Air cushion vehicle filtering backstepping trajectory tracking control method based on rleso
By adopting a filter backstep trajectory tracking control method based on RLESO, the position error constraint and disturbance problem of underactuated hovercraft in harsh environments is solved, achieving higher tracking accuracy and stability and improving control performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HUNAN UNIV OF SCI & TECH SANYA RES INST
- Filing Date
- 2023-04-03
- Publication Date
- 2026-06-23
Smart Images
Figure CN116500890B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of heading tracking technology, and specifically to a method for filtering backstepping trajectory tracking control of hovercraft based on RLESO. Background Technology
[0002] Hovercraft possess advantages such as low drag, high speed, excellent maneuverability, and good mobility, and have been widely used in ocean patrol, exploration, rescue, and salvage operations. They can navigate at high speeds in shallow waters, beaches, swamps, ice, and other environments inaccessible to other surface vessels. The main actuators of a hovercraft typically include two air propellers at the stern and a vertical air rudder mounted behind each propeller. The propellers primarily provide forward propulsion, while the rudders provide steering torque. Therefore, hovercraft are a typical underactuated vessel. Due to the lack of direct actuators for swaying motion, the tracking control design of hovercraft is extremely complex. Furthermore, hovercraft have very weak disturbance resistance and poor navigation stability, and are inevitably affected by various external disturbances such as wind, waves, and currents in practical applications. All these factors make the tracking control problem of underactuated hovercraft extremely difficult and challenging.
[0003] Over the past few decades, the trajectory tracking control problem of hovercraft has attracted widespread attention from scholars both domestically and internationally, leading to the proposal of many advanced control methods, such as sliding mode control, neural network control, fuzzy control, and backstepping control. Backstepping control is a recursive design method that divides the control design process into several steps. In each step, a control Lyapunov function is constructed, and then a virtual control law is designed until the final actual control law is reached. While this method offers a clear design process, the repeated differentiation of the virtual control variables during the design process can lead to complex differential calculations.
[0004] From a practical application perspective, hovercraft should be kept within a certain range while navigating on the water surface to prevent collisions or deviations from the intended course. If the system's constraints are not met, its performance will be affected, leading to decreased control performance, closed-loop instability, or even damage.
[0005] Existing technologies often only address a single problem of hovercraft and lack relevant patents to solve the trajectory tracking problem of underactuated hovercraft with positional error constraints and harsh environmental disturbances. Summary of the Invention
[0006] The technical problem to be solved by this invention is: This invention provides a filter backstep trajectory tracking control method for hovercraft based on RLESO, which can improve the safety performance and maneuverability of hovercraft, enable hovercraft to obtain better performance under the influence of harsh environments such as water surfaces, and improve the tracking accuracy of hovercraft.
[0007] To solve the above-mentioned technical problems, the technical solution proposed by this invention is as follows:
[0008] A hovercraft filtering backstepping trajectory tracking control method based on RLESO is proposed. First, a three-degree-of-freedom mathematical model of the hovercraft's motion is established. The actual trajectory information of the hovercraft is compared with the reference trajectory information to obtain the hovercraft's position error dynamic model. Based on the state information of the hovercraft's mathematical model, RLESO is designed to estimate and compensate for unknown environmental disturbances of the hovercraft. A time-varying BLF with a position error constraint function is constructed by combining the position error dynamic model. Then, based on the BLF, backstepping technology, and a second-order command filter, a hovercraft command filtering backstepping controller based on position error constraints is designed to achieve the hovercraft trajectory tracking control objective.
[0009] A further improvement to the above technical solution is as follows:
[0010] Preferably, in the above technical solution, the tracking control method includes the following steps:
[0011] Step S1: Establish a three-degree-of-freedom mathematical model of the hovercraft's motion.
[0012] Based on the motion of the hovercraft on the water surface, a mathematical motion model of the water surface motion is established for the three degrees of freedom of pitch, sway, and yaw in a fixed coordinate system and a hull coordinate system, including a kinematic model and a dynamic model.
[0013] Step S2, Obtain error dynamics
[0014] Based on the mathematical model established in step S1, the actual trajectory information of the hovercraft is collected and compared with the reference trajectory information to obtain the position error dynamic model of the hovercraft.
[0015] Step S3, Design RLESO
[0016] Based on the state information of the hovercraft mathematical model, RLESO is designed to estimate and compensate for unknown disturbances experienced by the hovercraft in harsh environments.
[0017] Step S4: Construct a BLF with a time-varying position error constraint function.
