An adaptive neural network trajectory tracking method for autonomous underwater helicopters

Abstract

The present invention discloses an adaptive neural network trajectory tracking method for an autonomous underwater helicopter, comprising: 1) constructing a dynamic model of the AUH, using a thrust distribution matrix to represent the impact of propeller failures, and generating the dynamic equations of the AUH represented by the state variables of the control system; 2) establishing an improved performance function and constructing an error transformation; 3) designing a state observer to estimate the state information required for the trajectory tracking control strategy, and introducing a radial basis function neural network to approximate the lumped uncertainty of the system; 4) constructing a trajectory tracking controller for the AUH based on the state observer. The preset performance control method proposed in the present invention can achieve the convergence speed, overshoot and tracking error of the original system meeting the preset performance when dealing with constrained control problems through the performance function and error transformation and the control of the unconstrained system. This makes it have excellent control performance on strictly constrained problems and gradually promotes its application in various fields.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater helicopter trajectory tracking, and in particular relates to an autonomous underwater helicopter trajectory tracking method using an adaptive neural network. Background Art

[0002] Autonomous underwater vehicles (AUVs) in the new era must adapt to the challenges brought about by the ever-changing operating environment and production methods. Scientific research and applications are no longer satisfied with using AUVs for local observations or searching for specific targets, but rather a comprehensive analysis of the deep sea, polar regions, and even the interaction between the lithosphere and the atmosphere. Traditional AUVs are mostly torpedo-type with poor low-speed maneuverability, and cannot effectively and fully meet the needs of ultra-maneuverable tasks such as seabed mobile observation networks, seabed resource exploration, seabed data and energy docking, and seabed contour surface cruising. To overcome this obstacle, researchers at Zhejiang University have developed a new type of AUV, called an autonomous underwater helicopter (AUH), which has excellent maneuverability and can operate in "seabed to seabed" mode.

[0003] The AUH is similar to a disc in appearance. Its unique shape, coupled with four vertical thrusters and four horizontal thrusters, makes it meet the requirements of super maneuverability. Compared with traditional AUVs, it has the functions of full-circle steering, fixed-point hovering, precise landing and free take-off and landing. Figure 1 As shown in the figure. Due to the rapid iteration and improvement of AUH, its diverse forms and functions have put forward higher requirements for underwater positioning, navigation and automatic control. Trajectory tracking, as an important component of AUH control system, is also one of the research hotspots in the AUV field. The complexity of the marine environment means that AUVs will inevitably encounter ocean current disturbances and may cause thruster failures. In addition, AUV fluid dynamics models based on commercial fluid calculation software or experimental measurements will also produce inevitable modeling uncertainties, which are detrimental to the control system. As a unique AUV, AUH must also consider the influence of the above factors when designing its trajectory tracking control strategy.

[0004] Commonly used algorithms in the field of AUV trajectory tracking control mainly involve various forms such as PID control, fuzzy control, sliding mode control, and adaptive control. The following will briefly describe the control schemes proposed in this field in recent years. For example, in the prior art, the literature [Patre BM, Londhe PS, Waghmare LM, et al. Disturbance estimator based non-singular fast fuzzy terminal sliding mode control of an autonomous underwater vehicle [J]. Ocean Engineering, 2018, 159: 372-387] designed a non-singular fast fuzzy terminal sliding mode controller with disturbance estimation to achieve finite-time convergence and robust control of the tracking error. The observed values ​​of the uncertain terms are used to compensate for model uncertainty and external disturbances. The literature [Liang X, Qu X, Hou Y, et al. Three-dimensional trajectory tracking control of an underactuated autonomous underwater vehicle based on ocean current observer [J]. International Journal of Advanced Robotic Systems, 2018, 15 (5): 1729881418806811] proposed a current observer based on a kinematic model to estimate unknown current disturbances, and integrated the estimation into the kinematic and dynamic equations of the AUV, thus realizing the three-dimensional trajectory tracking control of the underactuated AUV under unknown current disturbances. The patent application document with publication number CN105843224A provides an AUV horizontal plane path tracking control method based on the neural dynamic model backstepping method, which introduces the neural dynamic model theory, which has the characteristics of input and output smoothness; the virtual control quantity generated in the backstepping method design process flows through the neural dynamic model, thereby avoiding the complex derivation operation of the virtual control quantity.The literature [Chen JW, Zhu H, Zhang L, et al. Research on fuzzy control of path tracking for underwater vehicle based on genetic algorithm optimization [J]. Ocean Engineering, 2018, 156: 217-223] proposes an AUV trajectory tracking method based on the line of sight method. After optimization by the genetic algorithm, the fuzzy controller can effectively track the desired trajectory and has strong robustness against external disturbances. The patent application document with publication number CN108427414A proposes a horizontal plane adaptive trajectory tracking control method for an autonomous underwater vehicle. The method uses a high-gain state observer to estimate the speed and angular velocity of the AUV, and uses the high-precision approximation function of the radial basis function (RBF) neural network to compensate for the model parameter uncertainty and external interference. The AUV trajectory tracking problem is converted into a tracking problem in the polar coordinate system through coordinate transformation.

