Underwater vehicle trajectory tracking control method and system based on compression theory, medium and program

Abstract

The invention provides an underwater vehicle trajectory tracking control method, system, medium and program based on a compression theory, the underwater vehicle trajectory tracking control method based on the compression theory comprises the following steps: performing linear parameterization on a dynamic system of an AUV (Autonomous Underwater Vehicle) by selecting proper parameters, and then designing a proper adaptive rate and a controller based on the compression theory. According to the method, the adaptive rate only needs to meet enough excitation conditions, the parameter identification effect can be achieved, simultaneous convergence of the system trajectory and the parameters is ensured, the problem of parameter uncertainty in the trajectory tracking process is solved, and meanwhile a feasible scheme is provided for obtaining the AUV system parameters.

Description

Technical Field

[0001] The present invention belongs to the field of control, and in particular relates to an underwater vehicle trajectory tracking method, and more specifically to an autonomous underwater vehicle adaptive trajectory tracking control method based on compression theory. Background Art

[0002] Autonomous underwater vehicles (AUVs) can replace humans in performing high-risk and high-intensity operations underwater for a long time. Therefore, they have become an indispensable tool for humans to understand, explore and develop the ocean. They are widely used in various fields such as environmental monitoring, resource exploration, underwater rescue and salvage, military reconnaissance and strike, etc.

[0003] AUV trajectory tracking refers to designing a control algorithm to ensure that the AUV reaches and tracks a time-varying parameter trajectory. Compared with point stabilization and path following, trajectory tracking adds time constraints and is more suitable for certain occasions with strict time requirements, such as the deployment and recovery of AUVs within a limited time, tracking and observing ocean currents, etc., but its implementation is also more difficult and challenging.

[0004] At present, the trajectory tracking of AUV mainly faces the following challenges: parameter uncertainty, model uncertainty, external interference, input saturation and under-actuation. Parameter uncertainty mainly refers to the difficulty in obtaining the various hydrodynamic coefficients of the AUV model completely and accurately. At present, the main methods for obtaining hydrodynamic coefficients include potential flow theory, model test, computational fluid dynamics (CFD) and other methods. Among them, potential flow theory can only be applied to simple and regular structures, and is not very suitable for AUVs with complex shapes. Model tests are very expensive, and sometimes huge manpower, material and financial resources are invested but satisfactory results are difficult to obtain. The CFD method has high requirements on the ability, knowledge and skills of the users, and its reliability has not been fully verified.

[0005] As an effective method, adaptive control has been widely used in the field of control. By selecting appropriate parameters to linearly parameterize the system model, and designing the adaptive rate and adaptive controller on this basis, it can ensure that the system quickly reaches the expected state. At the same time, if the system parameters are unchanged and the designed adaptive rate meets certain conditions, the estimated value of the system parameter can converge to the true value, thereby achieving the effect of parameter identification. However, most adaptive rates currently need to meet the continuous excitation condition in order to achieve the effect of parameter identification, which is a very strict condition and difficult to achieve. Summary of the invention

[0006] In view of this, the present invention proposes an underwater vehicle trajectory tracking control method, system, medium and program based on compression theory to remedy the problems in the above-mentioned background technology. The specific technical solution is as follows:

[0007] The underwater vehicle trajectory tracking control method based on compression theory linearly parameterizes the dynamic system of the AUV by selecting appropriate parameters, and then designs a suitable adaptive rate and controller based on compression theory. The adaptive rate only needs to meet sufficient excitation conditions to achieve the effect of parameter identification, ensuring the simultaneous convergence of the system trajectory and parameters, solving the problem of parameter uncertainty in the trajectory tracking process, and providing a feasible solution for obtaining the AUV system parameters.

[0008] Step 1: Establish the kinematic and dynamic model of AUV;

[0009] The kinematic and dynamic models of the AUV are as follows:

[0010]

[0011] in is the state vector of the AUV in a fixed coordinate system, η 1 =[xyz] T is the displacement vector, is the posture vector. v = [uvwpqr] T is the velocity vector of the AUV in the body coordinate system, v 1 =[ucw] T is the linear velocity, v 2 =[pqr] is the angular velocity. J(η) is the transformation matrix.