[0018] Based on the position error dynamics model obtained in step S2, a BLF with a time-varying position error constraint function is constructed to ensure that the position tracking error is always within the constraint range.
[0019] Step S5: Design the instruction filtering and backstepping controller
[0020] Based on the BLF constructed in step S4, the expected value of the virtual control variable is derived by combining it with the backstepping technique. Combined with the second-order command filter, a hovercraft command filter backstepping controller based on position error constraints is obtained. The designed controller is used to achieve the hovercraft trajectory tracking control objective.
[0021] Preferably, in the above technical solution, the kinematic model and dynamic model in step S1 are as follows:
[0022] Three-degree-of-freedom kinematic model of a hovercraft in a fixed coordinate system:
[0023]
[0024] Three-degree-of-freedom dynamic model of the hovercraft in the hull coordinate system:
[0025]
[0026] In the formula, x, y, and ψ represent the northward, eastward, and bowward positions of the hovercraft in a fixed coordinate system, respectively; u, v, and r represent the pitching velocity, sway velocity, and bow roll angular velocity of the hovercraft, respectively; τ u , τ r These represent the sway control torque and the yaw control torque, respectively; β = d / m2, where d represents the hydrodynamic damping coefficient of the hovercraft. τ wu , τ wv , τ wr This represents the external disturbances caused by wind, waves, and currents to the hovercraft.
[0027] Preferably, in the above technical solution, the error dynamics model in step S2 is:
[0028]
[0029] In the formula, x d y d , ψ d For reference trajectory,
[0030] Preferably, in the above technical solution, in step S3, the RLESO is designed as follows:
[0031] The RLESO design for the underactuated hovercraft is as follows:
[0032]
[0033] In the formula, β i (i = 1, 2, 3) is the gain of the observer; pi (i = 1, 2, 3) are the auxiliary states of the observer; yes The observed values.
[0034] In the above technical solution, preferably, in step S4, the time-varying BLF with the position error constraint function is constructed as follows:
[0035]
[0036] In the formula, ρ is a given position error constraint function.
[0037] In the above technical solution, preferably, in step S5, the expected value u of the virtual control variable is derived by combining BLF with backstepping technique. d α d r d The expression is as follows:
[0038]
[0039] Define the error variable u of the virtual control variable e α e r e :
[0040]
[0041] In the formula, α is defined as α = v p sin(ψ e To avoid complex differential calculations of virtual control variables, the instruction filter is designed as follows:
[0042]
[0043] In the formula, ζ and ω n These are the damping ratio and bandwidth of the filter, Δ. i It is the input of the filter; z i and z id It is the output of the filter, i = u, r;
[0044] The designed instruction filtering and backstepping controller is as follows:
[0045]
[0046] In the formula, k3 and k5 represent controller parameters that are greater than zero.
[0047] The RLESO-based filtered backstep trajectory tracking control method for hovercraft provided by this invention has the following advantages compared with the prior art:
[0048] (1) The RLESO-based filtered backstepping trajectory tracking control method for hovercraft of this invention addresses the trajectory tracking problem of underactuated hovercraft with position error constraints and external disturbances. A command-based filtered backstepping control method based on RLESO is designed. RLESO is used to estimate and compensate for unknown disturbances experienced by the hovercraft in harsh environments such as the water surface, and a BLF is constructed to constrain the position tracking error. Based on this, a tracking controller is designed using the concept of backstepping technology. Furthermore, a second-order command filter solves the problem of complex differential calculation of virtual control variables in backstepping technology and keeps the hovercraft's position tracking error within a very small range. Compared with commonly used sliding mode control, the controller of this invention provides better transient performance for tracking errors.
[0049] (2) The RLESO-based filter backstep trajectory tracking control method of the present invention solves the constraint control problem of the hovercraft under the influence of external marine environmental disturbances, and improves the safety and control performance of the hovercraft.
[0050] (3) The RLESO-based air-cushion boat filter backstep trajectory tracking control method of the present invention avoids complex differential calculations of the controller by designing a second-order command filter. Attached Figure Description
[0051] Figure 1 This is a flowchart of the steps of the present invention.
[0052] Figure 2 This is a trajectory tracking curve of a certain type of hovercraft in an embodiment of the present invention.
[0053] Figure 3 This is a position tracking error constraint curve of a certain type of hovercraft in an embodiment of the present invention.
[0054] Figure 4 This is a dummy variable error curve diagram of a certain type of hovercraft in an embodiment of the present invention.
