Under-actuated AUV (Autonomous Underwater Vehicle) preset performance trajectory tracking control method and system based on RBF (Radial Basis Function) ocean current observer

Abstract

The invention discloses an under-actuated AUV (Autonomous Underwater Vehicle) preset performance trajectory tracking control method and system based on an RBF (Radial Basis Function) ocean current observer, and the method comprises the steps: building an under-actuated AUV three-degree-of-freedom model containing unknown time-varying ocean current interference, introducing a preset performance control theory, converting a constrained position tracking error into an unconstrained conversion error through an error transformation function, and obtaining an unconstrained position tracking error; and strict constraint on transient overshoot and steady-state errors is realized. Secondly, a finite time convergence ocean current observer based on an RBF neural network is designed, a nonlinear power term is introduced as a correction term, and rapid and high-precision estimation of unknown time-varying ocean current is achieved. And finally, based on a backstepping method strategy, designing a kinematics virtual control law and a dynamics actual control moment by using the conversion error and the ocean current estimated value. According to the method, the problems of uncontrollable AUV trajectory tracking transient performance and ocean current estimation lag in the prior art are solved, and the trajectory tracking precision and robustness of the under-actuated AUV under the complex ocean condition are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of underwater robot control technology, specifically to a method and system for trajectory tracking control of underactuated autonomous underwater vehicles (AUVs) that combines Prescribed Performance Control (PPC) with finite-time observer technology, considering unknown time-varying ocean current interference, model uncertainty, and strict performance constraints. Background Technology

[0002] Autonomous underwater vehicles (AUVs) are playing an increasingly important role in both military and civilian fields, such as marine resource exploration, seabed topography mapping, environmental monitoring, pipeline inspection, and military reconnaissance, due to their superior autonomous decision-making capabilities and flexible maneuverability. In these complex tasks, high-precision trajectory tracking control is the core foundation for AUVs to achieve autonomous operation. However, AUV trajectory tracking control faces several severe challenges. First, AUVs are typically underactuated systems, with their control input dimension being less than their three degrees of freedom in the horizontal plane. This means that the lateral (sway) motion of the AUV cannot be directly controlled and can only be indirectly adjusted through the yaw coupling effect, which greatly increases the complexity of controller design.

[0003] Secondly, the marine environment is complex and variable, and ocean current interference is unavoidable. Furthermore, ocean currents often exhibit significant time-varying and spatial non-uniformity. Ocean currents not only cause kinematic drift in AUVs but also act as external torques, causing dynamic disturbances. Simultaneously, the dynamic model of an AUV possesses strong nonlinearity and high coupling characteristics, and hydrodynamic parameters are difficult to obtain accurately, resulting in high model uncertainty and further reducing the system's robustness. To address these challenges, existing backstepping methods or conventional adaptive control methods, while ensuring asymptotic stability, cannot pre-set and strictly constrain the transient processes of tracking errors (such as initial overshoot and convergence speed), leading to problems such as large overshoot and long convergence times in the early stages of trajectory tracking. Moreover, for compensation of time-varying ocean currents, the convergence speed of traditional linear observers or conventional neural network observers is usually asymptotic. When facing rapidly changing and strong disturbances, the estimation lag is significant, making it difficult to meet the real-time compensation requirements of AUVs. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for trajectory tracking control of underactuated AUVs based on RBF current observers. By combining the PPC mechanism with a nonlinear fast observer based on RBF neural networks, the constrained trajectory tracking problem is transformed into an unconstrained stable problem. At the same time, the nonlinear power term is used to achieve fast and accurate compensation for time-varying ocean currents, solving the problems of difficult-to-guarantee transient performance of AUV trajectory tracking, insufficient estimation speed of time-varying ocean currents, and slow convergence of traditional observers in the above-mentioned background technology.

[0005] This invention provides the following technical solution: a pre-set performance trajectory tracking control method for underactuated AUVs based on RBF current observers, comprising the following operational steps:

[0006] Step S1: Construct a horizontal three-degree-of-freedom kinematic and dynamic model of the underactuated autonomous underwater vehicle that includes unknown time-varying ocean current disturbance terms.

