An AUV preset time trajectory tracking control method considering performance constraints and interference effects

Abstract

The application discloses an AUV preset time trajectory tracking control method considering performance constraints and interference influence, and relates to the technical field of trajectory tracking control.The application is to solve the problem that the existing AUV trajectory tracking control method is difficult to accurately complete trajectory tracking within the expected time.The application comprises the following steps: establishing an AUV kinematics model by using the six-degree-of-freedom position and posture of the AUV in an inertial coordinate system; combining the AUV kinematics model to establish an AUV dynamics model; establishing a performance function; converting the trajectory tracking error by using the performance function and the AUV dynamics model to obtain a trajectory tracking error vector; designing an adaptive lumped interference estimator by using the trajectory tracking error vector; and designing an adaptive posture tracking controller by using the trajectory tracking error vector and the adaptive lumped interference estimator.The application is used for AUV trajectory tracking control.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of trajectory tracking control, and particularly relates to an AUV preset time trajectory tracking control method considering performance constraints and interference effects. BACKGROUND

[0002] The ocean accounts for about 71% of the earth's surface, and is the largest ecosystem on earth, containing rich resources of marine oil and natural gas. However, the development of marine resources faces many problems and challenges, such as complex and changeable marine environment, existence of extreme harsh conditions such as high pressure and low temperature, which all increase the great difficulty for human beings to develop the ocean. As a special application of advanced robot technology under water, the autonomous underwater vehicle (AUV) has an important strategic position in marine resource exploration and marine environment monitoring. Many fine underwater task requirements also make the demand for the control accuracy and maneuverability of the AUV higher and higher. Among them, trajectory tracking is the most basic and primary task target of the AUV when performing tasks. In the process of trajectory tracking of the AUV, many problems will be encountered, such as external ocean current disturbance, AUV model uncertainty and the like, and fine and complex underwater tasks require the trajectory tracking process of the AUV to have higher control accuracy and faster response speed. Therefore, it has important engineering practical significance to carry out the research on the trajectory tracking control method of the AUV and design an advanced controller which has better control accuracy and faster response speed under the influence of various external interferences.

[0003] The trajectory tracking control of AUVs currently includes neural network control and fuzzy control methods. Neural network control methods have strong approximation ability for unknown nonlinear systems, especially for research objects that are disturbed by the external environment and have their own model uncertainties. The weight matrix, center parameter, and other parameters can be updated continuously through the reinforcement learning process. Literature (Zhou J J, Zhao X Y, Chen T, et al. Trajectory Tracking Control of an Underactuated AUV Based on Backstepping Sliding Mode With State Prediction [J]. Ieee Access, 2019, 7: 181983-181993.) takes AUV as the research object, combines the radial basis function neural network method with the state prediction sliding mode control method, estimates the external current disturbance and the model uncertainty of the system itself using the radial basis function neural network, and completes the trajectory tracking control by combining the non-singular terminal sliding mode technology. The simulation experiment at the end verifies that the radial basis function neural network has excellent approximation performance for nonlinear external disturbances and good trajectory tracking effect. However, this control method lacks control over the system convergence time, which is difficult to determine and design, and cannot limit the transient performance of the control system, which may cause the convergence time to exceed the expected time. Therefore, the trajectory tracking method of AUV based on neural network control has the problem of being difficult to complete trajectory tracking within the expected time, so this method cannot be applied in situations where the convergence time is strictly required. Fuzzy control is often applied to control systems that are difficult to model, and this control method has the characteristics of fast response and strong anti-interference ability. Literature (Elhaki O, Shojaei K. Neural network-based target tracking control of underactuated autonomous underwater vehicles with a prescribed performance [J]. Ocean Engineering, 2018, 167 (NOV. 1): 239-256.) takes an underactuated AUV as the research object, uses the Sigmoid function to construct the sliding mode term, and uses the backstepping method to design a sliding mode controller to solve the model uncertainty problem and effectively reduce the chattering phenomenon produced in the error convergence process of the system. Finally, the simulation experiment verifies that the controller has strong robustness in the trajectory tracking control of AUV.However, this lack of optimization of the entire trajectory tracking convergence performance, such as reducing overshoot, shortening the convergence time, reducing the steady-state error, etc., may produce an excessive overshoot, exceed the acceptable range in the convergence process, and cannot accurately complete the tracking task, and in serious cases may threaten the safety of the AUV itself. SUMMARY

[0004] The present application aims to solve the problem that the existing AUV trajectory tracking control method cannot accurately complete the trajectory tracking within the expected time, and proposes an AUV preset time trajectory tracking control method considering performance constraints and disturbance effects.

[0005] An AUV preset time trajectory tracking control method considering performance constraints and disturbance effects, specifically comprising:

[0006] Step one, establish an AUV kinematics model using the six-degree-of-freedom position and attitude of the AUV in the inertial coordinate system;

[0007] Step two, establish an AUV dynamics model in combination with the AUV kinematics model obtained in step one;

[0008] Step three, establish a performance function, convert the trajectory tracking error using the performance function and the AUV dynamics model, and obtain a converted trajectory tracking error vector, specifically:

[0009] Step three one, establish a performance function, specifically:

[0010] ρ(t)=(ρ0-ρ ∞ )e -kt +ρ ∞

[0011] ρ(t) satisfies the following conditions:

[0012] (1) ρ(t) is positive and strictly decreasing;

[0013] (2)

[0014] Where ρ0, k, ρ ∞ are preset normal numbers, and t is time;

[0015] Step three two, convert the trajectory tracking error using the performance function ρ(t) established in step three one and the AUV dynamics model, and obtain a converted trajectory tracking error vector;

[0016] Step four, design an adaptive lumped disturbance estimator using the trajectory tracking error vector obtained in step three, specifically:

[0017]

[0018] wherein, k di is a constant, i∈[1,6], i is the degree of freedom label, ε i is the transformation error of the i-th degree of freedom trajectory tracking, s i is the trajectory tracking error of the i-th degree of freedom;

[0019] Step five, using the trajectory tracking error vector obtained in step three and the adaptive lumped disturbance estimator obtained in step four to design an adaptive attitude tracking controller.

