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

Abstract

The application provides an underwater vehicle trajectory tracking control method and system based on compression theory, a medium and a program. The underwater vehicle trajectory tracking control method based on compression theory performs linear parameterization on a dynamic system of an AUV by selecting appropriate parameters, and then designs appropriate adaptive rates and controllers based on the compression theory. The adaptive rates only need to meet sufficient excitation conditions to achieve the effect of parameter identification, ensuring the simultaneous convergence of the system trajectory and the parameters, solving the parameter uncertainty problem in the trajectory tracking process, and providing a feasible scheme for obtaining the AUV system parameters.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of control, in particular relates to a kind of underwater vehicle trajectory tracking method, more specifically, a kind of adaptive trajectory tracking control method based on compression theory of autonomous underwater vehicle. BACKGROUND

[0002] Autonomous Underwater Vehicles (AUV) can replace human long time in underwater to carry out high-risk and high-intensity operation, thus has become the indispensable tool for human to understand, explore and develop ocean, has wide application in environmental monitoring, resource exploration, underwater rescue salvage, military reconnaissance strike and other fields.

[0003] AUV trajectory tracking refers to designing control algorithm to ensure that AUV reaches and tracks a time-varying parameter trajectory, compared with point stabilization and path following, trajectory tracking adds time constraint, and is more suitable for some occasions with strict time requirements, such as AUV deployment and recovery within limited time, tracking and observation of ocean current, but its implementation is more difficult and challenging.

[0004] Currently, AUV trajectory tracking mainly faces the following challenges: parameter uncertainty, model uncertainty, external disturbance, input saturation and under-actuation, etc. Among them, parameter uncertainty mainly refers to that it is difficult to completely and accurately obtain various hydrodynamic coefficients of AUV model. At present, the methods for obtaining hydrodynamic coefficients mainly 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 suitable for AUV with complex shape. Model test consumes huge cost, and sometimes huge manpower, material resources and financial resources are invested but satisfactory results are difficult to obtain. And CFD method has high requirements for the ability, knowledge and skill of users, and its reliability has not been fully verified.

[0005] Adaptive control as an effective method has been widely applied in the field of control, by selecting appropriate parameters to linearly parameterize the system model, on this basis, adaptive rate and adaptive controller are designed, which can ensure that the system quickly reaches the expected state. At the same time, if the system parameters are constant, and the designed adaptive rate meets certain conditions, the estimated value of system parameters can converge to the true value, so as to achieve the effect of parameter identification. But at present, most adaptive rates need to meet the continuous excitation condition to achieve the effect of parameter identification, and this condition is a very strict condition, which is difficult to achieve. SUMMARY

[0006] Therefore, the application provides an underwater vehicle trajectory tracking control method, system, medium and program based on compression theory, which makes up for the problems in the above background art, and the specific technical solutions are 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 appropriate adaptive rates and controllers based on compression theory. The adaptive rate only needs to meet the sufficient excitation condition, so as to achieve the effect of parameter identification, ensure the simultaneous convergence of the system trajectory and the parameters, solve the problem of parameter uncertainty in the trajectory tracking process, and provide a feasible scheme for obtaining the AUV system parameters.

[0008] Step 1: establish the kinematics and dynamics model of the AUV;

[0009] The kinematics and dynamics model of the AUV is as follows:

[0010]

[0011] wherein is the state vector of the AUV in the fixed coordinate system, η1=[x y z] T is the displacement vector, is the attitude vector. v=[u v w p q r] T is the velocity vector of the AUV in the body coordinate system, v1=[u c w] T is the linear velocity, and v2=[p q r] is the angular velocity. J(η) is the conversion matrix.

[0012]

[0013] wherein 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] wherein m is the mass of the AUV, is the inertia-related hydrodynamic force 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 are the first order damping coefficients, while X |u|u , Y |v|v , Z |w|w , K |p|p , M |q|q , N |r|r are the second order damping coefficients.

[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 mass and the center of buoyancy in the body-fixed coordinate system.