[0007] Preferably, an inertial coordinate system I-ξη and a volume coordinate system Bx are defined. b y b A three-degree-of-freedom kinematic and dynamic model of the AUV in the horizontal plane, considering time-varying ocean current disturbances, was established. The models explicitly include the ocean current velocity component in the inertial frame (d...). x ,d y ) and the dynamic disturbance term in volume coordinates (d u ,d v ,d r Based on this, the motion of the AUV in the horizontal plane consists of three degrees of freedom: longitudinal (Surge), lateral (Sway), and yaw.

[0008] Step S2: Define a preset performance function for the position tracking error, transform the original position error into an unconstrained conversion error, and derive the dynamic equation of the conversion error.

[0009] Preferably, by introducing Preset Performance Control (PPC) theory, a preset performance function ρ(t) for the position tracking error is defined. This function strictly sets the upper and lower bounds of error convergence, the minimum convergence rate, and the steady-state error range. Using a nonlinear error transformation function, the constrained original position error e is transformed into an unconstrained transformation error z, and the time-varying gain matrix Λ generated by the PPC transformation and the known dynamic term F are derived. z The dynamic equation for the conversion error.

[0010] Step S3: Construct a finite-time convergent ocean current observer based on RBF neural network, use RBF neural network to approximate ocean current components, output the estimated value of ocean current disturbance and compensate for it.

[0011] Preferably, for the unknown ocean current disturbance term included in the dynamic equation of the transformation error z, this invention designs a novel nonlinear fast observer. This observer utilizes a radial basis function neural network (RBFNN) to approximate the unknown ocean current dynamic function online, and couples the PPC transform gain Λ into the observer structure. Simultaneously, to improve the convergence performance of the observer, a nonlinear power term is introduced into the observer's correction term, specifically in the form of… and (where 0 < α < 1 < β), achieving finite-time convergence of observation errors. Compared to traditional linear correction terms, this nonlinear convergence acceleration term has the following advantages:

[0012] Fast convergence with large errors: When the observation error is large, terms with an exponent β > 1 converge quickly. It plays a dominant role, providing a larger feedback gain than the linear term, which prompts the system state to quickly enter the small error region;

[0013] Small error finite-time convergence: When the observation error is small, terms with an exponent of 0 < α < 1... This design plays a dominant role, with its derivative approaching infinity near the origin, thus avoiding the "tailing" phenomenon of asymptotic convergence at the end and achieving rapid convergence within a finite time. Through this design, the observer can quickly and accurately track and estimate time-varying ocean currents.

[0014] Step S4: Based on the error after preset performance conversion, the estimated value of ocean current disturbance and dynamic uncertainty parameters, a trajectory tracking controller is constructed using the backstepping strategy.

[0015] Preferably, it includes a kinematic virtual control law u designed for the conversion error z. rd ,v rd And the actual thrust τ designed for velocity error μ and torque τ r The control law is as follows:

[0016] Kinematic circuit: Designing a virtual control law u rd (desired longitudinal velocity) and v rd (Desired lateral velocity). In this step, ocean current observations are used directly. To compensate for drift caused by ocean currents, this invention selects the lateral velocity v in the design of the virtual control law. r As a virtual control object, rather than a heading angle-related quantity in traditional methods, this helps to handle the lateral error of underactuated systems more directly.

[0017] Dynamics Loop: To address the underactuated characteristics, a virtual control law ro for the bow roll rate r is designed using the coupled dynamics characteristics of the AUV. d In order to indirectly control the lateral velocity error ve Convergence. Finally, design the actual longitudinal thrust τ. u and bow roll torque τ r To achieve the desired longitudinal velocity u rd and virtual control law r d Tracking. A robust sign function term is introduced into the control law to overcome parameter uncertainties and residual disturbances in the dynamic model.

[0018] Step S5: Construct a composite Lyapunov function that includes transformation error, velocity error, observer error, and neural network weight estimation error, and perform system stability analysis and control law solution.

[0019] Preferably, using Lyapunov stability theory, a composite Lyapunov function incorporating conversion error, velocity error, observer error, and neural network weight estimation error is constructed, proving the uniform eventual boundedness (UUB) of all signals in the closed-loop system. Based on the boundedness of the conversion error, it is rigorously proven that the original position error e always remains within the performance boundary defined by the preset performance function ρ(t). Finally, based on real-time sensor data, the control law is solved and output to the actuator.

