A finite-time tracking method for underwater helicopters meeting preset performance

Abstract

The present invention discloses a finite-time tracking method for an underwater helicopter that meets preset performance, and belongs to the field of intelligent mechanical technology. The method comprises: establishing an inertial coordinate system and a motion coordinate system of the underwater helicopter; taking a combination of the speed of the underwater helicopter relative to the ocean current and the ocean current velocity as the speed state of the underwater helicopter according to data parameters in each coordinate system, and establishing a six-degree-of-freedom dynamic model of the underwater helicopter in combination with a propeller failure factor of the underwater helicopter; constructing a performance function and an error transformation relational expression, and utilizing the performance function to constrain the six degrees of freedom of the motion trajectory of the underwater helicopter; introducing an inverse tangent function and designing a disturbance observer to compensate for nonlinear disturbances caused by an external environment; and designing a finite-time preset performance controller of the underwater helicopter in combination with a preset performance method and a finite-time algorithm to control the underwater helicopter to track a desired trajectory.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent mechanical technology, and in particular relates to a limited-time tracking method for an underwater helicopter that meets preset performance. Background Art

[0002] In recent years, with the development of marine technology and the continuous upgrading of industrial systems and intelligent manufacturing, research on the intelligent and operational nature of underwater unmanned systems has entered a new stage. Autonomous underwater vehicles (AUVs), with their wide range, deep diving depth, reusability, strong autonomy, ease of maintenance, and high precision, have become increasingly important in marine engineering fields such as resource exploration, object observation, underwater patrols, regional mapping, and maritime rescue. They are also gradually becoming data and sample collection tools for scientific research such as marine environmental and biological analysis. Currently, a major research trend in the use of AUVs in marine engineering is to perform operations in complex environments, especially near-seabed environments, with high precision. In practical applications, AUVs are often required to perform complex trajectory tracking tasks, such as comprehensive underwater equipment inspections at offshore engineering bases and three-dimensional security patrols in the ocean. This not only requires the AUVs to have high maneuverability but also poses challenges to their motion control algorithms.

[0003] Currently, underwater helicopters, a subcategory of autonomous submersibles, utilize a variety of trajectory tracking control algorithms, primarily traditional PID control, sliding mode control, model predictive control (MPC), fuzzy control, and neural network control. However, these algorithms often fail to fully account for current velocity, uncertainty, and propeller failures; overuse reinforcement learning algorithms, resulting in excessive data volumes that compromise control speed and effectiveness; or, when applied to complex trajectories involving multiple degrees of freedom and multiple curves, suffer from performance degradation, resulting in limited practicality. Furthermore, it is important to note that these algorithms are limited in their applicability due to differences in motion characteristics, appendages, physical features, and operating modes between autonomous submersibles and traditional models. This makes it difficult to ensure that underwater helicopters can quickly and stably track complex three-dimensional trajectories involving hovering, takeoff and landing, and small rotation radii in subsea environments, hindering their superior maneuverability.

[0004] In summary, the current tracking methods for underwater helicopters usually overuse reinforcement learning algorithms when designing, resulting in an excessive amount of computing data, which occupies a large amount of underwater helicopter computing resources. In addition, the current tracking methods for underwater helicopters usually fail to fully consider the impact of ocean current velocity and underwater helicopter propeller failures on the accuracy of underwater helicopter tracking the desired trajectory, resulting in low tracking accuracy and poor anti-interference ability of underwater helicopters. Summary of the Invention

[0005] The purpose of the embodiments of the present invention is to provide a finite-time tracking method for an underwater helicopter that meets preset performance. The method can solve the technical problems that the existing tracking methods generally overuse reinforcement learning algorithms during design, resulting in an excessive amount of computing data and occupying a large amount of underwater helicopter computing resources. In addition, the current tracking methods for underwater helicopters generally fail to fully consider the impact of ocean current velocity and propeller failures of underwater helicopters on the accuracy of underwater helicopter tracking the desired trajectory, resulting in low tracking accuracy and poor anti-interference ability of underwater helicopters.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0007] An embodiment of the present invention provides a limited-time tracking method for an underwater helicopter that meets preset performance, comprising:

[0008] S101: Establish the inertial coordinate system and motion coordinate system of the underwater helicopter;

[0009] S102: Based on the data parameters of the underwater helicopter in the inertial coordinate system and the motion coordinate system, a six-degree-of-freedom dynamic model of the underwater helicopter is established by taking a combination of the speed of the underwater helicopter relative to the ocean current and the ocean current velocity as the speed state of the underwater helicopter, and in combination with a propeller failure factor of the underwater helicopter;