[0055] Figure 5 The dummy variable error α of a certain type of hovercraft during the application and implementation of this invention. e The convergence diagram.
[0056] Figure 6 The dummy variable error r of a certain type of hovercraft during the application and implementation of this invention e The convergence diagram.
[0057] Figure 7 When the present invention is applied, RLESO is used to address the disturbance τ. wu The observation effect diagram.
[0058] Figure 8 When the present invention is applied, RLESO is used to address the disturbance τ. wrThe observation effect diagram.
[0059] Figure 9 When the present invention is applied, RLESO is used to address the disturbance τ. wv The observation effect diagram.
[0060] Figure 10 The control input τ for a certain type of hovercraft during the application and implementation of this invention u Line graph.
[0061] Figure 11 The control input τ for a certain type of hovercraft during the application and implementation of this invention r Curve graph Detailed Implementation
[0062] The following provides a detailed description of specific embodiments of the present invention. It should be understood that the specific embodiments described herein are for illustrative and explanatory purposes only and are not intended to limit the scope of the invention.
[0063] Figure 1 The figure shows one embodiment of the RLESO-based air-cushion vehicle filtered backstepping trajectory tracking control method of the present invention, which includes the following steps:
[0064] Step S1: Establish a three-degree-of-freedom mathematical model of the hovercraft's motion.
[0065] Based on the motion characteristics of hovercraft on the water surface, a mathematical motion model of hovercraft is established in the fixed coordinate system and the hull coordinate system, as well as in the three degrees of freedom of pitch, sway and yaw, including: a three-degree-of-freedom kinematic model and a three-degree-of-freedom dynamic model.
[0066]
[0067] In the formula, x, y, and ψ represent the northward, eastward, and bowward positions of the hovercraft in a fixed coordinate system, respectively; u, v, and r represent the pitching velocity, swaying velocity, and bow roll angular velocity of the hovercraft, respectively; τ u , τ r These represent the sway control torque and the yaw control torque, respectively; τ w (t)=[τ wu , τ wv , τ wr ] T J(Ψ) represents the unknown disturbances experienced by the hovercraft in harsh environments such as on the water surface, and is the rotation matrix; M = M T >0, C(v) and D(v) are the ship's inertia matrix, Coriolis centripetal matrix, and hydrodynamic damping matrix, respectively. These matrices are all non-zero diagonal matrices, and their matrix forms are as follows:
[0068]
[0069]
[0070] Compared to d2, the hydrodynamic damping coefficients d1 and d3 are very small and therefore can be ignored, i.e., d1 = d3 = 0.
[0071] After performing simple algebraic reasoning, the mathematical model of the hovercraft established in this step can be written in the following form:
[0072] The three-degree-of-freedom kinematic model of the hovercraft in a fixed coordinate system is as follows:
[0073]
[0074] Three-degree-of-freedom dynamic model of the hovercraft in the hull coordinate system:
[0075]
[0076] In the formula, β=d / m2, where d represents the hydrodynamic damping coefficient of the hovercraft;
[0077] Step S2, Obtain the error dynamics model
[0078] Define the reference trajectory of a certain type of hovercraft as x d y d These are fully smooth time-varying functions and can be any continuous trajectory.
[0079] The required heading angle obtained from the reference trajectory is:
[0080]
[0081] Define the error variable as:
[0082]
[0083] Based on the hovercraft model and reference trajectory in step S1, the error dynamics model is as follows:
[0084]
[0085] In the formula, x d y d , ψ d For reference trajectory,
[0086] Step S3, Design RLESO
[0087] Hovercraft are susceptible to interference from the external environment during course tracking, resulting in poor controllability and low tracking accuracy. Using RLESO can eliminate peak phenomena in the initial stage of the system. Peak phenomena can lead to system performance degradation and even system instability.
[0088] The RLESO design is as follows:
[0089]
[0090] In the formula, β i (i = 1, 2, 3) is the gain of the observer; p i (i = 1, 2, 3) are the auxiliary states of the observer; yes The observed values.
[0091] Based on the hovercraft model in step S1 and the RLESO designed in this step, the error dynamics of RLESO are as follows:
[0092]
[0093] Step S4: Construct a barrier Lyapunov function (BLF) with a time-varying position error constraint function.
[0094] The time-varying BLF is constructed as follows:
[0095]
[0096] In the formula, ρ is a given position error constraint function.