[0005] The aforementioned literature proposes various control strategies for AUV trajectory tracking, achieving promising results and imparting a certain degree of stability and robustness to the trajectory tracking system. However, these strategies fail to consider or incompletely consider factors that affect control accuracy, such as current disturbances, modeling uncertainty, and thruster failures. Furthermore, due to the unique operational requirements of AUHs, including large-scale deployment, high-precision trajectory tracking, and seabed deployment, trajectory tracking control systems must not only achieve high steady-state accuracy but also rigorously control dynamic response to avoid collisions with the seabed and other AUHs. Summary of the Invention

[0006] The present invention proposes a control strategy based on a preset performance method to solve the trajectory tracking problem of the AUH under interference factors such as ocean current disturbances, modeling uncertainty, and propeller failure. In order to cope with the situation where the AUH speed and angular velocity state quantities are unmeasurable, a full-order adaptive state observer (LSO) is designed, and a radial basis function neural network (RBFNN) is introduced into the observer to deal with the influence of the total uncertainty of the system. At the same time, the relationship between the transformation error and the observed speed value is established with the help of the backstepping method, providing an application form of the preset performance method in output feedback control. The present invention adopts the following technical solutions:

[0007] An autonomous underwater helicopter trajectory tracking method using an adaptive neural network, comprising:

[0008] 1) Construct the dynamic model of the AUH, use the thrust distribution matrix to represent the impact of the thruster failure, and generate the dynamic equations of the AUH represented by the state variables of the control system;

[0009] 2) Establish an improved performance function and construct an error transformation;

[0010] 3) Design a state observer to estimate the state information required for the trajectory tracking control strategy, and introduce a radial basis function neural network to approximate the system lumped uncertainty;

[0011] 4) Construct the trajectory tracking controller of AUH based on the state observer.

[0012] Preferably, the kinetic model of AUH in step 1) is:

[0013]

[0014]

[0015] Where: M is the mass inertia matrix, η=[η x ,η y ,η z ,η φ ,η θ ,η ψ ] T is the AUH six-degree-of-freedom position and attitude vector in the inertial coordinate system, v = [v u ,v v ,v w ,v p ,v q ,v r ] T is the AUH velocity and angular velocity vector in the motion coordinate system, J represents the transformation matrix connecting the inertial coordinate system and the motion coordinate system, the C(v) matrix represents the Coriolis force and centripetal force of the AUH, the D(v) matrix represents the hydrodynamic damping part of the AUH, and g η The matrix represents the forces and moments generated by the AUH gravity and buoyancy, and τ represents the control forces and moments output by the AUH thrusters.

[0016] The impact of the AUH's thruster failure is expressed in the form of a thrust distribution matrix, defined as ΔB; the actual control force and torque are expressed as:

[0017] τ+Δτ=(B0-KB)u=(B0+ΔB)u

[0018] Where: B0 represents the nominal value of the AUH thrust distribution matrix, B is the thrust distribution matrix of the AUH, u represents the control output of the AUH thruster, K is a diagonal matrix whose element k is ii∈[0,1], represents the corresponding thruster failure degree, where 1 represents the highest failure degree and the thruster is completely ineffective;

[0019] The kinetic model of AUH can be rewritten as:

[0020]

[0021] Where: M η =MJ -1 , C Aη =C A (v r )J -1 , D η =D(v r )J -1 , subscript 0 represents the nominal value; F represents the total uncertainty of the system, which is expressed as follows:

[0022]

[0023] Where: represents the impact caused by ocean current disturbance; Δ represents the uncertainty value.

[0024] Furthermore, in step 1), represents the state variables of the control system, then the dynamic equation of AUH can be expressed using state variables:

[0025]

[0026] Where: H=[I n 0].

[0027] The present invention designs a new type of finite-time performance function, which can not only explicitly set the stable terminal time of the system, but also enable the designer to intuitively change the convergence rate of the system dynamic process by adjusting parameters. Preferably, in step 2), a finite-time performance function constraint tracking trajectory is established.

[0028]

[0029] in 0<k2<1;ρ0 and ρ ∞ are the values ​​of the performance function at the initial and end times, respectively; t f The time required for the performance function to reach the end value can be adjusted according to actual needs.

[0030] Let z i (t) = e i (t) / ρ i(t), a transformation error ε is defined on the interval (-∞,+∞) i (t):

[0031]

[0032] When the transformation error ε i When (t) is in the interval (-∞,+∞), z i (t) satisfies -1<z i (t)<1.

[0033] In step 3), RBFNN is introduced to approximate the system lumped uncertainty F, which includes ocean current disturbances, modeling uncertainty, and propeller failure. On the interval Ω, the RBFNN estimate of the system lumped uncertainty F can be expressed as:

[0034] F=W *T h(x N )+μ

[0035] Where: is the neural network input vector, h(x N )=[h1(x N ),h2(x N ),...,h j (x N ),...h m (x N )] T ∈R m , m is the number of hidden layer nodes in the network; h j (x N ) is usually expressed in the form of Gaussian basis function:

[0036]

[0037] Where: c j is the center vector of the jth node in the network, c j =[c j1 ,c j2 ,…,c jq ] T ,b j >0 is the base width value of node j. is the ideal weight matrix of the network, μ∈R n is the approximation error, and satisfies ||μ||≤μ * ,μ * is an unknown positive constant. For the weight matrix W∈R m×n , defined as:

[0038]

[0039] The state observer of step 3) is:

[0040]

[0041] Where: Represent the observed values ​​of state variables and output variables, L1 and L2∈R n is the diagonal gain matrix to be designed, Represents the estimated value of the system's lumped uncertainty F, and the input x of the neural network N can be expressed as Rewrite the observer in a more compact form:

[0042]

[0043] where A, C, and H are defined the same as in equation (7), and L = [L1, L2] T ;make Represents the state observation error, then:

[0044]

[0045] Where:

[0046] Preferably, the step 4) comprises:

[0047] First, define the error variable e1 = [e 11 ,e 12 ,...,e 16 ] T and e2

[0048] e1=x1-x d

[0049]

[0050] Where: x d =η d represents the expected trajectory of AUH, α1 represents the virtual control variable to be designed; through the performance function and error transformation in step 2), the transformation error ε can be obtained i ; For the transformation error ε i Taking the derivative, we can get:

[0051]

[0052] Where: Let ε=[ε1, ε2, ε3, ε4, ε5, ε6] T , R=diag[r1,r2,r3,r4,r5,r6], V=diag[v1,v2,v3,v4,v5,v6], further we get:

[0053]

[0054] Select appropriate gain matrix L, K1, K2 and parameter β to satisfy:

[0055]

[0056]

[0057]

[0058]

[0059] Then the observation error x e , transformation error ε, error e2 and weight estimation error All have boundaries.