[0010] S103: Constructing a performance function and an error transformation relationship, and using the performance function to constrain the six degrees of freedom of the underwater helicopter's motion trajectory;

[0011] S104: Introducing the inverse tangent function and designing a disturbance observer based on the inverse tangent function to compensate for the nonlinear disturbance caused by the external environment;

[0012] S105: Design a finite-time preset performance controller for the underwater helicopter based on the underwater helicopter's six-degree-of-freedom dynamics model, performance function, error transformation relation, and disturbance observer, combined with the preset performance method and finite-time algorithm;

[0013] S106: Using a finite time preset performance controller to control the underwater helicopter to track the desired trajectory.

[0014] In an embodiment of the present invention, when designing a method for tracking an underwater helicopter, the speed of the underwater helicopter relative to the ocean current and the overall ocean current velocity are used as the speed state of the underwater helicopter, and a six-degree-of-freedom dynamic model of the underwater helicopter is established in combination with the propeller failure factor of the underwater helicopter, fully considering the impact of unstable ocean current velocity and propeller failure factors on the tracking process of the underwater helicopter. In addition, a disturbance observer is designed by introducing a simple inverse tangent function to compensate for nonlinear disturbances, avoid excessive use of reinforcement learning algorithms, and reduce the amount of computational data. Then, a preset performance algorithm and a finite time algorithm are combined to design a finite time preset performance controller to track the desired trajectory, so that the underwater helicopter can converge quickly within a finite time, thereby improving the reaction speed of the underwater helicopter, and having high tracking accuracy and strong anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 The present invention provides a flow chart of a method for tracking underwater helicopters within a limited time, which satisfies preset performance.

[0016] The realization of the objectives, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0017] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0018] The finite time tracking method for an underwater helicopter that meets preset performance provided by an embodiment of the present invention will be described in detail below with reference to the accompanying drawings through specific embodiments and application scenarios.

[0019] Reference Figure 1 , which shows a flow chart of a method for tracking underwater helicopters in a limited time that meets preset performance, provided by an embodiment of the present invention.

[0020] An embodiment of the present invention provides a method for tracking an underwater helicopter in a limited time that meets preset performance, comprising:

[0021] S101: Establish the inertial coordinate system and motion coordinate system of the underwater helicopter.

[0022] S1011: Select any point on the sea level as the origin, and establish an inertial coordinate system with the north, east and center of the earth as the three positive axes.

[0023] S1012: Select the center of gravity of the underwater helicopter as the origin, and use the forward direction, rightward swing direction, and sinking direction of the underwater helicopter as the positive directions of the three axes to establish a motion coordinate system.

[0024] It can be understood that by establishing the inertial coordinate system and the motion coordinate system of the underwater helicopter, it is convenient to describe the degrees of freedom of the underwater helicopter, so that the various motion parameters of the underwater helicopter can be divided and calculated according to direction.

[0025] S102: Based on the data parameters of the underwater helicopter in the inertial coordinate system and the motion coordinate system, a combination of the speed of the underwater helicopter relative to the ocean current and the ocean current velocity is used as the speed state of the underwater helicopter, and combined with the propeller failure factor of the underwater helicopter, a six-degree-of-freedom dynamic model of the underwater helicopter is established.

[0026] It should be noted that as a branch of autonomous submersibles, the dynamic equations of underwater helicopters are generally represented by the Fossen outline six-degree-of-freedom nonlinear model. On this basis, it should be noted that when an underwater helicopter performs three-dimensional precision operations, its motion trajectory usually varies greatly in each degree of freedom. In addition, the ocean current velocity and its impact on the system also show complex time-varying characteristics, which in turn affects the accurate acquisition of the underwater helicopter's speed state. While retaining the nonlinear term of the ocean current disturbance in the dynamic equation, the speed state of the underwater helicopter is regarded as a combination of its speed relative to the ocean current and the ocean current velocity. The ocean current velocity is estimated through the underwater helicopter's current observer to more accurately describe the impact of the ocean current on the underwater helicopter's trajectory tracking system, thereby improving the tracking accuracy of the established six-degree-of-freedom dynamic model for the desired trajectory.