[0012]

[0013] Where M = diag (m 11 , m 22 , m 33 , m 44 , m 55 , m 66 ) is the mass matrix. C(v)=C RB (v)+C A (v) is the Coriolis force and centripetal force matrix:

[0014]

[0015] in m is the mass of the AUV, is the inertial hydrodynamic coefficient related to acceleration.

[0016] D(v) represents the damping matrix

[0017] D(v)=-diag(X u , Y v , Z w , K p ,M q , N r )

[0018] -diag(X |u|u |u|,Y |ν|v |v|,Z |w|w |w|,K |p|p |p|,M |q|q |q|,N |r|r |r|)

[0019] X u , Y v , Z w , ,K p , M q , N r is the first-order damping coefficient, and X |u|u , Y |v|v , Z |w|w , K |p|p , M |q|q , N |r|r is the second-order damping coefficient.

[0020] G(η) is the restoring force, which is expressed as:

[0021]

[0022] r G =[x G y G z G ] T and r B =[x B y B z B ] T are the position vectors of the center of gravity and the center of buoyancy in the body coordinate system.

[0023] τ=[τ 1 τ 2 τ 3 τ 4 τ 5 τ 6 ] T Refers to the forces and moments of each degree of freedom required to achieve the desired motion of the AUV. EIt represents the interference term in the AUV dynamics model, including internal interference caused by internal model uncertainty and parameter uncertainty, as well as external interference caused by wind, waves, currents, etc.

[0024] Step 2: Select appropriate system parameters to linearly parameterize the AUV's dynamic model:

[0025] According to the AUV model established in step 1, the dynamic equation model is rearranged into the following form:

[0026]

[0027] in is the system parameter vector, is the regression matrix. 1 =[m 11 m 22 m 33 m 44 m 55 m 66 d 1 d 2 d 3 d 4 d 5 d 6 d 11 d 22 d 33 d 44 d 55 d 66 ] T is a parameter related to added mass and damping, Θ 2 are parameters related to gravity, buoyancy, center of gravity coordinates, and center of buoyancy coordinates, Θ c is the interference vector in the fixed coordinate system.

[0028] d 1 =-X u , d 2 =-Y v , d 3 =-Z ω , d 4 =-K p , d 5 =-M q , d 6 =-N r ,

[0029] d 11 =-X |u|u , d 22 =-Y |v|v , d 33 =-Z |w|w , d 44=-K |p|p , d 55 =-M |q|q , d 66 =-N |r|r .

[0030] Θ 2 =[-WB) (x G Wx B B) (y G Wy B B) (z G W B B)] T .

[0031] When considering the influence of interference, we first give its expression in the fixed coordinate system, and then project it into the body coordinate system. This method is used to quantify the influence of interference on the motion of AUV, namely:

[0032] τ E =Φ c (η)Θ c

[0033]

[0034] is the regressor matrix, and the expression of each item is as follows:

[0035]

[0036] Note that the regression matrix are η, v and acceleration In order to eliminate the acceleration term, filtering is used. Definition:

[0037] τ f =f(s)τ

[0038] f(s)=s / (s+λ f ) is a linear stable filter, s is the Laplace operator, λ f is the gain of the filter. Therefore:

[0039] τ f =Φ f (η,v)Θ

[0040] Φ f (η, v) is the filtered regression matrix.

[0041] Step 3: Design a suitable adaptive rate and controller:

[0042] According to the dynamic model, the adaptive controller is designed as follows:

[0043]

[0044] where v r is the reference speed,

[0045] According to the selected parameter vector, the first five items on the right side of the adaptive controller are linearized to obtain:

[0046]

[0047] Apply the deterministic equivalence principle and replace the system parameter Θ in the adaptive controller with an estimated value Get the actual adaptive controller expression:

[0048]

[0049] Update online with the following adaptive rate:

[0050]

[0051] Where β(t) and Z(t) are auxiliary variables, Γ>0 and K Θ >0 is the diagonal gain matrix, ε m >0 is the memory factor of the adaptive rate. Prediction Error in

[0052] Step 4: Use the designed controller to perform adaptive trajectory tracking of the underwater vehicle.