[0020] On the other hand, the present invention provides an underactuated AUV preset performance trajectory tracking control system based on an RBF current observer, which executes an underactuated AUV preset performance trajectory tracking control method based on an RBF current observer, including: an environment perception and state acquisition module, a preset performance transformation module, a finite-time current observation module, a backstepping tracking control module, and an actuator drive module.

[0021] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0022] (1) Strictly controllable performance: Through the PPC mechanism, this invention achieves strict and adjustable constraints on the transient performance (overshoot, convergence speed) and steady-state performance (steady-state error range) of tracking error in underactuated AUV trajectory tracking for the first time, which greatly enhances the engineering practical value of the control system.

[0023] (2) Fast observation speed and high accuracy: This invention introduces a nonlinear convergence acceleration term into the RBF neural network observer and utilizes its different characteristics in the large and small error stages to achieve finite-time convergence of the observation error, which significantly improves the observer's ability to directly offset the influence of environmental interference on trajectory tracking and enhances the robustness of the system under complex sea conditions.

[0024] (3) Underactuated processing: The backstep controller designed for underactuated characteristics in this invention does not require a lateral thruster and achieves full-state constraint control by relying solely on longitudinal and yaw drives. It cleverly utilizes the dynamic response speed and steady-state estimation accuracy of the time-varying disturbance of yaw motion to lateral velocity.

[0025] (4) Strong anti-interference capability: This invention explicitly incorporates time-varying ocean currents into the controller design and performs feedforward compensation through an observer, thus achieving simultaneous convergence of position and attitude under underactuated conditions. Based on Lyapunov theory, a rigorous stability proof is given, ensuring the safety and reliability of the control system. Attached Figure Description

[0026] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0027] Figure 1 This is a schematic diagram of the overall structure of the underactuated AUV trajectory tracking control system provided in an embodiment of the present invention;

[0028] Figure 2 This is a schematic diagram of the kinematic model and coordinate system definition of an AUV in the inertial coordinate system and the volume coordinate system provided in this embodiment of the invention;

[0029] Figure 3 This is a schematic diagram comparing the straight-line trajectory tracking performance of AUVs under strong time-varying ocean current interference in the embodiments provided by the present invention;

[0030] Figure 4 This is a schematic diagram comparing the estimated and actual values ​​of unknown time-varying ocean current velocities obtained by the finite-time RBF observer provided in this embodiment of the invention.

[0031] Figure 5 This is a schematic diagram of the planar trajectory of an AUV tracking a figure-eight curve under complex ocean current interference, provided in an embodiment of the present invention.

[0032] Figure 6 This is a schematic diagram of the position tracking error and preset performance function envelope curve provided in the embodiment of the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Example 1

[0035] This invention provides the following technical solution: an underactuated AUV preset performance trajectory tracking control system based on an RBF ocean current observer, comprising:

[0036] The environmental perception and status acquisition module is used to acquire status information such as the AUV's position, attitude, and velocity.

[0037] The preset performance transformation module is used to convert position error into transformation error according to the set performance function;

[0038] The finite-time ocean current observation module has a built-in nonlinear fast ocean current observation algorithm for real-time output of ocean current estimates;

[0039] The backstepping tracking control module is used to calculate the control torque based on the conversion error, state information, and ocean current estimate.

[0040] The actuator drive module is used to respond to control commands and drive the thruster to move.

[0041] Example 2

[0042] Combination Figures 1-2 As shown, this invention focuses on underactuated AUVs in the horizontal plane. Under conditions of time-varying ocean currents and model uncertainties, it constrains the transient / steady-state performance of position errors through preset performance control (PPC), and achieves online estimation and compensation by combining an RBF neural network ocean current observer. Finally, it uses a backstepping method to construct the dynamic layer control input. This embodiment provides the following technical solution: a preset performance trajectory tracking control method for underactuated AUVs based on an RBF ocean current observer, including the following operational steps:

[0043] Step S1: Establish a mathematical model of the underactuated AUV, including the horizontal three-degree-of-freedom kinematic model and dynamic model of the underactuated autonomous underwater vehicle with unknown time-varying ocean current disturbance terms.