[0023] τ = [τ1 τ2 τ3 τ4 τ5 τ6] T denote the forces and moments in each degree of freedom required to achieve the desired motion of the AUV. τ E denote the disturbance terms in the AUV dynamics model, including internal disturbances due to internal model uncertainties and parameter uncertainties, as well as external disturbances due to wind, wave, current, etc.

[0024] Step 2: Choose appropriate system parameters to linearly parameterize the dynamics model of the AUV:

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

[0026]

[0027] where 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 the parameter related to the added mass and damping, Θ2is the parameter related to the gravity, buoyancy, center of gravity coordinates and center of buoyancy coordinates, Θ c is the disturbance vector in the fixed coordinate system.

[0028] d1 = -X u , d2 = -Y v , d3 = -Z ω , d4 = -K p , d5 = -M q , d6 = -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] Θ2= [-W-B) (x G W-x B B) (y G W-y B B) (z G W-z B B)] T .

[0031] In considering the influence of disturbance, its expression in the fixed coordinate system is given first, and then it is projected into the body coordinate system. Through this method, the influence of disturbance on the motion of AUV is quantified, i.e.

[0032] τ E = Φ c (η) Θ c

[0033]

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

[0035]

[0036] It is noted that the regressor matrix is a function of η, v and acceleration . In order to eliminate the acceleration term, filtering is used. Define:

[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, we have:

[0039] τ f = Φ f (η, v) Θ

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

[0041] Step 3: Design appropriate 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 parameter linearization is performed on the first five terms on the right side of the adaptive controller, and we can get:

[0046]

[0047] The system parameters Θ in the adaptive controller are replaced by the estimated values by applying the principle of deterministic equivalence The actual adaptive controller expression is obtained as:

[0048]

[0049] The online update is done by the following adaptation rate:

[0050]

[0051] where β(t) and Z(t) are auxiliary variables, Γ > 0 and K Θ > 0 are diagonal gain matrices, ε m > 0 is a memory factor of the adaptation rate. The prediction error where

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

[0053] The convergence properties of the AUV trajectory and system parameters are proved based on the compression theory as follows:

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

[0055]

[0056] For any initial condition:

[0057] (1) If λ z > 0, then Φ f (t) satisfies the sufficient excitation condition, which further makes η(t), v(t) and exponentially converge to η d (t), v r (t) and Θ, respectively.

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

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

[0060]

[0061] The formula is incorrect, and is modified as follows

[0062]

[0063] It can be shown that Thus the adaptive law can be rewritten as

[0064]

[0065] Combining the AUV system and the controller system, we have a virtual system:

[0066]

[0067] It is obvious that the virtual system has two special solutions: ξ1= [η T v T Θ T ] T and corresponding to the AUV system and the adaptive control system respectively.

[0068] The differential dynamics of the virtual system is

[0069]

[0070] where The Jacobian matrix J a，2 is

[0071]

[0072] Define the metric between two adjacent trajectories of the system as Its derivative with respect to time is is the symmetric part of J a，2 ,

[0073]

[0074] Since K p , K D and K Θ are all positive, according to the definition of Z(t), if λ z > 0, then Z(t) is uniformly positive definite, and if Φ f (t) satisfies the sufficient excitation condition, then J a，2，s is uniformly negative definite, thus we have The virtual system is contractive with the contractive rate When λ z > 0, the virtual system is contractive, while when λ z ≥ 0, the system is semi-contractive. For the former, η(t), v(t) and Θ(t) converge to η d (t), v r (t) and For the latter, η(t) and v(t) asymptotically converge to η d (t) and v r (t), while can only be kept bounded.

[0075] In the present application, the parameters selected when linearizing the dynamic model are

[0076] In the present application, in order not to lose generality, the initial estimated values of the system parameters are all set to zero, i.e.

[0077] In the present application, filtering techniques are used to eliminate the acceleration term in the regression matrix.

[0078] In the present application, the regression matrix only needs to satisfy a sufficient excitation condition to enable the estimated values of the system parameters to converge to the true values.

[0079] In the present application, the convergence characteristics between the actual system of the AUV and the adaptive control system are proved based on the construction of a virtual system according to the compression theory.