[0053] The following proves the convergence characteristics of AUV trajectory and system parameters based on compression theory:

[0054] According to the expressions of the adaptive controller and the adaptive rate, considering that the initial value of Z(t) is zero, Z(t) can be written as follows:

[0055]

[0056] For any initial conditions:

[0057] (1) If λ z >0, then Φ f (t) satisfies sufficient excitation conditions, so that η(t), v(t) and respectively converge exponentially to η d (t), v r (t) and θ;

[0058] (2) If λ z≥0, then η(t) and v(t) converge asymptotically to η d (t) and v r (t), and Can only remain bounded.

[0059] Proof: Combining the controller and the adaptive rate, the controller system can be rewritten as follows:

[0060]

[0061] The formula is wrong, modify it to the following form

[0062]

[0063] It can be proved Therefore the adaptation rate can be rewritten as:

[0064]

[0065] Combining the AUV system and the controller system, a virtual system can be obtained:

[0066]

[0067] Obviously, the virtual system There are two special solutions: 1 =[η T v T Θ T ] T and They correspond to the AUV system and the adaptive control system respectively.

[0068] The differential dynamics form of this virtual system is:

[0069]

[0070] in Jacobian matrix J a，2 for

[0071]

[0072] Defining metrics The square distance between two adjacent trajectories of the following system: Its derivative with respect to time is: For J a，2 The symmetrical part of

[0073]

[0074] Due to K p , K D and K Θare greater than zero. According to the definition of Z(t), if λ z > 0, then Z(t) is uniformly positive definite, Φ f (t) satisfies the sufficient incentive condition, then J a，2，s is uniformly negative definite, so we have The virtual system is compressed, the compression ratio When z > 0, the virtual system is compressed, and when λ z ≥0, the system is semi-compressive. For the former η(t), v(t) and Θ(t) converge to η exponentially. d (t), v r (t) and For the latter, η(t) and v(t) converge asymptotically to η d (t) and v r (t), and Can only remain bounded.

[0075] In the present invention, the parameters selected when the kinetic model is linearized are

[0076] In the present invention, in order to maintain generality, the initial estimated values ​​of the system parameters are set to zero, that is,

[0077] In the present invention, filtering technology is used to eliminate the acceleration term in the regression matrix.

[0078] In the present invention, the regression matrix only needs to satisfy sufficient excitation conditions to achieve the convergence of the estimated values ​​of the system parameters to the true values.

[0079] In the present invention, a virtual system is constructed based on compression theory to prove the convergence characteristics between the AUV actual system and the adaptive control system.

[0080] A computer system includes: 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 implement the described method.

[0081] A computer-readable storage medium stores computer-executable instructions, which are used to implement the method when executed.

[0082] A computer program comprises computer executable instructions, which are used to implement the method when being executed.

[0083] Compared with the existing technology, it has the following technical advantages:

[0084] 1. The AUV dynamics model is linearly parameterized by reasonably selecting parameters, and then the adaptive rate is designed to estimate the system parameters online, thus avoiding the influence of parameter uncertainty on trajectory tracking;

[0085] 2. The designed adaptive rate only needs to meet sufficient excitation conditions to achieve parameter identification, which is much looser than the continuous excitation that most adaptive rates currently need to meet, reducing the difficulty of parameter identification;

[0086] 3. When the system parameters remain unchanged or change very slowly, the combination of adaptive rate and controller can achieve the convergence of trajectory and parameters at the same time, which provides a solution for obtaining AUV system parameters;

[0087] 4. The design of the adaptive controller and the system convergence analysis are carried out based on the compression theory, which closely combines the design of the control system and the convergence analysis. Compared with the currently commonly used Lyapunov method, the difficulty of system design and analysis is greatly reduced.

[0088] 5. The present invention can ensure that the system quickly reaches the expected state.