[0027] S1021: Introducing the Fossen outline six-degree-of-freedom nonlinear model:

[0028]

[0029] Among them, M η =MJ -1 , M represents the inertial mass matrix, J represents the conversion matrix between the inertial coordinate system and the motion coordinate system; η = [η x ,η y ,η z ,η φ ,η θ ,η ψ ] T Represents the position vector and attitude vector of the underwater helicopter in the inertial coordinate system, represents the velocity and angular velocity vector of the underwater helicopter relative to the ocean current in the motion coordinate system; C RBThe matrix between the Coriolis force and the centripetal force of the underwater helicopter rigid body; C Aη =C A (v re )J -1 , C A The matrix representing the Coriolis force and centripetal force of the additional mass on the underwater helicopter; D η =D F (v re )J -1 , D F is the hydrodynamic damping matrix; g η is the force and torque vector brought by the gravity and buoyancy of the underwater helicopter; τ th The control force and torque provided to the thrusters of underwater helicopters.

[0030] S1022: Use the thrust distribution matrix ΔB to represent the impact of the thruster failure, and rewrite the actual control force and torque provided by the thruster as τ th +Δτ:

[0031] τ th +Δτ=(B0-K th B)u=(B0+ΔB)u Formula 2

[0032] Wherein, Δτ represents the abnormal thrust of the thruster, B represents the thrust distribution matrix of the underwater helicopter, B0 represents the nominal value of the thrust distribution matrix, u represents the control signal of the thruster, K th Represents a diagonal matrix, the diagonal matrix K th The element k in row i and column i thii ∈[0,1] represents the corresponding thruster failure degree.

[0033] It should be noted that thrusters are a crucial component of underwater helicopters and a major source of failure. Due to the complex operating environment of underwater helicopters and the various impacts that can occur at any time in the ocean, their thrusters are susceptible to various interferences and can experience various failures. When establishing a six-degree-of-freedom dynamic model for an underwater helicopter, different degrees of thruster failure are predicted and pre-incorporated into the calculation range of the six-degree-of-freedom dynamic model. This makes the established six-degree-of-freedom dynamic model of the underwater helicopter more fault-tolerant. This allows the model to track the desired trajectory even when faced with varying degrees of thruster failure, enabling better completion of various detailed tasks.

[0034] S1023: Determine the uncertainty of the Fossen outline six-degree-of-freedom nonlinear model, the impact of environmental disturbances and thruster failures.

[0035]

[0036] It is understandable that various factors affecting the underwater helicopter are combined and considered as a calculation factor to simplify subsequent calculations.

[0037] S1024: Rewrite the Fossen outline six-degree-of-freedom nonlinear model based on the actual control force, torque, and influence d to obtain Formula 4:

[0038]

[0039] Among them, C RBη0 , C Aη0 , D η0 and g η0 Represents C RBη , C Aη , D η and g η The standard value of .

[0040] S1025: Order Represents the state variables of the control system, and uses the state vector of the control system to represent the dynamic equation of the underwater helicopter:

[0041]

[0042] Where T represents the transpose operation, It represents the first-order derivative of the position state of the underwater helicopter, and x2 represents the velocity state of the underwater helicopter.

[0043] S1026: Integrate the dynamic equations of the underwater helicopter to obtain the dynamic model of the underwater helicopter:

[0044]

[0045] in,

[0046] S103: Construct a performance function and an error transformation relationship, and use the six degrees of freedom of the helicopter's motion trajectory constrained by the performance function.

[0047] S1031: Construct performance function ρ(t):

[0048] ρ(t)=(ρ0-ρ ∞ )exp(-kt)+ρ ∞ Formula 7

[0049] Among them, ρ0, ρ ∞ and k are pre-given positive constants.

[0050] It should be noted that the constructed performance function can constrain the six degrees of freedom of the underwater helicopter's trajectory, thereby reducing the underwater helicopter's motion amplitude and tracking error. k can be set according to actual needs. The value of k limits the minimum convergence rate of the underwater helicopter's tracking error. By adjusting the value of k, the underwater helicopter's response speed and flexibility can be improved.

[0051] S1032: The six degrees of freedom of the underwater helicopter's motion trajectory are constrained using the performance function. The established constraint relationship is:

[0052] -ρ i (t)<e i (t)<ρ i (t) Formula 8

[0053] Among them, e i (t) = x i -x di =η i -η di , x di =η di Defines the desired motion trajectory under the i-th degree of freedom, e i (t) defines the deviation between the actual motion trajectory and the expected motion trajectory in the i-th degree of freedom.