[0097] Step S5: Design the instruction filtering and backstepping controller
[0098] The virtual control variable is obtained by combining the BLF constructed in step S4 with the backstepping technique. Then, a second-order instruction filter is designed to solve the problem of complex differential calculation of the virtual control variable. Finally, the instruction filter backstepping controller is designed.
[0099] In order to stabilize the error variable x e y e The derivative with respect to V1 is:
[0100]
[0101] Define α = v p sinψ e Where u and α are considered as dummy control variables, their expected values are chosen as follows:
[0102]
[0103]
[0104] In the formula, k1 and k2 are constants greater than zero.
[0105] The derivative of V1 can be written as:
[0106]
[0107] Extend Lyapunov functions to
[0108]
[0109] In the formula, u e =uu d To avoid complex differentiation operations, an instruction filter is designed to make u d Its differential value z is obtained through a filter. ud .
[0110] The instruction filter is designed as follows:
[0111]
[0112] In the formula, ζ and ω n These are the filter's damping ratio and bandwidth, respectively. Δ u It is the input of the filter; z u and z ud It is the output of the filter.
[0113] Differentiate with respect to V2:
[0114]
[0115] Obtain the control torque τ u :
[0116]
[0117] In the formula, k3 is a constant greater than zero. The derivative of V2 can be written as:
[0118]
[0119] Further expand the Lyapunov functions:
[0120]
[0121] Differentiating V3 gives:
[0122]
[0123] definition in, The derivative can be written as:
[0124]
[0125] Expected value of choosing r:
[0126]
[0127] The derivative of V3 becomes:
[0128]
[0129] To stabilize r e Continue to expand the Lyapunov functions:
[0130]
[0131] In the formula, r e =rr d To avoid complex differential operations, let r d Its differential value z is obtained through a filter. rd Design a second-order instruction filter to make r d Its differential value z is obtained through a filter. rd .
[0132] The instruction filter is designed as follows:
[0133]
[0134] In the formula, ζ and ω n These are the filter's damping ratio and bandwidth, respectively. Δ r It is the input of the filter; z r and z rd It is the output of the filter.
[0135] Differentiate with respect to V4:
[0136]
[0137] Control torque τ can be obtained r :
[0138]
[0139] The stability analysis and position error constraint proof of the controller designed in this step include the following steps:
[0140] Step 1, Stability Analysis
[0141] Based on the control torque τ r , It can be written as:
[0142]
[0143] definition According to the inequality:
[0144]
[0145] available:
[0146]
[0147] In the formula, γ = min{k1, k2, k3, k4, k5}. Here, ι is bounded, and further, we can obtain:
[0148]
[0149] From the above equation, we can see that V4 is ultimately bounded, and by appropriately increasing the controller gain k, ι / 2γ can become arbitrarily small.
[0150] Step 2, the position error constraint meets the requirements.
[0151] The constructed barrier Lyapunov function satisfies the following condition:
[0152]
[0153] available:
[0154]
[0155] From the formula, we can deduce that:
[0156]
[0157] Therefore, the position error ρ e It is constrained within a given boundary ρ, and the position error constraint meets the requirements.
[0158] Step S6, Simulation Verification
[0159] The simulation verification environment for the RLESO-based air-cushion boat filter backstepping trajectory tracking controller designed in step S5 is set as follows:
[0160] The initial conditions for the hovercraft are x(t0) = 2m, y(t0) = 8m, ψ(t0) = 60°, and u(t0) = 0.3m / s.
[0161] Using a certain type of hovercraft as the simulation object, the present invention’s RLESO-based filtered backstep trajectory tracking control method for hovercraft is simulated and verified.
[0162] The parameters for the hovercraft model are selected as follows: m = 23.8 kg, I z =1.76kg / m 2 , Y v = -0.8612 kg / s, Y vv = -36.2823 kg / m, Y rv = -0.805 kg / m, d2=-(Y v +Y vv |v|+Y rv |r|).
[0163] The time-varying constraint function is chosen as ρ = 3exp(-0.3t) + 0.05. The parameters of the second-order command filter are chosen as ζ = 0.8, ω n =500. The control gain of the controller is selected as: k1=0.3, k2=0.1, k3=1, k4=1, k5=1; the gain of RLESO is selected as: β1=10, β2=10, β3=10.
[0164] The disturbance is: τ wu =0.5(1.5+sin(t)),τ wv =0.5(1.5+sin(t)),τ wr =0.5(1.5+sin(t)).
[0165] The reference trajectory can be any continuous trajectory; in this simulation, the reference trajectory is set to a circle.