[0044] In this embodiment, as Figure 2 As shown, the inertial coordinate system I-ξη and the volume coordinate system Bx are defined. b y b A three-degree-of-freedom kinematic and dynamic model of the AUV in the horizontal plane, considering time-varying ocean current disturbances, was established. The models explicitly include the ocean current velocity component in the inertial frame (d...). x ,d y ) and the dynamic disturbance term in volume coordinates (d u ,d v ,d r ).

[0045] For example, the motion of an AUV in the horizontal plane consists of three degrees of freedom: surge, sway, and yaw. Considering the time-varying ocean current disturbance component V in the horizontal plane... dxy =[d x ,d y ] T The kinematic equations of an AUV can be expressed as:

[0046]

[0047] Where (x,y) is the position in the inertial frame, and ψ is the bow angle; (u r ,v r (d) represents the velocity of the AUV relative to the ocean current in body coordinates; r represents the bow roll rate; (d) represents the speed of the AUV relative to the ocean current in body coordinates. x ,d y Let be the ocean current velocity component in the inertial frame of reference, assuming the ocean current is bounded, i.e.

[0048] Underactuated AUVs typically only have longitudinal thrust τ u and bow roll torque τ r There is no direct lateral driving force. Its dynamic equations can be expressed in the following form:

[0049]

[0050] Among them, u u ,v r and r represent the longitudinal velocity, lateral velocity, and yaw rate of the AUV relative to the ocean current in body coordinates, respectively, and m 11 ,m 22 ,m 33 X(·), Y(·), and Z(·) are the equivalent masses (including additional masses) of the AUV in the longitudinal, lateral, and yaw directions, respectively; X(·), Y(·), and Z(·) are the linear and nonlinear hydrodynamic damping coefficients in the corresponding directions; τ u ,τ r The longitudinal thrust and yaw moment control inputs are generated by the thrusters and servo motors; d u ,d v ,d r The disturbances are lumped disturbances at the dynamic level, including hydrodynamic disturbances caused by ocean currents and uncertainties in model parameters, and all disturbances are assumed to be bounded unknowns.

[0051] Step S2: Define a preset performance function for the position tracking error, transform the original position error into an unconstrained conversion error, and derive the dynamic equation of the conversion error.

[0052] In this embodiment, Preset Performance Control (PPC) theory is introduced, defining a preset performance function ρ(t) for the position tracking error. This function sets the upper and lower bounds of error convergence, the minimum convergence rate, and the steady-state error range. Specifically, through a nonlinear error transformation function, the constrained original position error e is transformed into an unconstrained transformation error z, and the time-varying gain matrix Λ generated by the PPC transformation and the known dynamic term F are derived. z The dynamic equation for the conversion error. This is determined by defining the reference trajectory as P. d =[x d ,y d ] T The reference tangential velocity is Reference heading Furthermore, define the volume coordinate system Bx b y b The position tracking error vector is as follows:

[0053]

[0054] From the kinematic relationship, the error dynamic equation can be obtained as follows:

[0055]

[0056] Where, η n Let e ​​be the position tracking error vector. x e y x represents the longitudinal and lateral position error components, respectively. d y d ψ represents the reference coordinates of the reference trajectory. e =ψ-ψ d Heading angle error.

[0057] Further define the preset performance function and error component e x ,e y Performance boundary function ρ x (t),ρ y (t):

[0058] ρ i (t)=(ρ i0 -ρ i∞ )e -l,t +ρ i∞ ,i∈{x,y}

[0059] Where, p i0 >0 represents the initial performance boundary, ρ i∞ >0 represents the steady-state performance boundary, l>0 represents the decay rate of the performance function, and the constraint condition is: -δ 1i ρ i (t) <e i (t)<δ2i ρ i (t). For example, using a logarithmic error transformation function, the constrained original position error e can be transformed. x ,e y Converting to unconstrained transformation error z x ,z y Its form is:

[0060]

[0061] Where, ξ i =e i / ρ i δ 1i >0、δ 2i >0 corresponds to the upper / lower bound scaling of the error, respectively.