[0054] Among them, e i (t) defines the deviation between the actual trajectory of the underwater helicopter and the expected trajectory in 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), then the six-degree-of-freedom trajectory vector η of the underwater helicopter is strictly limited to the performance boundary ±ρ i In addition, the parameter k in the performance function 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, an appropriate performance function ρ is designed. i (t) can obtain the desired system error response.

[0055] S1033: Construct error transformation equation:

[0056]

[0057] It should be noted that, to ensure that the tracking error of the underwater helicopter's dynamic system satisfies the performance function constraints, the designers equivalently transform the original dynamic system into a new one using an error transformation relation. By designing a controller that bounds the tracking error of the new dynamic system, it can be concluded that the tracking error of the original dynamic system also satisfies the performance function constraints, converging within an arbitrarily small, pre-defined region. Furthermore, the convergence rate and overshoot of the tracking error also meet the preset conditions of the performance function constraints.

[0058] S104: Introduce the inverse tangent function and design a disturbance observer based on the inverse tangent function to compensate for the nonlinear disturbance caused by the external environment.

[0059] It should be noted that in the design of trajectory tracking control strategies for underwater helicopters, compensating for nonlinear disturbances caused by the external environment is of great significance for ensuring the stable convergence of the system. Traditional disturbance observers often assume that the first-order derivative of the disturbance is bounded, making them unsuitable for delicate operations in complex environments. The unified approximation of nonlinear terms such as environmental disturbances, six-degree-of-freedom nonlinear model uncertainties, and thruster failures by neural networks is prone to excessive data volume, which in turn affects the rapidity and effectiveness of control. Therefore, this paper introduces a disturbance observer in the form of an inverse tangent function. This has a simple form, a smooth response, and good tracking effect for rapidly changing disturbances. It avoids the technical problem of large computational complexity when underwater helicopters process various nonlinear disturbances and is more suitable for the three-dimensional complex tracking operations of underwater helicopters.

[0060] S1041: Introducing the inverse tangent function:

[0061]

[0062] Among them, R, l1, l2, γ1 and γ2 are all design parameters greater than 0, and the symbol ^ represents the observed value of the variable;

[0063] S1042: Based on the inverse tangent function, the disturbance observer is designed as:

[0064]

[0065] in,

[0066] S105: Design a finite-time preset performance controller for the underwater helicopter based on the six-degree-of-freedom dynamic model, performance function, error transformation relation, and disturbance observer of the underwater helicopter, and in combination with the preset performance method and finite-time algorithm.

[0067] It can be understood that, based on the established six-degree-of-freedom nonlinear model of the underwater helicopter, and in combination with the preset performance method and the finite-time algorithm, the performance function and the disturbance observer are incorporated into the system of the preset performance controller, thereby improving the effectiveness of the established preset performance controller and the accuracy of tracking the desired trajectory.

[0068] S1051: Based on the dynamic model of the underwater helicopter, define the first tracking error between the position and attitude state of the underwater helicopter and its expected value as e1:

[0069] e1=x1-x 1d Formula 12

[0070] Taking the derivative of the first tracking error, we get:

[0071]

[0072] S1052: Substitute the error transformation formula into Formula 13 to obtain the derivative of the transformation error ε1:

[0073]

[0074] in, represents the first-order derivative of the performance function ρ1 with respect to time;

[0075] S1053: Design virtual control rate:

[0076]

[0077] Among them, k1 is the design parameter, is the first-order derivative of the desired motion trajectory x1;

[0078] S1054: Using the virtual control rate, define a second tracking error e2 between the speed and angular velocity state of the underwater helicopter and its expected value:

[0079] e2=x2-α Formula 16;

[0080] S1055: According to the terminal sliding mode principle and the finite time principle, the sliding film surface is defined as follows:

[0081]

[0082] Among them, sig(ε 1i ) a =sign(ε 1i )|ε 1i | a , e 2i represents the second tracking error e2 in the i-th degree of freedom, ε 1i Represents the transformation error ε1 under the i-th degree of freedom.

[0083] In traditional linear sliding mode control, once the system state reaches the sliding mode, it asymptotically approaches the origin along a designed exponential law, but its steady-state error does not converge to zero within a finite time. This paper proposes the concept of terminal sliding mode, replacing the traditional linear sliding mode with a nonlinear sliding mode. Its goal is to make the system state converge to the equilibrium point within a finite time.

[0084] The sliding surface is composed of the error between the underwater helicopter's output and the target. The convergence of the sliding surface means that the error converges to 0. The convergence of the sliding surface represents the convergence of the error.