[0060] In this application, the trajectory tracking controller is:

[0061]

[0062]

[0063] Where: B0 represents the nominal value of the AUH thrust distribution matrix, C RBη0 is the rigid body part of the AUH Coriolis force and centripetal force nominal matrix, C Aη0 is the part of the additional mass in the nominal matrix of AUH Coriolis force and centripetal force, D η0 is the nominal hydrodynamic damping matrix, g η0 Denote the forces and moments due to the nominal AUH gravity and buoyancy, x e1 is the observation error of the AUH position information, represents the known term consisting of error and system state, h is the Gaussian basis function, K2 is the gain matrix, and β is a constant.

[0064] Compared to existing technologies, the preset performance control method used in this invention, when dealing with constrained control problems, achieves the original system's convergence speed, overshoot, and tracking error meeting the pre-defined performance requirements through performance function and error transformation, as well as control of the unconstrained system. This results in superior control performance for strictly constrained problems, and is gradually being promoted and applied in various fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is the thruster configuration diagram of AUH;

[0066] Figure 2is the AUH trajectory tracking error curve (translational degree of freedom) under early thruster failure;

[0067] Figure 3 is the AUH trajectory tracking error curve (rotational degrees of freedom) under early thruster failure;

[0068] Figure 4 is the AUH trajectory tracking error curve (translational degree of freedom) under intermittent thruster failure;

[0069] Figure 5 AUH trajectory tracking error curve (rotational degrees of freedom) under intermittent thruster failure. DETAILED DESCRIPTION

[0070] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0071] Key technologies related to the method of this embodiment:

[0072] Inertial coordinate system: The origin can be selected at a certain point on the sea surface, and the positive directions of the three axes point to the north, east and the center of the earth respectively.

[0073] Motion coordinate system: The origin is taken at the center of gravity of AUH, and the positive directions of the three axes point to the forward direction, the right swing direction and the sinking direction respectively.

[0074] The nonlinear kinematic equations of AUH can refer to Fossen's outline six-degree-of-freedom nonlinear dynamic model:

[0075]

[0076]

[0077] Where: M is the mass inertia matrix, η=[η x ,η y ,η z ,η φ ,η θ ,η ψ ] T represents the six-degree-of-freedom position and attitude of AUH in the inertial coordinate system, v = [v u ,v v ,v w ,v p ,v q ,v r ] Trepresents the velocity and angular velocity of AUH in the motion coordinate system, J is the transformation matrix between the inertial coordinate system and the motion coordinate system, C(v) is the Coriolis force and centripetal force matrix of AUH, D(v) is the hydrodynamic damping matrix of AUH, g η are the force and torque vectors generated by the AUH gravity and buoyancy, and τ is the control force and torque generated by the AUH propulsion system.

[0078] Preset performance control: It is a method that maps the original "constrained" system into an equivalent "unconstrained" system using error transformation, and controls the stability of the "unconstrained" system so that the convergence speed, overshoot and tracking error of the original system can obtain preset performance.

[0079] Full-order adaptive state observer: It is an observer based on the model reference adaptive idea, which estimates the unknown state in the system by selecting appropriate feedback gain coefficients.

[0080] Radial Basis Function Neural Network: It is a feedforward neural network composed of an input layer, a nonlinear hidden layer (radial base layer) and a linear output layer. It uses radial basis functions and weight learning updates and can be applied to nonlinear function approximation, time series analysis, data classification processing system modeling and control and other fields.

[0081] Parameter definitions for this embodiment:

[0082] η=[η x ,η y ,η z ,η φ ,η θ ,η ψ ] T is the six-degree-of-freedom position and attitude value of AUH in the inertial coordinate system; J represents the transformation matrix between the inertial coordinate system and the motion coordinate system; v = [v u ,v v ,v w ,v p ,v q ,v r ] T represents the velocity and angular velocity of AUH in the motion coordinate system; M is the mass inertia matrix of AUH; C(v) is the Coriolis force and centripetal force matrix of AUH; D(v) is the hydrodynamic damping matrix of AUH; g η are the force and torque vectors generated by the AUH gravity and buoyancy; τ is the control force and torque generated by the AUH propulsion system; B is the thrust distribution matrix of the AUH; B0 is the nominal value of the AUH thrust distribution matrix; The constant part of the nominal value of the AUH thrust allocation matrix; is the matrix with unknown sign in the nominal value of the AUH thrust distribution matrix; u is the control output of the AUH thruster.

[0083] The autonomous underwater helicopter adaptive neural network trajectory tracking method in this embodiment includes the following steps:

[0084] The core of this invention is to design a trajectory tracking controller to enable the AUH to stably track the desired trajectory η, taking into account the ocean current disturbance, modeling uncertainty and propeller failure factors. d , while the tracking error e=η-η d The steady-state and dynamic responses meet the pre-set performance.

[0085] Step 1: Dynamic model transformation of AUH.