[0062] Further derivation of the transformed kinematic equations, according to the chain rule, yields... The derivative is expressed as:

[0063]

[0064] Where, ρ i For performance functions, Its time derivative, Let represent the time-varying gain generated by the PPC transformation, and it is known to be non-zero. The known dynamic term introduced for the change in the performance function is substituted into the above equation using the error dynamic equation. Expanding the above equation yields the equation based on the transformation error z:

[0065]

[0066] Among them, H x H y The dynamic term is known.

[0067] Step S3: Construct a finite-time convergent ocean current observer based on an RBF neural network.

[0068] In this embodiment, to address the unknown ocean current disturbance term included in the dynamic equation of the transformation error z, this invention designs a novel nonlinear fast observer. This observer utilizes a radial basis function neural network (RBFNN) to approximate the unknown ocean current dynamic function online and couples the PPC transform gain Λ into the observer structure. For observer design, the equation based on the transformation error z is rearranged into the following form:

[0069]

[0070] Where, η z To transform the error state vector, Fz (·) represents a known dynamic term of the system, η e V is the position error vector. r For virtual control input, g2(·) is the coordinate rotation matrix, V dxy For the ocean current disturbance to be observed, the above terms are defined as follows:

[0071] (1) State vector: η z =[z x ,z y ] T , where z x ,z y This is to transform the error components.

[0072] (2) Transformation gain matrix: Λ(t)=diag{G x G y}

[0073] (3) Known dynamic terms of the system:

[0074] (4) Virtual control input: V r =[u r ,v r ] T .

[0075] (5) Coordinate rotation matrix:

[0076] (6) Ocean current disturbance to be observed: V dxy =[d x ,d y ] T .

[0077] For example, the present invention designs a nonlinear fast observer based on an RBF neural network, which uses an RBF neural network to approximate ocean current components.

[0078] V dxy =W *T Φ(χ)+∈,||∈||≤∈ m

[0079]

[0080] Where, χ=[e x e y ] T Let Φ(χ) = [φ1(χ),…,φ1(χ),…,φ2 ... N (χ)] T , c i ,σ i These are the center and width parameters, respectively, Vdxy Let W be the ocean current disturbance vector to be observed. * It is an ideal weight matrix. is an online adjustable weight estimation matrix, ∈ is the bounded approximation error of the neural network, . The estimated value is obtained by approximating the unknown ocean current disturbance component through an RBF neural network. An observer is designed to estimate the state vector η. z The estimation of ocean currents is driven by observation errors, and the observer state vector is defined as η. p The observation error is Based on this, the following nonlinear fast observer is constructed:

[0081]

[0082] Wherein, the gain parameter k p ,k pα ,k pβ ,k pζ ,k ζα ,k ζβ ,K pζ >0, the exponent satisfies 0<α<1<β, Λ is the PPC transform gain matrix; ζ is the auxiliary state variable, taking... Based on the aforementioned observer structure, it can be seen that during Lyapunov analysis, there will be an intersection term relating to weight estimation error and ocean current disturbance. To eliminate this cross term and ensure system stability, the following adaptive weight update law is constructed: To eliminate Term, Adaptive Law We need to construct a new adaptive update law that can cancel out this term. Represented as:

[0083]

[0084] Wherein, the learning rate Γ is a symmetric positive definite matrix (or positive scalar), and Γ>0.

[0085] To improve the convergence performance of the observer, this invention introduces nonlinear power terms into the observer's correction terms, specifically in the form of: and (where 0 < α < 1 < β). This invention achieves finite-time convergence of observation errors by introducing a nonlinear power term. Compared to traditional linear correction terms, this nonlinear convergence acceleration term has the following advantages:

[0086] Fast convergence with large errors: When the observation error is large, terms with an exponent β > 1 converge quickly. It plays a dominant role, providing a larger feedback gain than the linear term, which prompts the system state to quickly enter the small error region;

[0087] Small error finite-time convergence: When the observation error is small, terms with an exponent of 0 < α < 1... This design plays a dominant role, with its derivative approaching infinity near the origin, thus avoiding the "tailing" phenomenon of asymptotic convergence at the end and achieving rapid convergence within a finite time. Through this design, the observer can quickly and accurately track and estimate time-varying ocean currents.