[0085] S1056: Calculate the finite-time preset performance controller based on the sliding surface and disturbance observer:

[0086]

[0087] in, b∈(0,1), k2 is the design parameter, sig(S i ) b =sign(S i )|S i | b .

[0088] It can be understood that by combining the error between the output of the underwater helicopter and the target and introducing the disturbance observer into the calculation of the finite-time preset performance controller, the errors caused by various complex disturbances are fully considered while ensuring the rapid convergence of the underwater helicopter, thereby improving the response speed and tracking accuracy of the underwater helicopter.

[0089] S106: Using a finite time preset performance controller to control the underwater helicopter to track the desired trajectory.

[0090] Among them, the underwater helicopter uses a finite-time preset performance controller to track the six degrees of freedom of the desired trajectory, and ensures that the first tracking error and the second tracking error converge to a small range of 0 within a finite time, and the error is always kept within the boundary of the pre-constructed performance function.

[0091] In an embodiment of the present invention, when designing a method for tracking an underwater helicopter, the speed of the underwater helicopter relative to the ocean current and the overall ocean current velocity are used as the speed state of the underwater helicopter, and a six-degree-of-freedom dynamic model of the underwater helicopter is established in combination with the propeller failure factor of the underwater helicopter, fully considering the impact of unstable ocean current velocity and propeller failure factors on the tracking process of the underwater helicopter. In addition, a disturbance observer is designed by introducing a simple inverse tangent function to compensate for nonlinear disturbances, avoid excessive use of reinforcement learning algorithms, and reduce the amount of computational data. Then, a preset performance algorithm and a finite time algorithm are combined to design a finite time preset performance controller to track the desired trajectory, so that the underwater helicopter can converge quickly within a finite time, thereby improving the reaction speed of the underwater helicopter, and having high tracking accuracy and strong anti-interference ability.

[0092] The foregoing is merely an embodiment of the present invention and is not intended to limit the present invention. It will be apparent to those skilled in the art that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are intended to be included within the scope of the claims of the present invention.

Claims

1. A finite time tracking method for an underwater helicopter that meets preset performance, characterized in that: include: S101: Establish the inertial coordinate system and motion coordinate system of the underwater helicopter; S102: Based on the data parameters of the underwater helicopter in the inertial coordinate system and the motion coordinate system, a six-degree-of-freedom dynamic model of the underwater helicopter is established by taking a combination of the speed of the underwater helicopter relative to the ocean current and the ocean current velocity as the speed state of the underwater helicopter, and in combination with a propeller failure factor of the underwater helicopter; The S102 specifically includes: S1021: Introducing the Fossen outline six-degree-of-freedom nonlinear model: Among them, M η =MJ -1 , M represents the inertial mass matrix, J represents the conversion matrix between the inertial coordinate system and the motion coordinate system; η = [η x ,η y ,η z ,η φ ,η θ ,η ψ ] T represents the position vector and attitude vector of the underwater helicopter in the inertial coordinate system, represents the velocity and angular velocity vector of the underwater helicopter relative to the ocean current in the motion coordinate system; C RB C represents the matrix between the Coriolis force and the centripetal force of the underwater helicopter rigid body; Aη =C A (v re )J -1 , C A D represents the matrix between the Coriolis force and the centripetal force of the additional mass on the underwater helicopter; η =D F (v re )J -1 , D F is the hydrodynamic damping matrix; g η is the force and torque vector brought about by the gravity and buoyancy of the underwater helicopter; τ th Control forces and torques provided to the propellers of the underwater helicopter; S1022: Use the thrust distribution matrix ΔB to represent the impact of the thruster failure, and rewrite the actual control force and torque provided by the thruster as τ th +Δτ: t th +Δτ=(B0-K th B)u=(B0+ΔB)u Formula 2 Wherein, Δτ represents the abnormal thrust of the propeller, B represents the thrust distribution matrix of the underwater helicopter, B0 represents the nominal value of the thrust distribution matrix, u represents the control signal of the propeller, K th Represents a diagonal matrix, the diagonal matrix K th The element k in row i and column i thii ∈[0,1] represents the corresponding thruster failure degree; S1023: Determine the uncertainty of the Fossen outline six-degree-of-freedom nonlinear model, the environmental disturbance, and the impact of the thruster failure d: S1024: Rewrite the Fossen outline six-degree-of-freedom nonlinear model according to the actual control force, torque, and the influence d to obtain Formula 4: Among them, C RBη0 , C Aη0 , D η0 and g η0 Represents C RBη , C Aη , D η and g η The standard value of S1025: Order Represent the state variables of the control system, and use the state variables of the control system to represent the dynamic equations of the underwater helicopter: Wherein, T represents a transpose operation, x.1 represents the first-order derivative of the position state of the underwater helicopter, and x2 represents the speed state of the underwater helicopter; S1026: Integrate the dynamic equations of the underwater helicopter to obtain a dynamic model of the underwater helicopter: in, S103: constructing a performance function and an error transformation relationship, and using the performance function to constrain the six degrees of freedom of the motion trajectory of the underwater helicopter; S104: Introducing an inverse tangent function and designing a disturbance observer based on the inverse tangent function to compensate for nonlinear disturbances caused by the external environment; S105: Designing a finite-time preset performance controller for the underwater helicopter based on the six-degree-of-freedom dynamic model of the underwater helicopter, the performance function, the error transformation relation, and the disturbance observer, in combination with a preset performance method and a finite-time algorithm; S106: Using the finite time preset performance controller to control the underwater helicopter to track the desired trajectory.