[0089] 6. The present invention is suitable for occasions with strict time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a schematic diagram of the fully driven six-DOF AUV model, the fixed coordinate system and the accompanying coordinate system;

[0091] Figure 2 It is the comparison between the actual trajectory and the expected trajectory of the AUV in the simulation with unchanged model parameters;

[0092] Figure 3 (a) is the convergence process of position tracking error during trajectory tracking;

[0093] Figure 3 (b) is the convergence process of posture tracking error during trajectory tracking;

[0094] Figure 4 (a) is the convergence process of linear velocity tracking error during trajectory tracking;

[0095] Figure 4 (b) is the convergence process of angular velocity tracking error during trajectory tracking;

[0096] Figure 5 (a) is the curve of control force change during trajectory tracking;

[0097] Figure 5 (b) is the curve of the change of control torque during trajectory tracking;

[0098] Figure 6 (a) is the variation curve of the estimation error of parameters 1-7;

[0099] Figure 6 (b) is the variation curve of the estimation error of parameters 8-14;

[0100] Figure 6 (c) is the variation curve of the estimation error of parameters 15-21;

[0101] Figure 6 (d) is the result of the variation curve of the estimation error of parameters 22-28;

[0102] Figure 7 This is the controller block diagram. DETAILED DESCRIPTION

[0103] An adaptive trajectory tracking control method for underwater vehicles based on compression theory.

[0104] Step 1: Establish the kinematic and dynamic model of AUV;

[0105] The AUV kinematic and dynamic models are as follows:

[0106]

[0107] in is the state vector of the AUV in a fixed coordinate system, η 1 =[xyz] T is the displacement vector, and η 2 =[φ θ ψ] T is the posture vector. v = [uvwpqr] T is the velocity vector of the AUV in the body coordinate system, v 1 =[uvw] T is the linear velocity, v 2 = [pqr] is the angular velocity, 0 3 refers to the 3×3 zero matrix, and J(η) is the transformation matrix.

[0108]

[0109]

[0110] Where M = M RB +M A =diag(m 11 , m 22 , m 33 , m 44 , m 55 , m 66) is the rigid body mass inertia matrix M RB and the fluid additional mass matrix M A C(v)=C RB (v)+C A (v) is the Coriolis force and centripetal force matrix:

[0111]

[0112] in m is the mass of the AUV, is the inertial hydrodynamic coefficient related to acceleration, and D(v) represents the damping matrix, which originates from the viscous friction generated by the AUV motion. Since the six-degree-of-freedom motion of the AUV is a strongly coupled, time-varying, and strongly nonlinear motion, the damping force it is subjected to is very complex and difficult to model accurately. Considering that the navigation speed of the AUV is generally not high, the high-order damping terms and coupling terms are ignored, and only the uncoupled first-order and second-order damping are retained, resulting in a simplified D(v) expression:

[0113] D(v)=-diag(X u , Y v , Z w , K p , M q ,N r )

[0114] -diag(X |u|u |u|,Y |v|v |v|,Z |w|w |w|,K |p|p |p|,M |q|q |q|,N |r|r |r|)

[0115] X u , Y v , Z w , K p , M q , N r is the first-order damping coefficient, and X |u|u , Y |v|v , Z |w|w , K |p|p , M |q|q , N |r|r is the second-order damping coefficient.

[0116] G(η) represents the restoring force, which comes from the gravity and buoyancy of the AUV. The gravity acts on the center of gravity r of the AUV. G =[x G y G z G ]T The buoyancy acts on the center of buoyancy r B =[x B y B z B ] T Generally speaking, these two do not coincide, and because the attitude of the spacecraft is constantly changing, the torque generated by gravity and buoyancy is also constantly changing. The expression of the restoring force G(η) is:

[0117]

[0118] Where W refers to the gravity of the spacecraft, B refers to the buoyancy, τ = [τ 1 τ 2 τ 3 τ 4 τ 5 τ 6 ] T Refers to the forces and moments of each degree of freedom required to achieve the expected movement of the AUV, usually generated by propellers, rudders, thrusters, vertical thrusters and other propulsion devices. Its essence is also a kind of fluid power, which is generated by the relative movement of these propulsion devices and the surrounding fluid medium.