[0086] The impact of AUH thruster failure can be expressed in the form of a thrust distribution matrix, defined as ΔB. Therefore, the actual control force and torque can be rewritten as τ + Δτ:

[0087] τ+Δτ=(B0-KB)u=(B0+ΔB)u (3)

[0088] Where: B0 represents the nominal value of the AUH thrust distribution matrix, B is the thrust distribution matrix of the AUH, u represents the control output of the AUH thruster, K is a diagonal matrix whose element k is ii ∈[0,1], represents the corresponding thruster failure degree, where 1 represents the highest failure degree and the thruster is completely ineffective. Therefore, equation (2) can be rewritten as:

[0089]

[0090] Where: M η =MJ -1 , C Aη =C A (v r )J -1 , D η =D(v r )J -1 , subscript 0 represents the nominal value; F represents the total uncertainty of the system, which is expressed as follows:

[0091]

[0092] Where: represents the impact caused by ocean current disturbance; Δ represents the uncertainty value.

[0093] make represents the state variables of the control system, then the dynamic equation of AUH can be expressed in the following form through the state variables:

[0094]

[0095] Rewrite (6) into a compact form:

[0096]

[0097] Where: H=[I n 0].

[0098] Step 2: Performance function and error transformation.

[0099] The goal of the pre-set performance control scheme is to make the six degrees of freedom trajectories of the AUH subject to the constraints of the performance function, as expressed by the following inequality.

[0100] -ρ i (t)<e i (t)<ρ i (t) (8)

[0101] Where: e i (t) = x i -x di =η i -η di , x di =η di Defines the expected trajectory under the i-th degree of freedom, e i (t) represents the deviation of the actual trajectory from the expected value of the i-th degree of freedom. If the error variable e i The initial value of (t) satisfies -ρ i (0)<e i (0)<ρ i (0), the six-degree-of-freedom trajectory vector of the AUH is strictly limited to the performance boundary ±ρ i Therefore, the ideal system error response can be obtained by constructing an appropriate performance function.

[0102] The present invention designs a new performance function in finite time form, which can be expressed as:

[0103]

[0104] in 0<k2<1. ρ0 and ρ ∞ are the values ​​of the performance function at the initial and end times, respectively. f The time required for the performance function to reach the end value can be adjusted manually according to actual needs.

[0105] Let z i (t) = e i (t) / ρ i (t), a transformation error ε is defined on the interval (-∞,+∞)i (t):

[0106]

[0107] Formula (10) shows that when the transformation error ε i When (t) is in the interval (-∞,+∞), z i (t) satisfies -1<z i (t)<1, that is, the transformation error ε i When (t) is bounded, inequality (8) is also satisfied when the transformation error is bounded. At this point, the control objective can be equivalently described as designing a controller to make the transformation error bounded. It is worth noting that the bound on the transformation error does not affect the response of the error variable.

[0108] From equation (7), we can see that when the transformation error ε i (t) is in the interval (-∞,+∞), then z i (t) satisfies -1<z i (t)<1, that is, the transformation error ε i When (t) is bounded, inequality (9) is also satisfied. In this case, the control objective can be equivalently expressed as designing a controller u so that the transformation error ε i (t) is bounded. Note that the error variable e i The response of (t) cannot be affected by the transformation error ε i The impact of the boundary of (t).

[0109] Step 3: Introduce the neural network observation system.

[0110] The present invention introduces RBFNN to approximate the system aggregate uncertainty F, which includes ocean current disturbances, modeling uncertainty, and propeller failure. On the interval Ω, the RBFNN estimate of the system aggregate uncertainty F can be expressed as:

[0111] F=W *T h(x N )+μ (11)

[0112] Where: is the neural network input vector, h(x N )=[h1(x N ),h2(x N ),...,h j (x N ),...h m (x N )] T ∈R m , m is the number of hidden layer nodes in the network. j (x N ) usually takes the form of Gaussian basis function, which is:

[0113]

[0114] Where: c j is the center vector of the jth node in the network, c j =[c j1 ,c j2 ,...,c jq ] T ,b j >0 is the base width value of node j. is the ideal weight matrix of the network, μ∈R n is the approximation error, and satisfies ||μ||≤μ * ,μ * is an unknown positive constant. For the weight matrix W∈R m×n , the ideal matrix W * Defined as:

[0115]

[0116] Step 4: Design a full-order adaptive state observer.

[0117] Position and attitude vector η and its first-order derivative is the state information required when designing the trajectory tracking control strategy of AUH. However, the complexity of the ocean environment leads to the first-order derivative of the position and attitude vectors It is difficult to measure directly. Therefore, the present invention introduces observer technology to estimate this variable. Since the control strategy design of AUH includes external disturbances and uncertainties, RBFNN is added to the LSO observer to approximate these uncertainties. For system (6), the RBFNN state observer is designed as follows.

[0118]

[0119] Where: Represent the observed values ​​of state variables and output variables, L1 and L2∈R n is the diagonal gain matrix to be designed, Represents the estimated value of the system's lumped uncertainty F, and the input x of the neural network N can be expressed as Rewrite the observer in a more compact form:

[0120]

[0121] where A, C, and H are defined the same as in equation (7), and L = [L1, L2] T .make Represents the state observation error, then:

[0122]

[0123] Where:

[0124] Step 5: Design a preset performance trajectory tracking controller.

[0125] In this step, the present invention constructs a trajectory tracking controller of the AUH based on the backstepping method and the preset performance method and the aforementioned RBFNN state observer (15).

