (b) fluctuated significantly because the target was making circular motion, which caused the target's aiming line to change continuously. As a result, the magnitude of the velocity on the target's aiming line estimated in the simulation also changed continuously, which caused a large error interference in the velocity estimation.

[0236] In summary, the simulation results above demonstrate that the target AUV horizontal plane guidance and control algorithm proposed in this section achieves good target guidance and tracking performance, and ensures that the position tracking error and angle tracking error converge to zero. Furthermore, from... Figure 11 As can be seen from the distance error curve between the docking AUV and the target in (a), the forward velocity of the AUV maintained good stability during rotation, which was particularly evident in circular path tracking with constantly changing angular velocity, fully demonstrating the independence of speed control. From Figure 9 (b) and Figure 12 The estimation results of the ocean current velocity in (b) also show that the adaptive rate designed in this section has a good estimation effect.

[0237] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for a slave AUV to track a master AUV based on sliding mode adaptive control, characterized in that... The steps are as follows: Step 1: Establish the kinematic and dynamic model of the AUV under the influence of ocean currents, decouple the motion of the AUV into horizontal plane motion and longitudinal plane motion, and obtain the equations of longitudinal plane and horizontal plane motion. Step 2: Design a SMAC-based longitudinal plane motion controller to control the input. , This enables the AUV to track a constant reference signal for depth and pitch angle. And to ensure the global stability of the tracking error, define For tracking error; The controller is: The adaptive law between system parameters and ocean current velocity is: in , These are the control parameters for adaptive control, and they are constant positive definite symmetric matrices. It is a positive definite diagonal matrix; Given a function matrix, and including the velocity of the AUV relative to the ocean current in the carrier coordinate system. , The pitch angle, middle It is a diagonal positive definite matrix. For the forward velocity only in the carrier coordinate system With pitch angle Related functions; for The estimated value; Ocean current speed The estimation error; For unknown parameter vector matrix, The result is the estimation of the parameters. The estimation error of the unknown parameter vector matrix; Step 3: Design a horizontal motion controller based on SMAC, including yaw angle control and speed control. The control objective of yaw angle control is to make the AUV's heading angle track the azimuth angle of the target. ),set up For heading angle error; the control objective of speed control is to maintain the distance between the AUV and the target AUV at a set value. )set up ; The yaw angle control law is as follows: The speed control law is as follows: Adaptive law In the yaw angle control law, The physical meaning of the mean parameter is the same as that mentioned above. for The estimated value; in , The coefficients of the constant term are set; This is the slug switching function; In the speed control law, , for The estimated value; , It is represented as the projection of the target AUV's velocity magnitude onto the aiming line of the docking AUV; = This is the sliding mode switching function. , These are the coefficients of the constant term; the physical meanings of the other parameters are the same as above. In the adaptive law, For the designed diagonal positive definite matrix, Adaptive parameters for ocean currents in the design; for and The estimation error is [value], and the physical meanings of the other parameters are the same as above; The above control system, under the control of the longitudinal plane motion controller, has the following function in the adaptive law: ; There will be That is, to ensure the global stability of the system; under the control of the horizontal plane motion controller, when ,satisfy There will be According to Lyapunov's lemma, the system is guaranteed to converge globally to the equilibrium point on the sliding surface. This ensures the global asymptotic stability of the aforementioned control system.

2. The method for tracking a master AUV by a slave AUV based on sliding mode adaptive control according to claim 1, characterized in that: The kinematic and dynamic model of the AUV under the influence of ocean currents is as follows: AUV kinematic model: AUV dynamics model: in Let be the ocean current velocity, and assume the ocean current is steady and irrotational; The velocity of the AUV relative to the ocean current in the carrier coordinate system; These are the position coordinates of the AUV in the ground coordinate system. The Jacobian matrix for AUV kinematics; , , These are the inertia matrix, Coriolis force and centripetal force matrix, and damping matrix, respectively. For resilience, The net force acting on the AUV.

3. The method for tracking a master AUV from a slave AUV based on sliding mode adaptive control according to claim 1, characterized in that: The motion of the AUV is decoupled into longitudinal plane motion, and the equation of longitudinal plane motion is obtained as follows: in, For the quality of AUV, This is the moment of inertia of the AUV's yaw angle. , , Add mass to the fluid of the AUV. , , , The fluid damping coefficient of the AUV. The buoyancy force acting on the AUV The force of gravity acting on the AUV. The coordinates of the AUV's center of gravity in the carrier coordinate system.

4. The method for tracking a master AUV by a slave AUV based on sliding mode adaptive control according to claim 1, characterized in that: The motion of the AUV is decoupled into horizontal surface motion, resulting in the equation of horizontal surface motion; In the formula, For the quality of AUV, Let the pitch angle be the moment of inertia. , Let be the coordinates of the AUV's center of gravity in the carrier coordinate system. , , Add mass to the fluid of the AUV. , , , , , The fluid damping coefficient is... Thrust in direction , Thrust in direction Yaw torque .

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