[0020] The beneficial effects of the present application are:

[0021] The present application first constrains the error by the performance function in the preset performance control technology, then obtains a new error variable through error conversion to simplify the subsequent derivation process, ensures that the new error e is the preset performance convergence when the preset performance converges, and then designs the preset time control for the new error and combines the adaptive lumped disturbance estimator to obtain the AUV preset time trajectory tracking controller u c , which ensures that the trajectory tracking error can achieve the desired effect. The present application unifies the ocean current disturbance and model uncertainty as external lumped disturbance, estimates the external lumped disturbance using the adaptive lumped disturbance estimator, and improves the convergence time limit by introducing the preset time control technology, so that the trajectory tracking error of the AUV converges to the preset steady-state error within the preset time, thereby completing the trajectory tracking within the desired time, which is closer to the actual engineering demand. The present application constrains the trajectory tracking error by introducing the preset performance method, ensures the preset transient performance and convergent steady-state performance, and combines the preset time control to constrain the convergence rate of the trajectory tracking error, further optimizes the trajectory tracking process from the time dimension, so that the steady-state error of the trajectory tracking error when converging is within the preset range and the overshoot is reduced, so that the overshoot is kept within an acceptable range during the convergence process, so that the AUV can accurately complete the trajectory tracking task within the desired time, avoiding the problem that the safety of the AUV is threatened. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 is the coordinate system defined for the AUV;

[0023] Figure 2 is the layout of the Xinghai Z3000 benthic AUV thruster;

[0024] Figure 3(a) is a curve graph of the AUV surge direction trajectory tracking error;

[0025] Figure 3(b) is a curve graph of the AUV sway direction trajectory tracking error;

[0026] Fig. 3(c) is a curve diagram of the heave direction trajectory tracking error of the AUV;

[0027] Fig. 3(d) is a curve diagram of the roll direction trajectory tracking error of the AUV;

[0028] Fig. 3(e) is a curve diagram of the pitch direction trajectory tracking error of the AUV;

[0029] Fig. 3(f) is a curve diagram of the yaw direction trajectory tracking error of the AUV;

[0030] Figure 4 Fig. 3(g) is an enlarged view of the six-degree-of-freedom trajectory tracking error curve of the AUV;

[0031] Figure 5 Fig. 3(h) is a curve diagram of the output control moment of the AUV propeller;

[0032] Figure 6 Fig. 3(i) is a curve diagram of the output control force of the AUV propeller;

[0033] Figure 7 Fig. 3(j) is a curve diagram of the trajectory in the surge direction of the AUV;

[0034] Figure 8 Fig. 3(k) is a curve diagram of the trajectory in the surge direction of the AUV;

[0035] Figure 9 Fig. 3(l) is a curve diagram of the trajectory in the heave direction of the AUV;

[0036] Figure 10 Fig. 3(m) is a curve diagram of the trajectory of the AUV in three-dimensional space;

[0037] Figure 11 Fig. 3(n) is a curve diagram of external interference. DETAILED DESCRIPTION

[0038] The coordinate system involved in the present application is shown in Fig. 1, and includes: an inertial coordinate system (E-ξηζ) and a moving coordinate system (O-XYZ). Figure 1

[0039] Inertial coordinate system (E-ξηζ): also known as "fixed coordinate system". The origin E can be selected at a certain point on the sea surface, the Eξ axis and the Eη axis are placed in the horizontal plane and are perpendicular to each other, and the Eξ axis points to the north. The Eζ axis is perpendicular to the Eξη plane and points to the center of the earth.

[0040] Moving coordinate system (O-XYZ): the origin O is taken at the center of gravity of the AUV, and the X axis, the Y axis and the Z axis are the intersection lines of the waterline plane, the transverse section and the centerline section passing through the origin. The X axis points to the longitudinal direction of the AUV and the bow direction is positive, the Y axis points to the transverse direction of the AUV and the starboard is positive, and the Z axis points to the downward direction of the AUV and the downward direction is positive.

[0041] ​Specific implementation one: the specific process of the AUV preset time trajectory tracking control method considering performance constraints and interference effects in this embodiment is as follows:

[0042] Step one, a kinematics model of the AUV is established by using the six-degree-of-freedom position and attitude of the AUV in the inertial coordinate system:

[0043] First, the linear velocity transfer matrix J1(η a ) and the angular velocity transfer matrix J2(η a ) are defined:

[0044]

[0045]

[0046] wherein, is the six-degree-of-freedom position and attitude of the AUV in the inertial coordinate system, x is the linear displacement of the AUV in the surge direction in the inertial coordinate system, y is the linear displacement of the AUV in the sway direction in the inertial coordinate system, z is the linear displacement of the AUV in the heave direction in the inertial coordinate system, is the angular displacement of the AUV in the yaw direction in the inertial coordinate system, θ is the angular displacement of the AUV in the pitch direction in the inertial coordinate system, and ψ is the angular displacement of the AUV in the yaw direction in the inertial coordinate system;

[0047] Then, the kinematics model of the AUV is established by using the linear velocity transfer matrix J1(η a ) and the angular velocity transfer matrix J2(η a ):

[0048]

[0049] wherein, J(η a ) is the conversion matrix between the inertial coordinate system and the motion coordinate system, V = [u, v, w, p, q, r] T is the velocity and angular velocity of the AUV in the motion coordinate system, u is the velocity of the AUV in the surge direction in the motion coordinate system, v is the velocity of the AUV in the sway direction in the motion coordinate system, w is the velocity of the AUV in the heave direction in the motion coordinate system, p is the angular velocity of the AUV in the yaw direction in the motion coordinate system, q is the angular velocity of the AUV in the pitch direction in the motion coordinate system, and r is the angular velocity of the AUV in the yaw direction in the motion coordinate system, O 3×3 is a zero matrix of three rows and three columns.