[0126] First, define the error variable e1 = [e 11 ,e 12 ,...,e 16 ] T and e2

[0127]

[0128] Where: x d =η d Represents the expected trajectory of AUH, and α1 represents the virtual control variable to be designed. Through the performance function and error transformation in step 2, the transformation error ε in equation (10) can be obtained i . For the transformation error ε i Taking the derivative, we can get:

[0129]

[0130] Where: Let ε=[ε1, ε2, ε3, ε4, ε5, ε6] T , R=diag[r1,r2,r3,r4,r5,r6], V=diag[v1,v2,v3,v4,v5,v6], we can further get:

[0131]

[0132] When we choose the appropriate gain matrix L, K1, K2 and parameter β to satisfy:

[0133]

[0134] Then the observation error x e , transformation error ε, error e2 and weight estimation error are all bounded (σ1, σ2, σ3, and σ4 are all positive constants). At this point, the six-degree-of-freedom trajectory tracking errors of the AUH are strictly limited within the boundaries defined by the performance function, which means that the control system achieves the desired dynamic performance and steady-state response.

[0135] The principles in this embodiment are as follows:

[0136] Kinetic model of UH:

[0137] The nonlinear kinematic equations of AUH can refer to Fossen's outline six-degree-of-freedom nonlinear dynamic model:

[0138]

[0139]

[0140] Where: J is the conversion matrix between the inertial coordinate system and the motion coordinate system, M is the mass inertia matrix, η = [η x ,η y ,η z ,η φ ,η θ ,η ψ ] T is the six-degree-of-freedom position and attitude of AUH in the inertial coordinate system, v = [v u ,v v ,v w ,v p ,v q ,v r ] T is the velocity and angular velocity of AUH in the motion coordinate system, C(v) represents the Coriolis force and centripetal force matrix of AUH, D(v) represents the hydrodynamic damping term of AUH, g η are the forces and moments generated by the AUH gravity and buoyancy, and τ is the control force and moment generated by the AUH thrusters.

[0141] The impact of AUH propulsion system failure is expressed in the form of a thrust distribution matrix, defined as ΔB. Therefore, the actual control force and torque can be rewritten as τ + Δτ:

[0142] τ+Δτ=(B0-KB)u=(B0+ΔB)u (3)

[0143] Where: B0 represents the nominal value of the AUH thrust distribution matrix, B is the thrust distribution matrix of the AUH, u represents the control output of the AUH thruster, and K is a matrix with an element of k ii The diagonal matrix ∈[0,1] represents the degree of propeller failure, where 1 represents the highest degree of failure and the propeller is completely ineffective. Therefore, equation (2) can be rewritten as:

[0144]

[0145] Where: M η =MJ -1 , C Aη =CA (v r )J -1 , D η =D(v r )J -1 , subscript 0 represents the nominal value; F represents the total uncertainty of the system, which is expressed as follows:

[0146]

[0147] Where: represents the impact caused by ocean current disturbance; Δ represents the uncertainty value.

[0148] make represents the state variables of the control system, then the dynamic equation of AUH can be expressed in the following form through the state variables:

[0149]

[0150] Rewrite (6) into a compact form:

[0151]

[0152] Where: H=[I n 0].

[0153] The core of the present invention is to design a controller u so that the position and attitude η of the AUH can still stably track the expected value η in the presence of ocean current disturbances, modeling uncertainty and propeller failure. d and make the tracking error e=η-η d The steady-state and dynamic responses meet the pre-set performance. To achieve this goal, the following reasonable assumptions need to be made:

[0154] Assumption 1: The lumped uncertainty of the system is bounded, that is, ||D||≤χ, where χ is an unknown positive constant.

[0155] Assumption 2: The actual position and attitude angle η of the AUH can be measured.

[0156] Assumption 3: Expected position and attitude angle η d Its first-order and second-order derivatives are known and bounded.

[0157] Energy function and error transformation construction:

[0158] Definition 1: If a smooth function ρ(t):R + →R satisfies monotonically decreasing and If the condition is met, then this function can be defined as a performance function.

[0159] A common performance function is as follows:

[0160] ρ(t)=(ρ0-ρ ∞ )exp(-kt)+ρ ∞ (8)

[0161] Where: ρ0, ρ ∞ and k are pre-given positive constants. The six degrees of freedom of the AUH motion trajectory are constrained by the performance function (8), as shown in the following inequality:

[0162] -ρ i (t)<e i (t)<ρ i (t) (9)

[0163] Where: e i (t) = x i -x di =η i -η di , x di =η di represents the desired motion trajectory under the i-th degree of freedom, e i (t) is the deviation between the actual motion trajectory and the expected value under the i-th degree of freedom. If the error variable e i The initial value of (t) satisfies -ρ i (0)<e i (0)<ρ i (0), the six-degree-of-freedom trajectory η of the AUH is strictly limited to the performance boundary ±ρ i (t). In addition, the parameter k i limits the minimum convergence rate of the tracking error, and ρ i∞ The upper bound of the allowed steady-state tracking error is given. Therefore, by designing an appropriate performance function ρ i (t) can obtain the desired system error response.

[0164] Definition 2: Based on Definition 1, if a smooth function ρ(t) is f Satisfying ρ(t)=ρ tf , where ρ tf is an arbitrarily small constant, t f is a time that can be set artificially, then ρ(t) can be called a finite-time performance function (FTPF).

[0165] According to Definition 2 and finite time theory, an improved performance function with finite time form is designed, which is defined as follows:

[0166]

[0167] Where: 0<k2<1, ρ0 and ρ ∞ are the values ​​of the performance function at the initial and final moments, t f The time required for the performance function to reach its endpoint can be adjusted manually according to actual needs. In order to ensure that (10) meets the definition of the performance function and has the above functions, it is necessary to verify that the designed improved performance function meets the monotonically decreasing condition and that the system represented meets the standard form of finite time convergence.