[0080] A computer system comprising: one or more processors, a computer readable storage medium storing one or more programs for execution by the one or more processors, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to carry out the method.

[0081] A computer readable storage medium storing computer executable instructions which, when executed, implement the method.

[0082] A computer program comprising computer executable instructions which, when executed, implement the method.

[0083] Compared with the prior art, the present application has the following technical advantages:

[0084] 1. By reasonably selecting parameters to linearly parameterize the dynamic model of the AUV, and then designing an adaptive rate to online estimate the system parameters, the influence of parameter uncertainty on trajectory tracking is avoided;

[0085] 2. The designed adaptive rate only needs to satisfy a sufficient excitation condition to achieve parameter identification, which is much more relaxed than the continuous excitation required by most current adaptive rates, thereby reducing the difficulty of parameter identification;

[0086] 3. In the case where the system parameters are constant or change very slowly, the adaptive rate and the controller can be combined to simultaneously achieve the convergence of the trajectory and the parameters, thereby providing a solution for obtaining the system parameters of the AUV;

[0087] 4. Based on the compression theory, the adaptive controller is designed and the system convergence is analyzed, so that the design and convergence analysis of the control system are closely combined together, compared with the Lyapunov method commonly used at present, the difficulty of system design and analysis is greatly reduced.

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

[0089] 6. The application is suitable for occasions with relatively strict time requirements. BRIEF DESCRIPTION OF DRAWINGS

[0090] Figure 1 is a schematic diagram of a full-drive six-degree-of-freedom AUV model, a fixed coordinate system and a body coordinate system;

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

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

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

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

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

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

[0097] Figure 5 (b) is the change curve of the control moment in the trajectory tracking process;

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

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

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

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

[0102] Figure 7 is a principle block diagram of the controller. DETAILED DESCRIPTION

[0103] An underwater vehicle adaptive trajectory tracking control method based on compression theory,

[0104] Step 1: Establish the kinematics and dynamics model of AUV;

[0105] The kinematics and dynamics model of AUV is as follows:

[0106]

[0107] Wherein is the state vector of AUV in the fixed coordinate system, η1=[x y z] T is the displacement vector, and η2=[φ θ ψ] T is the attitude vector. v=[u v w p q r] T is the velocity vector of AUV in the body coordinate system, v1=[u v w] T is the linear velocity, v2=[p q r] is the angular velocity, 03 indicates a 3×3 zero matrix, and J(η) is the conversion matrix.

[0108]

[0109]

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

[0111]

[0112] Wherein m is the mass of the AUV, is the inertia-related hydrodynamic coefficient related to acceleration, D(v) represents the damping matrix, which is derived from the viscous friction force generated by the AUV motion. Since the AUV's six-degree-of-freedom motion is strongly coupled, time-varying and strongly nonlinear, the damping force it receives is very complex and difficult to model accurately. Considering that the cruising 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 dampings are retained, to obtain the 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 is derived from the gravity and buoyancy of the AUV. The gravity acts on the center of gravity r G = [x G y G z G ] T , while the buoyancy acts on the center of buoyancy r B = [x B y B z B ] T , which generally do not coincide, and since the attitude of the vehicle is constantly changing, the moment 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 suffered by the vehicle, B refers to the buoyancy, τ=[τ1 τ2 τ3 τ4 τ5 τ6] T The force and torque required to achieve the expected motion of the AUV in each degree of freedom, usually generated by propellers, rudders, side thrusters, vertical thrusters, etc. Its essence is also a kind of fluid power, which is generated by the relative motion between these propulsion devices and the surrounding fluid medium.