[0050] Step two, the kinematics model of the AUV obtained in step one is combined to establish a dynamics model of the AUV, specifically:

[0051] Step two one, the dynamics equation of the AUV is expressed by using the six-degree-of-freedom nonlinear model based on the Fossen outline, as follows:

[0052]

[0053] M η = MJ -1 (η a ) (5)

[0054]

[0055] C Aη = C A (V r )J -1 (η a ) (7)

[0056] D η = D(V r )J -1 (η a ) (8)

[0057] g η = g(η a ) (9)

[0058]

[0059] V r = V - V c (11)

[0060] where M η , C RBη , C Aη , D η , is the intermediate matrix, is the second derivative of η a , g η , g(η a ) are the force and moment vectors generated by gravity and buoyancy, τ is the control force and moment generated by the propulsion system, M is the coefficient matrix, C RB (V) is the Coriolis and centripetal force and moment matrix of the rigid body, C A (V r ) is the Coriolis and centripetal force and moment matrix of the added mass, D(V r ) is the hydrodynamic damping matrix, V r is the velocity of the AUV relative to the ocean current, V c is the velocity of the ocean current in the moving coordinate system;

[0061] The six degrees of freedom nonlinear model in Fossen outline is used to represent the dynamics in this step from the literature (Fossen TI. Handbook of Marine Craft Hydrodynamics and Motion Control [M]. 2011.).

[0062] The coefficient matrix M in the above equation is composed of the rigid body mass and inertia matrix and the hydrodynamic added mass matrix, i.e. M = M RB + M A , M RB and M A The specific expressions are as follows:

[0063]

[0064]

[0065] Where M RB is the rigid body mass and inertia matrix, M A is the hydrodynamic added mass matrix, m is the AUV body mass, I X is the AUV inertia moment about the X axis, I Y is the AUV inertia moment about the Y axis, I Z is the AUV inertia moment about the Z axis, I XY is the AUV inertia product about the X and Y axes, I XZ is the AUV inertia product about the X and Z axes, I YZ is the AUV inertia product about the Y and Z axes, is the first order hydrodynamic coefficient about , is the first order hydrodynamic coefficient about , is the first order hydrodynamic coefficient about , is the first order hydrodynamic coefficient about , is the first order hydrodynamic coefficient about , is the first order hydrodynamic coefficient about ;

[0066] The Coriolis and centripetal force matrix is composed of the rigid body centripetal force matrix and the Coriolis-like force matrix, i.e. C(V) = C RB (V) + C A (V r ), C RB (V) and C A (V r ) The specific expressions are as follows:

[0067]

[0068]

[0069]

[0070] where C RB (V) is the rigid body centripetal matrix, C A (V r ) is the Coriolis-like matrix, and a1, a2, a3, b1, b2, b3 are intermediate variables.

[0071] The hydrodynamic damping matrix D(V r ) is given by

[0072] D(V r ) = -diag{D L + D Q |v|} (17)

[0073] D L = diag{X u , Y v , Z w , K p , M q , N r} (18)

[0074] D Q = diag{X uu , Y vv , Z ww , K pp , M qq , N rr} (19)

[0075] where D L is the linear motion drag coefficient matrix, D Q is the angular motion drag coefficient matrix, X u is the hydrodynamic coefficient for u, Y v is the hydrodynamic coefficient for v, Z w is the hydrodynamic coefficient for w, K p is the hydrodynamic coefficient for p, M q is the hydrodynamic coefficient for q, N r is the hydrodynamic coefficient for r, X uu is the hydrodynamic coefficient for u|u|, Y νν is the hydrodynamic coefficient for v|v|, Z ww is the hydrodynamic coefficient for w|w|, K pp is the hydrodynamic coefficient for p|p|, Mqq is the hydrodynamic coefficient about q | q |, N rr is the hydrodynamic coefficient about r | r | ;

[0076] the force and moment vectors generated by gravity and buoyancy, specifically:

[0077]

[0078] where W is the total gravity force on the AUV, B is the total buoyancy force on the AUV, Z B is the vertical coordinate value of the center of buoyancy;

[0079] Step two, on the basis of the established AUV dynamics model in step two one, considering the model uncertainty and ocean current disturbance, the AUV dynamics model is rewritten as follows:

[0080]

[0081]

[0082]

[0083] where M η0 is the nominal value of M η , B0 is the nominal value of the thrust distribution matrix, F is the total uncertainty of the system, C RBη0 is the nominal value of C RBη , C Aη0 is the nominal value of C Aη , D η0 is the nominal value of D η , g η0 is the nominal value of the force and moment vectors generated by gravity and buoyancy, u c is the control amount of the propeller, ΔM η , ΔC RBη , ΔC Aη , Δg η are the uncertainties of M η , C RBη , C Aη , g η , is the external ocean current disturbance d, term represents the AUV's own model uncertainty;

[0084] Then, define the intermediate variable then formula (21) is rewritten as follows:

[0085]

[0086]

[0087]

[0088]

[0089] wherein formula (23) is a transformed AUV dynamics model;

[0090] The purpose of the present application is to combine preset time control technology and preset performance control technology to design a new controller, and to optimize trajectory tracking effect from two dimensions of convergence time and control performance constraints.In addition, an adaptive lumped disturbance estimator is designed to estimate ocean current disturbance and model uncertainty.Combining actual engineering conditions, the following assumptions are made:

[0091] Assumption 1: the expected position and the first and second derivatives of the AUV attitude vector are all known bounded functions.