[0166]
[0167] The initial conditions for the hovercraft are set as follows: x0 = 2m, y0 = 8m, ψ0 = π / 3 rad, u0 = 0.3m / s, v0 = 0m / s, r0 = 0 rad / s. To further demonstrate the advantages of the proposed control method, an adaptive proportional-integral (PI) sliding mode (SM) control scheme is selected for comparison. This scheme combines adaptive technology, proportional-integral (PI) control, sliding mode (SM) control, and backstepping control to design an adaptive PISM controller. However, this controller requires repeated differentiation of the virtual control variables, resulting in computational complexity, and the chattering effect caused by sliding mode control still exists.
[0168] Figure 2 The image shows the trajectory tracking curve of a certain type of hovercraft under the tracking control method of this invention. By comparing it with the PISM control method, it can be seen that the curve of the hovercraft filtered backstep trajectory tracking control method based on RLESO of this invention enters the reference trajectory earlier in the initial stage, and has a faster response speed and better tracking performance compared with the PISM control method.
[0169] Figure 3 The image shows the position error constraint of a certain type of hovercraft under the tracking control method of this invention. Compared with the PISM control method, it can be clearly seen that the position error curve under the PISM control method exceeds the range of the constraint curve in the initial navigation stage of the hovercraft. However, the position tracking error curve of the hovercraft filter backstep trajectory tracking control method based on RLESO of this invention is always within the range of the constraint curve, and converges faster than the PISM curve.
[0170] Figure 4 The dummy variable error u of a certain type of hovercraft under the tracking control method of this invention is shown. e The convergence of the method, compared with the PISM control method, shows that the dummy variable error u under the RLESO-based hovercraft filtered backstep trajectory tracking control method of this invention is significantly better. e The curve converges to zero faster and more smoothly, while the dummy variable error u under the PISM method... e The curve fluctuates throughout.
[0171] Figure 5 The dummy variable error α of a certain type of hovercraft under the tracking control method of this invention is shown. e The convergence of the method, compared with the PISM control method, shows that the dummy variable error α under the RLESO-based hovercraft filter backstep trajectory tracking control method of this invention is significantly better. e The curve converges to zero more quickly and smoothly after a brief period of fluctuation, while the dummy variable error α under the PISM method... e The curve fluctuated throughout and ultimately did not converge to zero.
[0172] Figure 6 The dummy variable error r of a certain type of hovercraft under the tracking control method of this invention is shown. e The convergence results show that the dummy variable error r under the RLESO-based hovercraft filtered backstep trajectory tracking control method of this invention... e Curve and dummy variable error r under PISM control method e The curves can all converge to zero quickly and smoothly.
[0173] Figure 7-9 The diagram shows the observation of unknown disturbances experienced by hovercraft in harsh environments such as water surfaces using the RLESO designed in this invention. As can be seen from the graph, the two curves almost completely overlap. The RLESO designed under the RLESO-based hovercraft filter backstep trajectory tracking control method of this invention can quickly and accurately observe the disturbances experienced by the hovercraft.
[0174] Figure 10The control input τ of a certain type of hovercraft under this invention is shown. u The graph, compared with the PISM control method, shows the control input τ of the RLESO-based hovercraft filtered backstepping trajectory tracking control method of this invention. u The curve converges quickly and smoothly to zero, while τ under PISM control u The curve converges to zero with smaller fluctuations after a period of significant fluctuations.
[0175] Figure 11 The control input τ of a certain type of hovercraft under this invention is shown. r The graph, compared with the PISM control method, shows the control input τ of the RLESO-based hovercraft filtered backstepping trajectory tracking control method of this invention. r The curve converges quickly and smoothly to zero, while τ under PISM control r The curve converged to zero after fluctuating for a period of time.
[0176] The RLESO tracking control method of this invention performs real-time observation of system disturbances and incorporates the observed values into the feedback control for compensation, reducing the control system's dependence on the system model and making the controller more robust. Furthermore, the tracking control method of this invention solves the position error constraint problem of hovercraft under interference from harsh environments such as the water surface by combining BLF, backstepping technology, and a second-order command filter to design a command-filtered backstepping controller, thus enhancing the safety performance of the hovercraft. The tracking control method of this invention can significantly improve the steady-state performance of the hovercraft.
[0177] The above embodiments are merely preferred examples of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention should fall within the protection scope of the present invention.