2. The underwater helicopter finite time tracking method according to claim 1, characterized in that: The S101 specifically includes: S1011: Select any point on the sea level as the origin, and establish the inertial coordinate system with the north direction, the east direction and the direction pointing to the center of the earth as the positive directions of the three axes.

3. The underwater helicopter finite time tracking method according to claim 1, characterized in that: The S101 further includes: S1012: Select the center of gravity of the underwater helicopter as the origin, and use the forward direction, rightward swing direction, and sinking direction of the underwater helicopter as the positive directions of the three axes to establish the motion coordinate system.

4. The underwater helicopter finite time tracking method according to claim 1, characterized in that: The S103 specifically includes: S1031: Construct the performance function ρ(t): ρ(t) = (ρ0 - ρ ∞ ) exp(-kt) + ρ ∞ Equation 7 Among them, ρ0, ρ ∞ and k are pre-given positive constants.

5. The underwater helicopter finite time tracking method according to claim 4, characterized in that: The S103 also includes S1032: Using the performance function to constrain the six degrees of freedom of the motion trajectory of the underwater helicopter, the established constraint relationship is: -ρ i (t)<e i (t)<ρ i (t) formula8 Among them, e i (t) = x i -x di =η i -η di , x di =η di Defines the desired motion trajectory under the i-th degree of freedom, e i (t) defines the deviation between the actual motion trajectory and the desired motion trajectory in the i-th degree of freedom.

6. The underwater helicopter finite time tracking method according to claim 1, characterized in that: The S103 further includes: S1033: Construct error transformation equation:

7. The underwater helicopter finite time tracking method according to claim 6, characterized in that: The S104 specifically includes: S1041: Introduce the inverse tangent function: Among them, R, l1, l2, γ1 and γ2 are all design parameters greater than 0, and the symbol ^ represents the observed value of the variable; S1042: Based on the inverse tangent function, the disturbance observer is designed as follows: in, 8. The underwater helicopter finite time tracking method according to claim 7, characterized in that: The S105 specifically includes: S1051: Based on the dynamic model of the underwater helicopter, define a first tracking error between the position and attitude state of the underwater helicopter and its expected value as e1: e1=x1-x 1d Formula 12 Taking the derivative of the first tracking error, we get: S1052: Substitute the error transformation relationship into Formula 13 to obtain the derivative of the transformation error ε1: in, represents the first-order derivative of the performance function ρ1 with respect to time; S1053: Design virtual control rate: Among them, k1 is the design parameter, is the first-order derivative of the desired motion trajectory x1; S1054: Using the virtual control rate, define a second tracking error e2 between the speed and angular velocity state of the underwater helicopter and its expected value: e2=x2-α Formula 16; S1055: According to the terminal sliding mode principle and the finite time principle, the sliding surface is defined as: Among them, sig(ε 1i ) a =sign(ε 1i )|ε 1i | a , e 2i represents the second tracking error e2 under the i-th degree of freedom, ε 1i Represents the transformation error ε1 under the i-th degree of freedom.

9. The underwater helicopter finite time tracking method according to claim 8, characterized in that: The S105 further includes: S1056: Calculate the finite-time preset performance controller according to the sliding surface and the disturbance observer: in, a∈(0,1), b∈(0,1), k2 is the design parameter, sig(S i ) b =sign(S i )|S i | b .

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