[0092] Assumption 2: the lumped disturbance is unknown but bounded, that is, wherein k di is a known constant, and i=1, 2, 3, 4, 5, 6.

[0093] In the design process of the AUV controller, the present application mainly uses stability proof theory formula, Lyapunov stability theory considers a nonlinear system in continuous time:

[0094]

[0095] wherein x s ∈R n , f:R n ×R + →R n , x s is a state vector, t is time, and f(x s , t) is a function related to x s and t;

[0096] The Lyapunov stability theory in this step comes from the literature (Krstic M, Kokotovic P V, Kanellakopoulos I. Nonlinear and adaptive control design [M]. John Wiley & Sons, Inc, 1995.); the nonlinear system comes from the literature (Sánchez-Torres J D, Gómez-Gutiérrez D, López E, et al. A class of predefined-time table dynamical systems [J]. IMA Journal of Mathematical Control and Information, 2018.).

[0097] If the origin of the system is asymptotically stable within the convergence time T(x s0 ), and the convergence time function is bounded, that is, there is a normal number T c , such that the following conditions are met, and T c can be preset.

[0098]

[0099] The nonlinear system (3) is called stable within the preset time T c .

[0100] At time t0≥0, the initial value of the above nonlinear system is x s (t0; x s0 , t0) = x s0 , and the solution of the nonlinear system is x s (t; x s0 , t0). The solution can be divided into the following cases:

[0101] (1) bounded, assuming that there is a constant B(x s0 , t0) > 0, which satisfies:

[0102]

[0103] Where t0 is the initial time, and x s0 is the state vector at the initial time;

[0104] (2) stable, for any ε > 0, there is a constant value δ(ε, t0) > 0, which satisfies:

[0105]

[0106] Where, is xs0 perturbed state vector;

[0107] (3) asymptotically stable, there is a constant r(t0) > 0, and for any ε > 0, there is a constant T(ε, t0) > 0, satisfying:

[0108]

[0109] (4) unstable, there is a certain ε > 0, no matter how small the numerical δ(ε, t0) is, there is:

[0110]

[0111] Step three, establish a performance function, convert the trajectory tracking error by using the performance function and the deformed AUV dynamics model, so as to obtain the converted trajectory tracking error vector:

[0112] Define the trajectory tracking error e i (t):

[0113] e i (t) = η ai - η di

[0114] Wherein, e i (t) is the trajectory tracking error of the i-th degree of freedom at time t, and in the formula, η ai , η di Indicate η ai (t), η di (t), respectively, represent the actual position and attitude of AUV at time t and the expected position and attitude of AUV at time t;

[0115] In order to constrain the trajectory error of the AUV, the performance function is introduced as the upper and lower boundary of the AUV. The performance function is defined as follows:

[0116] For a continuous function ρ(t): R + → R, if the function satisfies the following two conditions:

[0117] (1) ρ(t) is positive and strictly decreasing;

[0118] (2)

[0119] Wherein, ρ ∞ is a predetermined normal number;

[0120] Then the function is a performance function, and a common performance function is as follows:

[0121] ρ(t) = (ρ0- ρ ∞ )e-kt + p ∞ (24)

[0122] where p0, k are preset constants;

[0123] The performance function is from the literature (Bechlioulis C P, Rovithakis G A. Prescribed performance adaptive control of SISO feedback linearizable system with disturbances [C]. Proceedings of 16th Mediterranean Conference on Control and Automation, 2008: 1035-1040.);

[0124] The tracking error is expressed by the performance function as:

[0125]

[0126] where 0 < d i < d i is the performance function coefficient of the i-th degree of freedom trajectory tracking, p i (t) is the performance function of the i-th degree of freedom trajectory tracking at time t, e i (t) is the i-th degree of freedom trajectory tracking error at time t;

[0127] According to the performance function formula (25), if the initial value of the tracking error satisfies 0 < |e i (0) | < p i (0), the parameter k i limits the minimum convergence rate of the tracking error, and p i∞ gives the upper and lower bounds of the allowed steady-state tracking error, and the overshoot of the system response will not exceed d i p i (t). Therefore, by designing appropriate performance function p i (t) and d i , the desired system error response can be obtained;

[0128] where e i (0) is the initial tracking error of the i-th degree of freedom, p i (0) is the initial tracking performance function value of the i-th degree of freedom, e i (t) is the i-th degree of freedom tracking error at time t;

[0129] In actual controller design, it is difficult and complicated to deal with the constraint inequality of the tracking error directly. Therefore, it is necessary to transform the error to obtain a new error transformation function S i (ε i ) to control the design of the controller and the constraint property does not change. The error transformation process is as follows:

[0130] Define the error transformation function S i (ε i ) with the following properties:

[0131] (1), S i (ε i ) is smooth and strictly monotonically increasing;

[0132] (2),

[0133] (3),

[0134] wherein ε i ∈(-∞,+∞), ε i is the transformed error, and a function S i (ε i ) satisfying the above conditions is given by the following formula:

[0135]

[0136] According to the characteristics of S i (ε i ), formula (26) can be equivalently expressed as:

[0137] e i (t) = p i (t) S i (ε i ) (27)

[0138] Because S i (ε i ) is strictly monotonically increasing, there exists an inverse function:

[0139]

[0140] If ε i can be controlled to be bounded, formula (25) can be guaranteed to be established, and the tracking error can be guaranteed to achieve the desired target under the constraint of the performance function p i (t). At this time, the tracking control problem of the system is transformed into the stable control problem of the closed-loop system with ε i as the variable.