[0119] τ E It represents the disturbances to which the AUV is subjected during its motion, including internal disturbances caused by system parameter uncertainty, model uncertainty, etc., and external disturbances caused by wind, waves, and ocean currents. When designing a controller, it is necessary to fully consider the robustness of the controller to disturbances, or to design a disturbance observer to estimate the total disturbance, and then compensate for the disturbance according to the results of the observer when designing the controller. The present invention assumes that the total disturbance to which the AUV is subjected during its motion is constant in a fixed coordinate system, and then maps it to the body coordinate system and adds it to the dynamic model of the AUV as an independent term.

[0120] Step 2: Linearize the parameters of the AUV dynamics model:

[0121] In the controller design process, an important step is to select a suitable parameter vector so that the system's dynamic model is linearly related to the selected parameters, which is called "linearly parameterized". According to the AUV model established in step 1, the dynamic equation model is rearranged into the following form:

[0122]

[0123] in is the system parameter vector, is the regression matrix. 1 =[m 11m 22 m 33 m 44 m 55 m 66 d 1 d 2 d 3 d 4 d 5 d 6 d 11 d 22 d 33 d 44 d 55 d 66 ] T is a parameter vector related to added mass and damping. 1 =-X u , d 2 =-Y v , d 3 =-Z w , d 4 =-K p , d 5 =-M q , d 6 =-N r , d 11 =-X |u|u , d 22 =-Y |v|v , d 33 =-Z |w|w , d 44 =-K |p|p , d 55 =-M |q|q , d 66 =-N |r|r Θ 2 is the parameter vector related to gravity, buoyancy, center of gravity coordinates and center of buoyancy coordinates, Θ 2 =[-(WB)(x G Wx B B)(y G Wy B B)(z G W B B)] T .

[0124] When considering the influence of interference, we first give its expression in the fixed coordinate system, and then project it into the body coordinate system. This method is used to quantify the interference suffered by the AUV, namely:

[0125] τ E =Φ c (η)Θ c

[0126]

[0127] Among them, 0 3×3 refers to a 3×3 zero matrix,

[0128] is the regressor matrix, and the expression of each item is as follows:

[0129]

[0130]

[0131] Note that the regression matrix are η, v and acceleration Here, we use the general method in robot control to filter the regression matrix to eliminate the dependence on acceleration. Definition:

[0132] τ f =f(s)τ

[0133] Here, f(s) = s / (s+λ f ) is a linear stable filter, s is the Laplace operator, λ f is the gain of the filter. Therefore:

[0134] τ f =Φ f (η,v)Θ

[0135] Φ f (η, v) is the filtered regression matrix.

[0136] Step 3: Design a suitable adaptive rate and controller:

[0137] Considering the ocean current disturbance, the expression of the designed adaptive controller is:

[0138]

[0139] where v r is the reference speed, η d Refers to the expected trajectory that the spacecraft needs to track, K D Refers to the control parameter, K P Refers to the control parameters.

[0140] According to the selected parameter vector, the first five items on the right side of the dynamic model are linearized to obtain:

[0141]

[0142] Apply the deterministic equivalence principle and replace the system parameters Θ in the ideal controller with estimated values The expression of the adaptive controller is obtained:

[0143]

[0144] Update online with the following adaptive rate:

[0145]

[0146] Where β(t) and Z(t) are auxiliary variables, and their initial values ​​are set to zero. If we have a certain understanding of the numerical range of system parameters, we can choose appropriate initial values ​​to speed up the convergence of trajectory and system parameters. In order to avoid loss of generality, the initial estimated values ​​of system parameters are set to zero, that is, In addition, Γ>0 and K Θ >0 is the diagonal gain matrix, ε m >0 is the memory factor of the adaptive rate. Prediction Error in

[0147] Step 4: Use the completed controller to perform adaptive trajectory tracking of the following vehicle.

[0148] Using compression theory to prove the convergence properties of trajectories and parameters

[0149] The convergence characteristics of the adaptive controller and the adaptive rate proposed in the present invention are proved by compression theory. Prior to this, two types of excitation conditions are explained and defined.