Claims
1. A method for filtering backstepping trajectory tracking control of a hovercraft based on RLESO, characterized in that, First, a three-degree-of-freedom mathematical model of the hovercraft's motion is established. The actual trajectory information of the hovercraft is compared with the reference trajectory information to obtain the position error dynamic model of the hovercraft. Based on the state information of the hovercraft mathematical model, RLESO estimation and compensation for unknown environmental disturbances of the hovercraft are designed. A time-varying BLF with position error constraint function is constructed in combination with the position error dynamic model. Then, based on the BLF, backstepping technology and second-order command filter, a hovercraft command filter backstepping controller based on position error constraint is designed to achieve the hovercraft trajectory tracking control objective. Among them, RLESO is designed based on the state information of the hovercraft mathematical model to estimate and compensate for the unknown disturbances experienced by the hovercraft in harsh environments. The RLESO design is as follows: ； In the formula, It is the gain of the observer; It is an auxiliary state of the observer; yes The observed values, These represent the pitching speed, swaying speed, and bow roll rate of the hovercraft, respectively. These represent the sway control torque and the yaw control torque, respectively.
2. The air-cushion vehicle filtered backstepping trajectory tracking control method based on RLESO according to claim 1, characterized in that, The tracking control method includes the following steps: Step S1: Establish a three-degree-of-freedom mathematical model of the hovercraft's motion. Based on the motion of the hovercraft on the water surface, a mathematical motion model of the water surface motion is established for the three degrees of freedom of pitch, sway, and yaw in a fixed coordinate system and a hull coordinate system, including a kinematic model and a dynamic model. Step S2, Obtain error dynamics Based on the mathematical model established in step S1, the actual trajectory information of the hovercraft is collected and compared with the reference trajectory information to obtain the position error dynamic model of the hovercraft. Step S3, Design RLESO Based on the state information of the hovercraft mathematical model, RLESO is designed to estimate and compensate for unknown disturbances experienced by the hovercraft in harsh environments. Step S4: Construct a BLF with a time-varying position error constraint function. Based on the position error dynamics model obtained in step S2, a BLF with a time-varying position error constraint function is constructed to ensure that the position tracking error is always within the constraint range. Step S5: Design the instruction filtering and backstepping controller Based on the BLF constructed in step S4, the expected value of the virtual control variable is derived by combining it with the backstepping technique. Combined with the second-order command filter, a hovercraft command filter backstepping controller based on position error constraints is obtained. The designed controller is used to achieve the hovercraft trajectory tracking control target.
3. The air-cushion vehicle filtered backstepping trajectory tracking control method based on RLESO according to claim 2, characterized in that, In step S1, the kinematic model and the dynamic model are as follows: Three-degree-of-freedom kinematic model of a hovercraft in a fixed coordinate system: ； Three-degree-of-freedom dynamic model of the hovercraft in the hull coordinate system: ； In the formula, These represent the hovercraft's northward, eastward, and bowward positions in a fixed coordinate system, respectively. These represent the pitching speed, swaying speed, and bow roll rate of the hovercraft, respectively. These represent the sway control torque and the yaw control torque, respectively. , This represents the hydrodynamic damping coefficient of the hovercraft; , , , m1 and m2 represent the external disturbances caused by wind, waves, and currents to the hovercraft; m1 and m2 represent the mass of the hovercraft in sway and roll, respectively; and m3 represents the moment of inertia of the hovercraft in bow roll.
4. The air-cushion vehicle filtered backstepping trajectory tracking control method based on RLESO according to claim 3, characterized in that, In step S2, the error dynamics model is as follows: ； In the formula, For trajectory tracking error, The heading angle required for the reference trajectory. The ideal speed for the hovercraft on the reference trajectory. .
5. The air-cushion vehicle filtered backstepping trajectory tracking control method based on RLESO according to claim 1, characterized in that, In step S4, the time-varying BLF with the position error constraint function is constructed as follows: ； In the formula, It is a given position error constraint function. .
6. The air-cushion vehicle filtered backstepping trajectory tracking control method based on RLESO according to claim 5, characterized in that, In step S5, the expected value of the virtual control variable is derived by combining BLF with backstepping technique. The expression is as follows: ； In the formula, and All are constants greater than zero; Define the error variable of the virtual control variable : ； In the formula, Defined as To avoid complex differential calculations of virtual control variables, the instruction filter is designed as follows: ； In the formula, and These are the filter's damping ratio and bandwidth, respectively. It is the input of the filter; and It is the output of the filter. ; The designed instruction filtering and backstepping controller is as follows: ； In the formula, This indicates a controller parameter that is greater than zero.