[0141] Let z i = e i(t) / p i (t), the error transformation function S i (t), the error transformation function S i is transformed into the following form:

[0142]

[0143] Let ε i The first and second order derivatives of time t are taken:

[0144]

[0145]

[0146]

[0147] where r i is an intermediate variable, e i , p i , S i -1 is is the second order derivative of the actual position and attitude of the AUV, is the second order derivative of the desired position and attitude of the AUV;

[0148] Since and p i (t) > 0, r i is always greater than zero, and the upper and lower bounds of r i are When the trajectory of the error e i (t) is strictly limited within the range of equation (25), r and are normal numbers.

[0149] The new error variable s ∈ R 6 can take the following form:

[0150]

[0151] In the formula, ε = [ε1, ε2, ε3, ε4, ε5, ε6] T , ε is the transformation error vector, ε i is the transformation error of the i-th degree of freedom trajectory tracking, λ = diag [λ1, λ2, λ3, λ4, λ5, λ6] > 0, λ is a pre-set controller parameter vector, λ i is the controller parameter of the i-th degree of freedom;

[0152] The transformed trajectory tracking error vector is obtained in combination with equation (23):

[0153]

[0154] L = [l1, l2, l3, l4, l5, l6] T

[0155]

[0156] R = diag[r1,r2,r3,r4,r5,r6]

[0157] Where R and L are intermediate vectors, l i The intermediate variables are s = [s1, s2, s3, s4, s5, s6], which is the trajectory tracking error vector. i It is the trajectory tracking error of the i-th degree of freedom;

[0158] So when controller u c When s is asymptotically convergent, ε i and It also converges asymptotically. The preset performance control method, by introducing a performance function and error transformation, enables the convergence speed, overshoot, and tracking error to obtain preset performance, thus relaxing the requirements for the selection of control parameters to a certain extent.

[0159] The convergence time can be preset and is independent of the initial state of the system. Before designing a preset time controller, the following lemma related to the stability of the preset time needs to be introduced.

[0160] Lemma 1: Consider a class of nonlinear systems make Let be a set containing the origin. For nonlinear systems... Construct a class of smooth positive definite function V defined on set U. a (x s If there exists a set For any x s If ∈U0\{0}, then V a (x s It can satisfy the following inequalities:

[0161]

[0162] Where λ a >0, λ b >0, T c >0, 0<β<1, 0<η b <+∞. Then, for nonlinear systems... It is time-stable. Additionally, there exists a positive constant θ. a <1, so that the state of the nonlinear system can be maintained within a preset time. Convergence. That is:

[0163]

[0164] and the lemma needed in the proof of Lyapunov stability.

[0165] Lemma 1 is from the literature (Wu C H, Yan J G, Shen J H, et al. Predefined-time attitude stabilization of receiver aircraft in aerial refueling [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, 68(10): 3321-3325.).

[0166] Lemma 2: For a vector x v ∈R n and a matrix Q n×n ∈R v , if the matrix Q is a positive definite symmetric matrix, then for any x v ≠0, the following inequality holds: T Qx v > 0 and v T Qx v satisfies the following inequality:

[0167] λ min (Q)||x v || 2 ≤ x v T Qx v ≤ λ max (Q)||x v || 2

[0168] Lemma 2 is from the literature (Rami M A, Zhou X Y. Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls [J]. IEEE Transactions on Automatic Control, 2000, 45: 1131-1143.).

[0169] Lemma 3: For any constant z c ∈R, there exists any positive real number ε a > 0, such that and usually take

[0170] Lemma 3 is from the literature (Polycarpou M M, Stable adaptive neural control scheme for nonlinear systems[J]. IEEE Trans. Autom. Control, vol. 41, no. 3, pp. 447-451, Mar. 1996.).

[0171] Step four, using the trajectory tracking error vector obtained in step three to design an adaptive lumped disturbance estimator, specifically:

[0172] The present application comprehensively considers the ocean current disturbance and model uncertainty as a lumped disturbance The hyperbolic tangent function is adopted to ensure that the estimated value and the actual value can converge smoothly and smoothly, and the expression of the adaptive lumped disturbance estimator is as follows:

[0173]

[0174] Wherein, ε i is the transformation error of the trajectory of the i-th degree of freedom, s i is the component of the vector s (trajectory tracking error of the i-th degree of freedom), k di is a constant.

[0175] Step five, using the trajectory tracking error variable obtained in step three and the adaptive lumped disturbance estimator designed in step four to design an adaptive attitude tracking controller, specifically:

[0176] Combined with the above lumped disturbance estimator and based on the preset performance control error form and the preset time control theorem form, the final AUV preset time trajectory tracking controller u c considering external disturbance and performance function constraint can be obtained:

[0177]

[0178]

[0179]

[0180] Wherein, λ min (R) is the minimum eigenvalue of the matrix R, T c is the preset time period, T c > 0, λ a > 0, λ b > 0, 0 < β < 1, β, λ a , λ b are positive constants.