[0150] Continuous Incentives: Regression Matrix is uniformly bounded if there exists λ z >0 and T>0 such that:

[0151]

[0152] Then the regression matrix is ​​said to satisfy continuous incentives.

[0153] Enough motivation: is uniformly bounded if there exists λ z >0 and T>0, such that:

[0154]

[0155] Then the regression matrix is ​​said to satisfy sufficient excitation.

[0156] The continuous excitation condition is a very important concept in adaptive control and system identification. It reflects the richness of the input signal spectrum. The input signal that meets the continuous excitation condition can stimulate the essential characteristics of the system, thereby achieving parameter convergence or system identification. However, it is not easy to design an algorithm that meets the continuous excitation condition. Therefore, many researchers study methods to achieve parameter convergence under weak excitation conditions. Sufficient excitation is a much weaker condition than continuous excitation. If continuous excitation is met, sufficient excitation must be met, and vice versa. In recent years, some scholars have also proposed other excitation conditions. Although they may differ in form, they are essentially not much different from sufficient excitation conditions.

[0157] Considering the adaptive control rate and parameter update rate proposed in this section, since the initial value of Z(t) is zero, Z(t) can be written as follows:

[0158]

[0159] For any initial conditions:

[0160] (1) If λ z >0, then φ f (t) satisfies sufficient excitation conditions, so that η(t), v(t) and respectively converge exponentially to η d (t), v r (t) and θ;

[0161] (2) If λ z ≥0, then η(t) and v(t) converge asymptotically to η d (t) and v r (t), and Can only remain bounded.

[0162] Proof: Combining the controller and the adaptive rate, the controller system can be rewritten as follows:

[0163]

[0164] In addition, it has been demonstrated in the literature Therefore the adaptation rate can be rewritten as:

[0165]

[0166] Combining the above two formulas, we can get a virtual system:

[0167]

[0168] Obviously, the virtual system There are two special solutions: 1 =[η T vT Θ T ] T and They correspond to the AUV system and the adaptive control system designed in this section respectively.

[0169] The differential dynamics form of this virtual system is:

[0170]

[0171] in Jacobian matrix J a，2 for

[0172]

[0173] measure The square distance between two adjacent trajectories of the lower system is defined as: Its derivative with respect to time is: For J a，2 The symmetrical part of

[0174]

[0175] Due to K p , K D and K Θ are greater than zero. According to the definition of Z(t), if λ z > 0, then Z(t) is uniformly positive definite, Φ f (t) satisfies the sufficient incentive condition, then J a，2，s is uniformly negative definite, so we have The virtual system is compressed, the compression ratio When z >0, the virtual system is compressed, and when λ z ≥0, the system is semi-compressive. For the former η(t), v(t) and Θ(t) converge to η exponentially. d (t), v r (t) and For the latter, η(t) and v(t) converge asymptotically to η d (t) and v r (t), and Can only remain bounded.

[0176] The specific simulation results are given below. The system parameters are as follows.

[0177]

[0178] First, the settings of various parameters in the simulation are explained. The constant vector of the total interference in the fixed coordinate system is Θ c=[-10 -20 8 5 10 20] T The remaining parameters are defined as: K p =0.2I 6 , K D =10I 6 , Γ=500I 28 , K Θ =600I 28 , ε m =800 and λ f =5. The initial state of AUV is defined as: η(0) = [15 2 2 0.1 0 0.1] T and v(0)=0 6×1 The initial guess values ​​of the system parameters are all zero, that is, The expected trajectory to be followed by the AUV is as follows:

[0179]

[0180] Next, the simulation results are presented and analyzed.

[0181] Figure 2 The actual and expected trajectories of the AUV are shown. It can be seen that the actual and expected trajectories of the AUV differ only in the initial period of time, and then the error between them decreases rapidly under the action of the controller until no obvious difference can be seen after they overlap. This shows that the adaptive controller proposed in the present invention has good performance and can complete the basic trajectory tracking task.

[0182] Figure 3 The tracking error curves of the AUV's position and attitude are shown. e =xx d It represents the tracking error of the longitudinal displacement, and the definitions of other symbols are similar. It can be seen that under the action of the controller, the tracking errors of the position and attitude of the AUV are rapidly reduced and converge in about 20s.