[0168] Proof: Considering the Lyapunov alternative function, the expression is as follows:

[0169]

[0170] Where: e ρ =ρ(t)-ρ ∞ . At t≤t f When, based on the performance function expression (10), we have V ρ Taking the derivative, we can get:

[0171]

[0172] Where: Since 0<k2<1, In addition, when e ρ ≠0, Therefore, based on the finite time theory, e ρ will converge to the zero region in finite time.

[0173] make Then formula (12) can be rewritten as follows:

[0174]

[0175] Integrating both sides of (13), we get:

[0176]

[0177] Where μ1μ2=4, and substituting into formula (14) we get:

[0178]

[0179] According to the definition of the performance function, when e ρ = 0, t = t f , at this time x ρ (t) = x ρ (t f )=0. Rearranging equation (15), we have:

[0180]

[0181] Therefore, it is concluded that ρ(t f )=ρ ∞ Compared with the commonly used exponential performance function (8), the improved performance function (10) designed by the present invention has the following obvious characteristics:

[0182] (1) The system's stable terminal time t can be explicitly set f , which is more intuitive for designers.

[0183] (2) For a given steady-state convergence time t f , the convergence rate of the system dynamic process can be changed by adjusting the parameters k1 and k2, making the adjustment of the dynamic response more flexible.

[0184] Let z i (t) = e i (t) / ρ i (t), a transformation error ε is defined on the interval (-∞,+∞) i (t):

[0185]

[0186] From equation (17), we can see that when the transformation error ε i (t) is in the interval (-∞,+∞), then z i (t) satisfies -1<z i (t)<1, that is, the transformation error ε i When (t) is bounded, inequality (9) is also satisfied. In this case, the control objective can be equivalently expressed as designing a controller u so that the transformation error ε i (t) is bounded. Note that the error variable e i The response of (t) cannot be affected by the transformation error ε i The impact of the boundary of (t).

[0187] Neural network approximation system:

[0188] The present invention introduces a radial basis function neural network (RBFNN) to approximate the system lumped uncertainty F, which is composed of ocean current disturbances, modeling uncertainty, and propeller failure. The RBFNN estimate of the system lumped uncertainty F on the interval Ω can be expressed as:

[0189] F=W *T h(x N )+μ (18)

[0190] Where: is the input vector of the radial basis function neural network, h(x N )=[h1(x N ),h2(x N),...,h j (x N ),...h m (x N )] T ∈R m , m represents the number of hidden layer nodes in the network. j (x N ) is expressed in the form of Gaussian basis function:

[0191]

[0192] Where: c j is the center vector of the jth node in the network, c j =[c j1 ,c j2 ,...,c jq ] T ,b j >0 is the base width value of node j. is the ideal weight matrix of the network, μ∈R n is the approximation error, and satisfies ||μ||≤μ * ,μ * is an unknown positive constant. At the same time, W * For W∈R m×n It is defined as follows:

[0193]

[0194] Assumption 4: There exists an ideal weight matrix W * Make ||μ||≤μ * when Where μ * is an unknown positive constant.

[0195] State Observer Design:

[0196] When designing the AUH trajectory tracking control strategy, the position and attitude vector η in the fixed coordinate system and its first-order derivative is the necessary status information. However, due to the complex marine environment, It is difficult to measure directly. Therefore, the present invention introduces an observer to estimate this variable. Since the control strategy design of AUH includes external disturbances and uncertainties, RBFNN is integrated into the LSO observer to approximate external disturbances and uncertainties. For system (6), the following RBFNN state observer is designed:

[0197]

[0198] Where: Represent the observed values ​​of state variables and output variables, L1 and L2∈Rn is the diagonal gain matrix to be designed, Represents the estimated value of the system's lumped uncertainty F, and the input x of the neural network N can be expressed as This writes the observer in a more compact form:

[0199]

[0200] where A, C, and H are defined the same as in equation (7), and L = [L1, L2] T ;make Represents the state observation error, we can get:

[0201]

[0202] Where:

[0203] Considering the AUH dynamic system (7) and the RBFNN state observer (21) to estimate the system state variable x, when the observer gain matrix L satisfies the following formula:

[0204] λ min (Q)-σ1>0 (24)

[0205] Where: Q = -(A-LH) > 0, σ1 > 0, and the weight estimation matrix is bounded, then the observation error x e will converge to a neighborhood of the initial value.

[0206] Proof: Considering the Lyapunov alternative function, the expression is as follows:

[0207]

[0208] Taking the derivative of V0 and substituting it into formula (23), we can obtain:

[0209]

[0210] According to assumption 4 and the characteristics of Gaussian function, we can get ||h(x N )||≤1, for any given constant σ1>0, the following inequality holds:

[0211]

[0212] We can get:

[0213]

[0214] because is bounded, so the observation error x e will converge to the set:

[0215]

[0216] According to the characteristics of RBFNN, the weight estimation matrix At t→∞, it will be equal to the ideal weight matrix Therefore, there is

[0217]

[0218] Preset performance trajectory tracking controller design:

[0219] Based on the aforementioned RBFNN state observer (22), backstepping method and preset performance method, a trajectory tracking controller for AUH is constructed.

[0220] First, define the error variable e1 = [e 11 ,e 12 ,...,e 16 ] T and e2:

[0221]

[0222] Where: x d =η d is the expected trajectory of AUH, and α1 is the virtual control variable to be designed. Through the above performance function and error transformation, the transformation error ε in equation (17) can be obtained i . For the transformation error ε i Taking the derivative, we get:

[0223]

[0224] Where: Let ε=[ε1, ε2, ε3, ε4, ε5, ε6] T , R=diag[r1,r2,r3,r4,r5,r6], V=diag[v1,v2,v3,v4,v5,v6], we get:

[0225]

[0226] The following steps give the specific analysis and derivation process.