[0119] τ E The disturbance suffered by the AUV during motion, including internal disturbance caused by system parameter uncertainty, model uncertainty, etc., and external disturbance caused by wind, wave, current. When designing the controller, the robustness of the controller to disturbance needs to be fully considered, or a disturbance observer is designed to estimate the total disturbance, and then the disturbance is compensated according to the results of the observer when designing the controller. The present application assumes that the total disturbance suffered by the AUV during motion is constant in the fixed coordinate system, and then it is mapped into the body coordinate system as an independent term added to the dynamics model of the AUV,

[0120] Step 2: Parameter linearization of AUV dynamics model:

[0121] In the process of designing the controller, an important step is to select a suitable parameter vector so that the dynamics model of the system is linearly related to the selected parameters, that is, so-called "linear parameterization". According to the AUV model established in step 1, the dynamics equation model is rearranged as follows:

[0122]

[0123] Where 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 the parameter vector related to the added mass and damping. 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 is a parameter vector related to gravity, buoyancy, center of mass and center of buoyancy, Θ2 = [- (W - B) (x G W - x B B) (y G W - y B B) (z G W - z B B)] T .

[0124] When considering the effect of disturbance, first give its expression in the fixed coordinate system, and then project it into the body coordinate system. Through this method, the disturbance suffered by the AUV is quantified, that is:

[0125] τ E = Φ c (η) Θ c

[0126]

[0127] where 0 3×3 is a 3x3 zero matrix,

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

[0129]

[0130]

[0131] It is noted that the regressor matrix is a function of η, v and acceleration . Here, a common method in robot control is adopted to filter the regressor matrix to eliminate the dependence on acceleration. Define:

[0132] τ f = f(s) τ

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

[0134] τ f = Φ f (η, v) Θ

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

[0136] Step 3: Design the appropriate adaptive rate and controller:

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

[0138]

[0139] where v r is the reference velocity, η d is the desired trajectory that the vehicle needs to track, K D is the control parameter, K P is the control parameter.

[0140] According to the selected parameter vector, the parameter linearization of the right side of the first five terms of the dynamic model can be obtained:

[0141]

[0142] By applying the certainty equivalence principle, the system parameters Θ in the ideal controller are replaced by the estimated values to obtain the expression of the adaptive controller:

[0143]

[0144] Update online through the following adaptive rate:

[0145]

[0146] where β(t) and Z(t) are auxiliary variables, and their initial values are set to zero. For If we have some understanding of the numerical range of the system parameters, we can choose appropriate initial values to speed up the convergence of the trajectory and system parameters. Here, in order to be general, the initial estimate of the system parameters is set to zero, i.e. In addition, Γ > 0 and K Θ > 0 are diagonal gain matrices, ε m > 0 is the memory factor of the adaptive rate. The prediction error where

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

[0148] Convergence properties of the trajectory and parameters are proved by using the contraction theory

[0149] The convergence properties of the adaptive controller and the adaptive rate proposed in this invention are proved by using the contraction theory. Before that, two types of excitation conditions are described and defined.

[0150] Persistent excitation: regression matrix is uniformly bounded if there exist λ z > 0 and T > 0 such that:

[0151]

[0152] The regression matrix is said to satisfy persistent excitation.

[0153] Sufficient excitation: is uniformly bounded if there exist λ z > 0 and T > 0 such that:

[0154]

[0155] The regression matrix is said to satisfy sufficient excitation.

[0156] The persistent excitation condition is a very important concept in adaptive control and system identification, which reflects the richness of the frequency spectrum of the input signal. The input signal that satisfies the persistent excitation condition can excite the essential characteristics of the system, so as to achieve parameter convergence or system identification. However, it is not easy to design an algorithm that satisfies the persistent excitation condition, so many researchers have studied methods to achieve parameter convergence under weak excitation conditions. Sufficient excitation is a much weaker condition than persistent excitation. Satisfying persistent excitation necessarily satisfies sufficient excitation, but the reverse is not necessarily true. In recent years, other excitation conditions have also been proposed by scholars. Although there may be differences in form, there is no big difference in essence from the sufficient excitation condition.

[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 condition:

[0160] (1) If λ z > 0, then φ f (t) satisfies the sufficient excitation condition, which further makes η(t), v(t) and exponentially converge to η d (t), v r(t) and Θ;

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

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

[0163]

[0164] In addition, it has been proven in the literature that Therefore, the adaptive law can be rewritten as:

[0165]

[0166] Combining the above two equations, a virtual system can be obtained as follows:

[0167]

[0168] It is obvious that the virtual system has two special solutions: ξ1= [η T v T Θ T ] T and correspond to the AUV system and the adaptive control system designed in this section, respectively.