[0183] Figure 4 The actual speed of the AUV is shown to track the reference speed, for example, u e =ux r It represents the tracking error of the longitudinal velocity, and the definitions of the other parameters are similar. It can be seen that both the linear velocity and the angular velocity converge quickly to the reference velocity.

[0184] Figure 5 It shows the control input required for each degree of freedom, τ i (i=1~6) represents the control input required for each degree of freedom. Figure 5It can be found that in the initial period of time, the tracking error is relatively large. In order to quickly track the expected trajectory, the required control input is also relatively large. As the tracking error decreases rapidly, the required control input also gradually decreases. When the actual trajectory tracks the expected trajectory, the control input also tends to stabilize.

[0185] Figure 6 The estimated results of the parameters are shown. i (i=1~28) represents the estimation error of the corresponding parameter. As can be seen from the figure, most parameters converged immediately after the simulation started, and a few parameters converged slowly. This is because in the problem of parameter identification, the system state needs to change continuously to fully reflect the characteristics of the system and drive the estimated value of the parameter to approach the true value. The greater the influence of the system parameters on the system state, the faster the convergence speed of the parameters. Conversely, the smaller the influence of the system parameters on the system state, the slower the convergence speed. When the AUV gradually tracks the expected trajectory, the system state in the regression matrix, i.e., the linear velocity and angular velocity, gradually tends to be stable, and the driving effect on the parameters gradually weakens. For some parameters that have little effect on the motion state of the AUV, the convergence speed slows down. The continuous excitation condition requires that the state of the system can maintain a relatively obvious change at any time, so as to continuously drive the estimated value of the parameter to approach the true value. However, when the system gradually reaches the expected state under the action of the controller, the system state will inevitably tend to be stable, so continuous excitation is more demanding. The sufficient excitation condition only requires the system state to maintain sufficient changes over a period of time to achieve parameter convergence, which is relatively easy to achieve.

[0186] The above results show that when the parameters of the system remain unchanged, the adaptive controller and adaptive rate proposed in the present invention can ensure the convergence of trajectory and parameters at the same time, that is, when the actual trajectory of the AUV converges to the target trajectory, the estimated value of the system parameter can also converge to the true value. At the same time, the adaptive rate proposed in the present invention only needs to meet sufficient excitation conditions to achieve parameter identification. Compared with the continuous excitation conditions that most of the current adaptive rates need to meet, sufficient excitation is much more relaxed and easier to meet. Therefore, the adaptive rate and adaptive controller proposed in the present invention provide an effective solution for obtaining AUV system parameters.

Claims

1. An underwater vehicle trajectory tracking control method based on compression theory, characterized in that: The system parameter vector Θ is selected to linearly parameterize the dynamic system of the AUV, and then the adaptation rate and controller are designed based on the compression theory to achieve adaptive trajectory tracking.

2. The underwater vehicle trajectory tracking control method based on compression theory according to claim 1 is characterized in that: The following steps are included: Step 1: Establish the kinematic and dynamic model of AUV; Step 2: Select the system parameter vector Θ to linearize the dynamic model of the AUV: Step 3: Design the adaptive rate and controller: Step 4: Use the designed controller to perform adaptive trajectory tracking of the underwater vehicle.