[0227] Step 1: Select the Lyapunov candidate function as follows:

[0228]

[0229] Where: p = R -1 , take the time derivative of V1 and substitute it into equation (33), we get:

[0230]

[0231] Design dummy control variable α1:

[0232]

[0233] Where: K1 is a positive definite gain matrix. Substituting equation (36) into equation (35), we can get:

[0234]

[0235] Apply Young's inequality:

[0236]

[0237] Where: σ2 is a positive constant. Substituting equations (28) and (38) into equation (37), we can obtain:

[0238]

[0239] Where: represents the largest positive definite eigenvalue.

[0240] Step 2: For further proof, define a new Lyapunov function V2.

[0241]

[0242] Calculate the first derivative of V2 with respect to time,

[0243]

[0244] In the formula: Γ=diag[τ1,τ2,...,τ n ] is the gain matrix. Note that:

[0245]

[0246] Where: Represents a known term. The adaptive law of the AUH trajectory tracking controller and weight matrix can be designed as follows:

[0247]

[0248]

[0249] Where: K2 is the gain matrix, β is a constant. Substituting equations (43) and (42) into equation (41), we can obtain:

[0250]

[0251] Similar to formula (38), we can get:

[0252]

[0253] Where: σ3, σ4 are positive constants. Substituting equations (38) and (46) into equation (45), we can further obtain:

[0254]

[0255] When choosing appropriate gain matrix L, K1, K2 and parameter β,

[0256]

[0257] Then the observation error x e , transformation error ε, error e2 and weight estimation error are all bounded and converge to the following sets:

[0258]

[0259] Combining the above definitions of the performance function and error transformation, it can be seen that the AUH's six-degree-of-freedom trajectory tracking error is strictly limited within the boundaries defined by the performance function, that is, the control system achieves the desired dynamic performance and steady-state response. Summarizing the above derivation and proof process, the following theorem is given:

[0260] For the AUH dynamic model (7), under the conditions of assumptions 1-4, the position and attitude quantities η in the fixed coordinate system are transformed into ε through error transformation and performance function. When the state observer, virtual control variable and controller are designed as Equations (22), (36) and (43) respectively, and the appropriate gains L, K1, K2, β are selected to satisfy inequality (48), the corresponding transformation error ε is ultimately bounded, and the tracking error e i Will be constrained within preset performance boundaries.

[0261] Simulation Example

[0262] In order to demonstrate the effectiveness of the trajectory tracking control method proposed in this paper, a fully driven AUH is introduced in the numerical simulation. The thruster arrangement of the AUH is as follows: Figure 1 As shown, 8 of the thrusters are of the same type, working independently and outputting thrust in both forward and reverse directions.

[0263] The initial state information, hydrodynamic coefficients and inertia coefficients of AUH are shown in Tables 1-3 respectively.

[0264] Table 1 Initial information of AUH

[0265]

[0266] Table 2 Hydrodynamic coefficients of AUH

[0267]

[0268] Table 3 Inertia coefficient of AUH

[0269]

[0270] The present invention assumes that within the AUH execution trajectory tracking range, the ocean current direction is the same as the positive direction of the x-axis in the inertial coordinate system, and the flow velocity expression is as follows:

[0271]

[0272] At the same time, the present invention quantifies the modeling uncertainty, and incorporates 20% of the model nominal value into the disturbance as a modeling error.

[0273] In order to verify that the designed controller is robust to the impact of thruster failure, two common thruster failure modes are introduced for simulation analysis, including thruster early failure and intermittent failure. Their respective expressions are as follows:

[0274]

[0275]

[0276] The desired AUH control performance is designed to be: (1) steady-state tracking error does not exceed 0.01; (2) maximum convergence time does not exceed 20s; (3) system response has no overshoot. Based on this, the performance function ρ can be determined. i (t) and δ i The values ​​of are shown in Table 4.

[0277] Table 4 Parameter values ​​of performance functions

[0278]

[0279] The gains of the state observer (21), trajectory tracking controller (43) and adaptive law (44) of AUH are as follows: L1 = diag[50; 50; 50; 50; 50], L2 = [800; 800; 800; 800; 800; 800], K1 = [0.1; 0.1; 0.1; 0.1; 0.1], K2 = [1; 1; 1; 1; 1; 1]. The number of hidden layer nodes of RBFNN is m = 7, and the basis width of Gaussian basis function is b. j =50, the center c is as follows:

[0280]

[0281] Under comprehensive consideration of the effects of modeling uncertainty, ocean current disturbance, thruster output saturation and thruster failure on AUH, the preset performance trajectory tracking controller (43), state observer (21) and adaptive law (44) proposed in the present invention are used to make the expected trajectory of AUH based on equation η d2 =[2sin(0.1t); 2cos(0.1t)-2; -0.5144t; 0; 0; 0], the simulation results are as follows Figure 2-Figure 5 shown.

[0282] from Figure 2-Figure 5 It can be seen that when the desired tracking trajectory is a spiral, the preset performance controller proposed in this invention can keep the trajectory tracking error within the boundaries preset by the performance function and converge to the preset steady-state control accuracy within the specified time. Combined with the analysis of operating conditions of thruster failure, in the case of an early thruster failure with a control time t less than 20 seconds, the designed control algorithm enables the AUH to quickly approach the preset trajectory, achieving the desired control objective.