[0169] The differential dynamics of the virtual system is given as follows:

[0170]

[0171] where The Jacobian matrix J a，2 is

[0172]

[0173] The metric is defined as the squared distance between two adjacent trajectories of the system as follows: The derivative of the metric with respect to time is given as follows: is the symmetric part of J a，2 ,

[0174]

[0175] Since K p , K D and K Θ are all greater than zero, according to the definition of Z(t), if λz > 0, then Z(t) is positive definite, Φ f (t) satisfies the sufficient excitation condition, then J a，2，s is negative definite, thus there exists The virtual system is compressive, with compression rate When λ z > 0, the virtual system is compressive, while when λ z ≥ 0, the system is semi-compressive. For the former, η(t), v(t) and Θ(t) converge exponentially to η d (t), v r (t) and For the latter, η(t) and v(t) asymptotically converge to η d (t) and v r (t), while 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 described. The constant vector of the total disturbance in the fixed coordinate system is Θ c = [-10 -20 8 5 10 20] T . The remaining parameters are defined as follows: K p = 0.2I6, K D = 10I6, Γ = 500I 28 , K Θ = 600I 28 , ε m = 800 and λ f = 5. The initial state of the AUV is defined as: η(0) = [15 2 2 0.1 0 0.1] T and v(0) = O 6×1 . The initial guess values of the system parameters are all zero, i.e. The expected trajectory to be tracked by the AUV is as follows:

[0179]

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

[0181] Figure 2The actual and expected trajectories of the AUV are shown. It can be seen that the actual and expected trajectories differ only for a short period initially. Subsequently, under the control of the controller, the error between the two rapidly decreases until they overlap and no significant difference is visible. This demonstrates that the adaptive controller proposed in this invention has good performance and can complete basic trajectory tracking tasks.

[0182] Figure 3 The figure shows the variation curves of the AUV's position and attitude tracking error, x e =xx d This represents the tracking error of longitudinal displacement; the definitions of other symbols are similar. As can be seen, under the control of the controller, the tracking errors of the AUV's position and attitude decrease rapidly, converging in approximately 20 seconds.

[0183] Figure 4 This demonstrates the tracking results of the AUV's actual speed against a reference speed, such as u. e =ux r This represents the tracking error of the longitudinal velocity; the definitions of the other parameters are similar. It can be seen that both the linear velocity and angular velocity converge rapidly to the reference velocity.

[0184] Figure 5 This shows the control inputs required for each degree of freedom, τ. i (i = 1 to 6) represent the control inputs required for each degree of freedom. Observation Figure 5 It can be observed that in the initial period, the tracking error is relatively large, and the required control input is also relatively large in order to quickly track the expected trajectory. However, as the tracking error decreases rapidly, the required control input gradually decreases, and the control input tends to stabilize after the actual trajectory tracks the expected trajectory.

[0185] Figure 6 The estimation results of the parameters, e, are shown. i(i = 1 ~ 28) represents the estimation error of the corresponding parameter. It can be seen from the figure that most of the parameters converge immediately after the simulation starts, and a small number of parameters have a slower convergence speed. This is because in the parameter identification problem, the system state needs to be constantly transformed to fully reflect the characteristics of the system, driving 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, and vice versa. When the AUV gradually tracks the expected trajectory, the system state in the regression matrix, i.e. the linear velocity and angular velocity, gradually stabilizes, and the driving effect on the parameters gradually weakens. For some parameters that have less influence on the motion state of the AUV, the convergence speed slows down. The continuous excitation condition requires that the state of the system can change at any time, thereby constantly driving 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 also tend to be stable, so continuous excitation is relatively harsh. The sufficient excitation condition only requires the system state to change enough within a period of time to achieve the convergence of the parameters, which is relatively easy to achieve.