3. The underwater vehicle trajectory tracking control method based on compression theory according to claim 2 is characterized by: The kinematic and dynamic models of the AUV are as follows: in is the state vector of the AUV in a fixed coordinate system, η1=[xy z]T is the displacement vector, is the attitude vector, v-[uvwp qr]T is the velocity vector of the AUV in the body coordinate system, v1=[u vw] T is the linear velocity, v2 = [pqr] is the angular velocity, J(η) is the transformation matrix, Where M = diag (m 11 , m 22 , m 33 , m 44 , m 55 , m 66 ) is the mass matrix, C(v)=C RB (v)+C A (v) is the Coriolis force and centripetal force matrix: in m is the mass of the AUV, is the inertial hydrodynamic coefficient related to acceleration, D(v) represents the damping matrix, D(υ)=-diag(X u ,Y v ,Z w ,K p ,M q ,N r )-diag(X |u|u |u|,Y |v|v |v|,Z |w|w |w|,K |p|p |p|,M |q|q |q|,N |r|r |r|) X u , Y v , Z w , K p , M q , N r is the first-order damping coefficient, and X |u|u , Y |v|v , Z |w|w , K |p|p , M |q|q , N |r|r is the second-order damping coefficient, G(η) is the restoring force, which is expressed as: r G =[x G y G z G ] T and r B =[x B y B z B ] T is the position vector of the center of gravity and the center of buoyancy in the body coordinate system, W refers to the gravity of the spacecraft, B refers to the buoyancy, τ=[τ1 τ2 τ3 τ4 τ5 τ6] T Refers to the forces and moments of each degree of freedom required to achieve the desired motion of the AUV, τ E It represents the interference term in the AUV dynamics model, including internal interference caused by internal model uncertainty and parameter uncertainty, as well as external interference caused by wind, waves and current.

4. The underwater vehicle trajectory tracking control method based on compression theory according to claim 2 is characterized in that: Step 2 specifically includes: According to the AUV model established in step 1, the dynamic equation model is rearranged into the following form: in is the system parameter vector, is the regression matrix, Θ1=[m 11 m 22 m 33 m 44 m 55 m 66 d1 d2 d3 d4 d5 d6 d 11 d 22 d 33 d 44 d 55 d 66 ] T is a parameter related to the added mass and damping, Θ2 is a parameter related to gravity, buoyancy, center of gravity coordinates and center of buoyancy coordinates, Θ c is the interference vector in the fixed coordinate system, d1=-X u ,d2=-Y v ,d3=-Z w ,d4=-K p ,d5=-M q ,d6=-N r ,d 11 =-X |u|u ,d 22 =-Y |v|v ,d 33 =-Z |w|w ,d 44 =-K |p|p ,d 55 =-M ｜q|q ,d 66 =-N |r|r 。Θ2=[-(W-B)(x G W-x B B)(y G W-y B B)(z G W-z B B)] T , When considering the influence of interference, we first give its expression in the fixed coordinate system, and then project it into the body coordinate system. This method is used to quantify the influence of interference on the motion of AUV, namely: t E =Φ c (h)I c is the regression matrix, and the expression of each item is as follows: Note that the regression matrix are η, v and acceleration In order to eliminate the acceleration term, filtering is used and defined as: t f =f(S)τ f(s)=s / (s+λ f ) is a linear stable filter, s is the Laplace operator, λ f is the gain of the filter, so: t f =Φ f (η,v)Θ Φ f (η, v) is the filtered regression matrix.

5. The underwater vehicle trajectory tracking control method based on compression theory according to claim 2 is characterized in that: Step 3 specifically includes: According to the dynamic model, the adaptive controller is designed as follows: where v r is the reference speed, η d Refers to the expected trajectory that the spacecraft needs to track, K D , K P Refers to the set control parameters; According to the selected parameter vector, the first five items on the right side of the adaptive controller are linearized to obtain: Apply the deterministic equivalence principle and replace the system parameter Θ in the adaptive controller with an estimated value Get the actual adaptive controller expression: Update online with the following adaptive rate: Among them, β(t) and Z(t) are auxiliary variables, and their initial values ​​are set to zero; the initial estimated values ​​of the system parameters are set to zero, that is, In addition, Γ>0 and K Θ >0 is the diagonal gain matrix, ε m >0 is the memory factor of the adaptive rate, the prediction error in 6. The underwater vehicle trajectory tracking control method based on compression theory according to any one of claims 1 to 5, characterized in that: The regression matrix satisfies the sufficient excitation condition.

7. A computer system, characterized in that include: 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 are enabled to implement the method of claim 6.

8. A computer-readable storage medium, characterized in that: Computer executable instructions are stored, and when the instructions are executed, they are used to implement the method of claim 6.

9. A computer program, characterized in that: The invention comprises computer executable instructions, which are used to implement the method of claim 6 when being executed.

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