[0088] Step S4: Based on the obtained estimates of ocean current interference components and conversion errors, a backstepping strategy is used for trajectory tracking controller.

[0089] In this embodiment, a kinematic virtual control law u designed for the conversion error z is included. rd ,v rd And the actual thrust τ designed for velocity error μ and torque τ r The control law is as follows:

[0090] Kinematic circuit: Designing a virtual control law u rd (desired longitudinal velocity) and v rd (Desired lateral velocity). In this step, ocean current observations are used directly. To compensate for drift caused by ocean currents, this invention selects the lateral velocity v in the design of the virtual control law. r As a virtual control object, rather than a heading angle-related quantity in traditional methods, this helps to handle the lateral error of underactuated systems more directly.

[0091] Dynamics Loop: To address the underactuated characteristics, a virtual control law ro for the bow roll rate r is designed using the coupled dynamics characteristics of the AUV. d In order to indirectly control the lateral velocity error v e Convergence. Finally, design the actual longitudinal thrust τ. u and bow roll torque τ r To achieve the desired speed u rd and r d Tracking. A robust sign function term is introduced into the control law to overcome parameter uncertainties and residual disturbances in the dynamic model.

[0092] For example, due to the introduction of Preset Performance Control (PPC), the goal of the controller design is to minimize the transformed error z. x ,z y Convergence, thus guaranteeing the original error e x ,e y To satisfy the preset performance envelope, the specific implementation process includes:

[0093] Designing a kinematic loop - virtual control law: selecting a law with respect to the transformation error η z =[z x ,z y ] T The positive definite function, represented as the Lyapunov function V1, is as follows:

[0094]

[0095] Differentiation yields Solve for the virtual control quantity u rd ,v rd As shown below:

[0096]

[0097] Where the gain parameter k z1 ,k z2 >0.

[0098] Substituting the above virtual control variables into V1, we can obtain...

[0099]

[0100] Among them, u e =u r -u rd ,v e =v r -v rd These represent the longitudinal velocity u of the AUV relative to the ocean current. r Its virtual control quantity u rd The error between them, and the lateral velocity v r Its virtual control quantity v rd The error between them, δ, is a bounded small quantity representing the error estimated by ocean currents. The introduced residual terms.

[0101]

[0102] in, This represents the error in ocean current estimation.

[0103] structure Selecting virtual control variable r d It is expressed as follows:

[0104]

[0105] Where, k v k is a positive constant. dv This is the sliding mode gain. Here, we assume u... r ≠0, meaning the AUV maintains longitudinal motion; substituting this into the equation yields... as follows:

[0106]

[0107] Where, d v This is the sliding mode gain.

[0108] structure Right now Solve for the longitudinal thrust τ u and bow roll torque τ r as follows

[0109]

[0110] Where, k u ,k r >0 represents the gain parameter, k du ,k dv ,k dr This is the sliding mode gain, used to compensate for dynamic disturbances d. u ,d v ,d r , sign(·) is the sign function, f u (u r ,v r ,r) and f r (u r ,v r r) are respectively:

[0111]

[0112] Among them, X u and N r These are the hydrodynamic damping parameters.

[0113] Step S5: Perform system stability analysis and solve the control law.

[0114] In this embodiment, using Lyapunov stability theory, a composite Lyapunov function incorporating conversion error, velocity error, observer error, and neural network weight estimation error is constructed, proving the uniform eventual boundedness (UUB) of all signals in the closed-loop system. More importantly, based on the boundedness of the conversion error, it is rigorously proven that the original position error e always remains within the performance boundary defined by the preset performance function ρ(t). Finally, based on real-time sensor data, the control law is solved and output to the actuator.