[0181] Step six, verify the preset time convergence characteristics of the adaptive attitude tracking controller designed in step five, specifically:

[0182] Theorem 1: For the AUV dynamics model considering the influence of ocean current disturbance and model uncertainty, under the action of the preset time trajectory tracking controller and the adaptive lumped disturbance estimator of the AUV, the trajectory tracking error of the AUV can converge within a preset time and reach a preset control precision.

[0183] Proof: Select the following Lyapunov function:

[0184]

[0185] Take the derivative with respect to time and substitute the control rate u c It can be obtained:

[0186]

[0187] From Lemma 2, we have:

[0188] λ min (R)||s|| 2 ≤s T Rs≤λ max (R)||s|| 2 (38)

[0189] Substituting formula (38) into formula (37) gives:

[0190]

[0191] Also:

[0192]

[0193] Substituting formula (34) into formula (40) gives:

[0194]

[0195] From Lemma 3, the above formula can be transformed as:

[0196]

[0197] Let Substituting formula (42) into formula (39) gives:

[0198]

[0199] It meets the form in Lemma 1, has preset time convergence characteristics, and the proof is complete.

[0200] Theorem 2: Under the above conditions, the trajectory tracking error of the AUV converges to a certain set within time, and the preset time convergence characteristic can be achieved by the controller u c The convergence time is preset

[0201] Proof: Rewrite equation (43) as:

[0202]

[0203] or

[0204]

[0205] Discuss two cases:

[0206] Case 1: When , there is:

[0207]

[0208] Case 2: When , there is:

[0209]

[0210] Next, stability analysis is performed for case 1. From equation (46), we have:

[0211]

[0212] Let s0 represent the initial state of the AUV system, and t(s0) represent the time from the initial state to system stability. Take the integral of both sides of equation (47) over t∈(0,t(s0)) to obtain:

[0213]

[0214] The right side of the expression is calculated as:

[0215]

[0216] Substitute equation (49) to obtain:

[0217]

[0218] Since , substitute equation (51) to obtain Therefore, under case 1, the AUV system converges to the set: within time.

[0219]

[0220] Similarly, according to the above derivation, in case two, the AUV system converges to the set in time

[0221]

[0222] In summary, the AUV preset trajectory tracking controller can ensure that the trajectory tracking error converges to the set in time

[0223]

[0224] Thus, the proof of Theorem 2 is complete.

[0225] Embodiment:

[0226] In order to verify the effectiveness of the present application, the "Star Sea Z3000" bottom dwelling AUV is selected for numerical simulation experiment. The full drive AUV and its propeller arrangement are shown in Figure 2 The hydrodynamic coefficients and inertia coefficients of the AUV are shown in Table 1 and Table 2, respectively. The hydrodynamic coefficients include inertia force coefficients, viscous force coefficients and added mass coefficients. Due to the existence of the actual propeller thrust upper limit, a saturation output thrust upper limit of 100N is set in the simulation experiment.

[0227] Table 1 AUV hydrodynamic coefficients

[0228]

[0229] Table 2 AUV inertia coefficients

[0230]

[0231] To solve the problem of ocean current disturbance and model uncertainty, the present application proposes an adaptive disturbance estimator to estimate it. In the simulation experiment, the nominal value of 20% is set as the model uncertainty influence, which is expressed as:

[0232]

[0233] The selected ocean current disturbance d is in the form of a triangular function, and the form of the set ocean current disturbance is as follows:

[0234]

[0235] The descending spiral trajectory is a commonly used trajectory in AUV simulation experiments, which includes multiple degrees of freedom of AUV movement. Therefore, the present application selects a spiral as the expected trajectory, and selects the expected trajectory η d as follows:

[0236]

[0237] The initial position and attitude η0 of the AUV are set as shown in Table 3;

[0238] Table 3 Initial Position and Attitude of AUV

[0239]

[0240] Based on the above AUV simulation model and the parameter settings for external interference, the parameters of the adaptive interference estimator were determined. d The ε parameter is set to k. d =[2,2,2,2,2,2] T ,ε=[0.1,0.1,0.1,0.1,0.1,0.1] T The parameters of the performance function are set to ρ0 = [1.8, 1.8, 2.3, 2.4, 1.8, 2.8], ρ ∞ =0.001, k=0.3. The preset parameters of the time trajectory tracking controller are set to β=0.5, T c =15, λ a =1,λ b =1. According to Theorem 2, the AUV trajectory tracking error will be at this point. It converges to the pre-set control steady state within a time limit of 21.210s.

[0241] Based on the parameters of the adaptive interference estimator, the parameters of the performance function, and the parameters of the preset time controller, the controller of the present invention was simulated and verified using numerical simulation software. The simulation results of the AUV preset time trajectory tracking controller considering external interference and performance function constraints are shown in Figures 3(a) to 3(b). Figure 11 As shown.