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

Claims

1. A trajectory tracking control method for an underwater vehicle based on the contraction theory, characterized in that: Specifically comprising the following steps, Step 1: establishing a kinematic and dynamic model of the AUV; Step 2: selecting a system parameter vector Θ to linearize the dynamic model of the AUV: Step 3: designing an adaptive rate and controller: Step 4: using the designed controller to perform adaptive trajectory tracking of the underwater vehicle; Step 3 specifically comprises, According to the dynamic model, the adaptive controller is designed as follows: where M is the mass matrix, v r is the reference velocity, J(η) is the transformation matrix, η is the state vector of the AUV in the fixed coordinate system, η d denotes the desired trajectory that the vehicle needs to track, K D , K P denotes the set control parameters; C(v) is the Coriolis and centripetal force matrix, D(v) represents the damping matrix, G(η) is the restoring force, τ E represents the disturbance term in the AUV dynamics model, including internal disturbances caused by internal model uncertainty and parameter uncertainty, as well as external disturbances caused by wind, wave and current, v is the velocity vector of the AUV in the body coordinate system; According to the selected parameter vector, the first five terms on the right side of the adaptive controller are parameter linearized to obtain: Wherein, Θ is a system parameter vector, Applying the certainty equivalence principle, the system parameter Θ in the adaptive controller is replaced by its estimate The actual adaptive controller expression is obtained: Online update by the following adaptive rate: where β(t) and Z(t) are auxiliary variables, both of which are initialized to zero; the initial estimate of the system parameters is set to zero, i.e. Moreover, Γ > 0 and K Θ > 0 is a diagonal gain matrix, ε m > 0 is a memory factor of the adaptation rate, the prediction error where Φ f (η, v) is the filtered regression matrix. 2.The trajectory tracking control method for an underwater vehicle based on the contraction theory according to claim 1, characterized in that: The kinematic and dynamic model of the AUV is as follows: where is the state vector of the AUV in the fixed coordinate system, η1= [xyz]T is the displacement vector, is the attitude vector, v = [u v w p q r] T is the velocity vector of the AUV in the body coordinate system, v1= [uv w] T is the linear velocity, v2= [p q r] 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) is the Coriolis force and centripetal force matrix: wherein m is the mass of the AUV, is an inertia-related hydrodynamic coefficient associated with acceleration, D(v) represents the damping matrix, D(v) = -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 a first order damping coefficient, while X |u|u , Y |v|v , Z |w|w , K |p|p , M |q|q , N |r|r is a second order damping coefficient, G(η) is the restoring force, and its expression is: 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-fixed coordinate system, W denotes the weight force acting on the vehicle, and B denotes the buoyancy force. T = [T1 T2 T3 T4 T5 T6] T denotes the forces and torques required to achieve the desired motion of the AUV, τ E denotes the disturbance term in the AUV dynamics model, including internal disturbances due to internal model uncertainty and parameter uncertainty, as well as external disturbances due to wind, wave, and current. 3.The trajectory tracking control method for an underwater vehicle based on the contraction theory according to claim 1, characterized in that: Step 2 specifically comprises, According to the AUV model established in step 1, the dynamic equation model is reorganized as follows: where 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 the parameter related to the added mass and damping, Θ2is the parameter related to the gravity, buoyancy, center of gravity coordinates and center of buoyancy coordinates, Θ c is the disturbance 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 the influence of disturbance is considered, first, its expression in the fixed coordinate system is given, and then it is projected into the body coordinate system, and the influence of the disturbance on the motion of the AUV is quantified through this method, that is: τ E = Φ c (η) Θ c is the regression matrix, each entry of which is expressed as follows: Note that the regression matrix is a function of η, v and acceleration To eliminate the acceleration term, a filter is employed, defined as: τ f = f(s)τ f(s) = s / (s + λ f ) is a linearly stable filter, s is the Laplace operator, λ f is the gain of the filter, thus: τ f = Φ f (η, v) Θ Φ f (η, v) is the filtered regression matrix.

4. The compressible theory based trajectory tracking control method for an underwater vehicle according to any one of claims 1-3, characterized in that: The regression matrix satisfies the sufficient excitation condition.

5. A computer system, characterized by One or more processors, a computer readable storage medium, and one or more programs stored therein, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method of claim 4. A computer executable instruction is stored, and the instruction is used to implement the method of claim 4 when executed.

6. A computer-readable storage medium, characterized in that: ​

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