[0115] Example 3

[0116] Combination Figures 3-4 As shown, in this embodiment, straight-line tracking is performed under sinusoidal ocean current interference. The reference trajectory is set as a straight line, and the ocean current is set as d. x=-1.2 sin(0.6t),d y = -1.5 cos(0.6t). For example... Figure 3 The tracking comparison results shown indicate that without observer compensation, the AUV experiences significant lateral drift due to ocean currents, causing its trajectory to deviate from the target line. Using the method of this invention, the AUV quickly corrects the deviation, and its trajectory coincides with the reference line, as shown... Figure 4 The comparison curves of the estimated performance of the observer shown demonstrate that in the initial stage, the observed values ​​converge rapidly to the true ocean current values. Although the ocean current is rapidly time-varying, the observer can still maintain a very small tracking error, proving the effectiveness of the nonlinear convergence mechanism in improving the dynamic response speed.

[0117] Combination Figures 5-6 As shown, this embodiment uses a figure-eight curve tracking method, and sets the reference trajectory as x. d = 2 sin(0.05t), y d =3 sin(0.1t), simulating complex manipulation scenarios. For example... Figure 5 As shown, the AUV can smoothly track a figure-eight trajectory, maintaining high tracking accuracy even at turns with significant curvature changes. Figure 6 The position error curve shown indicates that both the longitudinal and lateral errors converge to a very small neighborhood near zero (|e^(-1 / 2)) within a finite time. x |<0.05m,|e y The value of |<0.05m) and the value always converged within the preset performance envelope, verifying the robustness of the controller.

[0118] The control method proposed in this invention, based on preset performance control and a finite-time ocean current observer, solves the problem of estimating time-varying ocean currents by combining RBF neural networks with nonlinear convergence acceleration mechanisms. Furthermore, it addresses the problem of lateral uncontrollability by combining a backstepping preset performance controller with underactuated characteristics. Simulation results fully verify the superiority of this method in improving the trajectory tracking accuracy and robustness of AUVs. Simulation results show that:

[0119] The invention exhibits excellent observation performance: the finite-time ocean current observer designed in this invention introduces a nonlinear power term sgn. α The sgnβ(·) and sgnβ(·) can achieve fast and accurate estimation when ocean currents change drastically. The estimation error converges to the minimum neighborhood within a finite time, providing the controller with an accurate feedforward compensation signal.

[0120] This invention offers high trajectory tracking accuracy: by combining preset performance control (PPC), the original error is transformed into an unconstrained transformed error z through an error transformation function, and a transformation gain matrix is ​​introduced into the controller design. Experiments demonstrate that, whether tracking a straight line or a complex figure-eight trajectory, the AUV's position tracking error e always remains strictly within the funnel-shaped envelope constrained by the preset performance function ρ(t), effectively solving the problems of large initial overshoot and uncontrollable convergence speed inherent in traditional backstepping methods.

[0121] The underactuation treatment of this invention is effective: the dynamic control law designed for the lateral underactuation characteristics of AUVs utilizes the yaw rate r to control the lateral velocity error u. e The effective calming effect ensured the global asymptotic stability of the system.

[0122] In summary, this invention enables fast, stable, and high-precision trajectory tracking of underactuated AUVs under the dual influence of uncertain model parameters and strong external environmental interference, and has significant engineering application value.

[0123] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0124] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for tracking and controlling the preset performance trajectory of an underactuated AUV based on an RBF current observer, characterized in that: The following steps are included: Step S1: Construct a horizontal three-degree-of-freedom kinematic and dynamic model of the underactuated autonomous underwater vehicle that includes unknown time-varying ocean current disturbance terms; Step S2: Define a preset performance function for the position tracking error, transform the original position error into an unconstrained conversion error, and derive the dynamic equation of the conversion error; Step S3: Construct a finite-time convergent ocean current observer based on RBF neural network, use RBF neural network to approximate ocean current components, output the estimated value of ocean current disturbance and compensate in the feedforward path; Step S4: Based on the error after preset performance conversion, the estimated value of ocean current disturbance and dynamic uncertainty parameters, a trajectory tracking controller is constructed using the backstepping strategy; Step S5: Construct a composite Lyapunov function that includes transformation error, velocity error, observer error, and neural network weight estimation error, and perform system stability analysis and control law solution.