[0242] When using an AUV preset time trajectory tracking controller that considers external interference and performance function constraints, the AUV six-degree-of-freedom trajectory tracking error curve is as follows: Figures 3(a)-3(f) As shown, ρ and -ρ represent the upper and lower bounds of the trajectory tracking error, respectively; Figure 3(a) shows the trajectory tracking error curve in the AUV's pitch direction, Figure 3(b) shows the trajectory tracking error curve in the AUV's sway direction, Figure 3(c) shows the trajectory tracking error curve in the AUV's heave direction, Figure 3(d) shows the trajectory tracking error curve in the AUV's roll direction, Figure 3(e) shows the trajectory tracking error curve in the AUV's pitch direction, and Figure 3(f) shows the trajectory tracking error curve in the AUV's bow direction. Enlarged views at preset time points are shown below. Figure 4 As shown. By Figures 3(a)-3(f) It can be seen that the performance function constraint method proposed in this invention can ensure that the trajectory errors of the six degrees of freedom of the AUV are constrained within the upper and lower bounds of the performance function, and the final steady-state error also reaches the preset value. Figure 4It can be seen that the AUV preset time trajectory tracking controller proposed in this invention can track the trajectory within a preset time. This allows the six-degree-of-freedom trajectory tracking error to converge, achieving the preset time control effect. Figure 5 and Figure 6 The output control torque and control force curves of the AUV thruster are presented respectively. It can be seen that under the action of the above controller, the output force is within the set output saturation upper limit of 100N, which meets the actual requirements of the AUV. Figures 7 to 9 The trajectory curves of the AUV in the longitudinal, transverse, and helical directions are given, while Figure 10 The motion trajectory curve of the AUV in three-dimensional space is given, and the arrows in the figure indicate the direction of AUV motion. Figure 11 The effects of external disturbances on the AUV are demonstrated. It can be seen that the AUV preset time trajectory tracking controller designed in this invention, which considers external disturbances and performance function constraints, can ensure that the AUV moves to the desired trajectory under the influence of external ocean current disturbances and model uncertainties, thus achieving the trajectory tracking task.

[0243] The simulation results above demonstrate the effectiveness of the AUV preset time trajectory tracking controller of the present invention, which considers external disturbances and performance function constraints. It proves that the controller proposed in this invention can ensure that the AUV trajectory tracking error converges within a preset time and is constrained within the upper and lower bounds of the performance function under ocean current disturbances and model uncertainties, thereby achieving the desired trajectory tracking objective.

Claims

1. A method for AUV preset time trajectory tracking control considering performance constraints and interference effects, characterized in that... The specific process of the method is as follows: Step 1: Establish the kinematic model of the AUV using its six-degree-of-freedom position and attitude in the inertial coordinate system; Step 2: Establish the AUV dynamic model based on the AUV kinematic model obtained in Step 1; Step 3: Establish a performance function, and use the performance function and AUV dynamics model to transform the trajectory tracking error, obtaining the transformed trajectory tracking error vector, specifically: Step 31: Establish the performance function, specifically as follows: ρ(t)=(ρ0-ρ ∞ )e -kt +r ∞ ρ(t) simultaneously satisfies the following conditions: (1) ρ(t) is positive and strictly decreasing; (2) Where ρ0, k, ρ ∞ t is a preset positive constant, where t is time; Step 32: Use the performance function ρ(t) and AUV dynamics model established in Step 31 to transform the trajectory tracking error and obtain the transformed trajectory tracking error vector; Step 4: Design an adaptive lumped disturbance estimator using the trajectory tracking error vector obtained in Step 3, specifically as follows: Where, k di It is a constant, i∈[1,6], where i is the degree of freedom label, ε i It is the transformation error of the trajectory tracking of the i-th degree of freedom, s i It is the trajectory tracking error of the i-th degree of freedom; Step 5: Design an adaptive attitude tracking controller using the trajectory tracking error vector obtained in Step 3 and the adaptive lumped disturbance estimator obtained in Step 4.

2. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 1, characterized in that: The step one, which involves establishing the AUV's kinematic model using its six-degree-of-freedom position and attitude in the inertial coordinate system, specifically involves: in, x is the linear displacement of the AUV in the sway direction in the inertial coordinate system, y is the linear displacement of the AUV in the yaw direction in the inertial coordinate system, and z is the linear displacement of the AUV in the heave direction in the inertial coordinate system. θ is the roll angular displacement of the AUV in the inertial coordinate system, ψ is the pitch angular displacement of the AUV in the inertial coordinate system, and J(η) is the bow angular displacement of the AUV in the inertial coordinate system. a J1(η) is the transformation matrix between the inertial coordinate system and the moving coordinate system. a J2(η) is the linear velocity transfer matrix. a ) is the angular velocity transfer matrix, O 3×3 It is a 3x3 zero matrix, V = [u, v, w, p, q, r] T denoted as , where u is the velocity and angular velocity of the AUV in the moving coordinate system, v is the velocity of the AUV in the sway direction in the moving coordinate system, w is the velocity of the AUV in the heave direction in the moving coordinate system, p is the angular velocity of the AUV in the roll direction in the moving coordinate system, q is the angular velocity of the AUV in the pitch direction in the moving coordinate system, and r is the angular velocity of the AUV in the bow direction in the moving coordinate system.

3. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 2, characterized in that: The step two, which involves establishing an AUV dynamic model based on the AUV kinematic model obtained in step one, specifically involves: Step 2.1: Establish the dynamic model of the AUV, specifically as follows: M η =MJ -1 (η a ) V r =VV c Among them, M η C RBη C Aη D η , It is the intermediate matrix. It is η a The second derivative, It is η a The first derivative, g η It is a vector of forces and moments generated by gravity and buoyancy, M is a coefficient matrix, and C is a vector of forces and moments generated by gravity and buoyancy. RB (V) is the rigid body centripetal force matrix, τ is the control force and torque generated by the propulsion system, W is the total gravity acting on the AUV, B is the total buoyancy acting on the AUV, and Z... B It is the vertical coordinate value of the center of buoyancy, V. r V is the speed of the AUV relative to the ocean current. c It is the velocity of the ocean current in the moving coordinate system, I X It is the moment of inertia of the AUV about the X-axis of the motion coordinate system, I Y It is the moment of inertia of the AUV about the Y-axis of the motion coordinate system, I Z It is the moment of inertia of the AUV about the Z-axis of the motion coordinate system, I XY It is the product of inertia of the AUV about the X and Y axes of the motion coordinate system, I XZ It is the product of inertia of the AUV about the X and Z axes of the moving coordinate system, I YZ is the product of inertia of the AUV about the Y-axis and Z-axis of the motion coordinate system, and m is the mass of the AUV itself; Step 22: Based on the AUV dynamic model established in Step 21, the AUV dynamic model is rewritten to consider system uncertainties and ocean current disturbances.

4. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 3, characterized in that: The coefficient matrix M is as follows: M=M RB +M A Among them, M RB M is the rigid body mass and inertia matrix. A It is a hydrodynamic auxiliary matrix. It is about The first-order hydrodynamic coefficient, It is about The first-order hydrodynamic coefficient, It is about The first-order hydrodynamic coefficient, It is about The first-order hydrodynamic coefficient, It is about The first-order hydrodynamic coefficient, It is about The first-order hydrodynamic coefficient.

5. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 4, characterized in that: intermediate matrix C Aη Specifically: C Aη =C A (V r )J -1 (η a ) Among them, C A (V r ) is a Coriolis force matrix, where a1, a2, a3, b1, b2, and b3 are intermediate variables.

6. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 5, characterized in that: In step 22, based on the AUV dynamic model established in step 21, the AUV dynamic model is rewritten considering system uncertainties and ocean current disturbances, as follows: Among them, A,H, M is an intermediate variable. η0 It is M η The nominal value, u c It is the control quantity of the thruster, C RBη0 It is C RBη The nominal value, C Aη0 It is C Aη The nominal value, D η0 It is D η The nominal value, g η0 It is g η The nominal value of B0 is the nominal value of the thrust distribution matrix, and F is the total uncertainty of the system.

7. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 6, characterized in that: intermediate matrix D η Specifically D η =D(V r )J -1 (η a ) D(V r )=-diag{D L +D Q |ν|} D L =diag{X u ,Y v ,Z w ,K p ,M q ,N r } D Q =diag{X u|u| ,Y v|v| ,Z w|w| ,K p|p| ,M q|q| ,N r|r| } Among them, D(V) r ) is the hydrodynamic damping matrix, D L It is the linear motion drag coefficient matrix, D Q It is the angular motion drag coefficient matrix, X u It concerns the hydrodynamic coefficient of u, Y v It concerns the hydrodynamic coefficient of v, Z w It concerns the hydrodynamic coefficient of w, K p It refers to the hydrodynamic coefficient of p, M q It is the hydrodynamic coefficient related to q, N r It refers to the hydrodynamic coefficient of r, X u|u| It is the hydrodynamic coefficient of u|u|, Y ν|ν It concerns the hydrodynamic coefficient Z of v|v|. w|w| It concerns the hydrodynamic coefficient of w|w|, K p|p| It concerns the hydrodynamic coefficient of p|p|, M q|q| It concerns the hydrodynamic coefficient q|q|, N r|r| It refers to the hydrodynamic coefficient r|r|.

8. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 7, characterized in that: In step two two Specifically: Where, ΔM η ΔC RBη ΔC Aη Δg η They are M η C RBη C Aη g η The uncertainty value, It's due to interference from external ocean currents.

9. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 8, characterized in that: In step three-two, the performance function ρ(t) and the AUV dynamics model established in step three-one are used to transform the trajectory tracking error to obtain the transformed trajectory tracking error vector, specifically: First, define the trajectory tracking error e at time t for the i-th degree of freedom. i (t): e i (t)=η ai (t)-η di (t) Where, η ai (t) represents the actual position and attitude of the AUV at time t, η di (t) represents the expected position and attitude of the AUV at time t; Then, the trajectory tracking error e i (t) is transformed to obtain the transformed trajectory tracking error: λ=diag[λ1,λ2,λ3,λ4,λ5,λ6]>0 e=[e1,e2,e3,e4,e5,e6] T R = diag[r1,r2,r3,r4,r5,r6] L＝[l1,l2,l3,l4,l5,l6] T z i =e i (t) / ρ i (t) Where s is the transformed trajectory tracking error vector, s i ε is the trajectory tracking error of the i-th degree of freedom after transformation, and ε is the transformation error vector. It is the first derivative of ε. It is the second derivative of ε, ε i λ is the transformation error of trajectory tracking for the i-th degree of freedom, and λ is the controller parameter vector. i These are the controller parameters for the i-th degree of freedom, where L and R are intermediate vectors. i z i r i It is an intermediate variable. It is the error transformation function, e i (0) is the tracking error at the start time of the i-th degree of freedom, e i (t) is the tracking error at time t for the i-th degree of freedom, δ i ρ is the coefficient of the performance function for trajectory tracking in the i-th degree of freedom. i (t) is the performance function for trajectory tracking of the i-th degree of freedom. It is the second derivative of the actual position and attitude of the AUV at time t. It is the second derivative of the expected position and attitude of the AUV at time t.

10. The AUV preset time trajectory tracking control method considering performance constraints and interference effects according to claim 9, characterized in that: The fifth step, which involves designing an adaptive attitude tracking controller using the trajectory tracking error vector obtained in step three and the adaptive lumped disturbance estimator obtained in step four, specifically involves: Where, λ min (R) is the smallest eigenvalue of matrix R, T c It is a preset time period, T c >0, λ a >0, λ b >0, 0<β<1, β, λ a , λ b It is a constant.

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