[0283] The above description is only an example of a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An autonomous underwater helicopter trajectory tracking method using an adaptive neural network, characterized in that: include: 1) Construct the dynamic model of the AUH, use the thrust distribution matrix to represent the impact of the thruster failure, and generate the dynamic equations of the AUH represented by the state variables of the control system; The kinetic model of AUH in step 1) is: Where: M is the mass inertia matrix, η=[η x ,η y ,η z ,η φ ,η θ ,η ψ ] T is the AUH six-degree-of-freedom position and attitude vector in the inertial coordinate system, v = [v u ,v v ,v w ,v p ,v q ,v r ] T is the AUH velocity and angular velocity vector in the motion coordinate system, J represents the transformation matrix connecting the inertial coordinate system and the motion coordinate system, the C(v) matrix represents the Coriolis force and centripetal force of the AUH, the D(v) matrix represents the hydrodynamic damping part of the AUH, and g η The matrix represents the forces and moments generated by the AUH gravity and buoyancy, and τ represents the control forces and moments output by the AUH thrusters; The impact of the AUH's thruster failure is expressed in the form of a thrust distribution matrix, defined as ΔB; the actual control force and torque are expressed as: τ+Δτ=(B0-KB)u=(B0+ΔB)u Where: B0 represents the nominal value of the AUH thrust distribution matrix, B is the thrust distribution matrix of the AUH, u represents the control output of the AUH thruster, K is a diagonal matrix whose element k is ii ∈[0,1], represents the corresponding thruster failure degree, where 1 represents the highest failure degree and the thruster is completely ineffective; The kinetic model of AUH can be rewritten as: Where: M η =MJ -1 , C Aη =C A (v r )J -1 , D η =D(v r )J -1 , subscript 0 indicates nominal value, C RBη0 is the rigid body part of the AUH Coriolis force and centripetal force nominal matrix, C Aη0 is the part of the additional mass in the nominal matrix of AUH Coriolis force and centripetal force, D η0 is the nominal hydrodynamic damping matrix, g η0 represents the force and moment generated by the nominal AUH gravity and buoyancy; F represents the total uncertainty of the system, which is expressed as follows: Where: represents the impact caused by ocean current disturbance; Δ represents the uncertainty value; In the step 1), let represents the state variables of the control system, then the dynamic equation of AUH can be expressed using state variables: Where: H=[I n 0], x1 is the AUH position information η, x2 is the AUH speed information 2) Establish an improved performance function and construct an error transformation; In step 2), a finite-time performance function constraint tracking trajectory is established. in 0<k2<1;ρ0 and ρ ∞ are the values ​​of the performance function at the initial and end times, respectively; t f The time required for the performance function to reach the end value can be adjusted according to actual needs. Let z i (t) = e i (t) / ρ i (t), a transformation error ε is defined on the interval (-∞,+∞) i (t): When the transformation error ε i When (t) is in the interval (-∞,+∞), z i (t) satisfies -1<z i (t)<1; 3) Design a state observer to estimate the state information required for the trajectory tracking control strategy, and introduce a radial basis function neural network to approximate the system lumped uncertainty; In step 3), RBFNN is introduced to approximate the system lumped uncertainty F, which includes ocean current disturbances, modeling uncertainty, and propeller failure. On the interval Ω, the RBFNN estimate of the system lumped uncertainty F can be expressed as: F=W *T h(x N )+μ Where: is the neural network input vector, h(x N )=[h1(x N ),h2(x N ),...,h j (x N ),...h m (x N )] T ∈R m , m is the number of hidden layer nodes in the network; h j (x N ) is usually expressed in the form of Gaussian basis function: Where: c j is the center vector of the jth node in the network, c j =[c j1 ,c j2 ,...,c jq ] T ,b j >0 is the base width value of node j; is the ideal weight matrix of the network, μ∈R n is the approximation error, and satisfies ||μ||≤μ * ,μ * is an unknown positive constant; for the weight matrix W∈R m×n , defined as: The state observer of step 3) is: Where: Represent the observed values ​​of state variables and output variables, L1 and L2∈R n is the diagonal gain matrix to be designed, Represents the estimated value of the system's lumped uncertainty F, and the input x of the neural network N can be expressed as Rewrite the observer in a more compact form: where L = [L1, L2] T ;make Represents the state observation error, then: Where: 4) constructing a trajectory tracking controller of the AUH based on the state observer; The trajectory tracking controller is: Where: B0 represents the nominal value of the AUH thrust distribution matrix, C RBη0 is the rigid body part of the AUH Coriolis force and centripetal force nominal matrix, C Aη0 is the part of the additional mass in the nominal matrix of AUH Coriolis force and centripetal force, D η0 is the nominal hydrodynamic damping matrix, g η0 Denote the forces and moments due to the nominal AUH gravity and buoyancy, x e1 is the observation error of the AUH position information, represents the known term consisting of the error and the system state, h is the Gaussian basis function, K2 is the gain matrix, and β is a constant.

2. The autonomous underwater helicopter adaptive neural network trajectory tracking method according to claim 1, characterized in that: The step 4) comprises: First, define the error variable e1 = [e 11 ,e 12 ,...,e 16 ] T and e2 e1=x1-x d Where: x d =η d represents the expected trajectory of AUH, α1 represents the virtual control variable to be designed; through the performance function and error transformation in step 2), the transformation error ε is obtained i ; For the transformation error ε i Taking the derivative, we can get: Where: Let ε=[ε1, ε2, ε3, ε4, ε5, ε6] T , R=diag[r1,r2,r3,r4,r5,r6], V=diag[v1,v2,v3,v4,v5,v6], further we get: Select appropriate gain matrix L, K1, K2 and parameter β to satisfy: Then the observation error x e , transformation error ε, error e2 and weight estimation error All have boundaries.

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