2. The underactuated AUV preset performance trajectory tracking control method based on RBF ocean current observer according to claim 1, characterized in that: In step S1, by defining an inertial coordinate system and a volume coordinate system, a three-degree-of-freedom kinematic model and a dynamic model of the AUV horizontal plane considering time-varying ocean current disturbances are established respectively. These models include ocean current velocity components in the inertial coordinate system and uncertain disturbance terms of dynamic model parameters in the volume coordinate system.

3. The underactuated AUV preset performance trajectory tracking control method based on RBF ocean current observer according to claim 2, characterized in that: The three degrees of freedom in the horizontal plane three-degree-of-freedom kinematic model of an AUV include: longitudinal, lateral, and yaw.

4. The underactuated AUV preset performance trajectory tracking control method based on RBF ocean current observer according to claim 3, characterized in that: In step S2, by introducing a preset performance control theory, a preset performance function for the position tracking error is defined, and the upper and lower bounds of error convergence, minimum convergence speed, and steady-state error range are strictly set through the function.

5. The underactuated AUV preset performance trajectory tracking control method based on RBF ocean current observer according to claim 4, characterized in that: Step S2 also includes: using a nonlinear error transformation function to transform the constrained original position error into an unconstrained transformation error, and deriving the transformation error dynamic equation containing the time-varying gain matrix generated by the preset performance control theory transformation and the known dynamic terms. The nonlinear error transformation function is a logarithmic transformation function.

6. The underactuated AUV preset performance trajectory tracking control method based on RBF ocean current observer according to claim 5, characterized in that: The finite-time convergent ocean current observer constructed in step S3 uses a radial basis function neural network to approximate the ocean current components, uses the observation error to drive the estimation of time-varying ocean currents, and couples the transformation gain of the preset performance control theory into the observer structure.

7. The underactuated AUV preset performance trajectory tracking control method based on RBF ocean current observer according to claim 6, characterized in that: The finite-time convergent ocean current observer also includes: introducing a nonlinear power term into the correction term to achieve finite-time convergence of the observation error.

8. The underactuated AUV preset performance trajectory tracking control method based on RBF ocean current observer according to claim 7, characterized in that: The trajectory tracking controller constructed in step S4 includes: The kinematic virtual control law is designed to address the conversion error, specifically as follows: Design of kinematic loop: Design of virtual control law including desired longitudinal velocity and desired lateral velocity. Feedforward compensation of drift caused by ocean current by directly using ocean current observations. In the design of virtual control law, design of virtual control law for bow roll rate, and indirectly control the convergence of lateral velocity error by using kinematic coupling relationship. The dynamic thrust and torque control laws are designed to address velocity errors, specifically as follows: Design of dynamic loop: In view of the underactuated characteristics, the virtual control law of the yaw rate is designed by utilizing the coupled dynamic characteristics of the AUV to indirectly control the convergence of the lateral velocity error. Then, the actual longitudinal thrust and yaw moment are designed to track the desired longitudinal velocity and the virtual control law. At the same time, a robust sign function term is introduced into the control law to overcome the parameter uncertainty and residual disturbance in the dynamic model.

9. The underactuated AUV preset performance trajectory tracking control method based on an RBF ocean current observer according to claim 8, characterized in that: Step S5 involves system stability analysis and control law solution, including: using Lyapunov stability theory, constructing a composite Lyapunov function that includes conversion error, velocity error, observer error, and neural network weight estimation error; proving the uniform eventual boundedness of all signals in the closed-loop system; and based on the boundedness of the conversion error, proving that the original position error always remains within the performance boundary defined by the preset performance function. Finally, based on real-time sensor data, the control law is solved and output to the actuator.

10. A pre-set performance trajectory tracking control system for an underactuated AUV based on an RBF current observer, characterized in that: The method for tracking and controlling the preset performance trajectory of an underactuated AUV based on an RBF current observer, as described in any one of claims 1-9, includes: The environmental perception and status acquisition module is used to acquire the AUV's position, attitude, and velocity status information; The preset performance transformation module is used to convert position error into transformation error according to the set performance function; The finite-time ocean current observation module has a built-in nonlinear fast ocean current observation algorithm for real-time output of ocean current estimates; The backstepping tracking control module is used to calculate the control torque based on the conversion error, state information, and ocean current estimate. The actuator drive module is used to respond to control commands and drive the thruster to move.

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